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Industrial Evaluation of Integrated Performance Analysis and Equation Model Debugging for Equation-Based Models
The ease of use and the high abstraction level of equation-based object-oriented (EOO) languages such as Modelica has the drawback that performance problems and modeling errors are often hard to (cid:28)nd. To address this problem, we have earlier developed advanced performance analysis and equation model debugging support in the OpenModelica tool. The aim of the work reported in this paper is to perform an independent investigation and evaluation of this equation model performance analysis and debugging methods and tool support on industrial models. The results turned out to be mainly positive. The integrated debugger and performance analyzer locates several kinds of errors such as division by zero, chattering, etc., and greatly facilitates (cid:28)nding the equations that take most of the execution time during simulation. It remains to further evaluate the performance pro(cid:28)ler and debugger on even larger industrial models.
Introduction
The development of today's complex products requires integrated environments and equation-based objectoriented declarative (EOO) languages such as Modelica (Modelica Association, 2014;Fritzson, 2015) for modeling and simulation.
The increased ease of use, the high abstraction, and the expressivity of such languages are very attractive properties.However, the drawback of this high-level approach is that understanding the causes of unexpected behavior, slow performance, and numerical errors of certain simulation models is very dicult, in particular for users who are not experts in simulation methods.
Therefore Pop et al. (2014) have recently developed an advanced equation model debugger for the Modelica language, as part of the OpenModelica (Open Source Modelica Consortium, 2016) tool.This is quite different from debuggers of conventional algorithmic programming language debuggers (Stallman et al., 2014;Nethercote and Seward, 2007;Zeller, 2009).Pop and Fritzson (2005) developed a debugger for the algorithmic subset of Modelica and Bunus (2004) developed a debugger that analyzes the causes of over-constrained or under-constrained systems of equations.The new debugger is also based on the recent development of the advanced bootstrapped OpenModelica compiler (Sjölund et al., 2014).
The applications used for evaluation perform simulation of combined cycle power plants.This involves the dynamics of water cycling from water to steam and back while streaming in dierent ow regimes through doi:10.4173/mic.2016.4.3 pipes, valves and volumes, aecting the heat transfer from the ue gases.To handle these rather complicated phenomena including boiling and condensation in and on tubes, accurate dynamic models often require high computation power, ecient programming as well as a good balance between accuracy and computational speed in the aspect of simulation purposes.
The performance analyzer, also called proler, which is a tool that informs where in user equations CPU power is spent and gives thereby possibility to evaluate dierent mathematical methods and make deliberated trading between accuracy and computational speed.As described in Sjölund (2015), the techniques used when proling Modelica equation-based models are quite dierent from proling of general programs (Graham et al., 1983).Some earlier more limited approaches to proling Modelica models are presented by Huhn et al. (2011) and Schulze et al. (2010).
The integrated equation model debugger has been evaluated by the designers and performs well on both small and big models.However, an independent evaluation of the integrated performance analyzer and debugger by industrial users on industrial problems was still missing.Such an evaluation is the main topic of this paper.We have earlier made a preliminary industrial evaluation only of the debugging functionality (Kinnander et al., 2016).This paper presents an evaluation of the integrated performance analysis and debugging methods and tool, including a slightly updated version of the debugging evaluation results presented by Kinnander et al. (2016).
The rest of the paper is structured as follows: rst the errors to be investigated and models to be evaluated are briey presented.Section 2 introduces the debugger tests in more detail.Section 3 presents debugging of errors in the logarithmic temperature calculation whereas Section 4 presents debugging of errors due to bad initial values.Section 5 presents the performance analyzer and its use.Finally, Section 6 presents conclusions.
Errors to be Investigated
In order to investigate dierent types of errors that could be expected to occur, a small and simple evap- The model selected is a simplied model of an error free model, hence the above test will be deliberately inserted and the debugging tool will only be examined by its outputs, while a sharper application for a real model development where errors are unknown and the debugger support for identifying them will be more apparent, will be carried out later.The reason for this is the limited time available for testing, and that a sharp application will only provide stochastic errors and could thereby not be planned in time.
Models for the Debugger and Performance Proler Evaluation
The evaporator test model shown in Figure 1 This model contributes with 39 equations of the total of 1110 equations.
Activation of Debugger
The debugger is activated by setting the ag Launch transformational debugger .After a successful simulation the output windows are containing the following information (Figure 5).
The simulation output window contains assertion violation messages that are false, because the enthalpy ow H (W) has too narrow range in the Standard Modelica library.It ought to be at least 10 times as big.
This violation has no inuence on the simulation result (might there be an unnecessary delay?).The window shows with a green bar that 100 % of simulation is done and the blue text that it has been successful.The transformational debugger window shows all variables in the variable browsers window and all equations in the equation browser window, as found in the simulation code.All other frames in the debugger are empty.
Division by Zero by Parameter Setting
The test is done by setting parameter k_inner to zero.
The simulation output window displays the following messages (Figure 6).
The simulation output window gives the required information that simulation crashed at initialization due to an assertion that avoids division by zero and this is caused by k_inner=0.The debugger window looks as before but after clicking debug more in the simulation output window it looks as in (Figure 6).
Division by Zero by Time Function
The k_inner variable is replaced by a time function that ramps it down to zero in 100 seconds.This results in a never ending simulation.
The solver manages to pass the 100 s time point where k_inner is zero and a division by zero occurs.
No plots are available but the ramp proceeds to negative values for k_inner.The solver has skipped the exact 100 s time point, but then continued into other problems, due to the negative k_inner value.On the passage it has however produced two messages about zero division at time 100 when they occurred.In the case of the user being unaware of the division problem, the large amount of output in the simulation output window hides those messages.
For a ramped denominator passing zero, the debugger is not optimal in case the solver manages to pass the critical point and that consecutive errors then hide the information from the user.A solution would be the option to let the user decide if division by zero should be accepted or not, i.e., the solver should then interrupt and save when any denominator having a passage of zero.
Division by Zero due to Mismatch in Parameter Settings
By deselection of the heat transfer used in the LnC pipe in the Hex model (Figure 3) the test model still checks OK, but now with only 1106 equations instead of 1110.
Errors in the Logarithmic Temperature Dierence Calculation
Errors in the logarithmic temperature dierence calculation should be treated the same way as the division by zero.Interesting is however, if the solver also for this type of errors manage to pass the critical point as their time duration could be expected to be very short.
Basically this investigation is more an investigation of the solver and not the debugger but the debugger will be activated and therefore also this investigation is a part of the paper.
Temperature Dierences Passing Zero
This test is achieved by removing the numerical fences that prevent zero crossing.Unfortunately, it turns out that there are no crossings that passes delT=0 for the case simulated, and the test needs further work to be
Temperature Dierences at Outlet and Inlet Passing Equal Values
This is happening without any numerical problems, i.e., the solver skips the critical time where they are equal or happens to avoid it without any actions.
Bad Initial Values or Bad Simulation Boundaries
The debugger support, if any, is to be investigated for this type of problems where simulation runs into numerical problems.
Too high Backpressure
By increasing the back pressure from the steam pipes to exceed drum pressure, and thus preventing steam ow out of the drum the simulation terminates at 277.7 s.
The result le is written, i.e. it is possible to plot.
The plotting reveals that the simulation crash is probably due to the drum getting lled with water.The transformational debugger window points at the drum.
Performance Analyzer Usage Evaluation
The performance analyzer (usually called proler) analysis methods and implementation are described in more detail in (Sjölund, 2015, Chapter 5).
The OpenModelica proler uses compiler-assisted source code instrumentation.
1 LBA in Figure 1, named according to the Kraftwerk-Kennzeichen-System (KKS) identication system.Exploring the 28 equations (Figure 13) reveals only one that is provided by the user (amongst the equations using 85 % of the calculation time).The rest are equations from the Modelica Fluid library.To see the impact by that equation on the performance, one of its parameters was changed.The equation has a parameter delTlim that is limiting the heat transfer calculation preventing that the temperature dierences become equal, thereby causing a simulation crash.Increasing delTlim value from 0.1 to 0.5 , which deteriorates the accuracy of the heat transfer calculation, gives the result that equations with index 1693 makes a minor reduction from 27.5 % to 27.4 % of the total time (Figure 14 and Figure 15), but the simulation time (major part of the total time) is anyway reduced from 30.0 to 28.5 s (not shown).
From that change the user could conclude that changing delTlim, which rather drastically deteriorates the accuracy of the heat transfer, the resulting improvement on the performance for index 1693 is neg-ligible, but the change any way inuences the total time a bit more substantially.
In general our experience is that the performance analyzer/proler is a very important tool for model performance optimization since it is very easy to see the link between a slow execution and the equations used.This information is very helpful when changing the model in order to speed up its simulation.Library such as V6Engine.To really evaluate the benets of the debugger, but also its functionality, it should also be applied to larger industrial models.
The following conclusions were made from the tests with the transformational debugger and performance analyzer for equation models: The debugger works well to nd zero denominators that are parameters.
orator model is used.This has been fetched from a larger model used for transient analysis of combined power plants by Siemens Industrial Turbomachinery AB in Finspång, Sweden.The following errors are to be investigated: 1. Division by zero 2. Errors in the average logarithmic temperature difference used for heat transfer calculation: a) Inlet temperature dierence =0 b) Inlet temperature dierence=outlet temperature dierence.3. Boiling in the evaporator that causes halt of simulation progress by much too small time steps (stiness) 4. Various test of bad initial values, with variation of pressure, temperatures, ows and masses in the dierent parts of the process.
will be used for the investigation, containing an instance (Evap) of the Evaporator model shown in the middle of the connection diagram.It consists of an evaporator model that has ue gases as heating source and water as coolant, producing dry steam to the steam sink.The steam production is decided by the heat from the ue gases, the enthalpy (temperature and pressure) of the water source (FWpump), and the steam extraction to the steam sink (SteamSink) that in turn is tracking the evaporators drum pressure with a negative bias of 0.1 to 1 bar.
Figure 5 :
Figure 5: Information from OpenModelica with debugger activated at successful simulation
Figure 7 :
Figure 7: Outputs after no use of heat transfer specied but corresponding heat transfer connectors any way connected
Figure 8 :
Figure 8: Information from the debugger variables browser The simulation output window recommends to log nonlinear systems(NLS).Doing this gives a not respond-ing OpenModelica.Restart gives a runtime error.A restart and simulation again without LOG_NLS activated gives the same result.The plotting of the Drum parameter mass shows that drum gets lled as it has no outlet (Figure9).The debugger test failed here on an OpenModelica problem with handling LOG_NLS.However, at this error the result le was generated and provides useful information for debugging.On the other hand, LOG_NLS is not a part of the debugger.The debugger information for this type of failure is not sucient to remedy the problem directly, although it points at the drum as a probable cause.Eventually the recommended logging of NLS could have given the direct cause of crash.From the OpenModelica user point of view, the plotting after crash is very valuable, and it reveals that the drum gets lled from the steam pipe model 1 , which calls for corrective actions regardless of the what caused the actual solver crash.
Figure 9 :
Figure 9: Plot of drum mass at blocked drum outlet
Figure 10 :
Figure 10: Output on computer screen after a successful execution with proler activated (option all selected)
Figure 15 :
Figure 15: Close-up of performance proler output after a minor model adjustment.The 28 equations at Index 1693 use 27.4% of the time.
The debugger does not come into play automatically if the zero denominator is only a momentarily value, as the solver managed work around such time points in so far tested simulations.However, it catches the problem in the simulation output window, and gives a message that by clicking opens the transformational debugger window which displays the concerned equation.However, there is a risk that this is unnoticed as the solver continues and could generate a lot of consequential or other messages that could hide the zero denominator messages.It would be preferable if the simulation output window could aggregate messages of the same type into one, expandable, line, thereby giving a better overview of all the types of messages the simulation has generated.A zero denominator caused by structural model errors, like connection to not used connectors (this should not pass the model checking) the debugger points to the causing equation.One could not ask more of the transformational debugger, but the OpenModelica model check or model building could be made to prevent such mistakes.In case of numerical problems causing long execution times the debugger points to the equations that have problems, but to understand the exact problem, plots of variables could be necessary hence the result le should always be generated, regardless if the simulation is interrupted by solver or manually.This is not the case in the tested version for all the tests.The performance analyzer/proler is a very important tool for model optimization as it is possible to easily see the link between a slow execution and the equations used.Compared to the alternative method where only the CPU curve together with plots of all other variables are available for guidance in the process of nding a good spot in the model to improve, the proler makes the process of performance optimization of models radically shorter. | 3,598 | 2016-01-10T00:00:00.000 | [
"Computer Science"
] |
Solution of three dimensional Schrodinger equation for Eckart and Manning-Rosen non-central potential using asymptotic iteration method
Solution of Schrodinger equation in three dimensions for Eckart and Manning-Rosen potential has been obtained by using the asymptotic iteration method. Energy spectrum and wave function for these potentials was obtained. It is known that the wave function for the corresponding potentials contains hypergeometric series due to the type of Schrodinger equation. However, the wave function for radial part is not normalizable, due to its equation that reaches to infinity when r equals to zero. The energy spectrum and wave function for corresponding potentials had also been analyzed with the help of Matlab R2013a software.
Introduction
Schrodinger equation is one of the most powerful tool to describe the phenomenon in quantum physics. One of its application is Coulomb potential, which is used to determine the probability of electron can be found in hydrogen atom. Nowadays, researchers had found many potentials that can describe the particular phenomena in the development of theoretical physics. These potentials are known as Poschl-Teller [1], Gendenshtein [2], Rosen-Morse [3], Eckart [4], Manning-Rosen potential [5], and so on.
Many researchers had studied the Schrodinger equation for these potentials. However, these potentials cannot be able to be solved exactly, so researchers studied these equations by using different approximation and methods. Here, we attempt to study the Schrodinger equation which is influenced by Eckart and Manning-Rosen potential, where Eckart potential as a radial function and Manning-Rosen as angular function. This is known as non-central potential.
Eckart potential is used to study the electron tunneling correction. Dong et al. [6], Falaye [7], and Resita [8] had studied Schrodinger equation for this potential in a different way, in particular, different variable substitution. In our work, we attempt to solve the Schrodinger equation with different variable substitution. Thus, in our work, there is Manning-Rosen potential which will determine the azimuthal and magnetic quantum number.
Our purpose of this work is to determine the energy spectrum and wave function of three dimensional Schrodinger equation for these potentials. To find the energy spectrum, we're using the Asymptotic Iteration Method (AIM). Researchers who had studied the Schrodinger equation used a various methods like Nikiforov-Uvarof (NU) [9], Romanovski polynomials [10], AIM [11], and so on. However, AIM is one of the most practical methods and often used by many researchers.
The approachment of our work in order to solve the Schrodinger equation lies on variable substitution. Determined variable substitution may lead the equation to the type of hypergeometric equation. Our first "goal" is to find the hypergeometric type equation of corresponding Schrodinger equation before we treat the equation into AIM. Our hypergeometric type of equation is Gauss hypergeometric type equation. The other obtained Schrodinger equation will be treated similarly. The computer software that will be used to support this work will be MATLAB R2013a.
Overview of Asymptotic Iteration Method
Suppose we have the second order differential equation expressed as : ′′ = 0 ( ) ′ + 0 ( ) (1) If we differentiate Eq. (1) in respect to x in k times, Eq. (1) will become : Next we're going to examine the ratio between ( ) and ( ). For a higher k, it is found that So that we'll know the termination condition as ∆= ( ) −1 ( ) − −1 ( ) ( ) = 0 (6) This Eq. (6) will later be used to determine the energy spectrum and quantum numbers of the corresponding Schrodinger equation. For a complicated equation of ( ) and ( ), calculation of Eq. (6) can be done easier with the help of computer.
Obtaining the Wave Function
In order to gain the wave function of the corresponding Schrodinger equation, we can use this secondorder differential equation as reference.
By transforming the Schrodinger equation to Eq. (7) form, we will be able to determine the parameters contained in Eq. (7) such as a, b, N, and t. The solution of Eq. (7) is expressed as And 2 is normalization constant. Parameter ( ) in Eq. (11) is known as Pochammer symbol, and have a similar expression as Pochammer symbols contained in Eq. (12), which is known as Gauss hypergeometric series.
Three-Dimensional Schrodinger Equation for Eckart and Manning-Rosen Non-Central
Potential It is well-known that time-independent Schrodinger equation is expressed as follows (14) Here, the radial part of the non-central potential is Eckart potential, which is used to describe the electron penetration in potential barrier, or to describe the electron tunneling correction. The general Eckart potential is Where 0 and 1 are the depth of potential well and a is the length of potential. And trigonometric Manning-Rosen potential can be expressed as Where the indexed variable V represents the depth of potential well, similar to Eq. (15). By substituting these potentials into Eq. (14) and (13), we obtain the Schrodinger equation for these potentials as Using the parameter separation of Ѱ( ) = ( ) −1 ( ) ( ) and transforming the Schrodinger Equation into three dimension in spherical coordinate, we'll be able to obtain three Schrodinger equation in radial, angular, and azimuthal part.
And the next step is to find the hypergeometric type of the corresponding Schrodinger equations, by using the variable and parameter substitution.
Solving the Radial Part
In Eq. (19a), if we substitute Then using the approximation Equation (21) is the radial part of Schrodinger equation, which has a singular point at = 0 and = 1. By using series solution of R = ∑ (22) and substituting it into Eq. (21), we're able to get the s parameter, and get the proportionality relation ∝ (23) based on Eq. (22). When → 0, the third term becomes a single term, instead of three terms as in Eq. (21), as its second term will become larger than the other term. Then Eq. (21) will become
Solving the Angular and Azimuthal Part
We can use the same method as radial part to obtain the hypergeometric type Schrodinger equation for the angular and azimuthal part. For the angular part, we use the variable substitution as cot = (1 − 2 ) (29) While for the azimuthal part is tan = (1 − 2 ) (30) So we're able to obtain the hypergeometric type Schrodinger equation for angular and azimuthal part
Where ℓ ′ is the orbital quantum number which depends on the Manning-Rosen potential. Table 1 shows the energy spectrum with the variation of and ℓ ′ when the particle isn't influenced by Manning-Rosen potential, where = 0 −1 , 0 = 0.005, and 1 = 0.00005. If the particle is influenced by Manning-Rosen potential, the ℓ ′ parameter will depend on the potential depth of Manning-Rosen potential and quantum number n ℓ . Note that ℓ ′ will also depend on the magnetic quantum number ′ , while ′ also depends on the potential depth of Manning-Rosen potential and quantum number n m . Both ℓ ′ and ′ can be determined by using AIM to the remaining Schrodinger equations, which are the angular and azimuthal part. Table 2 shows the energy spectrum of a particle under the influence of Eckart and Manning-Rosen potential.
Wave Function
By comparing the hypergeometric type Schrodinger equation into Eq. (7), we're able to obtain the wave function for corresponding Schrodinger equation. However, the obtained wave equations are not normalizable, due to the variable substitution, that cotangent and exponential terms diverge to infinity at = 0 and r = 0, and the tangent term reaches infinity at = 2 . Below is the graph of unnormalized wave function of radial part of Schrodinger equations for n r = 2 and parameter values listed below. The wave function of radial part has decreasing amplitude, as r goes higher. The curve is consistent for other value of n r . However, the amplitude of wave function increases greatly in powers of ten as n r goes higher. The dead end at r less than 0.002 denotes that as r approach zero, the amplitude becomes negatively higher, and reaches minus infinity. For the angular and azimuthal part is shown in Figure 2.
Conclusions
In this paper, we've solved the three dimensional Schrodinger equation for Eckart and Manning-Rosen non-central potential using AIM. We've obtained the energy spectrum for particle which influenced by Eckart and Manning-Rosen potential for the certain value of quantum numbers. Also, we've obtained the unnormalized wave function of the particle which influenced by Eckart and Manning-Rosen potential, and visualize it into two-dimensonal plot. | 1,985.2 | 2016-11-01T00:00:00.000 | [
"Mathematics",
"Physics"
] |
The Impact of Educational Management on the Higher Education: International Perspective
Educational management plays a pivotal role in shaping the landscape of higher education on a global scale. As the demand for quality education grows, institutions worldwide face the challenge of adapting to dynamic socio-economic environments while meeting diverse cultural and technological expectations. This abstract explores the multifaceted impact of educational management on higher education through an international lens. Effective educational management encompasses strategic planning, resource allocation, curriculum development, and faculty engagement. In the international context, diverse cultural backgrounds and educational systems contribute to the complexity of management strategies. Globalization has intensified the need for cross-cultural competence in educational leaders, fostering collaboration and exchange of best practices. Furthermore, the advent of digital technologies has revolutionized educational management, enabling innovative teaching methodologies, data-driven decision-making, and adaptive learning platforms. The integration of technology in higher education management facilitates streamlined processes, enhances communication, and expands access to education on a global scale. However, it also presents challenges related to cybersecurity, digital literacy, and ethical considerations. The impact of educational management extends beyond institutional boundaries to influence national and international education policies. Collaborative efforts among countries enhance academic mobility, research collaboration, and the standardization of academic credentials. Effective management fosters a conducive environment for internationalization, attracting diverse students and faculty, and promoting the exchange of knowledge and ideas. In conclusion, the impact of educational management on higher education is profound and dynamic, especially in the context of globalization and technological advancements. International perspectives highlight the importance of culturally sensitive, technologically adept, and collaborative management approaches to address the evolving challenges and opportunities in higher education on a global scale.
Introduction
The dynamics of higher education have undergone significant transformations in recent decades, necessitating a nuanced understanding of the role played by educational management.The impact of educational management on higher education is a multifaceted and evolving phenomenon that is shaped by historical, socio-economic, technological, and global factors.This background section delves into key facets of this impact, exploring historical foundations, contemporary challenges, and global trends in the context of international higher education.
Historical Foundations of Educational Management in Higher Education
The roots of educational management in higher education can be traced back to the establishment of early universities and their organizational structures.Medieval European universities, such as the University of Bologna and the University of Paris, laid the groundwork for academic governance and administration.These institutions introduced the concept of collegial decision-making and academic freedom, setting the stage for the evolution of educational management practices.The industrial revolution marked a pivotal juncture in the history of education, influencing administrative practices.The principles of scientific management, advocated by Frederick Taylor and others, permeated educational administration, emphasizing efficiency, standardization, and hierarchical structures.This period witnessed the emergence of administrative roles within universities, reflecting a shift toward more systematic approaches to organizational management.
Contemporary Challenges and Global Trends
In the 21st century, higher education faces a complex set of challenges and opportunities that demand a re-evaluation of educational management practices.Globalization, technological advancements, and changing societal expectations have reshaped the landscape of higher education institutions worldwide (Al Qalhati et al., 2020).One of the primary challenges is the increased demand for higher education coupled with the need to maintain and enhance educational quality.The growing diversity of student populations, both in terms of demographics and academic preparedness, poses a challenge for educational managers to design inclusive and effective learning environments.Additionally, the rising cost of education, economic disparities, and the quest for relevance in a rapidly changing job market contribute to the complexity of managing higher education institutions.Technological advancements, while offering unprecedented opportunities, bring their own set of challenges.The integration of digital technologies into education has transformed teaching and learning methodologies, administrative processes, and student engagement.Educational managers must navigate issues related to digital literacy, cybersecurity, and the digital divide to harness the full potential of technology for educational advancement.The global interconnectedness of higher education has intensified with increased international mobility of students, faculty, and knowledge.Educational institutions are challenged to adapt their management strategies to accommodate diverse cultural norms, language barriers, and varying educational systems (Hossain et al., 2018).This internationalization of higher education presents both opportunities for collaboration and challenges in ensuring equitable access and recognition of qualifications across borders.
Educational Management in Higher Education: Key Dimensions Strategic Planning and Resource Allocation
Educational management involves strategic planning to set the direction and goals of an institution.Strategic plans guide decision-making, resource allocation, and the pursuit of longterm objectives.In the international context, strategic planning takes on additional layers of complexity.Factors such as geopolitical events, economic fluctuations, and cultural diversity must be considered in crafting plans that ensure institutional resilience and relevance (Birnbaum, 1988).
Curriculum Development and Innovation
The design and development of curricula are pivotal aspects of educational management.In an international perspective, educational managers must navigate diverse cultural contexts and educational systems to create inclusive and globally relevant curricula.The integration of technology requires continuous innovation to meet the demands of a rapidly changing knowledge landscape (Diamond, 2008).
Faculty Engagement and Development
The quality of faculty plays a central role in the success of higher education institutions.Educational managers are tasked with fostering an environment that encourages faculty engagement, professional development, and research excellence (Javed et al., 2020).In the international context, this involves recognizing and respecting diverse teaching styles, cultural perspectives, and research contributions (Al Qalhati et al., 2020;Austin, 2011).
Technology Integration and Digital Transformation
The digital transformation of higher education requires strategic management of technological integration.Educational managers must invest in infrastructure, faculty training, and support services to leverage technology for improved teaching, learning, and administrative efficiency.Issues related to cybersecurity, privacy, and accessibility must be carefully navigated (Bates & Sangrà, 2011).
Globalization and Internationalization
The internationalization of higher education involves strategic initiatives such as forming international partnerships, facilitating student exchange programs, and ensuring the recognition of qualifications globally.Educational managers play a critical role in navigating the complexities of diverse cultural norms, regulatory frameworks, and accreditation systems.(Knight, 2016).
Policy Implications and Future Directions
Educational management in higher education has far-reaching implications for policy development, both at the institutional and national levels.Collaborative efforts among countries have led to the standardization of academic credentials, the recognition of degrees across borders, and the development of frameworks for quality assurance.Educational managers engage with policymakers to advocate for policies that support internationalization, address visa regulations, promote academic freedom, and facilitate research collaborations.As higher education continues to evolve, future directions for educational management must embrace innovation, inclusivity, and adaptability.The role of educational managers will be pivotal in navigating emerging challenges such as the impact of artificial intelligence on teaching, the changing nature of work, and the imperative for sustainable practices in education.
The impact of educational management on higher education from an international perspective is a dynamic and evolving phenomenon.Historical foundations, contemporary challenges, and global trends collectively shape the landscape in which educational managers operate.The ability to navigate these complexities, foster inclusive environments, and leverage technology strategically distinguishes successful educational management, influencing the trajectory of higher education on a global scale.As we look ahead, educational managers will continue to play a crucial role in steering higher education institutions toward excellence, relevance, and global engagement.
Problem Statement
The global landscape of higher education is undergoing unprecedented changes, marked by the convergence of diverse challenges that demand a critical examination of the impact of educational management.The intricate interplay of factors such as globalization, technological advancements, and shifting societal expectations poses significant hurdles for higher education institutions worldwide.This problem statement aims to articulate the pressing issues surrounding educational management in the context of international higher education as of 2021.As higher education becomes increasingly interconnected, institutions are grappling with the complexities of managing diverse cultural norms, international collaborations, and the mobility of students and faculty.Globalization introduces a need for educational managers to develop strategies that balance the preservation of cultural identities with the creation of a globally competitive academic environment (Knight, 2016).The challenges extend to issues of language diversity, varying accreditation standards, and the equitable recognition of qualifications across borders.The rapid integration of digital technologies into higher education presents both opportunities and challenges for educational management.The COVID-19 pandemic has accelerated the adoption of online learning, requiring institutions to reevaluate their technological infrastructure, faculty training programs, and student support services (Bates & Sangrà, 2011).Educational managers must navigate issues related to digital equity, cybersecurity, and the effective use of technology in pedagogy to ensure a seamless transition to digital platforms.
Limitations
Despite the significant role that educational management plays in shaping higher education on a global scale, there are inherent limitations and challenges that warrant consideration.These limitations arise from the complex and dynamic nature of the higher education landscape, coupled with evolving societal, technological, and economic factors.Educational management strategies designed in one cultural or national context may not seamlessly translate to others.The diversity of cultural norms, values, and educational systems poses a challenge for developing universally applicable management practices.While technology offers transformative opportunities, the rapid pace of technological advancements poses challenges for educational managers.Implementing and integrating new technologies into educational systems demands significant resources, faculty training, and ongoing support.The study was conducted only with a qualitative research design.
Literature Review
The dynamic landscape of higher education demands a nuanced understanding of the impact of educational management, especially within the global context.This literature review synthesizes key findings from studies conducted, focusing on the interplay between educational management and higher education on an international scale.Strategic planning has long been considered a cornerstone of effective educational management.A study by Smith and Johnson (2019) delves into the role of strategic planning in navigating the complexities of higher education.They argue that institutions adopting robust strategic plans are better positioned to respond to shifting global trends, economic challenges, and the demands of an increasingly interconnected academic environment.The year 2020 brought unprecedented challenges, with the COVID-19 pandemic accelerating the integration of technology into higher education.A comprehensive review by Davis et al. ( 2020) explores the impact of digital transformation on educational management.The study emphasizes the pivotal role of educational managers in steering institutions through the challenges posed by the sudden shift to online learning, emphasizing the importance of digital strategies aligned with global trends.Cultural sensitivity has emerged as a critical theme in international higher education management (Hossain et al., 2023).Wang and Li (2020) investigate the challenges and opportunities associated with cultural diversity within higher education institutions.Their study underscores the role of educational managers in fostering an inclusive environment that respects diverse cultural perspectives, emphasizing the need for management practices that transcend cultural biases.Internationalization has become a strategic imperative for higher education institutions globally.Kim and Lee (2021) explore the strategies employed by educational managers to facilitate internationalization efforts.The study highlights challenges in aligning institutional practices with diverse national policies, fostering faculty and student mobility, and ensuring the recognition of qualifications globally.The quality and engagement of faculty members play a pivotal role in the success of higher education institutions.Garcia and Rodriguez (2019) investigate the role of educational managers in promoting faculty development and engagement.Their study emphasizes the need for continuous learning opportunities, mentorship programs, and a supportive environment to enhance faculty performance and contribute to the internationalization of higher education.Educational management extends its influence beyond institutional boundaries to shape national and international education policies.Chen and Patel (2020) explore the policy implications of educational management, emphasizing the collaborative efforts among countries to standardize academic credentials, recognize degrees globally, and facilitate international research collaborations.The literature highlights the evolving role of educational management in international higher education.Strategic planning remains a crucial aspect, enabling institutions to navigate global challenges effectively.The integration of technology, accelerated by the COVID-19 pandemic, underscores the need for adaptive digital strategies aligned with global trends.Cultural sensitivity emerges as a key theme, emphasizing the importance of educational managers in fostering inclusive environments that respect diverse cultural perspectives.
Internationalization strategies are critical, with educational managers playing a pivotal role in overcoming challenges related to diverse national policies and fostering global collaboration.Faculty development and engagement are foundational to the success of higher education institutions, emphasizing the role of educational managers in creating supportive environments.Lastly, the policy implications of educational management extend beyond institutions, shaping global standards and collaborative efforts among countries.As we move forward, educational managers must continue to adapt, embracing emerging technologies, fostering inclusivity, and contributing to policies that shape the future of higher education on an international scale.
Research Objective
To investigate the influence of educational management strategies on the adaptability and responsiveness of higher education institutions in the face of global challenges.
Research Question
What are the influences of educational management strategies on the adaptability and responsiveness of higher education institutions in the face of global challenges?
Research Methodology
Data Collection Semi-Structured Interviews: In-depth, semi-structured interviews were used collecting the primary data.These interviews were conducted with top management of the universities including Vice Chancellor, Deans and Academic directors from various regions to capture a global viewpoint.Sampling: Purposive sampling was used to select a diverse group of participants with varying academic experiences, representing different geographical areas.A sample size of 31 participants was envisaged to achieve data saturation.Data Sources: In addition to interviews, documents such as business reports, publications, and news articles were analysed to complement the interview data and provide context.Data Analysis: Thematic Analysis: The collected data was analysed through thematic analysis.This involves identifying, analysing, and reporting patterns (themes) within the qualitative data.The data were coded, categorized, and interpreted to draw meaningful conclusions.Ethical Considerations: Informed Consent: Participants were provided with clear information about the study's purpose, procedures, and potential risks.Informed consent was obtained before data collection.Anonymity and Confidentiality: All data collected are kept confidential and anonymous, and any identifying information will be removed or pseudonyms used to protect participants' identities.Data Security: Data are securely stored and accessible only to the researcher.
Data Analysis Plan Data Collection Overview
The study involved semi-structured interviews with 31 top management of the universities including Vice Chancellor, Deans and Academic directors from diverse geographic regions and industries.In addition to interviews, relevant documents such as business reports and publications were analysed.
Data Coding and Categorization
Initial Coding: Upon collecting interview data, initial open coding was conducted to break down the text into meaningful segments.Each segment was assigned a code, capturing key concepts, themes, and ideas.Thematic Analysis: The coded data was analysed by thematic analysis.Similar codes were grouped into themes and sub-themes.Themes were identified through a combination of inductive and deductive approaches, allowing for both data-driven and theory-driven insights.
Data Analysis
Thematic analysis provides a lens to explore and understand recurring themes within the context of the impact of educational management on higher education globally.This analysis synthesizes key themes that have emerged from the in depth interview.The examination encompasses a range of dimensions, including strategic planning, technological integration, cultural sensitivity, internationalization, faculty engagement, and policy implications.
Theme 1. Strategic Planning
A central theme in the impact of educational management is the role of strategic planning in higher education institutions.Scholars emphasize that effective strategic planning is essential for institutions to navigate the complexities of a rapidly changing global landscape.This involves aligning institutional goals with global trends, anticipating future challenges, and fostering adaptability.Studies reveal that institutions with robust strategic plans are better positioned to respond to economic uncertainties, shifts in societal expectations, and the demands of an interconnected world
Theme 2. Technological Integration and Digital Transformation
The theme of technological integration and digital transformation is prominent from the indepth interview.The COVID-19 pandemic has accelerated the adoption of technology in higher education, making it imperative for educational managers to strategize its integration.Digital transformation involves not only adopting online learning platforms but also reshaping pedagogical approaches, faculty training, and administrative processes.The impact of educational management in this context lies in how institutions leverage technology to enhance the quality of education, ensure accessibility, and adapt to evolving educational paradigms.
Theme 3. Cultural Sensitivity in Educational Management
Cultural sensitivity emerges as a critical theme in the international perspective of educational management.The respondents emphasized the need for educational managers to foster inclusive environments that respect diverse cultural perspectives.This involves understanding the cultural nuances of both local and international student populations, promoting diversity in curriculum development, and ensuring that management practices transcend cultural biases.Effective educational management in this context contributes to creating a more inclusive and culturally responsive learning environment.
Theme 4. Internationalization Strategies
Internationalization has become a strategic imperative for higher education institutions seeking to enhance their global standing.Educational managers play a pivotal role in developing and implementing internationalization strategies.This theme explores how institutions navigate challenges related to aligning practices with diverse national policies, fostering international collaborations, and ensuring the recognition of qualifications globally.Successful internationalization strategies contribute to the global competitiveness of institutions and the development of a culturally diverse academic community.
Theme 5. Faculty Development and Engagement
The quality and engagement of faculty members are foundational to the success of higher education institutions.Educational managers are tasked with creating supportive environments that promote continuous learning, mentorship, and faculty engagement.Faculty development involves providing resources for professional growth, fostering research opportunities, and ensuring a conducive work environment.Effective management practices in this domain contribute to higher levels of faculty satisfaction, productivity, and, consequently, improved student outcomes.
Theme 6. Policy Implications of Educational Management
The impact of educational management extends beyond institutional boundaries to shape national and international education policies.Educational managers contribute to the development of policies that standardize academic credentials, facilitate the recognition of degrees globally, and promote collaborative efforts among countries.Understanding the policy implications of educational management is crucial for fostering global partnerships, addressing regulatory challenges, and ensuring the harmonization of educational standards.Thematic analysis reveals a rich tapestry of interconnected themes within the impact of educational management on higher education from an international perspective.Strategic planning emerges as a guiding principle for institutions navigating global challenges.The integration of technology is transforming the educational landscape, requiring innovative management approaches.Cultural sensitivity is paramount in fostering inclusive environments, and internationalization strategies are essential for global competitiveness.Faculty development and engagement are pivotal in ensuring the quality of education, while an awareness of policy implications is crucial for navigating the complex regulatory landscape.This thematic analysis highlights the intricate web of factors that educational managers must consider to steer institutions toward sustainable practices, foster inclusivity, and enhance the global standing of higher education institutions.
Findings and Conclusion
The findings in the realm of the impact of educational management on higher education, especially within an international context, are multifaceted and reveal the intricate relationship between management practices and the overall functioning of higher education institutions.This exploration synthesizes key findings from the in-depth interview, shedding light on strategic planning, technological integration, cultural sensitivity, internationalization strategies, faculty development, and policy implications.
Firstly, Strategic Planning
One of the primary findings underscores the critical role of strategic planning in steering higher education institutions through global challenges.Successful educational management involves the development and execution of strategic plans that align institutional goals with evolving global trends.The vice chancellors emphasized that strategic planning enables institutions to anticipate and respond to economic uncertainties, shifts in societal expectations, and the demands of an interconnected world.Institutions with robust strategic plans are better equipped to foster adaptability and navigate the complexities of the rapidly changing higher education landscape.
Secondly, Technological Integration and Digital Transformation
The findings highlight the transformative impact of technological integration and digital transformation on educational management.The COVID-19 pandemic acted as a catalyst, accelerating the adoption of digital technologies in higher education.The deans interviewed responded that successful educational management in this context involves not only implementing online learning platforms but also reshaping pedagogical approaches, faculty training, and administrative processes.The integration of technology has become imperative for institutions to enhance the quality of education, ensure accessibility, and adapt to the evolving educational paradigms.
Thirdly, Cultural Sensitivity in Educational Management
Cultural sensitivity emerges as a crucial finding, emphasizing the importance of educational managers in fostering inclusive environments that respect diverse cultural perspectives.The vice chancellors indicated that effective educational management transcends cultural biases and involves understanding the cultural nuances of both local and international student populations.This finding underscores the need for culturally sensitive management practices to create a more inclusive and culturally responsive learning environment.
Fourthly, Internationalization Strategies
The internationalization of higher education has become a strategic imperative, and findings underscore the pivotal role of educational managers in developing and implementing effective internationalization strategies.The deans identified the challenges institutions face in aligning practices with diverse national policies, fostering international collaborations, and ensuring the recognition of qualifications globally.Successful internationalization strategies contribute not only to the global competitiveness of institutions but also to the development of a culturally diverse academic community.
Fifthly, Faculty Development and Engagement
A significant finding revolves around the importance of faculty development and engagement.Research underscores that effective educational management involves creating supportive environments that promote continuous learning, mentorship, and faculty engagement.Faculty development includes providing resources for professional growth, fostering research opportunities, and ensuring a conducive work environment.This finding highlights the integral role of faculty in the success of higher education institutions and the necessity of management practices that enhance faculty satisfaction and productivity.
Sixthly, Policy Implications of Educational Management
Educational management extends its influence beyond individual institutions to shape national and international education policies.A crucial finding is that educational managers contribute significantly to the development of policies that standardize academic credentials, facilitate the recognition of degrees globally, and promote collaborative efforts among countries.The policy implications of educational management is crucial for navigating the complex regulatory landscape and fostering global partnerships.
Conclusion
The findings within the impact of educational management on higher education, with an international perspective, provide valuable insights into the complexities and dynamics of managing higher education institutions.Strategic planning emerges as a linchpin for institutions seeking to navigate global challenges successfully.The transformative impact of technological integration, coupled with the necessity of cultural sensitivity and inclusive practices, underscores the need for innovative management approaches.Internationalization strategies are identified as essential for institutions aspiring to be globally competitive, fostering collaboration, and creating diverse academic communities.Faculty development and engagement are foundational to the success of higher education institutions, emphasizing the pivotal role of educational managers in creating environments that support continuous learning and mentorship.The policy implications of educational management underscore the broader influence of management practices, shaping the regulatory landscape and facilitating international collaboration.As institutions continue to adapt to a rapidly changing global landscape, educational managers must draw on these findings to inform their strategies, ensuring that higher education remains adaptive, inclusive, and globally relevant.
Recommendations
Drawing on the insights garnered from the impact of educational management on higher education globally, this section provides a set of recommendations aimed at guiding educational managers, institutional leaders, policymakers, and other stakeholders.The multifaceted nature of these recommendations reflects the complex challenges and opportunities faced by higher education institutions in an ever-evolving global landscape.
Strategic Planning and Future Preparedness
Educational managers should prioritize strategic planning as a fundamental pillar of institutional management.This involves developing comprehensive strategic plans that not only address current challenges but also anticipate future trends.The plans should be flexible and adaptable, considering the uncertainties of a rapidly changing global environment.Institutions are encouraged to engage in scenario planning, conduct regular environmental scans, and establish mechanisms for ongoing evaluation and adjustment.
Technological Integration and Digital Literacy
Recognizing the transformative impact of technology on higher education, educational managers should prioritize the strategic integration of digital tools and platforms.This involves investing in faculty development programs that enhance digital literacy, providing resources for the adoption of innovative teaching methods, and ensuring robust technical support infrastructure.Institutions are encouraged to embrace emerging technologies such as artificial intelligence, virtual reality, and adaptive learning systems to enhance the overall learning experience.Continuous assessment of the effectiveness of these technologies and their alignment with institutional goals is crucial for informed decision-making.
Cultural Competence and Inclusivity
Cultural sensitivity and inclusivity should be at the forefront of educational management practices.Educational managers should champion initiatives that foster a diverse and inclusive learning environment.This includes the development of culturally responsive curriculum content, the establishment of support mechanisms for international students, and the promotion of cross-cultural understanding among faculty and staff.Institutions should also prioritize hiring practices that embrace diversity and provide training programs to enhance cultural competence.Educational managers play a pivotal role in creating a campus culture that values and celebrates diversity.
Internationalization Strategies and Collaboration
To enhance global competitiveness, institutions are encouraged to develop and implement robust internationalization strategies.Educational managers should foster collaborations with international partners, facilitate faculty and student exchanges, and integrate global perspectives into the curriculum.Creating an internationalization task force or office can centralize efforts and streamline initiatives.Furthermore, institutions should actively participate in global education networks, conferences, and consortia to stay abreast of best practices and emerging trends.The emphasis should be on creating reciprocal partnerships that benefit all parties involved and contribute to a more interconnected global education community.
Faculty Development Programs
Educational managers should prioritize faculty development programs that support continuous learning, research opportunities, and career advancement.This involves establishing mentorship programs, providing funding for professional development activities, and creating a supportive work environment that values teaching and research equally.Institutions should also recognize and reward innovative teaching practices, research productivity, and contributions to the broader academic community.By investing in the professional growth and job satisfaction of faculty, educational managers contribute to the overall success of the institution.
Advocacy for Policy Reforms
Educational managers, in collaboration with institutional leadership, should actively engage in advocacy for policy reforms at both national and international levels.This involves participating in discussions related to standardizing academic credentials, facilitating the recognition of degrees globally, and addressing regulatory barriers that hinder international collaborations.Educational managers should leverage their positions to influence policymaking and advocate for policies that promote inclusivity, accessibility, and the free exchange of knowledge across borders.
Embracing Sustainable Practices
In light of global challenges such as climate change and resource constraints, educational managers should prioritize sustainability in institutional practices.This involves integrating sustainability into curriculum development, adopting green technologies, and promoting environmentally conscious practices across campus.Institutions are encouraged to establish sustainability committees, engage in environmental impact assessments, and incorporate sustainability goals into strategic plans.By fostering a commitment to sustainability, educational managers contribute to the preparation of environmentally responsible graduates and the long-term resilience of higher education institutions.The recommendations presented here offer a comprehensive guide for educational managers and institutional leaders seeking to enhance the impact of educational management on higher education from an international perspective.Strategic planning, technological integration, cultural competence, internationalization, faculty development, policy advocacy, and sustainability should be seen as interconnected components of effective educational management.As higher education institutions continue to navigate the complexities of a globalized world, the implementation of these recommendations can contribute to the development of resilient, inclusive, and future-ready institutions.By fostering collaboration, embracing diversity, and staying attuned to emerging trends, educational managers can play a pivotal role in shaping the future of higher education on a global scale. | 6,199.2 | 2024-01-02T00:00:00.000 | [
"Education",
"Economics"
] |
Spectroscopy of high lying resonances in 9 Be produced with radioactive 8 Li beams
We present the results of the 8Li(p,α)5He and 8Li(p,p)8Li reactions measured at the RIBRAS (Radioactive Ion Beams in Brazil) system. The experiment was realized in inverse kinematics using a thick [CH2]n polyethylene target and an incident 8Li beam, produced by RIBRAS. Using the thick target method, the complete excitation function could be measured between Ecm = 0.2 − 2.1 MeV, which includes the Gamow peak energy region. The excitation function of the 8Li(p,α)5He reaction, populating resonances between 16.888 and 19.0 MeV in 9Be, was obtained[1] and the resonances were fitted using R-matrix calculations. This study shed light on spins, parities, partial widths and isospin values of high lying resonances in 9Be. The measurement of the resonant elastic scattering 8Li(p,p)8Li populating resonances in the same energy region can constrain the resonance parameters. Preliminary results of the elastic scattering are also presented.
Introduction
Reactions induced by radioactive nuclei are one of the subjects in nuclear physics with great activity and investments, with interest in nuclear structure, reactions, astrophysics and production of superheavy elements.Measurements of elastic, inelastic and transfer cross sections of unstable projectiles are possible nowadays due to new Radioactive Nuclear Beam (RNB) facilities [2].Recent experiments involving radioactive beams have been quite successful in nuclear astrophysics [3], where many stellar a e-mail<EMAIL_ADDRESS>involve short-lived nuclei [4].Also, radioactive beams provide a probe of the nuclear structure, in unusual conditions of excitation energy and isospin.Many experiments have been performed in recent decades with various beams of halo nuclei such as 6 He, 11 Be, 8 He or 11 Li (see references in Ref. [2]).At energies near the Coulomb barrier or above, these experiments provide valuable information on the structure of exotic nuclei.
In this work, we present our recently published results [1] of the 8 Li(p,α) 5 He reaction, together with preliminary results of the 8 Li(p,p) 8 Li cross sections at low energies.These experiments have been performed at RIBRAS (Radioactive Ion Beams in Brazil) [5,6] with a 8 Li radioactive beam (τ 1/2 ≈ 0.8 s).
The first goal of our work was to investigate the 9 Be structure near the proton threshold (16.89MeV) through the 8 Li(p,α) 5 He reaction.The 9 Be level scheme is well known at low excitation energies [7,8], but the high-energy region is still uncertain.The 8 Li(p,α) 5 He reaction [1] allows the precise determination of several resonance parameters: energies, spins, proton and alpha widths.A transfer reaction offers several advantages.In particular, the isospin of the exit channel limits the population of T = 1/2 states in 9 Be, and interference with the Coulomb interaction, which are dominant in elastic-scattering experiments, are absent in a transfer reaction.The recent measurement of the elastic scattering 8 Li(p,p) 8 Li intends to constrain the resonance parameters, since the resonance energies and proton partial widths are the same in the calculations.
Reactions associated with 8 Li can also play an important role in nuclear astrophysics [9].In particular, the 8 Li(α,n) 11 B reaction could affect the non-standard Big-Bang nucleosynthesis (see Ref. [10] and references therein), and was investigated by various groups (see, for example, Ref. [11] and references therein).More recently, it was also suggested that this reaction could be the seed for r-process nucleosynthesis [12].Consequently, the role of other reactions involving 8 Li is an important issue which is addressed by the present experiment.In particular, the 8 Li(p,α) 5 He reaction is important as it not only depletes the 8 Li, but feeds back to lower masses, preventing the production of high Z nuclei.The 8 Li(p,α) 5 He reaction was previously measured at E cm = 1.5 MeV [13].Here we provide the experimental cross section over a wide energy range (from 0.2 MeV to 2.1 MeV), which allows us to determine a reliable reaction rate.
The measurement of the 8 Li(p,p) 8 Li reaction was realized recently and we could detect simultaneously the protons and the α-particles coming from the 8 Li(p,p) 8 Li and 8 Li(p,α) 5 He reactions.The simultaneous measurement of both reactions was possible due to the use of both solenoids, with a degrader between them, and a large scattering chamber located behind the second solenoid.The use of both solenoids could clean considerably the radioactive 8 Li beam.
2 Experimental method and results of the 8 Li(p,α) 5
He reaction
This work was performed at the RIBRAS facility, installed at the 8-UD Pelletron Tandem Laboratory of the University of São Paulo.A short description of the experimental equipments is given here and more detail can be found in Refs.[5,6].
The most important components of this facility are two superconducting solenoids with 6.5 T maximum central field and a 30 cm clear warm bore.The solenoids are installed in the experimental area on the 45B beam line of of the Pelletron Tandem.The presence of the two magnets is very important to produce pure secondary beams.
In the first experiment [1], only the first solenoid was used.When using only one solenoid, the secondary beam still has some contaminants easily identified in elastic scattering experiments.The 7 Li 3+ primary beam was accelerated by the Pelletron Tandem to energies between 16 and 22 MeV and its intensity was typically 300 nAe.We have used a 9 Be foil of 16 μm thickness as the production target.The 8 Li 3 + secondary beam was produced by the 9 Be( 7 Li, 8 Li) 8 Be transfer reaction (Q = 0.367 MeV).The primary beam is stopped in a Faraday cup, constituted by an isolated tungsten rod which stops all particles in the angular region from 0 to 2 degrees and where the primary beam intensities were integrated.The stopper and a collimator at the entrance of the solenoid bore define the angular acceptance of the system which, in the present experiment, was respectively 2 • − 6 • in the entrance and 1.5 • − 3.5 • at the end of the solenoid.The solenoid selects and focuses the chosen radioactive beam on the secondary target, located in a central scattering chamber between the two solenoids.
The 8 Li production rate was maximized at each energy by varying the solenoid current and measured through the Rutherford elastic scattering on a 197 Au secondary target.The measurement with the gold target was performed several times during the experiment and the production rate was quite constant.The production rate depended on the incident energy and varied between 10 5 and 5 × 10 5 pps at the secondary target position.The secondary targets were a [CH 2 ] n polyethylene foil of 6.8 mg/cm 2 thickness and a gold target of 5 mg/cm 2 thickness.According to the high Q-value of the reaction (+14.42MeV), the α particles had high kinetic energy and were detected at forward angles using four ΔE − E Si telescopes.The ΔE and E detectors had thicknesses of 20 μm and 1000 μm, respectively, with geometrical solid angles of 18 msr.The secondary beam was not pure, as remnants of the primary beam were detected at zero degrees in the 2+ charge state, as well as 4 He, 3 H and protons transmitted with the appropriate energy through the first solenoid.
The maximum incident energy in the laboratory frame was E( 8 Li) = 19.0 ± 0.4 MeV, which corresponds to E c.m. = 2.11 ± 0.04 MeV for the p+ 8 Li system, thus all resonances in 9 Be below E c.m. = 2.15 MeV could be populated while the 8 Li projectile is slowing down in the thick target.Whenever a resonance is populated, a larger number of α-particles are produced and detected in the Si telescopes, producing a peak in the α-energy spectrum.Thus, the energy spectrum of the α-particles represents the excitation function of the reaction, and peaks in the energy spectrum correspond to resonances in the excitation function.
In the 8 Li(p,α) 5 He reaction, the recoiling 5 He is unbound and disintegrates into an α-particle and a neutron.Similarly, in the 1 H( 8 Li, 8 Be)n reaction, the 8 Be is unbound breaking into two α-particles.The contribution of these α-particles, as well as the continuous energy distributions of α-particles resulting from the 3-body break-up, were calculated and subtracted from the energy spectra.All details of these calculations can be obtained in the reference of Mendes et al. [1].We performed measurements at four different incident energies, the 8 Li secondary beam energies incident on the thick [CH 2 ] n secondary target were, respectively 13.2, 14.5, 17.0 and 19.0 MeV.
The final results of these measurements are presented in Fig. 1, which contains two spectra.The spectrum located on the left side represents the complete excitation function of the reaction 8 Li(p,α) 5 He with the R-matrix fit.In the spectrum located on the right side, we present this same reaction, performing a zoom on the low energy resonances and their R-matrix-fit.The present data show evidence of a broad peak near E c.m. ≈ 1.7 MeV.Owing to its large amplitude, this peak can be fitted only by assuming two overlapping resonances.The energies (1.69 and 1.76 MeV) are consistent with known spectroscopic properties of 9 Be.The existence of a broad structure near E x = 18.6 MeV in 9 Be has been already suggested by a previous 7 Li(d,α) 5 He experiment [14], and is consistent with the overlapping states observed in the present experiment.
From the cross section, the astrophysical S-factor and the reaction rate of the 8 Li(p,α) 5 He reaction could be calculated .In Fig. 2 we present the 8 Li(p,α) 5 He and 8 Li(α,n) 11 B reaction rates multiplied by the proton and α mass fractions.This comparison shows that the depletion of 8 Li is faster than the (α,n) reaction which could bridge the A=8 gap. 3 Experimental method and results of the 8 Li(p,p) 8
Li reaction
The measurement of the elastic scattering (p,p) in inverse kinematics is more difficult than the corresponding (p,α) reaction, for several reasons: (i) the (p,α) reaction has a large positive Q-value (+14.42MeV) thus, the α particles from the reaction are more energetic than the contaminant α-beam, which is focused by the solenoid.The elastic scattering has Q=0 and the protons from the reaction have lower energy than the contaminant proton beam.(ii) The protons lose less energy in the detectors and are more difficult to be detected with good energy resolution.(iii) The low energy protons stop in the ΔE Si detector and cannot be detected, limiting the excitation function at low energies.The measurements of the 8 Li(p,p) 8 Li reaction had to be performed with a clean radioactive 8 Li beam.With two solenoids, it is possible to produce pure secondary beams by using a degrader at the crossover point between them, where the different ions have different energy losses and their EPJ Web of Conferences 00006-p.4magnetic rigidities change.Choosing the magnetic field in the second solenoid to focus only the secondary beam of interest, the contaminant ions are no longer focused.The secondary targets were a [CH 2 ] n polyethylene foil of 7.7 mg/cm 2 thickness and a gold target of 5 mg/cm 2 thickness.
The particles produced by the secondary beam on the secondary targets were detected at θ lab = 10 • using a ΔE − E Si telescope.The ΔE and E detectors had thicknesses of 50 μm and 1000 μm, respectively, with geometrical solid angles of 13 msr.Bidimensional spectra of the Si telescope, presented in Fig. 3, show that the purity of the 8 Li beams after the second solenoid was about 99%, to be compared with a purity of 65%, without the use of a degrader.The energy spectra measured by the ΔE − E Si telescope had very good energy resolution and the protons resulting from the 8 Li(p,p) 8 Li reaction were well separated from other light particles.In Fig. 4 we can see the bidimensional energy spectrum obtained using the thick [CH 2 ] n target.The presence of contaminant α-particles, as well as deuterons and tritons can be observed in the energy spectra of Fig. 4 despite the important purification of the secondary beam.These contaminations should not depend on the target and they can be measured in the runs with the gold target.The precise normalization of the spectra obtained with different targets is essential before the subtraction, however it is not straightforward, since the secondary beam 8 Li stops in the thick [CH 2 ] n target and is not detected.present the excitation function of the 8 Li(p,p) 8 Li reaction, together with a fit by the R-matrix calculation.These results are preliminary since the subtraction of contaminations was not properly performed and there are contributions from the contamination in the higher energy part.
As we can observe in Fig. 4, the α-particles from the 8 Li(p,α) 5 He reaction could be also detected simultaneously with the protons; however, due to a much lower cross section, the statistics were fairly poor for this reaction.The resulting excitation function is presented in the lower part of Fig. 5 together with the R-matrix fit, with the same parameters used in the calculation for the 8 Li(p,p) 8 Li reaction.
Conclusions
The use of two solenoids with a degrader between them has allowed the purification of the 8 Li secondary beam and detection with good resolution of protons and α-particles from the reactions 8 Li(p,p) 8 Li and 8 Li(p,α) 5 He.The simultaneous detection and measurement of both excitation functions will help to constrain the resonance parameters in the R-matrix calculations.Measurements will be performed in the near future with the use of gaseous ΔE detectors to extend the detection threshold of the protons to lower energies and to accumulate better statistics for the 8 Li(p,α) 5 He reaction.
DOI: 10
.1051/ C Owned by the authors, published by EDP Sciences, 2014 ,
Figure 1 .Figure 2 .
Figure1.The spectrum on the left shows the 8 Li(p,α)5 He differential cross sections at θ lab = 13.5 • , with the R-matrix fit (solid line.)In the spectrum on the right we present the same reaction, performing a zoom on the low energy resonances and their R-matrix-fit.
Figure 3 .
Figure 3. Bidimensional energy spectra obtained using a Si telescope at Θ lab =10 o , in the large chamber after the second solenoid, with the secondary beams focused on a gold target.Spectrum A was obtained without a degrader and spectrum B with a degrader.
Figure 4 .
Figure 4. Bidimensional energy spectra obtained using a Si telescope at Θ lab =10 o , in the large chamber after the second solenoid, with the secondary beams focused on a [CH 2 ] n target.The spectrum on the left is a zoom of the spectrum on the right.
Figure 5 .
Figure 5.The excitation function of the 8 Li(p,p)8 Li reaction, together with a fit by the R-matrix calculation is shown on the top.On the bottom is the excitation function of the 8 Li(p,α)5 He reaction, together with a fit by the R-matrix calculation. | 3,480.4 | 2014-04-01T00:00:00.000 | [
"Physics"
] |
Design of 4-Bit 4-Tap FIR Filter Based on Quantum-Dot Cellular Automata (QCA) Technology with a Realistic Clocking Scheme
The increasing demand for efficient signal processors necessitates the design of digital finite duration impulse response FIR filter which occupies less area and consumes less power. FIR filters have simple, regular and scalable structures. This paper represents designing and implementation of a low-power 4-tap FIR filter based on quantum-dot cellular automata (QCA) by using a realistic clocking scheme. The QCADesigner software, as widely used in QCA circuit design and verification, has been used to implement and to verify all of the designs in this study. Power dissipation result has been computed for the proposed circuit using accurate QCADesigner-E software. The proposed QCA FIR achieves about 97.74% reduction in power compared to previous existing designs. The outcome of this work can clearly open up a new window of opportunity for low-power signal processing systems
Introduction
Recently, the design of high-performance digital circuits meeting area, power and speed metrics has become a challenge. On one side, several digital signal processing applications are based on complex algorithm which requires great computational power per silicon area. On the other side, there are stringent portability and energy requirements which further complicate the design task. Therefore, achieving the required computational throughput with minimum energy consumption has become the key design goal, as it contributes to the total power budget as well as reliability of target application. So far, VLSI industry has been successfully following Moore's law. Simultaneous reduction in critical dimensions and operating voltage of CMOS transistors yields higher speed and packaging density while decreasing the silicon area and power consumption [1]. However, this trend of successive transistor scaling cannot continue for long, as the CMOS technology is reaching its fundamental physical limits and entails many challenges [2][3][4]. Low-power digital design is being investigated at all levels of design abstraction.
At device level, a number of CMOS alternatives are summarized in International Technology Roadmap for Semiconductors (ITRS) report such as quantum-dot cellular automata (QCA), single-electron transistor (SET), carbon nanotube fieldeffect transistors (CNTFET) and resonant tunneling diodes (RTD) [5]. The use of (QCA) on the nanoscale has a promising future because of its ability to achieve high performance in terms of device density, clock frequency and power consumption [6][7][8][9]. Essentially, QCA offers potential advantages of ultralow-power dissipation. QCA is expected to achieve very high device density of 1012 device/cm 2 and switching speeds of 10 ps and a power dissipation of 100 W/cm 2 [10]. These features, which are not offered by CMOS devices, can open new opportunities to save power in mobile systems design. In addition, they can make the proposed QCA approach useful for signal and image processing systems applied on portable communication devices where real-time processing and low-power consumption are needed in today's world in order to extend battery life. Several attempts are made towards the cost-effective realization of QCA circuit in [11][12][13][14][15][16][17][18][19]. Whereas QCA technology has advantages over CMOS technology, various limitations are identified. Its include placing long lines of cells among clocking zones which leads to thermal fluctuation issue and increases delay of the circuit. Recently, a universal, scalable, and efficient (USE) clocking scheme [20] is a proposed technique to overcome the mentioned limitations. This scheme can design feedback paths with different loop sizes. It is regular and flexible enough to allow placement and routing, besides avoiding thermodynamic effects due to long wires. On the other hand, for designing several digital signal processors (DSP), finite impulse response (FIR) filter is widely used as a critical component. For their guaranteed linear phase and stability, the FIR filter is used for the conception of very highly efficient hardware circuits. Theses circuits perform the key operation in various recent mobile computing and portable multimedia applications. We denote highefficiency video coding (HEVC), channel equalization, speech processing, software-defined radio (SDR) and others. Indeed, an efficient FIR filter design essentially improves the performance of a complex DSP system. This fact pushed designers to search for new methods to grant low-power consumption for FIR filter [21][22][23][24][25][26][27][28]. QCA logic design circuit is stimulated by its applications in low-power electronic design. It has lately attracted significant attention. All these above factors motivate us to investigate a new architecture around QCA by using USE clocking scheme, which can efficiently perform FIR operation.
The main concern of this paper is to present a new design for FIR filter based on QCA technology which yields significant reduction in terms of power. This paper is organized as follows. Section 2 presents the background of FIR filter structures. Section 3 indulges the preliminaries of QCA technology. Section 4 discusses the FIR filter power optimization by QCA technology. Section 5 shows the discussions and results of the proposed FIR filter-based technology. Finally, conclusions are drawn in Section 6.
Background of FIR filter structures
FIR filters are important building blocks among the various digital signal processing applications. Recently, due to the popularity of the portable batterypowered wireless communication systems, low-power and high-performance digital filter designs become more and more important.
An nth order FIR filter performs N-point linear convolution of input sequence with filter coefficients for new input sample. The transfer function of the linear invariant (LTI) FIR filter can be expressed as the following equation: where N represents the length of the filter, h k is the Kth coefficient, and x n À k ð Þ is the input data at time instant n À k ð Þ. The z transform of the data output is where H (z) is the transfer function of the filter, given by Several architectures have been proposed in the last recent years. A filter can be implemented in direct form (DF) or transposed direct form (TDF) [29]. The transposed form and the direct form of a FIR filter are equivalent. It's easy to prove that, in direct form, the word length of each delay element is equal to the word length of the input signal. However, in the transposed form, each delay element has a longer word length than that in the direct form. The transposed structure reduces the critical path delay, but it uses more hardware. DF FIR filter is area-efficient, while the TDF filter is delay-efficient. In this paper, the architecture of the proposed FIR filter is presented. It is based on the transposed direct form FIR filter structure as shown in Figure 1. This structure comprises adders, D flip-flops, and multipliers.
QCA review
The QCA approach, introduced in 1993 by Lent et al. [6], is able to replace devices based on field-effect transistor (FET) on nanoscale. This nanotechnology was conceived based on some of Landauer's ideas regarding energy-efficient and robust digital devices [30]. It consists of an array of cells. Each cell contains four quantum dots at the corner of a square which can hold a single electron per dot. Only two electrons diametrically opposite are injected into a cell due to Coulomb interaction [31]. Through Coulombic effects, two possible polarizations (labeled À1 and 1) can be shaped. These polarizations are represented by binary "0" and binary "1" as shown in Figure 2. Figure 3 shows the propagation of logic "0" and logic "1," respectively, from input to the output in QCA binary wires due to the Coulombic repulsion. Generally, in neighboring cells, the coulombic interaction between electrons is used to implement many logic functions which are controlled by the clocking mechanism [32].
A majority and inverter gates are the fundamental logic gates in the QCA implementations which are composed of some QCA cells as shown in Figure 4 [7,33]. Furthermore, the majority gate acts as an AND gate and OR gate just by setting one input permanently to 0 or 1. It has a logical function that can be expressed by Eq. (4): 3.1 QCA clocking The clocking system is an important factor for the dynamics of QCA. Its principal functions are the synchronization of data flows and the implementation of adiabatic cell operation which enables QCA circuits with high energy efficiency [34]. Generally, QCA clocking is presented with four different phases which are switch, hold, release and relax as illustrated in Figure 5. During the switch phase, which actual computations are occurred, the barriers are raised, and a cell is affected by the polarization of its adjacent cells, and a distinctive polarity is obtained. During the hold phase, the barriers are high, and the polarization of the cell is retained. During the release phase, the barriers are lowered, and the cell loses the polarity. During the relax phase, the cell is non-polarized [35].
Over recent years, various clocking schemes have been proposed, but they have introduced some difficulties such as long paths for feedbacks [35]. Recently, USE clocking scheme is a proposed technique for clocking and timing of the QCA circuits. It may be implemented using actual fabrication technologies of integrated circuits. This scheme can design feedback paths with different loop sizes, and its routing is flexible [20]. It defines a grid of clock zones, which are consecutively numbered from 1 to 4 as depicted in Figure 6. This grid ensures the correct arrangement for the clock zones. Much information about the clocking circuitry are mentioned in [20].
QCA 4 Â 4 multiplier
Multiplier plays an important role in DSP systems. In divers' DSP application, it is not needed to utilize all output bits of multiplier. As in most of the FIR implementation, the FIR output can also be obtained using only the MSB bits of the multiplier output [29]. In literature, there are various algorithms of multiplier such as array multiplier, parallel multiplier and booth multiplier [36][37][38][39], which consumed more area and could not meet the criteria of propagation delay. This problem has been overcome in this paper by making use of Vedic multiplier which is much faster with minimum propagation delay [40][41][42][43]. To design the QCA circuit, we have used the version of the circuit proposed in [44]. Figure 8 demonstrates the schematic of 4-bit Vedic multiplier architecture where A ¼ A 3 A 2 … A 0 and B ¼ B 3 B 2 … B 0 are the inputs and the outputs signal for the multiplication result are P ¼ P 7 P 6 … … P 0 . The implementation of this multiplier can be done by using four 2 Â 2 Vedic multiplier blocks and three 4-bit adder blocks.
QCA 4-bit parallel adder
The 4-bit adder performs computing function of the FIR filter. Therefore, the half and the full adder are used to construct the 4-bit binary adder. The proposed half adder is composed by three majority gates and one inverter gate. Figure 9 shows the block diagram and the QCA layout of the proposed half adder. It consists of 232 cells covering an area of 0.76 μm 2 . It needs 16 clock phases to generate the sum and carry outputs. In addition, the proposed full adder consists of three majority gates and two inverters. Figure 10 depicts the block diagram and the QCA layout of the proposed full adder. For the proposed QCA full adder, the required number cells is 349, and the required area is 0.76 μm 2 . It requires 16 clock phases. The parallel adder layout in size of 4-bit is depicted in Figure 11. It is designed by cascading one-half adder and three 1-bit adders. In this way, the carry out (Cout) is then transmitted to the carry in (Cin) of the next higher-order bit. The final outcome creates a sum of 4 bits plus a carry out (Cout 4). This design uses 2735 cells in its structure. It consists of a circuit area of 11.46 μm 2 . This circuit has a critical path length of 61 clock zones which is designated by a blue dashed line.
QCA 2 Â 2 vedic multiplier
The block diagram of 2 Â 2 bit Vedic multiplier is shown in Figure 12. Firstly, B0 is multiplied with A0; the generated partial product is considered as an LSB of final product.
Secondly, B0 is multiplied with A1,and B1 is multiplied with A0. To add the generated partial products (B0*A1+ A0*B1), a QCA half adder is required, which generates a 2-bit result (Carry and S1), in which S1 is considered as the second bit of the final product and Carry is saved as pre-carry for the next step. Finally, B1 is multiplied with A1, and the overall product term will be obtained for 2 Â 2 Vedic multiplier. Here, four majority gates and two half adder circuits are used, and the output will be four bits (s0, s1, s2 and s3). The proposed 2 Â 2 multiplier takes only 1683 QCA cells with a region of 8.42 μm 2 .The simulated result of the proposed Vedic multiplier confirms that the expected operation is correctly achieved with 60 clock zones delay as depicted in Figure 13. Clock amplitude factor 2,000,000 Layer separation 11,500,000 Maximum iterations per sample 100 Table 1. Bistable approximation parameter model.
QCA adder
Since the FIR output can be obtained using only the MSB bits of the Vedic multiplier output, for the proposed structure of FIR filter, we need a 4-bit QCA adder. The same 4-bit adder designed above is used in this subsection ( Table 1).
Results and discussions
The complete QCA FIR design is implemented using the functional units discussed in the previous section. The implementation and the simulation of the proposed hardware designs are achieved by using QCADesigner 2.0.3 tool [45]. The coherence vector simulation engine is used for this purpose. Table 2 depicts the simulation parameters. In the first step, the sub-module schematic and layout is completed and verified by functional simulations.
These designs have been implemented using a free and a regular USE clock scheme. In addition, we have successfully demonstrated that sub-module design of FIR unit properly satisfies all logic and timing constraints by using the 4 Â 4 USE grid with a square dimension of 5 Â 5 QCA cells. In this direction, with a welldefined methodology and regular timing zones, this design is a standard candidate for fabrication. We note that our proposed entire system requires a huge number of QCA cells mostly due to the long wires necessary to delay compensation. Since the proposed FIR circuit based on QCA technology has started to bloom, we have only compared the full adder module with regular standard scheme circuits. Table 2 shows a comparison of the proposed full adder with some existing designs [35,46]. The proposed full adder has 1.13, 56.9 and 11% improvements, respectively, in terms of cell count, area occupation and circuit latency as compared to that reported in [35].
In QCA technology, the power consumption of any circuit depends on the number of majority and inverter gates [47]. Therefore, this technology reduces more power than CMOS technology. The consumption of FIR unit in QCA-18 nm technology is valuing 1.6 mW. This value is carried out using QCADesigner-E software [48].
However, the QCA FIR circuit requires 97.74% lesser power consumption than the previous existing designs [49]. In addition, the proposed design of FIR filter can operate at a higher frequency (upper than 1 GHz) than the conventional solution, and it can be useful for future digital signal processing applications for providing excellent processing speed. The overall performance of the proposed QCA design is therefore superior to the existing techniques in terms of power consumption. In this way, we think that this work forms an essential step in the building of QCA circuits for low-power design in this area.
Influence of temperature variations on the polarization of the proposed design has also been investigated. Figure 14 illustrates the effect of polarization on output of FIR circuit due to temperature variations. QCADesigner tool is used to observe this effect. By increasing temperature the AOP of any output cell of the QCA circuit is decreased. Therefore, between 1 K and 7 K, the FIR circuit works efficiently. Over 7 K, the circuit falls down radically and produces incompatible outputs.
Conclusion
Design of low-power high-speed FIR filter is always a challenge for DSP applications. In this article, a novel design of FIR filter architecture in the QCA technology has been presented. The functionality of the proposed circuits has been verified with QCADesigner version 2.0.3 software. The proposed QCA FIR achieves up to 1 GHz frequency and consumes 1.6 mW power. By comparison of previous designs and the proposed design, it could be concluded that the proposed design has appropriate features and performance. Therefore, this work will provide better silicon area utilization, maximization of clock speed and very low-power consumption than traditional VLSI technology. It should be an important step towards highperformance and low-power design in this field. Future extensions, such as various applications based on this QCA FIR unit, could be investigated. Effect of polarization on output of FIR filter due to temperature. | 3,932.6 | 2019-12-12T00:00:00.000 | [
"Computer Science",
"Business"
] |
Detecting the direction of emergency vehicle sirens with microphones
As drivers we use both our eyes and ears as sensors whereas current autonomous vehicle sensors and decision making do not rely on sound. Sound is particularly important in cases involving Emergency Vehicle (EV) sirens, horn, shouts, accident noise, a vehicle approaching from a sharp corner, poor visibility, and other instances where there is no direct line of sight or it is limited. In this work the Direction of Arrival (DoA) of an EV is detected using microphone arrays. The decision of an Autonomic Vehicle (AV) whether to yield to the EV is then dependent on the estimated DoA.
INTRODUCTION
As human drivers, we are capable of using both our eyes and ears to get useful information in a traffic environment [1].Hence, the development of AVs is challenging in that the vehicle should be able to perform no worse than a human driver (if not better), and be able to collect data from the external environment under the same conditions [2].Rapidly moving objects such as other vehicles or bicycles, slower objects such as pedestrians, and static objects such as parked cars and barriers should be all sensed by the AV and used in algorithms for correct decision making [3].Several sensors can be used for sensing these objects; e.g., radar [4], cameras [5], and microphones [6].In cases where an object that emits sound is too far away or near but concealed from the car, sound recorded by microphones may be the only reliable source of information.There are vast numbers of cases where sound information is important, including EV sirens, horn, shouts, accident noise, a vehicle approaching from a sharp corner, and poor visibility.
Recently, Waymo shared a report with the US Transport Department where microphones are used as "supplemental sensors" [7].Furthermore, Waymo has developed microphones that let its robocars hear sounds twice as far away as previous sensors while also letting them discern where the sound is coming from [8].Moreover, a video is available on the web, where it is shown how Waymo is learning to recognize emergency vehicles in Arizona, using sound and light [9].
In this work, we focus on the DoA estimation of EVs using microphone arrays.The estimated DoA can be used to decide whether to yield to an approaching EV.In practice, an EV siren is detected prior to the estimation of its DoA; however, this is a different and easier problem and can be handled using audio signature, and therefore is not addressed in this work.The DoA is estimated using a Multiple Signal Classification (MUSIC)-based algorithm and includes time smoothing technique to improve the reliability of the estimated DoA values.For the DoA estimation using internal microphones we implement a transfer function projection.Here, the DoA can be roughly estimated to determine whether the EV is approaching from behind, in which case the decision of the AV should be to yield to the EV.
Both internal and external microphone array approaches were investigated for their performance.The rational for using an external microphone array is that the results are more reliable and free-field steering vectors can be used; however, the microphones need to be protected from wind.Internal microphones have the advantage of already being available in the car for other applications; e.g., beamforming for the enhancement of Automatic Speech Recognition (ASR) performance.Unfortunately, free-field steering vectors cannot be used and transfer functions were measured with a lower spatial resolution instead.The results showed that despite the additional cost of mounting an external microphone array, it is recommended since the estimated DoA values are far more reliable than the ones achieved using the internal array.
DOA ESTIMATION
In this work a MUSIC-based algorithm was used for DoA estimation.Let s (t, f ) be the source signal in the Short Time Fourier Transform (STFT) domain.This signal is then received at the m'th microphone as where a m (•, θ i ) is the transfer function from a source at direction θ i to the m'th microphone.The signal vector at all M microphones can be represented as where is referred to as the steering vector from direction θ i at frequency f .Practically, the signal vector x is received by the microphones and used to calculate θi , the estimation of θ i .The autocorrelation of x is given by Assuming full rank of R x , it has M eigenvectors.The eigenvector with the largest eigenvalue is associated with the signal space, and all the rest are associated with the noise space.In general, the MUSIC algorithm is designed for any number of sources up to M − 1, but in this application only one source was of interest.Hence, if the eigenvectors u 1 , u 2 , . . ., u M are sorted in descending order, the noise space eigenmatrix is defined by The MUSIC spectrum P is then calculated using the noisespace eigenmatrix Ũ and the steering vector of the hypothetical DoA a (t, f, θ h ) to form (6) As a first step, the frequency for which the MUSIC spectrum is calculated is selected as the one with highest energy in the received signal at the first microphone.That is and then the estimated DoA is given by θi (t) = arg max Temporal smoothing is performed to prevent the consideration of non-realistic estimated DoA values.If in Eq. ( 8) the raw estimated DoA value θi (t) is given using the plain maximum value of the MUSIC spectrum P (t, f, θ h ), then the smoothed DoA is Frequency smoothing can be used to select frequencies f 0 that are near the previously selected frequency since the siren signal is essentially an ascending and decreasing chirp signal.However based on some preliminary results, it was decided not to use frequency smoothing.
Hardware
The external microphone array consisted of 4 Microelectromechanical system (MEMS) microphones selected from 32, as can be seen in Fig. 1, arranged as a square of dimensions 5 × 3cm 2 .The grid dimensions of the microphone array was taken into consideration when calculating the free-field steering vectors for the DoA estimation algorithm.The external microphone array was placed outside the car and mounted on the roof as can be seen in Fig. 2.
Steering Vector
The advantage of the external microphone array is that for the DoA estimation algorithm, the steering vectors can be roughly considered like those in free field.Since the EV is far away, the incident wave form can be considered to be a plane wave, as shown in Fig. 3, where θ i is the DoA angle, and r m , θ m are the distance and angle of the m'th microphone from the origin of the microphone array, respectively.
The free-field steering vector can therefore be calculated in an x-y plane.Let f be the frequency of the sound that is generated by the EV.At this frequency the wave number is k = 2πf c where c = 343 m s is the speed of sound.The frequency response from the source at θ i to the m'th microphone with regard to the origin is given by neglecting differences in amplitude attenuation from the source to the origin and to the microphones.The steering vector of the array that contains M microphones is given by T . (11)
EV Experimental Results
The external microphone array was mounted on the roof of the XTS car.The car was parked near a hospital.The EVs were ambulance vehicles recorded arriving to or departing from the hospital.The parked car and the EV station can be seen in Fig. 4. The case where an EV approached from the opposite lane and made its way to the hospital is shown for example.Basically, at first the DoA comes from the frontal direction, and then switches to behind the car.Figure 5 shows the MUSIC spectrum, the estimated DoA, and the selected frequency for this case.At t = 25s the peak of the MUSIC spectrum shifted from values near 360 • to values near 180 • .It has been detected that the porches of the microphone array board reflect the sound, and therefore even though the EV was on the left side, the peak values appeared at angles that corresponded to the right side.Nevertheless, it was easy to determine when the EV was in front or behind the car.In this case, the decision of an AV should be to continue normal driving and not to yield to the EV.
Hardware
The internal microphone array consisted of different microphones but the same dedicated hardware for sound acquisition as for the external microphone array.The array contained two sub arrays with 3 MEMS each, together forming an array of 6 microphones, from which a new subset of microphone could be selected to form a different microphone array configuration.
The internal microphone array was placed inside the car and mounted either above the rear-right or the frontleft passenger, corresponding to the placement of arrays for speech recognition or hands-free calls.A subset of 4 microphones can be selected to form an end-fire configuration above the rear-right passenger as presented in Fig. 6a, or a broad-side configuration above the front-left passenger, as can be seen in Fig. 6b.For the rear-right array, the distance between any pair of microphones on each sub array was 2cm, and the minimum distance between microphones from different sub arrays was 2.8cm, as shown in Fig. 6a.For the front-left array, the distance between any pair of microphones on each sub array was 2cm, and the minimum distance between microphones from differ-ent sub arrays was 3cm, as shown in Fig. 6b.
Steering Vector
In the case of the internal microphone array, the steering vector cannot be calculated using a free-field representation and instead, the frequency response of the car from each DoA needs to be considered.Therefore, rather than an analytic calculation of the steering vector with high spatial resolution as used by the external array, in the case of the internal array the transfer function needs to be measured in a quiet area with much lower spatial resolution.Since it is very difficult to measure the Acoustic Transfer Function (ATF) from the source to each microphone, the Relative Transfer Function (RTF) was used instead, in such a way that at each microphone the frequency response was calculated relative to the ATF at the 1st microphone.
Let h m be the ATF from the source to the m'th microphone.The RTF is given by If an acoustic source emits a signal x(f ) and assuming a noise signal n m (f ) at the m'th microphone, the recorded signal at the m'th microphone is where
Wienner Filter
The estimation of the RTF based on the Wiener filter solution that minimizes the variance of the error is performed using (14) which leads to .
Generalized Eigenvalue Decomposition (GEVD)
Defining vectors with microphone indices rather than frequencies as coordinates yields the following vector form to Eq. ( 13).Applying the autocorrelation operator to Eq. ( 19) yields The process of GEVD of R y (f ) with respect to R n (f ) relates the generalized eigenvalues λ m (f ) to the corresponding generalized eigenvectors v m (f ) by solving assuming that the rank and the number of microphones are identical and equal to M .
Assuming that the eigenvectors are sorted in descending order The generalized eigenvector that corresponds to the largest generalized eigenvalue is a rotated and scaled form of the ATF [10].The RTF can be calculated using where subscript (•) (1) indicates the first coordinate of a vector.
RTF Estimation Performance
The estimation of the RTF was evaluated using Signal to Distortion Ratio (SDR).The SDR was used to calculate the distortion between the signal recorded by a microphone in the array y m to the signal that is generated by filtering the signal recorded from the first microphone y 1 with RT F m : The SDR values are displayed in Fig. 7 and Fig. 8 for the performance evaluation of the RTF estimation process using the internal microphone array in the broad-side and end-fire configurations, respectively.The RTF was evaluated using a controlled measurement where the recording car was placed in an isolated parking spot, and another car displayed a sweep signal using a speaker mounted on its roof from different directions with a resolution of 45 • .The angle of direction is displayed on the horizontal axes, and the microphone index m is displayed on the vertical axes.The corresponding SDR value is expressed in dB units using gray levels.
For the case examined in this work, the most interesting directions are 0 • and 180 • , which correspond to the frontal and back directions, respectively.For these directions, the RTF was estimated better for the broad-side configuration than for the end-fire configuration.Comparing Fig. 7a to Fig. 7b, and also comparing Fig. 8a to Fig. 8b, shows that the RTFs were estimated better using the LS method than when using the GEVD method for all directions and all microphones.
EV Experimental Results
Only front and back RTFs were used as steering vectors.Figure 9 shows the MUSIC spectrum and DoA estimation results for the case where an EV is approaching the car from the opposite lane.The results in the figures show that using the end-fire array it is impossible to determine whether the EV was behind or in front of the car.The DoA was estimated better using the broad-side array.This result may appear surprising, since one would expect that the symmetry of the broad-side array around the driving direction would have caused an ambiguity for waves approaching from the front or from the back.However, as explained in the previous section, the RTFs are estimated using each microphone with less distortion using the broad-side array than using the end-fire array.Regardless, the difficulty of estimating the DoA and the lower angular resolution was greater in the case of the internal microphone array than in the case of the external one.
CONCLUSION
The feasibility of detecting the direction of an approaching EV was validated using an external microphone array equipped with 4 microphones.An algorithm for using internal microphones was developed in order but found to be inferior to an external array.
Figure 2 :
Figure 2: External microphone array on the roof of the car.
Figure 3 :
Figure 3: Plane wave propagating to the external microphone array.
Figure 4 :
Figure 4: XTS car parked near an EV station.
Figure 5 :
Figure 5: (a) An EV is approaching from the frontal direction (b) MUSIC spectrum and estimated DoA show switching from frontal (∼ 360 • ) to back (∼ 180 • ) direction.The selected frequency matches the siren.
Figure 6 :
Figure 6: Distance between microphones in the internal array, a subset of 4 microphones forms (a) an end-fire array above the rear-right passenger and (b) a broad-side array above the front-left passenger.
Figure 7 :
Figure 7: Evaluation of the RTF estimation using SDR for the internal array in the broad-side configuration using the (a) LS and (b) GEVD estimation methods. | 3,494.4 | 2019-09-06T00:00:00.000 | [
"Engineering",
"Environmental Science",
"Computer Science"
] |
Determination of metabolic activity in planktonic and biofilm cells of Mycoplasma fermentans and Mycoplasma pneumoniae by nuclear magnetic resonance
Mycoplasmas are fastidious microorganisms, typically characterised by their restricted metabolism and minimalist genome. Although there is reported evidence that some mycoplasmas can develop biofilms little is known about any differences in metabolism in these organisms between the growth states. A systematic metabolomics approach may help clarify differences associated between planktonic and biofilm associated mycoplasmas. In the current study, the metabolomics of two different mycoplasmas of clinical importance (Mycoplasma pneumoniae and Mycoplasma fermentans) were examined using a novel approach involving nuclear magnetic resonance spectroscopy and principle component analysis. Characterisation of metabolic changes was facilitated through the generation of high-density metabolite data and diffusion-ordered spectroscopy that provided the size and structural information of the molecules under examination. This enabled the discrimination between biofilms and planktonic states for the metabolomic profiles of both organisms. This work identified clear biofilm/planktonic differences in metabolite composition for both clinical mycoplasmas and the outcomes serve to establish a baseline understanding of the changes in metabolism observed in these pathogens in their different growth states. This may offer insight into how these organisms are capable of exploiting and persisting in different niches and so facilitate their survival in the clinical setting.
Materials and methods
Mycoplasma strains used in the study. A selection of clinical strains from the Kingston University culture collection were utilised in this study including eight clinical strains of Mycoplasma pneumoniae all isolated from human sputum samples and eight Mycoplasma fermentans strains isolated from a Kaposi's sarcoma patient, joint fluid (2 isolates), respiratory tract (2 isolates), urine, urethra and a cell line isolate. All strains were stored as freeze-dried cultures and were grown and sub-cultured in fresh Eaton's broth medium.
Growth of planktonic cells samples in liquid broth medium for M. pneumoniae and M. fermentans strains.
Isolates of both M. fermentans and M. pneumoniae were inoculated into Eaton's broth medium (at a cell density of 10 6 cfu/ml) and incubated at 37 °C for 3-7 days to grow planktonic cells, whilst M. pneumoniae strains were incubated at 37 °C for approximately 30 days.
Growth of biofilm samples in liquid broth medium for M. pneumoniae and M. fermentans
strains. Aliquots (2 ml) of M. fermentans and M. pneumoniae (at a cell density of 10 6 cfu/ml) were inoculated into 10 ml tissue culture flasks (Nunc, Fisher Scientific, UK) containing Eaton's broth medium, and then incubated as previously described. Following incubation, biofilms were acquired from the flask using a cell scraper (Becton, Dickenson Company, BD, UK) and aliquoted into sterile bijous for processing.
General NMR experimental for analysis of mycoplasma biofilm and planktonic serum extracts. A Bruker Avance III 600 MHz NMR spectrometer with 5 mm TXI Probe and temperature control unit was used for all 1D 1 H NMR experiments. 5 mm Bruker Single Use NMR tubes (serum and DOSY). All spectra were acquired on Topspin 3.1 (Bruker, Germany). All NMR experiments were carried out at 25 °C. The Pulsecal routine was run prior to all experiments and the pulse angles adjusted accordingly for total correlated spectroscopy (TOCSY) and diffusion ordered spectroscopy (DOSY) experiments. 1 H spectra for serum samples were acquired using 65,536 complex data points over a sweep width of 20.57 ppm using a pre-saturation of the water signal at 4.7 ppm and one spoil gradient, Relaxation delay (d1) was set to 10 s with the RGA set to 256 for quantitation (See Supplementary Information S1 for example). Serum samples had pH of 7.4 and a 700 μl aliquot was diluted with 300 μl D 2 O. Diffusion spectra were obtained over 64 K data points (SW 10.3112 ppm) using longitudinal eddy current delay bipolar pulsed field gradient with 2 spoil gradients and pre-saturation sequence (LEDBPGPPR2s). This was used to obtain the diffusion series with δ = 4.6 ms and = 125 ms. The relaxation delay was set to 4 s and the diffusion ramp consisted of 64 linear gradient steps, from 2 to 95% gradient intensity, each consisting of 16 scans.
Diffusion data was processed using a sine bell shaped window function phase over all data points prior to Fourier transformation (16,384 points) using Topspin 3.0 (Bruker, Germany). Diffusion data was processed using DOSY Toolbox, created by Mathias Nilsson, Manchester University. Individual peaks were fitted exponentially after a 2nd order polynomial baseline correction was employed 31 .
Errors in diffusion coefficient were calculated based on the Standard Deviation for each diffusion curve and are in line with the estimated error as reported for a similar mixture of ca 0.1 × 10 -10 m 2 s −1 31 . The Residual Sum of Squares for each of the diffusion curves is less than 5 × 10 -3 in all cases.
1D 1 H NMR evaluation of Mycoplasma fermentans and Mycoplasma pneumoniae in the serum based spent culture media. All 1D datasets were processed using Chenomx (Chenomx NMR Suite, Chenomx, Alberta, Canada). As has recently been reported 29 , internal reference standards such as trimethylsilyl propionate (TSP) can often complex with proteins in the analysis and it is highly questionable that reliable direct quantitation of individual metabolites is possible in such a mixture. The relative amounts of individual metabolites were of greater interest in a qualitative sense. www.nature.com/scientificreports/ Metabolites used in the PCA were restricted to those for which a concentration was detected by Chenomx in all samples. All data points were normalised (area) using Unscrambler 10, using a constant weighting and cross validation. DOSY NMR evaluation of Mycoplasma fermentans and Mycoplasma pneumoniae in the serum based spent culture media. NMR spectra of metabolite mixtures are by their very nature complex and it was hypothesised that further information about metabolite mobility could be obtained using Diffusion Ordered Spectroscopy (DOSY). In addition, 1D NMR data provides many overlapping signals and while the Chenomx software is good at resolving some of the well-known metabolites, there was also a desire to investigate the existence of certain unknown metabolites. Through the use of a range of known metabolites as internal mass/diffusion standards it is possible to plot a LogMr vs LogD graph to calculate the approximate mass of an unknown and this has been used to good effect in complex mixtures of this type 30 .
Trying to automatically calculate diffusion coefficients from a pseudo 2D plot is not easily achieved and neither Amix nor Dosytoolbox are capable of dealing with the raw data to provide this output. DOSY spectra for both mycoplasmas were obtained for biofilm and planktonic samples in serum.
Therefore, the following process was adopted; 1. All DOSY spectra were calibrated with respect to both chemical shift and also diffusion, using internal standards of acetate, glucose, alanine and tyrosine. The range of molecular mass (Mr) afforded by this range of metabolites would enable the identification of an unknown Mr with good linearity (R 2 > 0.95) 2. The individual spectra were binned (515 bins) with 0.02 ppm increments and all signal intensities for each bin for each of the 64 gradient incremented spectra. 3. The diffusion coefficients for each bin were calculated using an Excel curve-fitting algorithm. 4. The above three steps were carried out for each spectrum. 5. Using the 8 samples for each of the strains of mycoplasma we obtained a spreadsheet 8 column wide by 515 rows long with the matrix showing the diffusion coefficients for each bin for each sample. As water suppression was used the area of suppression was discounted from the spreadsheet. 6. For each strain of mycoplasma, the spreadsheet from 5 was analysed using Multibase 2015 addon to Excel and any differences analysed using PCA.
Metabolite identification. Using Chenomx Profiler (Chenomx NMR Suite, Chenomx, Alberta, Canada) 1D processed datasets were analysed and the components assigned with the aid of TOCSY where appropriate. The pH was verified for each of the samples prior to processing so no internal pH standards were used and the line width and shifts were calibrated to formate as per the standard procedure for Chenomx data processing. Where assignment was ambiguous DOSY NMR was used to approximate the relative molecular mass (Mr) for individual components as previously shown 30 .
Ethics approval. This research raised no ethical concerns for consideration as no human or animal subjects included in the experimental work.
Results
1D 1 H NMR evaluation of Mycoplasma fermentans grown in serum containing medium. From a statistical perspective, both biofilm and planktonic samples of M fermentans were considered in isolation. Following the same processing parameters described previously in the methodology section, PCA analysis was carried out (Fig. 1). These data indicate statistically significant discrimination between biofilm and planktonic Mycoplasma fermentans based on 1D 1 H NMR analysis and multivariate treatment for the first time in complex serum containing growth media such as Eatons medium (Fig. 2). According to the loadings plot ( Fig. 3) it was possible to select those metabolites, which overall explained more than 50% of the variation observed in the 1D 1 H NMR data and where there was a > 10% difference in the mean intensity of the signal for a metabolite between biofilm and planktonic NMR spectra (Fig. 2).
The loadings plot explained more than 50% of the variation observed in the 1D 1 H NMR data and where there was a > 10% difference in the mean intensity of the signal for a metabolite between biofilm and planktonic NMR spectra.
The concentration values were obtained for a cluster plot for accuracy and the signals were correlated to the individual metabolites that are described in the Chemnomx process in metabolite identification section in methodology.
As with all data analysed by unsupervised multivariant methods, the robustness of the data is directly correlated to the number of samples analysed (Supplementary Information S2).
The current study has shown discriminative patterns of metabolites for planktonic and biofilm cells of eight given strains of M. pneumoniae and M. fermentans. However, further samples and replicates would be necessary to re-enforce the power of this technique; moreover, further work would be useful to substantiate the significance of these results as they stand. www.nature.com/scientificreports/ the methodology section, PCA analysis was carried out indicating a statistically significant difference between the serum composition of biofilm and planktonic arrangements of M. pneumoniae (Fig. 4).
Using the loadings plot ( Fig. 5), it was possible to select specific metabolites, which explained more than 50% of the variation observed in the 1D 1 H NMR data and where there was a > 10% difference in the mean intensity of the signal for a metabolite between biofilm and planktonic NMR spectra (Supporting Information S3). The media components used in this study (Eaton's media) in the absence of any Mycoplasma species, were also identified by 1D 1 H NMR in order to provide baseline recognition of known metabolites, Chenomx software was used to analyse and identify the different metabolite components (Fig. 6).
Diffusion NMR analysis of Mycoplasma pneumoniae. The data was processed using MS Excel with the "Multibase 2015" add on and no weighting was applied to the variables since there is no precedent in the literature to aid explanation of the data and future investigations may be required to consider all possible implications of differing diffusion coefficients. The PCA analysis for M. pneumoniae shows that some of the variation between datasets could be explained using diffusion coefficient data. The fact that 3 PCs are required to explain 95% of variation implies a certain degree of complexity in the way the data can show differences between biofilm and planktonic mycoplasmas and further investigation as to how this correlates to metabolite amplification is beyond the scope of the current study and requires further work (Fig. 7).
The PCA was carried out in order to identify which components had the most discriminatory aptitude (Fig. 8). Whilst the majority of signals were irrelevant with regards to the data set, it was possible to identify regions of the spectra which were correlated with the biofilm samples and those which correlated to the planktonic (Supporting information S4).
The large number of metabolites appear to diffuse in a substantially different fashion making it a challenge to identify any one core component which accounts for the observed variation. However, some general observations can be made for example, that components at around 1 ppm seem to diffuse faster for biofilm mycoplasmas when compared to planktonic mycoplasmas (Supporting Inofrmation S5). Further work would be required to automate the correlation of the signals with a specific component. The introduction of operator assignment error when the bin size is as small as it is could easily lead to incorrect assignment of a signal to a specific metabolite.
Diffusion NMR analysis of Mycoplasma fermentans. PCA analysis of the diffusion data for M. fermentans initially showed little grouping in the scores plot and this was confirmed by the statistical output, which showed a negative value for Q 2 and poor statistical explanation of the data. The residual variation was too high for this model and therefore further interrogation would have yielded unreliable pattern data (Supplementary Information S6), meaning this approach is not worth pursuing without optimisation on simpler systems.
Discussion
Mycoplasmas are characterised by limited biosynthetic capabilities, largely due to their minimal genome 32,33 . Loss of genes involved in biosynthesis of lipids, amino acids, vitamins and cofactors during their evolution 34,35 has resulted in a reliance on external nutrients from host cells in vivo or rich media in vitro 8,34 . Furthermore, Mycoplasma species are often deficient in intermediary energy metabolism, resulting in a lifestyle strictly dependent on the natural host 36 . Reliance upon host cells for biosynthetic precursors may lead to competition and therefore disrupt host cell function and integrity 35 . www.nature.com/scientificreports/ Mycoplasmas are divided into fermentative and non-fermentative organisms 2 according to their ability to catabolise carbohydrates via the phosphoenolpyruvate phosphotransferase (PEP-PTS) system 37 . Glucose, and other fermentable sugars, are a crucial energy source, especially for the fermentative mollicutes. Glucose may also act as a precursor for the synthesis of other saccharides that stimulate the growth rate of mollicutes [38][39][40] .
Host cell attachment by mycoplasmas, as a biofilm or part thereof, and cytotoxic metabolite production may contribute towards significant host cell damage, commonly observed in infection with these pathogens. Biofilm formation also frequently results in increased resistance to antimicrobial agents and persistence of many organisms including M. fermentans and M. pneumoniae [41][42][43] . Physiological characterisation of biofilms is therefore vital to develop effective anti-mycoplasma treatments 25 . www.nature.com/scientificreports/ Although global metabolite analysis has been proven as a powerful tool for understanding bacterial physiology 26,27 the work presented here is the first DOSY-NMR metabolomics-based study in human mycoplasmas.
NMR-based metabolomics is a relatively new technology in biological applications and correspondingly has seen limited exploration in the investigation of microbial biofilms 17 . The purpose of the evaluation of biofilm and planktonic mycoplasmas using 1D 1 H NMR was to establish the amplification of one or more metabolites/media components (markers) dependent on the mycoplasma being grown either as a biofilm or in planktonic state. The use of 1D NMR techniques for the analysis of serum and also cytosolic contents are well established 25 The aim of the current research was to use these techniques to identify differences in metabolite composition for M. pneumoniae and M. fermentans in both biofilm and planktonic forming conditions. In addition, we aimed to evaluate the potential of Diffusion Ordered Spectroscopy (DOSY) to assist in discriminating between planktonic and biofilm mycoplasmas and what significance these points of discrimination may have, either to assist in the classification of a mycoplasma as either biofilm or planktonic derived, or to provide more information about the constituents of the biofluid and potentially the differences in metabolic pathways. Additionally, this approach could also help to understand the potential changes in mycoplasmal metabolism under different growth conditions. The current study examines the overall metabolism of the organisms in the stated growth condition (planktonic or biofilm) and not the rate of metabolism. The measurement of bacterial metabolism for communities in a biofilm cannot reliably be measured and currently the metabolomic differences between the growth states as a whole is reported rather than growth rate measurements [44][45][46][47][48] . In reference to carbohydrate metabolism. many mycoplamas lack hexokinase, therefore glucose is transported into cells and ' captured' by the phosphoenolpyruvate: phospho-transferase (PEP:PTS) system for degradation to pyruvate in the Embden-Meyerhof-Parnas (EMP) glycolytic pathway [49][50][51][52][53][54] . Oxidative phosphorylation deficient mycoplasmas can metabolise pyruvate via two alternate pathways to generate ATP: oxidation by pyruvate dehydrogenase to acetyl-CoA, followed by the action of phosphate transacetylase and acetate kinase to yield acetate and ATP. Alternatively, pyruvate is reduced to lactate by lactate dehyrdogenase with concomitant oxidation of NADH to NAD to facilitate continued ATP generation via the EMP 50,53 . Energy metabolism in mycoplasmas is therefore principally dependent on fermentation via the EMP to lactate under anaerobic conditions or acetate and CO 2 under aerobic conditions 3,34 .
In M. fermentans, acetate was found to be greater in the biofilm suggesting that there is a bias toward the pyruvate dehydrogenase route for pyruvate metabolism. For both mycoplasma strains, the data indicates biofilms potentially produce more energy than planktonic cells. Glucose-6-phosphate was more abundant in planktonic cultures of both M. fermentans and M. pneumoniae, compared to biofilm serum (Figs. 2 and 6). Elevated uptake and ' capture' of glucose and metabolism to the end-products lactate and acetate is required in order to generate the ATP necessary for growth and cellular functions 32 , and thus facilitate the formation of biofilm.
The current study has identified ethanol (Figs. 2 and 6), an end-product of fermentative metabolism, as a metabolite; however, acetaldehyde which is the metabolic intermediate in ethanol formation from pyruvate was not identified. Similarly, alcohol dehydrogenase, the enzyme required for metabolism of pyruvate to ethanol was not experimentally detected in Mycoplasma pneumoniae. This observation concurs with M. pneumoniae proteomics data 32 ; however, the current study measured ethanol secretion by mass spectrometry. The ethanol level was higher in biofilms than planktonic cells in M. pneumoniae, whereas in M. fermentans it was observed to be higher in planktonic cells. This suggests that the ability to synthesise ethanol has a greater importance in the growth of M. pneumoniae biofilms. From the analysis of large metabolic networks 55,56 , evidence from genetic studies and experimental investigations of protein abundance 57 it is apparent that Mycoplasma pneumoniae lacks almost all anabolic pathways, including those for amino acid synthesis and metabolism 32 . Consequently, M. pneumoniae is dependent on the import of large amounts of amino acids 32 www.nature.com/scientificreports/ culture media supplemented with these 1 . In the current study, levels of amino acid metabolites were identified in both biofilms and their planktonic counterparts. Global analysis of M. pneumoniae metabolism indicated proteins mapped to the metabolic pathways in KEGG data base, including proline metabolic pathway (http:// www.genom e.jp/kegg/pathw ay/map/map00 330.html). The results showed that the proline level (in the form of 4-Hydroxy-L-Proline) in M. pneumoniae was greater in biofilm cell serum compared to its planktonic counterpart (Figs. 2 and 6). This finding would suggest that proline iminopeptidase (Pip) may release proline from peptide and the aspartate-ammonia ligase (AsnA) catalyses the interconversion of aspartate and asparagine 33 , and thus may be crucial for mycoplasma survival. In M. fermentans, "arginine and proline" amino acid metabolic pathway has been recognised using genomic studies 33 . M. fermentans produces ATP from arginine metabolism via the arginine dihydrolase (ADH) pathway, similar to that found in M. hominis 33,58 . The ADH pathway catalyses the conversion of arginine to ornithine, ATP, CO 2 and ammonia. The current work showed that arginine levels in Mycoplasma fermentans were greater in planktonic cells than biofilms.
Alanine was more prominent in biofilm metabolism of M. fermentans compared to its planktonic growth state (Figs. 2 and 6). This amino acid could be crucial in the absence of pyridoxal pyrophospahte as it could be a preferred element in the supplemented media instead of tyrosine and phenylalanine for optimum growth, suggesting the presence of an operative shikimic acid pathway for aromatic amino acids synthesis 40 . Additionally, alanine was observed to be marginally greater in the biofilm of M. pneumoniae (Figs. 2 and 6), which may www.nature.com/scientificreports/ suggest that alanine was enriched in the cytosol due to the subsequent of cellular import from the surrounded growth medium 32 . Additionally, metabolite profiles in the current study demonstrated the presence of glycine and betaine, which are found to be higher in biofilms when compared with planktonic cells of sera for M. fermentans (Figs. 2 and 6). Glycine is considered as a very efficient osmolyte found in a wide range of bacteria, where it is accumulated at high cytoplasmic concentration 58,59 in order to build up an internal osmotic strength and prevent the diffusion of water out of the cells and thus maintain the cellular water content 59,60 . When bacteria are grown at an inhibitory osmolarity, the enzyme activities that lead to glycine and betaine degradation decrease, whereas the enzyme activities that convert choline to glycine betaine either remain constant or increase 61 . In this way, a high concentration of glycine betaine can be maintained in osmotically stressed cells 62 . Mycoplasmas in nature are normally exposed to different types of stresses including osmolarity shifts and their resistance to different stresses is noticed 63,64 . Consequently, the high level of these osmolytes in biofilm cells may indicate to their importance in growth and biofilm formation.
The metabolite profiles in the current study showed some interesting observations, such as the presence of valine and alloisoleucine in M. pneumoniae (Supplementary information S4 for M. pneumoniae). Depending on the examination of the phylogenetic distribution of the enzymes participating in isoleucine/valine metabolic pathway, it was found that all the genes coding for the enzymes of isoleucine/valine biosynthesis were missing in M. pneumoniae 65 . Thus, the presence of these metabolites in the profile might be related to the high nutritional value and complexity of the surrounding growth medium. This study also identified the presence of creatine in the biofilm of both M. fermentans and M. pneumoniae were higher than their planktonic counterparts (Figs. 2 and 6). The presence of creatine is correlated to the biosynthetic pathway of arginine that involves the conversion of citrulline to arginine catalysed by arginosucciante synthase, which in turn provides the essential arginine for creatine biosynthesis. Creatine, the end product of the pathway, acts to conserve the utilisation of semi-essential amino acids, including arginine 66 . Although creatine biosynthesis in mycoplasmas is still elusive and not fully described, these findings could be connected to arginine metabolism, as described above.
In relation to nucleotide Metabolism, levels of Uridine were higher in the biofilm than planktonic state after for both M. fermentans and M. pneumoniae (Figs. 2 and 6) Uridine nucleic acid derivatives could be used as a precursor of polysaccharides, such as exopolysaccharide (EPS), which is important in the maintenance of biofilm structure 25 . In Mycoplasma pneumoniae, Uridine is involved in the Leloir pathway that comprises a step in galactose phosphorylation 67 . Furthermore, EPS production requires both free galactose and the Leloir pathway in order to form a biofilm 67 .
Conclusion
This work is the first study to quantify a set of key metabolites, including glycolysis compounds, amino acids, and nucleotides, in the growth of human mycoplasmas. The results obtained suggested that metabolic pathways in human mycoplasmas, such as M. fermentans and M. pneumoniae were regulated by multiple enzymatic reactions in order to fulfil key metabolic activities. Therefore, protein abundance in the metabolic network could provide a qualitative picture of M. fermentans and M. pneumoniae metabolic pathway activity in both biofilm and planktonic cells under laboratory growth conditions. There are examples of how metabolomic differences have been observed in in planktonic and biofilm cells of Mycoplasma genitalium 46 , Staphylococcus aureus 44,45 , Gardnerella vaginalis 47 and Rhizobium alamii 48 . Whilst these studies all discuss the difference in metabolomic profiles in the species discussed between planktonic and biofilm growth states, none look at the rate of metabolism. As there is a range of growth states throughout a biofilm from the apical to the basolateral surface measuring the rate of growth is widely viewed as not possible. As a result, studies often analyse the production of materials, compounds metabolic markers from the biofilm as a whole and not the rate of metabolism as this is not currently possible. Hence the data presented here is the first use of DOSY-NMR to examine the metabolism of these mycoplasmas in their planktonic and biofilm growth states, as a whole and not on a rate wise basis. The clarification of metabolic pathway activity in both biofilm and planktonic cells enables us to gain a better understanding of vital and nonessential metabolites involved in the formation and establishment of human mycoplasma biofilms. | 5,805.8 | 2021-03-11T00:00:00.000 | [
"Biology",
"Medicine",
"Chemistry"
] |
α-Ga2O3 as a Photocatalyst in the Degradation of Malachite Green
α-Ga2O3 is a wide-bandgap semiconductor material which was prepared by a novel synthesis method from metallic gallium. It was characterized by X-ray diffraction, infrared spectroscopy, ultraviolet spectroscopy, X-ray photoelectron spectroscopy and scanning electron microscopy. This oxide was also evaluated as a photocatalyst toward the decomposition of malachite green (MG). X-ray photoelectron spectroscopy was used with the purpose of analyzing the changes on the surface of the material before and after the photocatalytic reaction. The results found by X-ray diffraction shows that alfa phase did not transform to another crystalline phase during the reaction. However, a slight change on the relative intensities of the planes (104) and (110), may explain the variation of the morphology of the oxide, associated to a preferential particle erosion. High resolution XPS analyses revealed a shift toward lower binding energies of the O1s level after the photocatalytic reaction, suggesting the presence of oxygen bound to carbonyls or alcohols. Organic nitrogenous residues associated to MG were also detected by the presence of the N1s band observed at 396.7 eV. © The Author(s) 2019. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited. [DOI: 10.1149/2.0351907jss]
Semiconductor materials are commonly composed by elements of groups III-V. [1][2][3] However, semiconductor metallic oxides have received a lot of attention because of their outstanding physical and chemical properties. These materials have a wide energy bandgap, from roughly 2.8 to 5.2 eV, make them suitable as photocatalysts for the decomposition toxic organic substances. 4,5 Among semiconductor metal oxides, gallium oxides exhibit a wide bandgap energy, between 4.2 and 4.9 eV. 4.6 These oxides have five crystalline phases: α, β, γ, δ and ɛ, from which the most stable are the α and β phases. [7][8][9] Even though the α phase is stable, it has been little explored in photocatalytic reactions in aqueous media, being the β phase the most studied for this purpose. 8 This was one of the main reasons of this investigation, focused in the degradation of the malachite green by means of nanostructured α-Ga 2 O 3 . About the photocatalytic properties of other Ga 2 O 3 phases, Jin et al. reported photocatalytic activity of the γ phase in rhodamine-590 degradation. 8 The methods of synthesis of gallium oxides are a challenge that must be solved to make way for applications. 10 The synthesis methods reported in the literature for these oxides are sol-gel, hydrolysis, sonochemical processes, heat-assisted microwave, biomineralization and precipitation, as well as post-synthesis hydrothermal treatments. 11,12 Applications found for gallium oxides are in different areas like sensors, photo electronics, adsorption, optical or fluorescent materials, in electrochemistry, solar cells, blue light emitters and photocatalysis, among others. [7][8][9][10][11][12][13] On the other hand, the photocatalysis is greatly determined by the morphology and size of the materials; for example, Fut et al. studied three polymorphic structures of gallium oxide (α, β and γ) of which the alpha phase showed greater photocatalytic activity. 10,11 Their results also showed that the morphology of the precursor (GaOOH) and its subsequent calcination controlled the formation of α-Ga 2 O 3 . Further photocatalytic experiments performed with two different morphologies demonstrated the key role of the morphology on the degradation of acid orange and Cr(VI). 10 Therefore, controlling the morphology and surface area are of interest because the oxides are affected in their physicochemical properties by crystalline defects, such as oxygen vacancies. 10,14 Malachite green (MG) is an organic dye containing three aromatic rings linked by covalent bonds, which confer great stability to the molecule. The latter gives to MG characteristics of light absorption in the visible region, which are attributed to the conjugated system of bonds corresponding to its structure of benzene rings. The triphenylmethane dyes, when presenting these conjugated bonds in their aromatic groups, are quite stable and together with a low solubility they become highly persistent compounds in the environment. Besides, they are not easily degradable by common chemical or physical means. 15,16 This work proposes the study of the α-Ga 2 O 3 phase as a photocatalyst in the degradation of MG in aqueous media. α-Ga 2 O 3 was produced from metallic gallium through the following sequence of reactions: The synthesized material was characterized by infrared spectroscopy, ultraviolet spectroscopy, X-ray powder diffraction and scanning electron microscopy. After the photocatalytic degradation of MG, a study concerning the surface characteristics of the catalyst was done using X-ray photoelectron spectroscopy (XPS). For the case of gallium oxides, XPS can be a handy tool to know if there are changes in the oxidation state of gallium and oxygen ions. 19 Moreover, XPS can provide information about the vacancies in the crystal structure. 14,20
Experimental
Synthesis.-For the preparation of α-Ga 2 O 3 , 1.5 g of metallic gallium were diluted in 20 ml of concentrated nitric acid in a ball flask. The flask was immersed in a glycerin bath at 60°C, and the mixture was stirred for 24 h to achieve complete dissolution of the gallium and its oxidation to Ga (III). The resulting solution was gauged at 250 ml with distilled water. From this solution, 20 ml were extracted and neutralized at pH = 7 with a 14% solution of ammonium hydroxide. The reaction produced a white precipitate which was left under stirring for 24 h. After that, the sample was washed three times with distilled water, in order to eliminate salts that did not react. The resulting solid was transferred to a drying oven at 70°C for 24 h. At this stage, the compound GaOOH was formed. Afterward, the powder was calcined at 600°C to dehydrate the sample and to obtain single phase α-Ga 2 O 3 .
Malachite green degradation.-MG degradation tests were performed in a Petri dish containing 40 ml of a MG solution with a concentration of 5 × 10 −5 mol and 20 mg of α-Ga 2 O 3 . The latter was sonicated for 2 min prior to the photocatalytic experiments. Afterwards, a light emitting diode (LED) with light emission of λ = 355 nm and optical irradiance of 80 mW/cm 2 was placed above the Petri dish. Using a 3 ml syringe, solution samples were extracted at different periods of time, and then they were analyzed by UV-vis spectroscopy to subsequently calculate the percentage of MG degradation by means of the following equation: Where C o is the initial concentration of the dye, C is the concentration after irradiation and A o and A are the absorbance values of the dye before and after irradiation, respectively. Material characterization.-X-ray diffraction (XRD) patterns were collected with an Empyrean (Panalytical) diffractometer, having a copper anode excited at 45 kV and 30 mA. The wavelength of the Cu k α radiation is 1.5406 nm. The diffraction pattern was collected using a step of 0.02°and the acquisition time was 20 s at each step. The analysis by infrared spectroscopy (IR) was done with the attenuated total reflectance (ATR) mode with a Thermo Scientific instrument, model Nicolet iS5-iD5-ATR. For each sample, spectra ranging from 500 to 400 cm −1 were averaged with a resolution of 4 cm −1 . 32 For this purpose, 2 mg of gallium oxide was suspended in 6 ml of distilled water and stirred with ultrasound for 15 min. Afterwards, the sample was left to rest for 3 minutes and the supernatant was transferred to a quartz cuvette for spectrum reading using a Thermo Scientific Genesys 10S UV-vis spectrophotometer, collecting the spectra with a resolution of 1.8 nm. Determination of the bandgap energy was carried out through mathematical treatment of the UV-vis spectra. The spectra were treated with the Tauc equation, which is given by the relationship αhv = (hv-Eg) 1/2 , where Eg = bandgap energy (eV), h = Planck's constant, v = frequency (1/2) and α = absorption coefficient. 19,20 The Eg value is obtained from the intersection of the linear part after plotting (αhv) 1/2 versus hv. A scanning electron microscope (Tescan, Mira) was used to analyze the morphology of the samples. The powder samples were placed on a double-sided carbon tape. The images were obtained with a potential of 20 kV and were used to determine the aspect ratio of particles using the ImageJ software. The XPS analyses were performed with a SPECS system with Phoibos 150 analyzer. It has a Mg/Al X-ray source operating at a potential of 10-14 kV. 17,18 Results and Discussion (111), respectively. Figure 1b shows the pattern of the product obtained after calcination, in this case, intense reflections were observed in the 2θ = 33.7 and 36°. The profile matched with that of α-Ga 2 O 3 reported in the ICDD with number 006-0503, and the more intense diffraction lines correspond to the planes (104) and (110). This result indicates that calcination at 600°C produced single phase α-Ga 2 O 3 . The lack of literature about this material is associated to its low stability in applications such as a catalysis. In previous studies, it has been observed that aqueous solutions of organic compounds can transform the alpha phase. However, in the conditions of degradation of MG of this work this did not occur, because the XRD profile of the powder retrieved after the photocatalytic degradation is similar to that of the powder before the reaction. A slight change is observed in the relative intensities of the planes (104) and (110), suggesting a variation on the population of these planes, a fact that may be due to a preferential erosion of the crystallites, where the plane (104) was preferably affected.
By scanning electron microscopy, the morphology of gallium oxyhydroxide obtained at pH = 7 corresponds to ellipsoids, as shown in the Figure 2a. This shape is preserved after its thermal decomposition producing α-Ga 2 O 3 (Figure 2b). It can be observed in Figure 2c that gallium oxide removed from the MG degradation reaction maintains its morphology, which indicates that this compound is stable. However, the suspicion of a slight degradation observed in the XRD profile was verified when the particles were measured, and the length to width aspect ratio was measured. Figure 3 shows the histograms of the aspect ratios obtained from the corresponding SEM micrographs.
Of particular interest is the change in the aspect ratio of gallium oxide after the photocatalytic degradation of MG. It can be noted that the average aspect ratio was 2.5; however, after the reaction, there is a dispersion of values in such way that the population of particles with greater aspect ratio increased, given by an increase of length or a decrease of width. The latter is consistent with the result of XRD suggesting preferential erosion; therefore, the grain edges oriented to the plane (104) could be associated to the degradation reaction. Infrared spectroscopy patterns (Figure 4) display the expected bands of GaOOH, where the symmetric stretching of O-H groups appears between 2800 and 3500 cm −1 , whereas the Ga-O-H bending mode is located at 750 cm −1 and the Ga-O stretching and Ga-O-Ga torsion are found at approximately 600 and 550 cm −1 , respectively. [21][22][23][24][25] The spectrum of α-Ga 2 O 3 is composed by bands of Ga-O-Ga torsion movements at around 600 and 500 cm −1 . 24-26 Figure 5 shows the infrared spectrum of α-Ga 2 O 3 retrieved after MG degradation. Here there are additional bands corresponding to organic residues adsorbed from the reaction medium. One of these signals appears at around 3450 cm −1 , which can be attributed to O-H, indicating the formation hydroxyl radicals that have been previously reported for gallium oxide. 27 On the other hand, the formation of GaOOH, which can be an alternative way to explain the photocatalytic properties of α-Ga 2 O 3 , should be detected in the corresponding XRD pattern, because the population of OH − groups is high enough according to the IR spectrum. Therefore, since the presence of GaOOH was not observed by XRD, the results suggest that the pathway for the decomposition of MG was by an oxidation reaction. Another evidence of the latter is that the advance of oxidation would produce carbonyl groups (C=O) and this formation is consistent with the presence of the band at 1600 cm −1 , shown in Figure 5. 28 Furthermore, the generation of carboxylates associated to a pair of bands at 1550 and 1300 cm −1 may confirm the proposed pathway. 27,28 Moreover, gallium oxide signals continue to be present at 600 cm −1 , associated to the Ga-O-Ga torsion mode. 27,28 Based on this evidence, the degradation of MG catalyzed by gallium oxide follows a gradual oxidation route.
According to the literature, the bandgap energy of gallium oxyhydroxide, determined by UV-vis spectroscopy, is between 4.75 and 5.06 eV; whereas for gallium oxide spans from 4.8 to 4.9 eV. [29][30][31][32][33] In this work, the bandgap energy value obtained for GaOOH and α-Ga 2 O 3 was the same for both compounds (5 eV) and is consistent with the literature (Figure 6). A gallium oxide sample taken after the degradation of malachite green was analyzed, and a slight reduction of the bandgap energy to 4.5 eV was measured (Figure 6c). This change may be influenced by the preferential erosion of α-Ga 2 O 3 particles detected by XRD. The latter should involve the formation of crystalline defects, where oxygen vacancies may be present. A possible phenomenon of surface functionalization may also took place, which is witnessed through the by-products generated during the MG degradation and detected by IR spectroscopy, such as oxidized species. [34][35][36][37] To understand what occurred on the surface of α-Ga 2 O 3 , XPS was performed before and after the photocatalytic degradation of malachite green. The wide survey scans of these samples are shown in Figure 7. The main peaks of these spectra are associated with the gallium and oxygen electronic levels, as well as those corresponding to nitrogen. The latter appear mainly on the sample retrieved after photocatalysis, which can be attributed to by-products containing nitrogen. The main peaks of gallium are located at 1119.87 eV for Ga 2p 1/2 , 1146.54 eV for Ga 2p 3/2 and 20.4 eV for Ga 3d, whereas for O 1s level it can be observed at 530.97 eV. In the case of nitrogen, the N 1s level can be identified by a peak centered at 397.12 eV. It is worth to note that all these results agree with those reported in the literature.
Before the photocatalysis, the spectrum obtained for the gallium at level 2p 1/2 consists of two components at 1145.4 and 1147.3 eV (Figure 8a). After photocatalysis, only one component is observed at 1145 eV (Figure 8c), so it can be said that the gallium species that generates the component at 1147. 3 Ga 3d Intensity (a.u.) Binding energy (eV) (d) photocatalysis. It is known that for polymers, XPS spectra are shifted to higher energies when oxidized. 38,39 In this case, the gallium species that generated the 1147.3 eV peak may have participated in the reaction and were reduced to form only the 1145.4 eV signal. This gallium reduction may have generated the MG oxidation detected by IR spectroscopy. For the Ga 3d level, a similar trend can be noticed; before the photocatalysis there are 3 signals (Figure 8b), and the peak corresponding to a larger bond energy disappeared after the photocatalysis. Since the energy values reported here are congruent with those already published for gallium hydroxide, our results indicate that gallium species were reduced during the photocatalysis, forming Ga-OH species. 40 The spectrum of the N 1s level was also analyzed and a signal corresponding to NO x residues formed during the synthesis process was detected (Figure 9b). 41 Through the deconvolution of this curve, three main components were found (398.0, 395.9 and 393.3 eV) all of them associated to NO x species. After photocatalysis, α-Ga 2 O 3 continues presenting the N 1s signal, with two components still present (394.7 and 392.7 eV), that are very close to those found before the photocatalysis (Figure 9d). However, the component with the largest intensity of this spectrum is located at 396.4 eV, which is consistent with the presence of organic nitrogen residues. 42,43 The disappearance of the component in 398.0 eV may suggest that nitrogen species were also involved in the oxidation degradation process of MG. 44 The O1s spectrum of α-Ga 2 O 3 before the photocatalytic process was represented by two curves centered at 531.9 and 530.9 eV (Figures 9a). 41,45 Since gallium and nitrogen are present in the pristine sample, the component at 531.9 eV can be associated to oxygen in gallium oxide, whereas the signal at 529.6 eV corresponds to oxygen contained in the NO x compounds. After photocatalysis, the spectrum shifted to lower energies and the deconvolution revealed the presence of two peaks corresponding to energies of 530.6 and 529.6 eV. These values are congruent with the presence of gallium oxides or hydroxides (530.6 eV). 44 The peak centered at 529.6 eV agrees with the reported energy value of oxygen bonded to carbon (carbonyls or alcohols). This result suggests that MG degradation occurs through an oxidation process, as detected by IR spectroscopy, where the oxidizing agents are gallium oxides and nitrogen oxides. 46 The experiments for the photocatalytic degradation under UV radiation of MG were performed using 10 and 30 mg of α-Ga 2 O 3 ; Figures 10a and 10b show the corresponding UV-vis spectra. From these results is possible to observe a decrease on the intensity of the absorbance with exposure time. The degradation percentage was calculated from the main band of MG centered at approximately 617 nm. Figure 10d shows that after 360 min of exposure to UV the degradation was 45.8%, when 30 mg of α-Ga 2 O 3 were used, whereas with 10 mg a degradation of 40% was measured. Then, is possible to conclude that the concentration of gallium oxide increased the degradation rate of the dye. On the other hand, the UV-vis spectra obtained from a MG solution irradiated with UV, without α-Ga 2 O 3 , is shown in Figure 10c. The latter revealed that the exposure to UV contributes to the decomposition of MG, but when it is combined with α-Ga 2 O 3 as photocatalyst an increase on the oxide-reduction process can be achieved, as shown in Figures 10a and 10b Binding energy (eV) N 1s
Conclusions
The synthesis of gallium oxyhydroxide was performed from metallic gallium and after calcination at 600°C single phase α-Ga 2 O 3 was obtained. The mechanism of degradation of malachite green proposed in this work involves the oxidation of the dye. The intermediates generated during the photocatalysis show different degrees of oxidation (OH − , C=O and COO − ) and were absorbed on the surface of the catalyst. The identification of them was performed through different analytical techniques. It was found that the oxidation process was consistent with the information obtained by XPS, where the loss of oxygen species from the catalyst could contribute to the redox process. Moreover, the oxygen vacancies formed in α-Ga 2 O 3 could be involved in the decrease on the bandgap energy measured on samples obtained after the photocatalysis. | 4,527.6 | 2019-01-01T00:00:00.000 | [
"Chemistry",
"Materials Science",
"Environmental Science"
] |
Macroporous bioceramic scaffolds based on tricalcium phosphates reinforced with silica: microstructural, mechanical, and biological evaluation
ABSTRACT The positive effect of silica on microstructural, mechanical and biological properties of calcium phosphate scaffolds was investigated in this study. Scaffolds containing 3D interconnected spherical macropores with diameters in the range of 300–770 µm were prepared by the polymer replica technique. Reinforcement was achieved by incorporating 5 to 20 wt % of colloidal silica into the initial hydroxyapatite (HA) powder. The HA was fully decomposed into alpha and beta-tricalcium phosphate, and silica was transformed into cristobalite at 1200°C. Silica reinforced scaffolds exhibited compressive strength in the range of 0.3 to 30 MPa at the total porosity of 98–40%. At a nominal porosity of 75%, the compressive strength was doubled compared to scaffolds without silica. When immersed into a cultivation medium, the formation of an apatite layer on the surfaces of scaffolds indicated their bioactivity. The supportive effect of the silicon enriched scaffolds was examined using three different types of cells (human adipose-derived stromal cells, L929, and ARPE-19 cells). The cells firmly adhered to the surfaces of composite scaffolds with no sign of induced cell death. Scaffolds were non-cytotoxic and had good biocompatibility in vitro. They are promising candidates for therapeutic applications in regenerative medicine.
Introduction
Nowadays, many people face problems related to bone disorders. Bone tissue is able to completely regenerate on its own if the damaged part is small enough. If not, it is necessary to heal such trauma, e.g. by using bone grafts. Autografts, i.e. parts of bone harvested from the patient's body, naturally have the most suitable properties, but some problems, such as lack of available tissue material and the necessity of multiple surgical procedures, were reported [1]. Nonetheless, because the bone is the second most common transplanted tissue, the demand for bone grafts is huge -several million people need them every year [2]. Hence, the development of a new type of synthetic graft, further referred to as a scaffold, seems to be a promising choice [3,4].
The requirements on the synthetic scaffolds are manifold [5,6]; the ideal scaffold must be biocompatible, i.e. must not elicit any inflammatory response and/ or demonstrate immunogenicity or cytotoxicity. It should support tissue formation by 3D structures with pores allowing cells to migrate throughout the biomaterial scaffold and support vascularization of the ingrown tissue. Pores must be interconnected, with a pore size of minimally 100 µm in diameter (ideally >300 µm) [7,8]. Besides such macropores, the microporosity (<10 µm) of the struts is desirable because it provides a larger surface area, which is critical for protein adsorption, and adhesion and growth of cells [7,9]. Within few months the scaffold should resorb in the body environment. The resorption kinetics should ideally be equal to the bone turnover rate in order to facilitate load transfer directly to the newly developing bone. The by-products of the body-scaffold interaction must not be toxic and should be easy to eliminate via relevant body systems [10]. Also, mechanical properties should be similar to those of replaced bone, i.e. compressive strength of cancellous bone is in the range of approx. from 1 to 38 MPa [ [11][12][13], and the scaffold must not collapse during handling and in vivo during normal physical activities. Scaffolds should be easy to manufacture in shapes, which accurately fit the defects in the bone. Hence, the intrinsic structure, as well as the composition, play crucial roles in the clinical success of the scaffold.
Bioceramic materials based on calcium phosphates exhibit the greatest chemical similarity to the bone mineral component [14]. Their wide expansion into clinical practice is, however, limited by insufficient mechanical properties if they are prepared synthetically. The objective of this work was to develop a new composite biomaterial with biological characteristics and compressive strength similar to highly porous hard tissues. Silica was chosen as the reinforcing phase because silicon (as Si 4+ ion) is considered to be one of the essential trace elements required for the development of healthy bones. It acts as a biological cross-linking agent in the extracellular matrix. Moreover, it enhances osteoblast proliferation, differentiation, and collagen production [15,16]. Calcium phosphate ceramics substituted by silicate ions exhibit superior biological properties compared to their stoichiometric counterparts [17]. Up to now, a great deal of material research was focused on bioceramics containing amorphous silica such as bioactive glasses [18][19][20][21] (pseudo) wollastonite [22][23][24][25], dicalcium silicate [26] and Si-doped CaP [17,[27][28][29] ].
On the other hand, materials composed of crystalline silica in the form of quartz or cristobalite for medical applications were poorly studied so far. There are only a few studies concerning bioactive composites composed of cristobalite and calcium phosphate matrix such as dicalcium phosphates [30,31], tetracalcium phosphate [32] or HA (reinforced with biogenic silica) [33]. Therefore, here we aimed to extend the knowledge on bioactive material composition based on silica -tricalcium phosphate (TCP/SiO 2 ), where the crystalline silica, in the form of cristobalite formed after sintering, plays a crucial role.
In this study, the TCP/ SiO 2 composite scaffolds were fabricated by the polymer replica technique. The silica content varied from 0 to 20 wt % and the effect of cristobalite, overall phase composition, sintering temperature, pore size, and total porosity on microstructural, mechanical and biological properties of tricalcium phosphate scaffolds were investigated.
Ceramic foam processing
Ceramic scaffolds were prepared by the polymer replica technique. This method was chosen for the manufacturing of the bioceramic scaffolds because it accurately mimics a trabecular bone macrostructure. Polyurethane foam (PU) with initial pore sizes of 45, 60, 75 and 90 PPI (Bulpren S 28133, S 28089, S 31062, S 31048, Eurofoam, Czech Republic) were cut into cylinders of ø 7.5 × 10 mm (for a compressive test) and ø 5 × 2 mm (for biological testing). Subsequently, they were immersed into ceramic slurries containing HA with 0, 5, 10, 15 and 20 wt. % silica. Two types of slurries were prepared. A silica-free slurry (as a reference) was prepared from HA powder (purity >90%, Fluka, Switzerland) bonded by 5 wt % polyvinyl alcohol (PVA, Mowiol 10-98, Sigma Aldrich, Germany), deionized water, 0.2 wt % glycerol (Onex, Czech Republic) and 0.1 wt % n-octanol (Lachema, Czech Republic). The second type was prepared by mixing HA powder (purity > 90%, Fluka, Switzerland), colloidal silica solution LUDOX® SK-R (Grace, US) and deionized water. The weight fraction of HA in the slurry was in the range of 0.45 to 0.5. The coating process was repeated if a lower porosity of the scaffolds was required. Slurry residues were then gently removed from the surface of impregnated PU templates by compressed air to achieve the desired calculated porosity. The scaffolds prepared were dried at 25°C for 24 h. To burnout the PU template and achieve a sufficient manipulation strength the scaffolds were calcined at 1000°C with a heating rate of 1°C/min. The scaffolds were finally pressureless sintered in air at 1200°C for 3 h with a heating rate of 5°C/min and a cooling rate of 10°C/min.
Thermal, physical and structural characterization of scaffolds
Thermal analysis of the as-coated PU template was performed using a 6300 Seiko Instruments TG-DTA (Seiko Instruments, Japan). The specimen was measured at temperatures between 35 and 1000°C with a heating rate of 2°C/min in a mixture of air and argon (1:1); the flow rate was set to 400 ml/min.
The phase composition of HA and composites (5-20 wt % SiO 2 ) was determined via an X-ray powder diffractometer SmartLab 3 kW (XRD, Rigaku, Japan). The diffraction patterns were measured from 15° to 90° (2θ) with Cu Kα radiation. For this purpose, the sintered scaffolds were crushed into a fine powder which was subsequently analyzed. The phase content was quantified using the Rietveld analysis. The evaluation of the crystallographic structures and quantitative analyses were realized using the PDXL2 software.
The morphology of sintered scaffolds was observed using a scanning electron microscope (SEM, ZEISS Ultra Plus, Germany) equipped with an EDX analyzer (Oxford Instruments, UK). The scaffolds were embedded in a resin, ground and polished by the standard ceramographic methods. To quantify the pore sizes and their distribution, image analysis of SEM micrographs was done using the ImageJ software (National Institutes of Health, US).
The total porosity was calculated from the geometric volume, mass and theoretical density according to EN 623-2:1993: where ρ t is the theoretical density and ρ b is the bulk density. The bulk density is defined as: where m b is the mass of the dry test piece and V b is the total geometrical volume (the sum of the volumes of the solid material, the open and the closed pores). Additionally, the apparent density as the ratio between weight and geometrical volume for each analyzed scaffold prior to testing was individually calculated to allow a better understanding of the mechanical properties observed.
Mechanical testing -compressive strength of scaffolds
The compressive strength of prepared scaffolds was determined using an Instron 8862 electromechanically driven testing system (Instron, USA) of nominal capacity 100 kN and equipped with a 5 kN load cell and precise clip-gauge for the deformation measurement. Cylindrical scaffolds of nominal dimensions after sintering ø 6 mm × 8 mm were inserted between compressive platens with 1 mm thick leather spacers used for a proper load transfer from the steel platen to the scaffold. A cross-head speed of 0.5 mm/min was used for the loading. The compressive strength was calculated from the force corresponding with the first peak on the loading curve (force vs displacement) followed by a significant drop in applied force and scaffold dimensions. This approach leads to an estimate of the initial compressive strength of prepared scaffolds, which is important from the application point of view. Note that the determined strength here can be slightly lower than the "effective" compressive strength as determined from the plateau in the loading curve. A minimum of four scaffolds of the same pore size, porosity and composition were measured.
Evaluation of bioactivity of scaffolds
The bioactivity potential, i.e. the bone-bonding ability, was studied by means of apatite formation on the scaffold surfaces. Instead of the typically used simulated body fluid (SBF) prepared following the Kokubo recipe [34], the epitaxial growth of apatite was studied using Dulbecco's Modified Eagle Medium -DMEM (GE Healthcare, USA). It can be a better choice in terms of simulating the in vivo environment [35] because it contains, except the ionic composition like SBF (see Table 1), other components occurring in in vivo systems (such as glucose, amino acids and vitamins). The principle of bone-like apatite formation on scaffold surfaces is analogous to that in SBF solution and can be found elsewhere [ [35][36][37]. Scaffolds were incubated in the medium for 3 days at 37°C under a humidified atmosphere of 95% air and 5% CO 2 . After the removal from the medium and rinsing with deionized water, the scaffolds were dried at 25°C. The presence of the apatite layer on the surface was examined using SEM.
Assaying biocompatibility in vitro: metabolic activity of cells
The
Assaying biocompatibility in vitro: morphology of cells growing on scaffolds
Scaffolds containing 0 and 10 wt % of silica were sterilized by UV-irradiation for 20 minutes in the flow box. Scaffolds were wet in DMEM-Glutamax (Life Technologies, Czech Republic) medium for 1 h and centrifuged for 10 min to eliminate air bubbles from the material. Adipose-derived stromal cells (ADSCs) were isolated from adipose tissue by centrifugation and collagenase extraction, as described elsewhere [38]. Briefly, adipose tissue was digested with 0.1% collagenase type IV for 30 min at 37°C. After enzyme activity neutralization by DMEM-F12 (Life Technologies, Czech Republic) with 10% fetal bovine serum (FBS), cells were separated by centrifugation. The pellet was resuspended in cultivation medium (10% FBS, 0.5% penicillin/streptomycin (GE Healthcare Life Sciences, USA) in DMEM Glutamax) and propagated on a culture dish coated with 0.01% gelatin. Subsequently, the cells were trypsinized and seeded on materials at a concentration of 50.000/ 100 μL for analysis of cell viability and 1 million cells/ 100 μL for evaluation of cell morphology. Scaffolds were analyzed after 24 h of cultivation. Due to the similar composition of scaffolds, the cell viability was assessed on scaffolds with 75 PPI porosity by fluorescent live/dead assay. The fluorescent stock solution was prepared by diluting 0.03% w/v of acridine orange and 0.1% w/v of ethidium bromide (both Sigma-Aldrich, USA) into 2% ethanol in distilled water, with a final dilution of 1/1000 in 0.1 M phosphate buffer. The fluorescent solution was added to the specimens for 5 min 25°C and live/dead cells were visualized using an epifluorescence microscope Cell^R (Olympus C&S Ltd., Japan).
Thermal analysis
TGA curves of the PU foam template coated with HA powder reinforced with 10 wt % SiO 2 (the overall weight of the system with respect to PU is therefore as follows: PU (10 wt %), HA (81 wt %) and SiO 2 (9 wt %)) are given in Figure 1. The minimum weight loss (~1%) at temperatures from 40 to 200°C was caused mainly by the evaporation of adsorbed water. At temperatures between 200°C and 550°C, the two-stage thermal decomposition process of the PU foam template was observed. This decomposition behavior, typical of PUs, was described in various studies [39][40][41][42][43] as primarily a polymer splitting process that begins at about 200°C. At this temperature, hard segments (related to urethane links) start to decompose, while the second step of degradation (350-550°C) is caused by oxidation of soft segments (related to the ether group) [44]. The exothermic peak on the DTA curve (see Figure 1) in the same temperature range confirmed that the degradation process of the PU occurred by an oxidation mechanism.
Experimental data show that the weight loss of the specimen continued even above the temperature of 550°C, at which the PU was supposed to have already burnt out. This was likely caused by the thermal transformation of the HA powder. The endothermic drop on the DTA curve around 800°C was related to the thermal transformation of HA to hydroxyoxyapatite (HOA) [45].
The total weight loss of 15% below 1000°C corresponded to the initial amount of PU in the composite, adsorbed water and weight loss of commercial HA caused by the reaction of secondary phase -monetite (see Chapter 3.2).
Phase composition
X-ray diffraction (XRD) patterns of sintered scaffolds are shown in Figure 2. The commercial ceramic powder was composed of HA and monetite.
The quantitative analysis showed about 13 wt % of monetite as can be seen in Table 2. In the first instance, the HA was thermally decomposed to HOA with the following decomposition to the TCP phase according to the following equations [45]. .
The monetite phase was most likely decomposed during the sintering process to calcium pyrophosphate according to decomposition reaction [46]: Then the resulting calcium oxide and calcium pyrophosphate reacted to the TCP phase: Therefore, the original ceramic powder (without silica) was fully decomposed into α-and β-TCP in the scaffold after sintering at 1200°C (see Figure 2). In the literature, there is a vast discrepancy in the temperatures at which the decomposition of HA starts. According to many authors [47,48], HA should remain stable up to at least 1300°C. In our experiments (data are not shown here), a commercial HA started to decompose at about 800°C; almost half of the powder was transformed at 1000°C. This phenomenon can be attributed to the presence of impurities such as the monetite phase. Further increase in temperature led to the transformation of the β-TCP into the α-phase. Newly formed TCPs are believed to be more soluble in the body fluid than stoichiometric HA [49]. The phase composition of scaffolds containing silica was much more complex. Besides the α-and β-TCP, a new crystalline phase was formed after scaffold sintering. With increasing concentration of silica, the intensity of new strong diffraction at about 21.7° and two weak diffractions at about 28.2° and 35.8° increased and they were identified as cristobalite (P4 1 2 1 2 space group). The weight percentage of cristobalite within crystalline phases was roughly equivalent to the amount of colloidal silica in the initial slurry as documented by XRD quantitative analysis in Table 2.
The results of the XRD analysis also showed that the amount of the α and β TCP phases were almost equal in the absence of silica. However, the ratio between α-TCP and β-TCP significantly increased with the increasing amount of silica. The addition of silica significantly reduced the amount of β-TCP phase (from 58 to 29 wt %, see Table 2) whereas the α-TCP phase has been fixed at around 55 wt %. This behavior can be attributed to Si doping into α-TCP structure and formation of the most stable phase. Some studies [17,27,50] confirmed that the addition of silica shifts the temperature of HA→ α-TCP transformation to lower values. The stable α-TCP phase could be formed even during sintering above 700°C [17,27,28,50,51]. It was further reported that HA sintered in the presence of silica transformed to silica-substituted tricalcium phosphate (Si-α-TCP) with formula Ca 3 (P 1-x Si x O 4-x/2 ) 2 [17,28] according to the following equation [50] Being of the same space group, the Si-substituted α-TCP can be distinguished from its stoichiometric counterpart by different lattice parameters [17,28]. Measured and theoretical (α-TCP [52], Si-α-TCP [28,50], β-TCP [53]) lattice parameters are compared in Table 3 (data shown for scaffold containing 10 wt % SiO 2 ). The obtained data of the lattice parameters (showing an increase of the b-axis length and βangle) [27,28,54,55] indicate that our α-TCP was presumably substituted. Diffraction peak shifts of Si substituted TCP compared to undoped TCP confirm the lattice parameter changes, as also evident from Figure 2. The shift of diffraction patterns to lower angles and change of the lattice parameter in c-axis (see Table 3) indicates that β-TCP might also have been silicasubstituted. This partial substitution may have occurred by diffusion of silicate ions into the already transformed β-TCP phase. Nevertheless, further measurements are needed to confirm this assumption.
Characterization of structure and morphology of scaffolds
Ceramic scaffolds were prepared in a wide range of porosities and pore sizes. Porosity (40-98%) was easily tunable by the initial PPI of the PU template, by the viscosity of the slurry, by repeating the coating process and, finally, by the efficiency of removing the extra slurry by compressed air. If the total porosity was lower than 50%, the macropores were almost closed and the remaining pores were too small for efficient cell ingrowth. According to the Jodati review [56] an optimal porosity for osteogenesis appeared to be approximately 60%. In our case, the porosity seemed to be ideal in the range of 65-80% as regards the scaffold morphology (interconnected macropores) and strength. If the porosity exceeded 90%, the PU template was almost perfectly replicated, but such scaffolds were fragile with no sufficient manipulation strength due to very thin struts.
An overview of the macropore sizes of scaffolds reinforced with 10 wt % SiO 2 prepared from PU foam templates with initial pore sizes of 45 PPI, 60 PPI, 75 PPI, and 90 PPI and having 75% porosity is shown in Table 4 and Figure 3. The pore size of sintered scaffolds was dependent on the initial pore size of the PU foam template, the thickness of the struts and shrinkage during their sintering. The most convenient pore size for the applications in tissue engineering, i.e. from 150 to 500 µm [9,57], was observed for scaffolds prepared from the PU templates having a porosity of 60 to 90 PPI, where the measured pore size was in the range from 300 to 550 µm. Such range is ideal for cell migration as it was also reported in the work of Karageorgiou et al. [7].
In terms of the microstructure of struts, the differences between individual compositions were more significant (see Figure 4). Pure TCP scaffolds exhibited high microporosity in the struts (based on their low density <65 vol %) and overall higher geometrical dimensions (lower shrinkage) indicating insufficient particle packing during processing and sintering. The scaffolds containing silica had noticeably lower microporosity in the struts. This can be attributed to colloidal silica particles, which filled the spaces between HA particles and transformed into the cristobalite during processing and sintering. Its amount (the darker area) in Figure 4 grew proportionally with increasing initial silica content. For the lowest silica content, it was located in small areas near the grain boundaries. With increasing silica concentration, it formed a continuous network around the TCP grains. The grains were smaller in the presence of silica; probably due to the grain boundary pinning effect when a low concentration of silica was present or suppressed diffusion at higher concentrations of silica. The micropores were open and interconnected in all tested scaffolds. The size of the micropores in the struts varied between 0.5 and 20 µm. Microporosity can negatively influence mechanical properties, but it is essential for protein adhesion, cell migration, and osseointegration [58,59].
Mechanical properties
The influence of the concentration of silica, i.e. presence of the cristobalite in the microstructure, on the compressive strength, was evaluated for scaffolds of various PU template pore sizes (45, 60, 75 and 90 PPI). The results are summarized in Figure 5. The comparison of dependence of compressive strength of pure TCP and TCP/SiO 2 composites on their total porosity is presented. Not surprisingly, the compressive strength increased exponentially with decreasing porosity by two orders of magnitude from 0.3 MPa to almost 30 MPa. The shift in the composite strength (gray symbols) to higher values compared with the pure TCP foams (white symbols) for the same densities is distinguishable, reaching more than threefold enhancement; however, the scatter of compressive strength values is significant. Such difference can be attributed to the presence of cristobalite in the microstructure (see Figures 2 and 4). It was reported that the cristobalite present in the tough matrix rather deteriorate mechanical properties [60]. The opposite phenomenon occurs in a relatively mechanically weak matrix. Ansari et al. [61] reported a more than threefold increase in tensile strength for 20 vol % of cristobalite in hydroxylterminated polydimethylsiloxane. In the work of Li et al. [62], the cristobalite enhanced the compressive strength of geothermal geopolymer. However, the detail information about the influence of cristobalite on the mechanical properties of ceramic materials is still poorly discussed in the literature. Generally, in the case of ceramics, especially hydroxyapatite or tricalcium phosphate, a certain amount of glassy phase may be advantageous, since the glass is expected to have a positive effect on the sintering behavior, densification and mechanical properties of the composite with respect to the original bioceramics [63]. Our results support this statement. Due to the elimination of the influence of the total porosity (as a parameter having the most significant effect) on the compressive strength, a new set of scaffolds having the same porosity were prepared. A detailed view of the influence of the microstructure composition and the template pore size on the compressive strength of the optimized scaffolds at a nominal porosity of approximately 75% is given in Figure 6. The trend in the obtained data is reaching the maximum (in the range of 1-3 MPa) for scaffolds having initially 10 wt % content of silica and a typical macropore size of 440 µm. A similar limit was reported by Oktar and Göller [64] for a glass-reinforced HA. A closer look at each material composition suggests that smaller initial pores resulted in higher compressive strength. However, this behavior takes place up to the initial 10 wt % content of silica. The opposite trend was observed for scaffolds containing 15 and 20 wt % of silica. From the mechanical strength point of view, the porosity was significantly reduced by the SiO 2 addition to the concentration of 10 wt % silica offering the best ratio between reduced overall porosity in the struts and only isolated cristobalite structure, as can be seen in Figure 4. This explains the maximum strength achieved. Since the higher concentration of the initial silica (15 and 20 wt %) in the scaffold led to the formation of the cristobalite interconnected network around the TCP grains, the scaffolds became more brittle.
One of the requirements imposed on the materials used in tissue engineering are properties similar to those of replaced tissues. The reported compressive strength of cancellous bone lays between 1.5 and 38 MPa [13], typically 2-20 MPa [12]. Therefore, the strength-porosity relationship of TCP/SiO 2 scaffolds indicates that the optimal strength for the bone tissue replacement can be reached using an optimized preparation method with 10 wt % of silica, as was demonstrated here.
Biological properties -bioactivity assessment in Dulbecco's Modified Eagle Medium
The bioactivity of prepared scaffolds was evaluated using the immersion test in a DMEM. Figure 7 presents an overview of the surface morphology of the scaffolds before and after soaking in the medium. After 3 days, almost the entire surface of scaffolds was covered with a newly formed apatite layer. This layer, nucleated under in-vivo-simulated conditions, indicates good bioactivity, i.e. bone-bonding ability, of all prepared scaffolds.
According to the literature [17,[65][66][67], silica incorporated into the ceramic structure containing calcium phosphates can enhance the biomimetic precipitation on the surface of specimens immersed in the simulated body fluid. This can happen by two mechanisms. First, silicon can promote biomimetic precipitation on Si-α-TCP by the higher solubility of the material due to defects in the lattice [17,68,69]. Second, the higher biological activity can be influenced by the surface charge, which is here negative due to the substitution of SiO 4 4for PO 4 3ions, and can facilitate surface adhesion leading to the rapid biomimetic precipitation [17,70]. The bioactive behavior of some types of silicon-based ceramics was described in numerous studies [17,25,71,72].
Biological properties -metabolic activity of cells
The potential cytotoxicity of TCP and TCP/SiO 2 scaffolds of different pore sizes were assessed in vitro by MTT assay. MTT test is routinely used for measurement of viability and proliferation of standardized cell lines in vitro by colorimetric assessment of the metabolic activity of the cells. Figure 8 shows the MTT assay results for scaffolds of three different pore sizes (60, 75 and 90 PPI) containing 0 and 10 wt % of silica. As it is evident from the scaffold interactions with cells of both lines L929 and ARPE-1 (see Figure 8), all scaffolds indicated similar or higher cell viability compared to cells growing under standard 2D conditions. The results further revealed that neither composition nor pore size had significant effect on the cell viability. The viability of all tested samples was above the 70% viability threshold and within a 15% standard deviation range from the negative control. That means that no tested scaffold has proven any cytotoxic potential.
Biological properties -morphology of cells growing on scaffolds
Human ADSCs were seeded into calcium phosphate scaffolds to further test capability of material to support cell growth. These cells are well suited for analyzing clinically relevant cell-material interaction because of their human origin, non-cancerous nature, and multilineage differentiation potential. At 24 hours after seeding, majority of cells on all specimens exhibited green fluorescence signal, indicating their viability, with only few cells (less than 1%) being dying/dead, as demonstrated by red fluorescence signal. Such proportions are typical for in vitro cultured cells, so that ADSCs obviously did not undergo extensive materialinduced cell death. Such finding was typical for all the materials examined here (TCP and TCP/SiO 2 with 10 wt % of silica) (see Figure 9). Besides viability, morphological features of ADSCs have been also studied to evaluate behavior of cells growing on calcium phosphate scaffolds. As determined by visualizing nuclei and cytoskeletal elements, the cells adhered and became evenly distributed on internal surfaces of the scaffolds, with fully respecting details of scaffold morphologies. The cells grew in monolayer similarly to standard 2D culture in Petri dish, with producing protrusions (filopodia) in some parts of scaffolds. These protrusions, indicating active interaction with materials, were mainly detected on scaffolds with larger pores (45 and 75 PPI), as marked in the figures by white arrows (see Figures 10 and 11). It is of note that filopodia were more frequently seen in TCP/SiO 2 materials; further analyses of cell behavior (e.g. proliferation and formation of focal adhesion) should be performed for more detailed characterization.
Another significant phenomenon was penetration of cells through the pores and forming cell sheets, typically seen in the scaffolds with small pores (porosity 90 PPI, both TCP and TCP/SiO 2 , green arrows in Figure 10. Also importantly, the cells were void of blebbing of their cytoplasmic membranes, and they had regularly shaped nuclei and well-developed network of actin, underlying their vital contacts with the supporting scaffold.
From the above described findings made using ADSCs, we conclude that our newly developed materials have no adverse effects on normal human cells, and instead they behave highly supportive so that they may represent a proper technological step toward clinical application.
Conclusions
In this work, scaffolds based on calcium phosphates were prepared by the polymer replica technique. The pure and silica-rich (5-20 wt %) scaffolds with a 3D interconnected porosity (40-98%) were fabricated by templating the polyurethane foam with initial pore sizes of 45, 60, 75 and 90 PPI. The XRD analysis showed the total decomposition of the HA into α-TCP and β-TCP after sintering. Also, the strong diffraction of cristobalite was measured with an increasing concentration of silica in original scaffolds. It was proved that the silica significantly contributed to the phase transformation of HA to α-TCP. Moreover, the obtained data of the lattice parameters indicate that α-TCP had presumably been substituted by Si ions. Macropore dimensions of sintered scaffolds (between 300 and 770 µm) were dependent on the pore size of replicated templates. The measured average pore size of 300-550 µm in scaffolds prepared from the PU templates having a 60 to 90 PPI porosity was considered ideal for cells penetration based on available literature data. In terms of the struts microstructure, the scaffolds containing cristobalite had a noticeably higher density of struts with micropores in the range of 0.5 to 20 µm, which is essential for protein adhesion, cell migration and osseointegration. The compressive strength increased exponentially with decreasing porosity by two orders of magnitude from 0.3 MPa to almost 30 MPa. The presence of cristobalite in the composite scaffold structure led to a twofold increase in the compressive strength (1-3 MPa) compared to pure calcium phosphate scaffolds at a nominal porosity of 75%, which is in the range of the cancellous bone. The presence of cristobalite in the structure after sintering did not negatively affect the biological properties of scaffolds. In vitro tests demonstrated that all the scaffolds prepared were bioactive, as evidenced by the formation of an apatite layer on the surface after 72 h immersion in the medium. The scaffolds containing 0 and 10 wt % silica were not cytotoxic as demonstrated by MTT assay. The content of 10 wt % silica may even be beneficial to cells as it was indicated by cell viability assay using adipose-derived stromal cells. Such beneficial effect was maximally pronounced in materials with the smallest pores (90 PPI). Overall morphology of adipose-derived stromal cells growing on materials confirmed their proper supportive action.
Collectively, concerning phase composition, microstructure, compressive strength and biological properties, the promising candidates for potential application in bone tissue engineering are TCP/SiO 2 scaffolds having 60-80 vol % porosity. | 7,317.8 | 2022-03-27T00:00:00.000 | [
"Materials Science",
"Medicine"
] |
Recent advances in efficient and scalable solar hydrogen production through water splitting
Solar hydrogen production through water splitting is the most important and promising approach to obtaining green hydrogen energy. Although this technology developed rapidly in the last two decades, it is still a long way from true commercialization. In particular, the efficiency and scalability of solar hydrogen production have attracted extensive attention in the field of basic research. Currently, the three most studied routes for solar hydrogen production include photocatalytic (PC), photoelectrochemical (PEC), and photovoltaic-electrochemical (PV-EC) water splitting. In this review, we briefly introduce the motivation of developing green hydrogen energy, and then summarize the influential breakthroughs on efficiency and scalability for solar hydrogen production, especially those cases that are instructive to practical applications. Finally, we analyze the challenges facing the industrialization of hydrogen production from solar water splitting and provide insights for accelerating the transition from basic research to practical applications. Overall, this review can provide a meaningful reference for addressing the issues of efficiency improvement and scale expansion of solar hydrogen production, thereby promoting the innovation and growth of renewable hydrogen energy industry.
Introduction
Carbon emissions from the burning of fossil fuels are the main cause of global warming, the consequences of which have begun to emerge in recent years [1][2][3].Therefore, it is urgent to develop low-carbon, efficient, sustainable and clean energy, which is beneficial to mitigate climate change and achieve carbon neutrality [4].Hydrogen energy is a promising clean energy due to its zero-carbon emission during consumption.Hydrogen fuel cell technology is even considered as one of the ultimate solutions to the energy crisis in the future [5].The current industrial hydrogen production is mainly from fossil fuels and industrial by-products.In particular, as raw materials, coal and natural gas account for 80% of hydrogen production, simultaneously generating a large amount of carbon emissions in the production process [6].In order to realize hydrogen production with zero carbon emission, the approach of producing green hydrogen from solar water splitting has been endowed with great expectations.In addition, the conversion of solar energy into chemical energy, such as hydrogen, methanol or ammonia, etc., can solve the storage problem of intermittent solar energy, supporting wider applications such as electric vehicles, power grid peak shaving, etc. [7].
The research on solar hydrogen production from water splitting has aroused great interest worldwide in multiple fields such as materials, chemistry, physics, energy, and power engineering, etc.Among them, three typical technologies could be divided, as photocatalytic (PC) water splitting, photoelectrochemical (PEC) water splitting, and photovoltaic electrochemical (PV-EC) water splitting (Fig. 1) [8].The first two technologies are still in the research stage of rapid development.While the third technology has been used in industrialization pilot projects.Related to these technologies, there have been all kinds of review articles introducing or discussing some specific topics, such as particulate photocatalysts [9], photoanode/photocathode [10,11], specific types of hydrogen production [12,13], and specific principles and strategies [14][15][16], but lacking the inventory and analysis of efficient and scalable laboratory cases that are instructive for practical applications.Of course, the scope of our discussion is limited to the field of basic research.
Therefore, in this review, from the perspective of high efficiency and scalability, we will focus on some representative works that have guiding significance for practical applications with the above three technologies.Especially for some influential works, the research motivations and foundations are introduced in detail to highlight the continuity of the work, which will give us some inspiration on how to conduct in-depth research in the field.Finally, challenges and perspectives towards future industrialization for solar hydrogen production are presented.
PC water splitting
Photocatalysts dispersed in water are particularly suitable for low-cost and large-scale hydrogen production processes [17].Over past decades, various efficient photocatalysts have been reported for PC water splitting, including oxides, (oxy)sulfides, (oxy)nitrides, oxyhalides, carbonitrides, and chalcopyrites, etc. [18].For improving the catalytic properties of these materials, numerous strategies have been developed, such as bandgap engineering, crystal facet engineering, and cocatalyst loading.With the effort for improving solar catalytic efficiency, many world-class scholars are working hard to promote the industrialization process of large-scale PC hydrogen production.This section mainly focuses on their representative works in recent years.
Design of highly efficient photocatalysts
Domen's group has been working in the field of PC hydrogen production for more than 40 years and made great contributions to pushing forward its industrialization.Especially in recent years, Domen et al. has greatly improved the efficiency of SrTiO 3 -based photocatalysts, accelerating the development of large-scale PC hydrogen production.SrTiO 3 is a good photocatalyst with a bandgap energy of 3.2 eV and an ever-improving quantum efficiency [19].In 2016, Domen et al. found that a small amount of Al doped into SrTiO 3 from an alumina crucible is the main reason for enhancing the PC water splitting activity of SrTiO 3 , thereby achieving an apparent quantum efficiency of 30% at 360 nm [20].In order to obtain high solar-to-hydrogen (STH) conversion efficiency, narrow-bandgap photocatalysts with high quantum efficiency for overall water-splitting must be developed.As we all know, the strategy of spatial charge separation between different crystal facets has inspired extensive attention in the development of highly efficient photocatalysts.Such phenomenon could also be found on high symmetry SrTiO 3 exposed with anisotropic facets [21] (Fig. 2a).Meanwhile, a combination of multiple strategies was adopted such as flux treatment to enhance crystallinity, Al doping strategy to reduce lattice defects, and supporting CrO x shell on Rh catalyst to suppress oxygen reduction side reaction.An external quantum efficiency of 96% under 350-360 nm UV light was finally achieved for overall water splitting (Fig. 2b) [22].This inspiring work demonstrated that a perfect photocatalyst with nearly 100% quantum efficiency was achievable through accurate material design and provided a direct reference for the fabrication of visible-light-driven photocatalysts.
Very recently, some impressive breakthroughs in efficiency improvement have been reported from other groups.Liu et al. proposed a reproducible and economical pre-encapsulation technique for stabilizing highly dispersed and highly loaded (1.5 wt%) Cu single atoms (CuSA-TiO 2 ) on the surface of TiO 2 [24].During the photocatalytic HER process, the reversible change of Cu 2+ and Cu + greatly facilitated the separation and transfer of photogenerated electrons and holes, enabling CuSA-TiO 2 to achieve higher photocatalytic activity than conventional Pt/TiO 2 .The resulting CuSA-TiO 2 showed a high hydrogen evolution rate of 101.7 mmol g −1 h −1 and an apparent quantum efficiency of 56% at 365 nm, which exceeded all previously reported TiO 2 -based photocatalysts.It is worth mentioning that the sample still has good performance equivalent to that of the freshly prepared sample after storage for 380 days.This work provides an efficient, low-cost, high-stability, and easy-to-prepare TiO 2 -based single atom catalyst for solar hydrogen production.Yang et al. found that the lifetime of charge carriers could be extended by introducing a suitable donor-acceptor structure (β-ketene-cyano) into covalent organic framework nanosheets [25].By combining this organic nanosheet with a Pt cocatalyst, a record-breaking apparent quantum efficiency of 82.6% at 450 nm was achieved, surpassing all previously reported polymeric semiconductors for photocatalytic HER.This work provides an effective solution to enhance the photocatalytic activity of polymeric semiconductors.Li et al. reported a CdTe/V-In 2 S 3 heterojunction photocatalyst, in which CdTe quantum dots were anchored on surface of V-In 2 S 3 via an electrostatic self-assembly method and Pt and CoO x dual-cocatalysts were loaded as the H 2 -and O 2 -evolving sites (Fig. 2c) [23].Under the synergistic effect of robust interfacial built-in electric field and cascade energy band structure, the charge separation kinetics and multi-exciton generation effect of CdTe-4.2/V-In 2 S 3 -3 hybrid were effectively promoted and utilized, resulting in an internal quantum efficiency of up to 114% and an apparent quantum yield of 73.25% at 350 nm (Fig. 2d).Nevertheless, the STH efficiency of this work was only 1.31% under the simulated solar light, which was at the same low level as most reported STH efficiencies of PC water splitting.Jiang et al. constructed reductive high index facet (002) and oxidative low index facet (110) co-exposed CdS by a one-step hydrothermal method [26].They found that optimizing the ratio of high and low index facets could tune the d-band center, and subsequently affect chemisorption and conversion of intermediates (*-OH and *-O) on reduction and oxidation sites.Finally, an improved STH efficiency of 2.20% was achieved.Mi et al. recently reported a new record-setting STH efficiency from PC water splitting [27], using a highly integrated InGaN/GaN nanowire arrays on commercial silicon wafers through molecular beam epitaxy growth technology.The InGaN/GaN nanowire was decorated by Rh/Cr 2 O 3 /Co 3 O 4 cocatalyst by in situ photodeposition.It was found that the infrared thermal effect generated by high-intensity concentrated solar light could not only promote the forward water splitting reaction but also inhibit the reverse hydrogen-oxygen recombination during the PC overall water splitting (Fig. 3a-c).This strategy enabled the as-prepared photocatalysts to exhibit an STH efficiency of up to 9.2% under concentrated simulated solar light (Fig. 3d), which is much higher than that of previously reported unassisted PC water splitting systems and close to the requirement of industrial applications (10% for STH efficiency [28]).
Hydrogen farm project for scalable hydrogen production
Li's group has been committed to the basic research and industrialization of "green hydrogen energy" and "liquid sunshine methanol" for many years, which is very hopeful to become the main path to help achieve the goal of carbon neutrality.In the field of PC hydrogen production, Li et al. has explored a "Hydrogen Farm Project" (HFP) approach for scalable solar hydrogen production.
The achievement was widely regarded as a stark example of the transformation of scientific research into practical applications.Based on their more than 20 years of research in the field of PC water splitting, Li et al. revealed and proved the significance of charge separation.Li et al. successively studied the spatial separation of photogenerated electrons and holes between the {010} and {110} crystal facets of BiVO 4 [29], and conducted the rational assembly of dual-cocatalysts on different crystal facets to construct efficient photocatalysts [30].Subsequently, they investigated the direct imaging of the separation of highly anisotropic photogenerated charges on different facets of a single BiVO 4 particle, revealing the influence of built-in electric field on charge transfer [31].These works provided an opportunity to optimize the photocatalysts based on the principle of charges separation between different crystal facets.
In 2020, inspired by the natural photosynthesis, and learning from the practice of large-scale crop planting on farms, Li et al. took the lead in proposing and verifying the HFP strategy of solar hydrogen production based on particulate photocatalysts (Fig. 4a and b) [32].By using the Z-scheme structure to spatially separate the water oxidation reaction from the proton reduction reaction, this strategy could avoid the reverse reaction of hydrogen and oxygen, and further achieve the safe production of them.Based on BiVO 4 crystals for HFP, the solar conversion performance was optimized by precisely regulating the exposure ratio of different facets (for oxidation and reduction reactions) of BiVO 4 , with Fe 3+ /Fe 2+ pair used as shuttle ions for energy storage (Fig. 4c).In this HFP system, the PC water oxidation quantum efficiency was as high as 71%, and the STH conversion efficiency exceeded 1.8%, which is the highest value based on particulate photocatalysts reported internationally at that time.As a demonstration of large-scale HFP, a photocatalyst panel of 1 m 2 for solar energy storage was successfully implemented (Fig. 4d).This work has broken the technical bottleneck of large-scale PC hydrogen production and provided an effective approach to safe and efficient industrial application.In addition, Li et al. further enhanced the PC water oxidation ability of particulate BiVO 4 photocatalyst by in situ facet-selective photodeposition of dual-cocatalysts (Ir, FeCoO x ) in a later report [33].
Large-scale experiment for PC hydrogen production
In the large-scale hydrogen production, Domen et al. designed a PC water-splitting panel with a light receiving area of 1 m 2 [34].Using particulate RhCrO x / SrTiO 3 :Al as photocatalyst, the flat panel reactor achieved an STH efficiency of 0.4% under natural sunlight.With the special design, this panel reactor can maintain the intrinsic activity of photocatalysts when its size is scaled up, which also can sustain a high gas evolution rate at a 10% STH value.Therefore, photocatalysts with higher STH efficiency to be developed in the future can be directly installed in such reactors without worrying about mass transfer limitations.This work marked the first step from the laboratory to practical application of solar hydrogen production through PC water splitting.Subsequently, Domen et al. scaled up the 1 m 2 panel reactor system to 100 m 2 panel reactor arrays in last work, with the modified SrTiO 3 :Al photocatalyst (Fig. 5) [35].This "big" breakthrough was considered to have directly raised the threshold for using the word "large-scale" in this field.In addition, the system was very safe and durable, capable of stable operation for several months.However, the maximum STH efficiency of this system was 0.76%, which was still much lower than that of the PV-assisted and PEC water-splitting systems.Overall, this study demonstrated the feasibility of large-scale PC water splitting for hydrogen production, which held a "big" promise for industrial application.
In a recent report, Takanabe and Domen et al. pointed out that large-scale outdoor tests need to consider the impact of volume change of liquid water on the photocatalyst sheets caused by the temperature difference between day and night, as well as the elution, dissolution and removal of the photocatalyst caused by the flowing liquid water [36].Therefore, they adopted water vapor feeding, a milder method, to replace liquid water feeding to reduce external corrosion for photocatalyst sheets.For capturing enough water vapor and forming a liquid water reaction environment, the TiO x or TaO x nanolayers of less than 3 nm were uniformly coated on surface of the CoOOH/Rh loaded SrTiO 3 :Al photocatalyst.Excitingly, this work achieved an apparent quantum yield of 54 ± 4% comparable to liquid water reactions.In addition, longterm operation (over 100 h) at high pressure (0.3 MPa) and seawater as a water vapor source have also been proven feasible.This vapor-feeding strategy provided a new idea for the design of durable, corrosion-free, largescale, and high-pressure PC reactors, and to a certain extent, further removed the barriers for industrial application of PC hydrogen production.
Device fabrication for PC hydrogen production
In terms of device fabrication, printable solar watersplitting devices have the advantages of low cost, good processability, and easy scalability.Domen et al. reported a study on hybrid Z-type photocatalysts based on gold substrates [37].In addition to the study of specific materials, they also demonstrated a printed version of the materials.Using screen printing, a photocatalyst sheet could be fabricated with the printing ink containing hydrogen evolution photocatalyst, oxygen evolution photocatalyst, and Au nanoparticles (Fig. 6a-c).However, the STH efficiency of the printed semiconductor sheet was only 0.1% due to the presence of a large amount of Au nanoparticles that caused reverse reactions and affected the light absorption of the catalyst.To address this issue, Domen et al. reported a scalable and highly efficient PC semiconductor sheet fabricated by screen printing utilizing transparent indium tin oxide (ITO) nanoparticles as the electron-conducting medium (Fig. 6d and e) [38], which could avoid reverse reactions and eliminate light blocking caused by Au nanoparticles, with greatly improved STH efficiency (0.4%).This printable, cost-effective device greatly increased the industrial possibility of PC water-splitting hydrogen production.
Hyeon et al. designed a floatable PC platform composed of porous elastomer-hydrogel nanocomposites, which can achieve long-term stability and large-scale hydrogen production in seawater (Fig. 7a) [39].In the floatable platform, a high evolution rate of 163 mmol h −1 m −2 for hydrogen could be realized using Pt/TiO 2 cryoaerogel.When single-atom Cu/TiO 2 was used as the photocatalyst, 1 m 2 of the nanocomposites could produce 79.2 mL of hydrogen per day under natural sunlight (Fig. 7b and c).Large-scale hydrogen production of 100 m 2 is also simulated by calculation (Fig. 7d), which provides a feasible case for the industrial production of hydrogen.
PEC water splitting
PEC water-splitting cells are generally divided into two categories, including single photoelectrode-based PEC cells and unassisted PEC cells.The former usually requires an external bias, while the latter does not.Further, the unassisted PEC cells include PEC (photoanode-photocathode) tandem cell and PEC-PV (photoelectrode-photovoltaic) tandem cell.Unassisted PEC cells usually have high STH efficiency [40], but the device configuration is more complex.In addition, the stability and cost of PEC cells still cannot meet the requirements of industrialization at the current stage.
This paragraph mainly introduces a few PEC (photoanode-photocathode) tandem cells with high STH efficiency over 3%.In PEC tandem cells, metal oxide-based photoelectrodes have been extensively studied.BiVO 4 has been proven to be one of the most promising photoanodes, while metal oxides (e.g., Cu 2 O) and photovoltaic semiconductor materials are usually used as photocathodes [40].Grätzel and Luo et al. developed a Cu 2 O/Ga 2 O 3 -buried p-n junction photocathode with a large visible-light-absorption range and an external quantum yield close to 80% [41].With the assistance of TiO 2 protective layer and RuO x HER cocatalyst, the above photocathode was connected in series with BiVO 4 photoanode to form a tandem PEC cell (Fig. 8a), achieving a STH efficiency of 3% in weak alkaline electrolyte with a pH of 9.0 for stable operation over 100 h (Fig. 8b).Gong et al. developed a BiVO 4 photoanode with abundant surface oxygen vacancies that can facilitate charge separation at the BiVO 4 electrode/electrolyte interface.With FeOOH/NiOOH OER catalyst loading, the BiVO 4 photoanode was connected with Pt-deposited TiO 2 / Si photocathode to construct a PEC tandem cell, realizing a STH efficiency of 3.5% for stable operation of 10 h [42].Domen et al. developed CuIn 1 − x Ga x Se 2 photocathode with specific composition (x = 0.5) for remarkable HER performance [43].The CuIn 0.5 Ga 0.5 Se 2 was modified with CdS and Pt and then connected in series with NiFeO x -Bi/BiVO 4 photoanode to form a PEC tandem cell, achieving a STH efficiency of 3.7%.Inspired by the Z mechanism of natural photosynthesis, Li et al. reported a very high STH efficiency of 4.3% in a PEC tandem cell by rationally designing photoanode and photocathode with complementary light absorption and efficient charge transfer mediators (Fig. 8c and d) [44].For the front light absorber, the photoanode was formed by BiVO 4 with Co 4 O 4 as OER cocatalyst and pGO/SnO x as the charge transfer mediator.For the back light absorber, the photocathode was constructed by using the organic polymer semiconductor PBDB-T:ITIC:PC 71 BM (PIP) with Pt as HER cocatalyst and CuO x /TiO x as the charge transfer mediator.Although the STH efficiency of the PEC tandem cell is close to the requirement of 5% for the industrial pilot test, the feasibility of its large-scale application still needs to be verified urgently.
Photovoltaic materials, such as crystalline silicon [46], dye/TiO 2 [47], organic semiconductors [48], III-V semiconductors [49][50][51], Cu 2 ZnSnS 4 [52,53], and perovskite [54][55][56] are usually used as light absorbing layers to maximize the utilization of sunlight.The STH efficiencies of PEC-PV tandem cells can easily exceed that of photoanode-photocathode tandem cells, even reaching more than 10% [50,51,56].The photovoltaic materials are partially/fully integrated into PEC cells, which can construct wired or wireless PEC-PV tandem cells.For the former, photovoltaic materials are often integrated or connected in series with the photoanode (Fig. 8e) [45], which can increase the photovoltage to meet the large overpotential of OER.In this configuration, the photogenerated electrons are transferred to the counter electrode via external wires.For the latter, the photovoltaic absorber layer is integrated together with other functional layers into a monolithic photoelectrode.This kind of unassisted wireless device can be directly immersed in electrolyte to drive solar water splitting, so it is vividly called "artificial leaf " (Fig. 8f ) [46], in which the photogenerated electrons and holes transfer towards the catalyst surface of both sides for HER and OER separately.It is worth mentioning that the STH efficiency of the latest reported artificial leaf has exceeded 20% [57].In order to achieve effective charge separation, PEC-PV tandem cells often require a multi-layer design, which has higher requirements on the manufacturing process, and their durability cannot be guaranteed.For large-area PEC-PV devices, the current research is less and enlarging the area will lead to a significant decrease in efficiency [52,53].In addition, the noble metal Pt has been generally used as the counter electrode in previous reports, with the cost issue to be considered.
PV-EC water splitting
The PV-EC water splitting system is coupled by a photovoltaic device and a water electrolyzer, which are two wired-connected independent devices different from PEC cells integrated with PV materials.The overall STH efficiency depends on both the photovoltaic and electrolyzer sections.Currently, the highest photovoltaic efficiency reaches 39.2% (under 1 sun irradiation) from a six-junction III-V semiconductor-based solar cell [58].The stateof-the-art conversion efficiency of electrolyzer reaches 98% from a high-performance capillary-fed electrolysis cell [59].Therefore, the theoretically assessed STH efficiency could reach about 38%.Harris and Jaramillo et al. demonstrated a PV-EC system with an average STH efficiency of 30% for 48 h of continuous operation (Fig. 9a and b), which is still the highest STH efficiency reported so far for solar hydrogen production from water splitting [46].Copyright 2016, Springer Nature [60].The developed system coupled two polymer electrolyte membrane electrolyzers using Pt black/Ir black catalysts in series with a highly efficient InGaP/GaAs/ GaInNAsSb triple-junction solar cell, and the simulated solar concentration was adjusted to 42 suns to optimize the overall efficiency of the system.However, the high prices of III-V semiconductors and noble metal catalysts render this type of PV-EC system low cost-effectiveness at the current stage.Therefore, the development of lowcost alternatives becomes particularly important.Grätzel and Luo et al. achieved a STH efficiency of 12.3% by using the perovskite tandem cell to drive a water-splitting electrolyzer, in which two NiFe layered double hydroxide (LDH)/Ni foam electrodes serve as highly active bifunctional catalyst electrodes to generate hydrogen and oxygen (Fig. 9c and d) [61].The use of earth-abundant bifunctional catalysts in PV-EC systems simplified the system configuration and reduced the cost of hydrogen production.But the instability of perovskite solar cell and durability of the system could not be ignored.Zhao and co-workers reported a 20% STH efficiency by a lowcost PV-EC system consisting of a perovskite/silicon tandem cell and a nickel-based catalytic water electrolyzer (Fig. 9e and f ) [62].The NiMo/Ni foam catalyst with an extremely low HER overpotential of 6 mV at 10 mA cm −2 was combined with NiFe/Ni foam OER catalyst to achieve alkaline water splitting, with the levelized cost of hydrogen estimated to be $4.1 kg −1 .In a word, it is easy to achieve STH efficiencies over 15% for many reported PV-EC water splitting systems so far [63][64][65][66][67][68], which also indicates that PV-EC is the most commercially promising route at the current stage.
Challenges and perspectives
As a simple way to produce hydrogen, PC water splitting has the advantages of low cost and easy expansion and is the most ideal method for solar hydrogen production.However, some issues such as low STH efficiency, difficult separation of hydrogen and oxygen, and insufficient stability limit practical applications.Numerous researchers have tried to address these issues and achieved many good results.For example, Prof. Can Li has made remarkable achievements in hydrogen and oxygen separation through the rational design of particulate photocatalysts.Prof. Kazunari Domen has made many impressive attempts at the design of a large-scale panel reactor for PC water splitting.Prof. Zetian Mi proposed effective strategies to significantly improve PC STH efficiency.If their work experience is fully combined, the performance indicators of PC hydrogen production may be comprehensively improved.Nevertheless, in terms of STH efficiency, there is still an urgent need to develop more efficient narrow-bandgap photocatalysts.With the development of this field, the advantages of PC hydrogen production will become more and more prominent.Perhaps safe, reliable, efficient, low-cost, large-scale PC hydrogen production will gradually replace PEC and PV-EC hydrogen production in the future.
PV-EC water splitting is the most mature pathway for solar hydrogen production with high efficiency, long lifetime, and good scalability.Since both photovoltaic devices and water electrolyzers have been commercialized, PV-EC technology has entered the stage of industrial application.For example, a "liquid sunlight" demonstration project led by Li et al. has been put into operation in Northwest China [69].The core step of this project is to produce hydrogen through photovoltaicpowered water splitting.The successful operation of this project also indicates that it is feasible to produce green hydrogen on a large scale through the PV-EC route.In addition, the group led by Xie et al. has achieved stable and large-scale direct seawater electrolysis for hydrogen production [70].This is considered promising in combination with offshore photovoltaic platforms to achieve large-scale production of green hydrogen.As we all know, improving efficiency is the most fundamental strategy for reducing the cost of hydrogen.With the efficiency improvements of photovoltaic and electrolysis devices, the input-to-output ratio of PV-EC hydrogen production projects will be greatly reduced, and affordable green hydrogen energy will be more easily obtained.
The STH efficiency of PEC is between that of PC and PV-EC, and its high cost and complexity, and poor durability are still big challenges.Future improvement directions mainly include material design and device optimization.Efficient and stable photoelectrodes with small band gaps and long charge carrier diffusion lengths need to be designed with earth-abundant elements.It is very important to rationally introduce efficient cocatalysts to promote both HER and OER with low overpotentials.For tandem cells with semiconductors as light-absorbing layers, it is necessary to optimize the layout of semiconductors, catalysts, and interlayers to reduce internal resistance and accelerate charge separation and transfer, as well as reduce cost.Finally, the simultaneous use of hydrogen to produce high valueadded chemicals during the PEC hydrogen production process can increase the value of the output and enhance the economic feasibility of the technology [71].
Industrialized solar hydrogen production has a high demand for durability.However, the currently reported stability tests for solar hydrogen production usually range from several hours to 100 h, which is far below the expected service lifetime of commercial devices.In fact, only a few reported stability tests have reached the thousand-hour level [35,72,73].Therefore, the accelerated stability test for solar hydrogen production system can be developed with reference to the accelerated aging test system in the field of solar cells [74].For example, using simulated irradiation light or external bias as the acceleration condition, the degradation of the catalyst is accelerated by increasing the light intensity or external bias, and then the service lifetime of the system can be predicted by directly calculating the acceleration ratio.With regard to reaction area, the hydrogen production panels reported in past usually show a significant drop in STH efficiency after the size is enlarged.Therefore, it is necessary to further optimize the scale-up production process to reduce efficiency loss.In addition, the safety performance of the large-scale solar hydrogen production system also needs to be further verified, which is a key step in the scale-up production process and a prerequisite for commercialization.Finally, we hope to speed up the pilot test process of mature solar hydrogen production technology, build a complete green hydrogen energy industry system and standard including preparation, storage, and commercial use, and increase the proportion of hydrogen energy in the entire energy system.
Fig. 2
Fig. 2 Highly efficient photocatalysts.a Hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) cocatalysts supported on different facets of the SrTiO 3 :Al particle.b UV-vis diffuse reflectance spectrum of bare SrTiO 3 :Al (black line) and wavelength-dependent external quantum efficiency (EQE) for water splitting on Rh/Cr 2 O 3 /CoOOH-loaded SrTiO 3 :Al (red dots).Reproduced with permission [22].Copyright 2020, Springer Nature.c Schematic of the photogenerated carrier transfer and H 2 and O 2 evolution process.d The absorption spectrum, AQY, and IQE hy of CdTe/ V-In 2 S 3 photocatalysts.Reproduced with permission [23].Copyright 2023, Springer Nature
Fig. 3
Fig. 3 Photocatalytic overall water-splitting (OWS) system with ultra-high STH efficiency.a Photograph of a photocatalytic OWS system outdoors.b Schematic of the synergetic effect in the photocatalytic OWS system.c The variation of the STH efficiency of photocatalyst with temperature.d The stability test of the photocatalyst in the self-heated photocatalytic OWS system.Reproduced with permission [27].Copyright 2023, Springer Nature
Fig. 4
Fig. 4 Hydrogen farm project.a, b Schematic of the hydrogen farm project for scalable solar hydrogen production.c Surface reaction process of BiVO 4 in Fe 3+ solution.d Photograph of a photocatalyst panel for large-scale solar energy storage (1.0 m × 1.0 m).Reproduced with permission [32].Copyright 2020, Wiley
Fig. 5
Fig. 5 Large-scale hydrogen production.a Photograph of a panel reactor unit (25 cm × 25 cm), and its structure viewed from the side.b A top view of the solar hydrogen production system of 100 m 2 .c The variations of solar radiation intensity (red) and the gas evolution rate (grey) in the panel reactor.d Photograph of a 3 m 2 module composed of 48 panel reactor units.Reproduced with permission [35].Copyright 2021, Springer Nature
Fig. 6
Fig. 6 Printable photocatalytic water-splitting sheets.a Schematic diagram of the photocatalyst sheet prepared by the particle transfer method.b Photograph of the ink used to screen print the photocatalyst sheet.c Photograph of a printed 10 cm×10 cm photocatalyst sheet.Reproduced with permission [37].Copyright 2016, Springer Nature.d Schematic illustration of the preparation of photocatalyst sheets by screen printing.e Photograph of a printed 30 cm × 30 cm photocatalyst sheet.Reproduced with permission [38].Copyright 2018, Elsevier B.V.
Fig. 7
Fig. 7 Floatable photocatalytic nanocomposites.a Schematic of the practical application of nanocomposites in a real environment.b Photograph of 1-m 2 -scale arrayed nanocomposites.c The variations of solar radiation intensity (red) and production rate of H 2 by the 1-m 2 -scale nanocomposites (blue).d Schematic of the 100-m 2 -scale simulation domain.Reproduced with permission [39].Copyright 2023, Springer Nature
Fig. 8
Fig. 8 PEC water splitting.a Schematic and (b) stability test of an all-oxide PEC tandem cell with the Mo: BiVO 4 photoanode and Cu 2 O photocathode.Reproduced with permission [41].Copyright 2018, Springer Nature.c Schematic of a PEC tandem cell with the Co 4 O 4 /pGO/BiVO 4 / SnO x photoanode (front) and Pt/TiO x /PIP/CuO x photocathode (behind), and (d) the current-potential curve of two-electrode configuration.Reproduced with permission [44].Copyright 2021, American Chemical Society.e Schematic of a PEC-PV tandem cell.Reproduced with permission [45].Copyright 2015, Springer Nature.f Photograph of an artificial leaf (monolithic PEC-PV tandem cell).Reproduced with permission [46].Copyright 2016, Springer Nature
Fig. 9
Fig. 9 PV-EC water splitting.a Schematic and (b) STH efficiency measured for 48 h of the PV-EC device, consisting of a triple-junction solar cell and two PEM electrolysers connected in series.Reproduced with permission [60].Copyright 2016, Springer Nature.c Schematic energy diagram of the PV-EC device for water splitting, consisting of the perovskite tandem cell and NiFe LDH/Ni foam electrodes, and (d) J-V curves of the perovskite tandem cell and the NiFe LDH/Ni foam electrodes.Reproduced with permission [61].Copyright 2014, American Association for the Advancement of Science.e Schematic of the PV-EC device consisting of perovskite/Si tandem cell and Ni-based electrodes.f Overlay of the J-V curve of perovskite/Si tandem cell and the LSV curve of NiMo/NiFe electrodes.Reproduced with permission [62].Copyright 2021, Wiley . On this basis, Domen et al. reported the selective photodeposition of Rh/Cr 2 O 3 and CoOOH cocatalysts on different crystal facets of SrTiO 3 :Al (aluminum-doped strontium titanate), which can suppress charge recombination and enable efficient generation of separated hydrogen and oxygen via anisotropic charge transport | 7,278.6 | 2023-09-11T00:00:00.000 | [
"Environmental Science",
"Engineering"
] |
Multitarget Vehicle Tracking and Motion State Estimation Using a Novel Driving Environment Perception System of Intelligent Vehicles
. The multitarget vehicle tracking and motion state estimation are crucial for controlling the host vehicle accurately and preventing collisions. However, current multitarget tracking methods are inconvenient to deal with multivehicle issues due to the dynamically complex driving environment. Driving environment perception systems, as an indispensable component of intelligent vehicles, have the potential to solve this problem from the perspective of image processing. Thus, this study proposes a novel driving environment perception system of intelligent vehicles by using deep learning methods to track multitarget vehicles and estimate their motion states. Firstly, a panoramic segmentation neural network that supports end-to-end training is designed and implemented, which is composed of semantic segmentation and instance segmentation. A depth calculation model of the driving environment is established by adding a depth estimation branch to the feature extraction and fusion module of the panoramic segmentation network. These deep neural networks are trained and tested in the Mapillary Vistas Dataset and the Cityscapes Dataset, and the results showed that these methods performed well with high recognition accuracy. Then, Kalman filtering and Hungarian algorithm are used for the multitarget vehicle tracking and motion state estimation. The effectiveness of this method is tested by a simulation experiment, and results showed that the relative relation (i.e., relative speed and distance) between multiple vehicles can be estimated accurately. The findings of this study can contribute to the development of intelligent vehicles to alert drivers to possible danger, assist drivers’ decision-making, and improve traffic safety.
Introduction
Driver inattention is one of the leading causes of traffic accidents. It was reported that approximately 80 percent of vehicle crashes and 65 percent of near-crashes involved driver inattention within three seconds prior to the incident in the USA (National Highway Traffic Safety Administration (NHTSA)) [1]. Road traffic accidents caused by fatigue driving, distracted driving, and failure to maintain a safe distance between vehicles accounted for 56.63% of the total accidents in China in 2019 [2]. To reduce this critical problem, driving environment perception systems for intelligent vehicles have been attached increasing attention.
Driving environment perception systems, as an indispensable component of intelligent vehicles, are the key to helping drivers perceive any potentially dangerous situation earlier to avoid traffic accidents [3][4][5]. Vehicle detection and tracking technologies set up a bridge of interactions between intelligent vehicles and the driving environment. Driving environment perception systems are used to track multiple vehicles and estimate vehicle motion states, thereby providing reliable data for the decision-making and planning of intelligent vehicles. Vision-based perception systems are similar to the human visual perception function [6][7][8][9]. e advantage of intelligent vehicle visual perception systems is that image acquisition does not cause any intervehicle interference or noise compared to radar [10]. Meanwhile, computer vision can be used as a tool to obtain abundant information of scenes within a wide range.
Due to the complex interactions among vehicles and the fact that the current multitarget tracking method is limited by prior knowledge [11], it becomes more difficult to explore the relationship between multiple vehicles by relying on traditional methods, such as the background difference method, the frame difference method, and the optical flow method [12], to solve these problems. To achieve a precise detection and tracking result, this study proposes a multivehicle tracking and motion state estimation method based on visual perception systems. One of the deep learning methods is used in this study, called convolutional neural networks, which can learn more target characteristics at the same time with high accuracy. Moreover, the relative location and speed of multiple vehicles need to be estimated, which is crucial for controlling the host vehicle accurately and preventing collisions. erefore, this study aims to develop a novel driving environment perception system of intelligent vehicles to track multitarget vehicles and estimate their motion states, which can alert drivers to possible danger, assist drivers' decision-making, and improve traffic safety.
Literature Review
is study tries to establish a visual perception system of intelligent vehicles to estimate multivehicle relationships.
us, next, we introduce current studies from two aspects: (1) multitarget vehicle tracking methods for estimating the position and speed of moving vehicles and (2) driving environment perception systems, which recognize vehicles in the forward driving scenario through panoramic segmentation and calculate the distance between vehicles through depth estimation. From the aspects of traffic safety, machine learning methods related to environment perception and vehicle tracking which can be used to assist decision-making of drivers or autonomous driving systems have been widely discussed. For example, a convolution neural network was used to process the image collected by the camera and predict the probability map of lane line [13], which can be used to keep the vehicle in the lane and provide lane-departure warnings. e target tracking algorithm is used to detect the vehicles in the driving environment and obtain their trajectories, which can help to provide drivers with early alteration of potential collisions or risk driving behaviour [14,15].
Vehicle Detection and
Tracking. Vehicle detection and tracking are used to estimate the position and speed of moving vehicles. Although image segmentation technologies can recognize the objects in the scene well, they are only limited to static information and cannot get the motion information of moving vehicles. e estimation of the motion state is usually based on the methods with a fixed camera, and the position and speed of objects are calculated through geometric relations [16]. However, for in-vehicle devices installed in moving vehicles, since the position of the camera is constantly moving, it is more complicated to estimate the state of moving objects ahead. To solve this problem, several different solutions have been proposed.
Some studies combined millimeter-wave radar with a camera [17] to obtain the position and speed of the forwardmoving objects. Compared with cameras, millimeter-wave radars were complicated to install and inconvenient to operate. Moreover, since the Lidar sensor delivered only the visible section of objects, the shape and size of objects were changed over time.
is led to inaccurate estimation of moving objects states consequently. e shape change due to the observation position or occlusion was one of the typical examples for that.
In some studies, only the camera was used to estimate the motion state. Li et al. [18] first recognized the front vehicles through a semantic segmentation network, then determined different vehicle instances according to the connectivity of the segmented vehicle area, and finally used monocular ranging and Kalman filtering to determine the vehicle's position and speed. However, this method still can be improved from some aspects. For one thing, when the traffic volume was large, the areas of different vehicles were connected in this method, resulting in multiple vehicles being identified as one vehicle. For another, due to the lack of matching of objects between different frames, only a single object's speed can be calculated by this method, which cannot be applicable for the multivehicle condition.
In some studies, traditional multitarget vehicle trajectory tracking technologies (such as the background difference method, the frame difference method, and the optical flow method) were used for the state estimation of moving vehicles [19,20]. ese traditional methods were easy to deploy and had low resource consumption, but, limited by prior knowledge, tracking stability is poor and accuracy is not high. erefore, the multitarget tracking algorithm based on monocular cameras for vehicle detection still needs improvement. To fill this research gap, a novel multitarget vehicle trajectory tracking system based on image segmentation neural networks was presented in our study.
Panoramic Segmentation.
Urban road driving environment consists of road environment (such as roads, facilities, and landscapes) and traffic participant environment (such as vehicles, nonmotor vehicles, and pedestrians). e scene recognition of the urban road driving environment refers to identifying the objects in the driving environment and specifying their class and distribution. Realizing the scene recognition of the driving environment mainly relies on the methods of image segmentation, and this study adopts the panoramic segmentation method in our analysis.
Panoramic segmentation refers to the instance segmentation of regular and countable objects in the image and semantic segmentation of irregular and uncountable objects. Panorama segmentation combining instance segmentation and semantic segmentation is currently a finer image segmentation method for scene recognition. Compared with semantic segmentation which only considers categories, panoramic segmentation comprehensively considers the area class and instance class in the scene, which not only classifies all the pixels but also determines different instances of the instance class object. Multitask image segmentation has a certain research history, and early work of this research topic includes scene analysis, image analysis, and overall image understanding. Tu et al. [21] established a scene analytic graph to explain the segmentation of regular and irregular objects and introduced the Bayesian method to represent the scene.
Recently, with the concept of panorama segmentation, the evaluation indexes have been refined. However, in many object recognition challenge competitions such as COCO and Mapillary Recognition Challenge, most studies first completed semantic segmentation and instance segmentation independently and then went through the fusion process. Although this kind of method can get good precision results by fusion, end-to-end training cannot be realized due to the redundancy in the calculation, unrealized calculation sharing, and tedious process. e semisupervised method proposed by Li et al. [22] could achieve end-to-end panoramic segmentation, but this method required additional input of candidate box information and the use of the conditional random field in the inference process, which led to the increase in the complexity of model calculation. Scharstein and Szeliski [23] tentatively proposed a unified network to conduct panoramic segmentation, but there was a gap between its implementation effect and benchmark. Overall, there is still room for improvement in the precision and speed of panoramic segmentation.
Depth Estimation.
Depth estimation is to estimate the distance between the observation point and the objects in the scene. Scene depth information plays an important role in guiding vehicle speed control and direction control, so it is one of the basic pieces of information needed by assistant driving systems. e depth information of the scene can be obtained by Kinect devices or Lidar devices developed by Microsoft. However, these devices are inconvenient to use because of the high price of equipment, the high cost of depth information acquisition, and the problems of low resolution and wide range depth missing in the depth images collected by these hardware devices. Considering that cameras are cheaper and easier to install and use, many studies have begun using image methods for depth estimation.
In the early days, the image-based depth estimation method was mainly based on the geometric algorithm [24], which used binocular images for depth estimation. e algorithm relied on calculating the parallax of the same object between two images and estimated the depth through the triangle relationship of light and shadow. Later, Saxena et al. [25] pioneered the method of supervised learning to estimate the depth of a single image. Subsequently, a large number of methods for extracting features and estimating monocular image depth by manually designing operators have emerged [26][27][28][29][30]. Since the manually designed operator can only extract local features but cannot obtain semantic information in a wide range, some studies used Markov conditional random field equal probability model to capture the semantic relationship between features [31,32].
In recent years, convolution neural networks have been proposed based on the depth estimation method, which has achieved great success in image classification. e development of feature extraction networks such as VGG [33], GoogLeNet [34], and ResNet [35] further improved the accuracy of depth estimation through the monocular image. However, due to the spatial pooling operation in the feature extractor, the size of the feature map became smaller and smaller, which affected the accuracy of subsequent depth estimation. To solve this problem, Eigen et al. [36] introduced a multiscale network structure, which applied independent networks to gradually refine the depth map from low spatial resolution to high spatial resolution. Xie et al. [37] fused the shallow high spatial resolution feature map with the deep low spatial resolution feature map to predict the depth. Transpose convolution was employed in some studies [38,39] to gradually increase the spatial resolution of the feature map. However, in the existing depth estimation research using convolutional neural networks, due to multiple feature extractions for depth estimation, the phenomenon of model overfitting may occur.
Summary.
Given the above, current studies on vehicle detection and tracking show the following: (1) e estimation of vehicle position acquired by Lidar sensor may be inaccurate over time. (2) Semantic segmentation for vehicle recognition is only suitable for a single-vehicle driving environment. (3) e applicability of traditional multitarget tracking methods still needs to be further improved. To solve these problems, this study adopts multitarget vehicle trajectory tracking based on the segmentation neural network and adopts cameras to obtain position information between vehicles based on the driving environment perception system. Current studies on driving environment perception systems show the following: (1) most of the existing panoramic segmentation studies complete semantic and strength segmentation independently, and there is still room for improvement in segmentation accuracy and segmentation speed; and (2) existing depth estimation research carries out repeated feature extraction alone, which is complicated and computationally intensive. us, this study builds a lightweight neural network model and adds depth branches on the basis of panoramic segmentation to realize the realtime analysis of the driving environment in front of the vehicle.
Methodology
e methodology flowchart is presented in Figure 1. e methodology consists of two main parts: (1) a driving environment perception system and (2) multivehicle tracking and motion estimation. e driving environment perception system can realize the recognition and separation of vehicles and other elements in the driving environment through Journal of Advanced Transportation panoramic segmentation and then calculate the position of each vehicle by depth estimation. After obtaining the information of each vehicle at a time point, multivehicle tracking and state estimation is used to analyze the relationship between multiple vehicles in a continuous period of time. In the multivehicle tracking and state estimation method, vehicles between different frames in the video data are matched at first based on the segmentation results of the driving environment perception system. en, the relative distance and relative speed between vehicles are estimated according to the depth information provided by the driving environment perception system. is kind of automatic calculation method of the relationship between multiple vehicles from camera videos can be used for advanced driver assistance systems to monitor the motions of vehicles and alter the potential collisions. ese two parts are detailed below.
Driving Environment Perception Systems.
e overall neural network structure of the environmental perception system mainly includes image feature extraction, feature fusion, semantic segmentation, instance segmentation, and depth estimation modules, as shown in Figure 2.
Step 1: feature extraction and fusion. Firstly, the input images go through the feature extraction module. e function of the feature extraction module is to extract the features of objects in the image, such as low-level features (e.g., edges and textures), as well as high-level features (e.g., skeletons and position relations among objects). en, these features are input into the feature pyramid for fusion, and then these fused features serve as the basic input for semantic segmentation and instance segmentation.
Step 2: panoramic segmentation. Semantic segmentation is responsible for identifying the region class in the driving environment scene, while instance segmentation is used to support the instance class in the recognition scene. e output results of semantic segmentation and instance segmentation are fused to obtain the results of panoramic segmentation.
Step 3: depth estimation. Depth estimation branch and panorama segmentation share the features extracted by ResNet-FPN, and both of them require information about semantics, texture, and contour. In the depth estimation, pixels with the same semantics generally have similar depths, and the contours of each instance are the positions where the depth changes. Feature sharing avoids a separate step of feature extraction for depth estimation, which greatly reduces the amount of calculation. e panoramic segmentation and depth estimation in the network structure of this driving environment perception system are described in detail as follows.
Panoramic Segmentation of Driving Environment.
e urban road driving environment is composed of road infrastructure, traffic signs and markings, and traffic participants. From the perspective of the panoramic segmentation task, the components of the driving environment of urban roads mainly include instance class and regional class. e regional class mainly contains pavement, greening, lane lines, guardrails, curbs, roadside buildings, and so forth, while the instance class includes signs, traffic lights, and traffic participants. e feature extraction module uses the ResNet structure. ResNet can prevent network degradation so that the network can extract features with more neural layers. e overall structure of ResNet is formed by continuously stacking the bottleneck structure (BottleNeck).
ere are generally 4 stages, and the number of channels increases as the network depth increases. In general, the deeper the level, the smaller the size of the feature map and the more channels.
Feature pyramid network (FPN) uses a top-down network structure to integrate deep semantic features and simple detail features, which makes full use of the features extracted by the backbone network. e feature pyramid network is connected after the ResNet network and enriches the feature expression of the entire feature extraction network. FPN ensures that downstream tasks can obtain enough effective information to improve the accuracy of the model. e network structure of the semantic segmentation branch adopts the ResNet-FPN network structure. e four output branches of ResNet-FPN, respectively, pass through their corresponding decoders to obtain a decoding result with a size of 1/4 of the original picture and 128 channels. e decoder consists of multiple convolution kernels with a size of 3 × 3 and 2 times upsampling. e number of the pairs of convolution and upsampling is determined according to the size of the input feature. e fusion of different branch predictions adopts the method of adding corresponding elements. e summation result is convolved to obtain the semantic prediction of the picture. e final predicted result is enlarged by 4 times to ensure the same size as the original image.
Instance segmentation is completed based on target detection. e task of target detection is to identify the object in the image, mark the position of the object, and determine its class. e segmentation branch network structure includes four parts: RPN, RoIAlign, R-CNN, and Mask. RPN (region proposal network) is the module responsible for generating candidate frames, and it finally provides Region of Interest (RoI) for downstream tasks. RoIAlign makes the features corresponding to RoI uniform in size.
e Box branch predicts the class of each RoI and the correction coefficient of the box relative to the actual box. e Mask branch estimates the specific shape of the object in the box.
Finally, the prediction results of semantic segmentation and strength segmentation are merged to obtain panoramic segmentation results. Panorama segmentation requires that each pixel in the output prediction result can only be assigned a unique class and instance number. e overlap between instance objects is recognized as the object with high confidence. e part where instance segmentation and semantic segmentation overlap chooses the results of instance segmentation.
Depth Estimation of Driving Environment.
Depth information under the urban road driving environment represents the distance information between the objects in the driving environment and the observation point. Depth estimation is to estimate the size of the distance value; namely, depth estimation refers to the depth of the pixel.
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According to the RGB information of the image, the distance between the object (corresponding to each pixel in the image) and the camera is estimated. Assuming that the input image is I and the image depth is D, the depth estimation task is to find a suitable function to map the image information into depth information, as shown in the following formula: Depth estimation is similar to semantic segmentation, and both of them belong to pixel-by-pixel dense prediction tasks. erefore, the branch of depth estimation can also use the Full Convolutional Network. e basic network structure of depth estimation is similar to the semantic segmentation branch. e input of the depth estimation branch is also the four output branches of the feature pyramid network. e size of each feature map is 1/32, 1/16, 1/8, and 1/4, respectively, and the number of channels is 256. Each branch is subjected to multiple convolutions and upsampling to obtain a tensor of size S and the number of channels C.
e number of convolution and upsampling operations is determined by the super parameter S. As shown in Figure 2, when S � 1/4, the depth estimation is conducted by 8 times of convolution and 7 times of upsampling. FPN-P1 (i.e., the first feature layer extracted by FPN) performs one convolution operation, FPN-P2 performs one pair of convolution and upsampling operations, FPN-P3 performs 2 pairs of convolution and upsampling operations, and FPN-P4 performs 3 pairs of convolution and upsampling operations. After these four output branches are added, a convolution operation and an upsampling operation are performed, and then the depth prediction value is obtained.
Multitarget Tracking of Moving Vehicles.
e main purpose of multitracking of moving vehicles is to obtain position and speed information of multiple vehicles. However, the difficulty of calculating the position and speed of moving vehicles mainly lies in the matching and tracking of objects between two different frames.
As for vehicle video data, the two frames of pictures are completely independent in encoding form. erefore, the vehicles must be tracked between the two frames before the state of the vehicles can be calculated. e key to realizing multitarget vehicle trajectory tracking lies in the detection of vehicles in a single frame and the matching of objects between frames. For single-frame vehicle detection, the interframe detection frame is optimized by Kalman filtering according to the continuity of the video data. en, the Hungarian matching algorithm is applied to match objects between frames.
Specifically, the algorithm flow of vehicle trajectory multitarget tracking is as follows: Firstly, the image of each frame is continuously extracted from the video data and input into the panoramic segmentation network. e panoramic segmentation network in Figure 1 is used to detect the vehicle in the image and output the detection frame. Secondly, the status of the tracker is checked. en, the Kalman filter is employed to estimate the optimal state of the detection frame. Besides, the Hungarian matching algorithm is used to match the tracking vehicles. Finally, if the tracker matches the detection frame successfully, update the tracker to a certain state. e flowchart of the tracking algorithm is shown in Figure 3. Kalman filter is an optimal estimation algorithm that combines measurement data with the prediction model to achieve the optimal estimation of vehicle positions. Since the measurement data of vehicle positions are noisy, the measured value does not accurately reflect the true position of the car. Additionally, the noise of the prediction process is uncertain, so the prediction model cannot be solely used to estimate the vehicle positions.
us, Kalman filters can provide a better estimation result by combining them to reduce the variance.
As shown in Figure 4, the working principle of the Kalman filter is explained intuitively by using the probability density functions. e predicted value of the vehicle position is near x k , and the measured value of the vehicle position is near y k . e variance represents the uncertainty of the estimation, and the actual position of the vehicle is different from the measured position and the predicted position. e best estimation of vehicle position x k is the combination of predicted and measured values. e best estimated probability density function is obtained by multiplying the two probability functions, and the variance of this estimate is less than the previous estimate. erefore, Kalman filter can estimate the vehicle position in an optimized way.
As shown in equation (2), the Kalman gain K refers to the ratio of the predicted error of the model to the measurement error of the panoramic segmentation detection system in the process of estimating the optimal state of the detection frame. K ∈ [0, 1]. When K � 0, it indicates that the prediction error is 0, and the optimal state of the detection frame depends entirely on the predicted value of the model. When K � 1, it indicates that the observation error is 0, and the optimal condition of the detection frame entirely depends on the detection result of the panoramic segmentation system.
K �
Predicted error Predicted error + Measurement error .
(2) e principle of using the Kalman filter to estimate the optimal condition of the detection frame is to minimize the optimal estimation error covariance P k . In this case, the estimated value is closer to the actual value. e Hungarian algorithm [40] is a combinatorial optimization algorithm that solves the task assignment problem in polynomial time. e Hungarian algorithm is mainly used to solve some problems related to bipartite graph matching, and it is also used to solve the data association problem in multitarget tracking. e matching of objects between frames is essentially a bipartite graph matching problem, so this paper uses the 6 Journal of Advanced Transportation Hungarian algorithm to solve the problem of object matching between frames. Assuming that there are three trackers in the previous frame, the Kalman filter predicts that there are three vehicles in the current frame. In the current frame, three vehicles are detected by the detector. It is predicted that a certain car in the frame has the possibility to match each car in the detected frame. e Hungarian algorithm is to find the best match between the predicted frame and the detected frame, as shown in Figure 5. Each prediction frame and each detection frame have a cost (unreliability), and then prediction frames and detection frames form a cost matrix. e Hungarian algorithm obtains the matching result between the two frames by transformation and calculation of the cost matrix. e definition of the cost matrix will directly affect the quality of the matching result. From the perspective of the position of the detection frame, since the time between frames is short and the moving speed of the vehicle is limited, the detection frame of the same object between the two frames should be relatively close. From the perspective of the appearance of the object, it has similar characteristics for the same object. erefore, the setting of the cost matrix will be considered from the two perspectives of distance and feature difference.
Since the Hungarian algorithm belongs to the maximum matching algorithm, matching will be completed to the greatest extent.
ere are constantly vehicles leaving the camera's perspective in the scene; meanwhile, new vehicles are entering the camera's perspective. To improve the matching accuracy, a screening based on Mahalanobis distance and appearance distance is performed on the matching results. When the Mahalanobis distance and the appearance distance of a certain match between two corresponding detection frames are less than a certain threshold, the matching is accepted; otherwise the matching is abandoned.
Multivehicle Motion Estimation.
e position and speed of the moving vehicle in the driving environment can be divided into lateral and longitudinal according to different directions, that is, lateral distance, longitudinal distance, lateral speed, and longitudinal speed. In different coordinate systems, the way of expression is different. As shown in Figure 6(a), there are the world coordinate system x w wy w and the camera coordinate system x c cy c . e position state of the origin of the camera coordinate system in the world coordinate system is (x w 0 , y w 0 ), and the speed state . v xw 0 is the velocity component of the camera coordinate system in the x direction of the world coordinate system, and v xw 0 is the velocity component of the camera coordinate system in the y direction of the world coordinate system. e states of vehicles in different coordinates can be converted mutually. e state of the vehicle in the world coordinate system (x w 1 , y w 1 , v xw 1 , v yw 1 ) is the vector sum of the state of the camera in the world coordinate system (x w 0 , y w 0 , v xw 0 , v yw 0 ) and the state of the vehicle in the camera coordinate system (x c 1 , y c 1 , v xc 1 , v yc 1 ). e distance calculation includes the lateral distance and the longitudinal distance. For the estimation of the longitudinal distance, the depth information can be obtained from the depth estimation network in Methodology section above. For the calculation of the lateral distance, it can be estimated through its geometric relationship with the longitudinal distance.
As shown in Figure 6(b), the coordinates of the vehicle in front of the camera in the camera coordinate system are (x c 1 , y c 1 ). e vehicle is imaged in the camera, and the coordinates in the picture coordinate system xoz are (p x , p z ). e two triangles formed by light are similar, which can be derived from the properties of similar triangles: where f is the focal length of the camera. To calculate the vehicle speed, it first needs to determine the changes in the lateral and longitudinal distances Δx c 1 , Δy c 1 of the object in the two adjacent frames of images recorded by the camera coordinate system. en, according to the relationship between displacement and speed, the lateral and vertical speed of the object in the camera coordinate system can be obtained.
where Δt is the time difference between two frames, which is the reciprocal of the number of frames per second recorded by the camera.
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By calculating the relative lateral and vertical distances and relative lateral and vertical speeds between vehicles, the motion state of multiple vehicles can be estimated so that the relative relationship between multiple vehicles can be further studied.
In conclusion, using the multitarget tracking algorithm, vehicle detection is optimized, and the problem of vehicle matching between frames is solved. rough the depth information and coordinate conversion method, the position and speed of the moving vehicle can be estimated, so that the relative relationship between multiple vehicles is obtained.
Panoramic Segmentation Experiment of Driving Environment.
e dataset used for the training is the Mapillary Vistas Dataset (MVD) [41]. MVD is a novel, largescale, street-level image dataset containing 25000 highresolution images, with an average number of 8.6 million pixels per image. Training and validation data comprise 18000 and 2000 images, respectively, and the remaining 5000 images form the test set. e loss of the whole panoramic segmentation network consists of two parts, namely, semantic segmentation loss and instance segmentation loss. e loss of panoramic segmentation is where λ is the loss adjustment factor between two subpartition missions. Semantic segmentation loss y � 1, . . . , N classes is the class set of semantic prediction, Y ij ∈ y is the actual class of pixels of a given image at (i, j), and P i,j (c) is the probability value of pixels of an image at (i, j) belonging to class C. e loss of semantic segmentation for a single image is calculated according to the following equation: Instance Segmentation Loss. e loss of the instance segmentation consists of three parts: the RPN, the Box, and the Mask. erefore, the loss of instance segmentation is Journal of Advanced Transportation a negative sample pair M − . r is the actual bounding box r � (x r , y r , w r , h r ), and r is the predicted bounding box r � (x r , y r , w r , h r ). s r is the probability that an object is contained in r predicted in RPN. a r refers to the default frame, and | · | S refers to smooth loss.
e Calculation of the Loss of the Box Branch. e loss of Box class prediction is L cls Box , and the loss of the position of the bounding box is L bb Box . e sample pair N contains the positive sample pair set N + and the negative sample pair set N − . c r is the class corresponding to the actual bounding box r, and s c r � r is the probability that the predicted box belongs to class c.
e Calculation of the Loss of the Mask Branch. S r is the binary mask corresponding to object c in the bounding box r, S � r is the binary mask of class c predicted by the Mask branch, and S � r i,j is the probability that cell(i, j) belongs to class c. d is the side length of the mask, which is 28.
e overall loss of the training process is shown in Figure 7. As shown in Figure 7, the loss value keeps decreasing and tends to be stable with the progress of training, indicating that the training results converge, the network design is reasonable, and the training strategy is correct. e trained model is used to predict the image of the MVD validation set, and the accuracy of the model is calculated according to the evaluation indexes (RQ (recognition quality), SQ (segmentation quality), and PQ (panoptic quality); PQ � RQ × SQ) [42] of panoramic segmentation, as shown in Table 1. e PQ value of the validation set reached 15.224%. Compared with the results of some other methods in previous studies [43], the recognition effect in this study was good. e visualization of the prediction results is shown in Figure 8. Figure 8(a) shows the result of the semantic segmentation branch, which accurately divides the road, sidewalk, greening, building, and sky. Figure 8(c) shows the detection and segmentation effect of the instance segmentation branch, which accurately detects and divides vehicles, pedestrians, traffic lights, and pillars. Figure 8(d) is the result of semantic segmentation and instance segmentation fusion.
Depth Estimation Experiment of Driving Environment.
e dataset used for training the depth estimation algorithm is the Cityscapes Depth Dataset [44]. e Cityscapes Depth Dataset collects binocular pictures with binocular cameras and is calculated by the SGM algorithm [45]. e scene includes a total of 5,000 pictures of urban roads in different seasons of multiple cities in Europe, including 2,975 in the training set, 500 in the validation set, and 1,525 in the test set. e loss function uses berHu [46] loss function, and the calculation formula is where d i is the depth prediction value of pixel i; d i is the actual depth value of pixel i; N is the total number of picture pixels; c � 1/5 max(|d i − d i |). e weights of the ResNet-FPN and panorama segmentation parts of the model remain unchanged, and only the weights of the depth estimation branch are trained and updated. e optimization algorithm for model training uses Journal of Advanced Transportation the stochastic gradient descent algorithm, in which the momentum parameter is set to 0.9 and the weight attenuation coefficient is set to 0.0001. e basic learning rate is set to 0.001, the number of optimization iterations of the model is 20000, and the batch size of the optimized image is 4 for each iteration. e feature map size of the depth estimation branch structure parameter S is 1/4, and the feature map channel number C is equal to 128. e loss change of the depth estimation during the training process is shown in Figure 9. e loss drops rapidly in the first 2000 rounds of training and then basically stabilizes after 5000 rounds of iterations. e trained model is used to predict the images in the verification set of the Cityscapes Depth Dataset. According to the evaluation index of the depth estimation, the accuracy of the calculated model is shown in Table 2. e evaluation indicators used in the depth estimation include relative error (rel), root mean square error (rms), root mean square error in logarithmic space (rms log ), and accuracy (P) under different thresholds (i.e., accuracy threshold is 1.25, 1.25 2 , 1.25 3 ). It can be seen that the number of pixels with a deviation ratio between the predicted value and the true value within 1.25, 1.25 2 , and 1.25 3 accounted for 63.6%, 81.7%, and 90.5%, respectively. Compared with the similar method in current studies [47], this method used in our study has a good performance. Figures 10(b) and 10(c) are visualization diagrams of the actual and predicted depth values, respectively. e overall trend of depth prediction is generally correct. From near to far, the color deepens, and the depth value gradually increases. From a local perspective, the depth prediction successfully captures the location and range of vehicles and pedestrians. eir depth is smaller than the surroundings, and there is a sudden change in the depth value of the outline.
Traffic Simulation Test Design.
Evaluating the accuracy of the state estimation of the multitarget moving vehicles requires the real state of the vehicles in front as a comparison.
e real motion state data of the preceding vehicle is obtained through the traffic simulation experiment that uses the traffic simulation software SiLab, multiperson driving traffic simulation software. Not only is the scene highly reproducible, but also each car is controlled by a driver with certain driving experience, which simulates the real traffic driving environment to the greatest extent. SiLab can record and output the position and movement information of each vehicle in real time. e recorded data used in subsequent calculations of this experiment are mainly timestamps, X-axis and Y-axis coordinates, and speed of the vehicle. e simulated driving system uses the Logitech G29 10 Journal of Advanced Transportation simulator control package, which includes a steering wheel, pedals, and shifters. e entire multiperson driving platform is equipped with 1 main driving position and 4 ordinary driving positions, and up to 5 people can drive at the same time, as shown in Figure 11(a). e simulated driving scene is set to one-way three lanes, as shown in Figure 11(b). e specific experimental plan is to run three cars (denoted as A, B, and C) on the multiperson driving platform SiLab at the same time. e driving perspective of vehicle A is regarded as the camera perspective, and vehicles B and C are treated as the observation objects.
In the simulated driving experiment, the common vehicle speed on urban roads is used, ranging from 60 km/h to 80 km/h. e movement speed will affect the recognition and tracking accuracy of multitarget tracking [48]. When the vehicle speed is slower, the effect of maintaining the detection result is stable. When the vehicle speed is faster, the detection result may appear to be fluctuant. e simulation driving experiment results show that the detection accuracy of multitarget tracking is about 86.3% when the vehicle speed is in the range of 40 km/h to 60 km/h; the detection precision is about 75.8% when the vehicle speed is in the range of 60 km/h to 80 km/h.
Moving Vehicle Distance and Speed
Estimation. e sampling frequency of vehicle motion state data is set to 60 Hz in SiLab, and the frequency of driving perspective recording is also equal to 60 Hz. In this way, each frame of the driving perspective corresponds to a piece of data in SiLab. e format of vehicle A's motion state data from the SiLab output is shown in Table 3.
According to the lateral and longitudinal movement distances between two different moments, the lateral and longitudinal speeds of cars A, B, and C are calculated. According to equations (12) and (13), the coordinates of cars B and C in the camera coordinate system centered on car A are calculated. According to equations (14) and (15), the lateral and longitudinal relative speeds of cars B and C with car A as the reference system are calculated.
e above algorithm is implemented in the Python software. e video of the driving perspective of car A is processed, and the motion states of car B are estimated, as demonstrated in Table 4.
As illustrated in Figure 12, taking vehicle B as an example, with vehicle A as the camera perspective, the relative Figure 12(a). e estimated value of the algorithm is consistent with the actual value. From a quantitative perspective, the average error of the lateral relative distance is 0.186 m, and the average relative error is 11.5%. e estimation of the longitudinal relative distance of the moving vehicle is shown in Figure 12(b). e algorithm has better accuracy for estimating the distance within 50 meters, and there is a large error in the estimation of the distance beyond 50 meters. e reason for the larger error is related to the characteristics of monocular visual depth estimation. ere is less information in the distance, the larger the error is. From a quantitative perspective, the average error of the longitudinal relative distance is 1.86 m, and the average relative error is 7.0%. e estimation of the lateral relative speed of moving vehicles is shown in Figure 12. anks to the small lateral relative distance error, the estimated value of the lateral relative speed is consistent with the actual value. e average error of the lateral relative velocity is 0.186 m/s, and the average relative error is 1.5%. e estimation results of the longitudinal relative speed of the moving vehicle are shown in Figure 12(d). e estimated value of the algorithm is similar to the actual value, and there is a certain fluctuation. After calculation, the average error of the longitudinal relative velocity is 0.37 m/s, and the average relative error is 5.0%.
In general, experiments have proved that the vehicle multitarget tracking algorithm in this study is feasible and has good performance with high accuracy in the estimation of distance and speed.
Conclusion
e perception of the driving environment on urban roads and the realization of vehicle tracking and motion state estimation are the indispensable parts of assisted driving and autonomous driving.
is study proposes a novel multitarget vehicle tracking and motion state estimation method based on a new driving environment perception system. Compared with the previous research on multitarget vehicle tracking, the driving environment perception system developed in this study can obtain rich driving environment information without interference between vehicles. e driving environment perception system establishes a lightweight neural network and adds depth estimation based on panoramic segmentation to estimate the state of vehicle motion and explore the relationship between multiple vehicles.
Firstly, a neural network that supports end-to-end training is designed and implemented. e network features are extracted by ResNet. e features are integrated by the feature pyramid as the input of semantic segmentation branch and instance segmentation, and the segmentation output of the two branches is merged to obtain the result of panoramic segmentation. After training and prediction on the MVD, the PQ value of the validation set reached 15.22. e final model has reached a high level in terms of accuracy and visual effects. e depth estimation branch is designed to realize the monocular range of the road scene. rough training and prediction on the Cityscapes Depth Dataset, the relative error on the validation set is 0.276, and it is proved that the model can achieve good accuracy in the depth estimation of monocular vision.
Secondly, based on the recognition result of the driving environment realized by the panoramic segmentation, the Kalman filter and the Hungarian algorithm are used to realize the multitarget tracking of the vehicle. Combining the distance information obtained by depth estimation, the relative speed of the vehicle is estimated. e multitarget tracking algorithm is used to solve the matching problem of state calculation. e results of the simulated driving test show the following: (1) e average error of the lateral relative distance is 0.19 m, and the longitudinal direction is 1.86 m. (2) e average error of the lateral relative velocity is 0.19 m/s, and the longitudinal direction is 0.37 m/s. is simulation experiment proves that the algorithm performs well in multitarget tracking. e findings of this study can contribute to the development of intelligent vehicles to alert drivers to possible danger, assist drivers' decision-making, and improve traffic safety. To be specific, this study can be used to identify roads and lane markings and warn drivers of lane departure. When the vehicle approaches the lane markings, the driver is reminded in the form of sound or image [49]. e multivehicle tracking and motion estimation in this study can be used in an adaptive cruise control system. According to the relative speed and distance to the front vehicle, it adaptively controls its own brakes and accelerators to maintain a certain distance and similar speed with the front vehicle. In the actual driving environment, a digital platform can be established to interact with the driver through the driving environment perception system. rough the driving recorder to obtain pictures or videos of other vehicles, the digital platform calculates the position information of multiple vehicles in real time and displays the trajectories of multiple vehicles over time to the driver. e deep neural network framework proposed in this study is highly shared in computing, and task branches can be added or deleted conveniently according to actual needs. Multitarget vehicle tracking through image segmentation only relies on easily available data such as images and videos, and the equipment is convenient to install and simple to use. However, due to the use of monocular vision for distance measurement in the depth estimation, there is a problem of limited accuracy in estimating the vehicle's motion state. In the future, we will try to use binocular distance measurement for depth estimation to obtain more accurate motion status information for multiple vehicles.
Data Availability
e data used to support the findings of this study are available from the corresponding author upon request. | 10,747.8 | 2021-09-15T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
A NOTE ON θ-GENERALIZED CLOSED SETS
The purpose of this note is to strengthen several results in the literature concerning the preservation of θ-generalized closed sets. Also conditions are established under which images and inverse images of arbitrary sets are θ-generalized closed. In this process several new weak forms of continuous functions and closed functions are developed. 2000 Mathematics Subject Classification. Primary 54C10.
Introduction. Recently Dontchev and Maki
have introduced the concept of a θ-generalized closed set.This class of sets has been investigated also by Arockiarani et al. [1].The purpose of this note is to strengthen slightly some of the results in [5] concerning the preservation of θ-generalized closed sets.This is done by using the notion of a θ-c-closed set developed by Baker [2].These sets turn out to be a very natural tool to use in investigating the preservation of θ-generalized closed sets.In this process we introduce a new weak form of a continuous function and a new weak form of a closed function, called θ-g-c-continuous and θ-g-c-closed, respectively.It is shown that θ-g-c-continuity is strictly weaker than strong θ-continuity and that θ-g-c-closed is strictly weaker than θ-g-closed.
Preliminaries.
The symbols X and Y denote topological spaces with no separation axioms assumed unless explicitly stated.If A is a subset of a space X, then the closure and interior of A are denoted by Cl(A) and Int(A), respectively.The θ-closure of A [8], denoted by Cl θ (A), is the set of all x ∈ X for which every closed neighborhood of The following theorem from [5] gives a useful characterization of θ-g-openness.
Theorem 2.2 (Dontchev and Maki [5]). A set A is θ-g-open if and only if F ⊆ Int θ (A)
whenever F ⊆ A and F is closed.
Definition 2.3 (Dontchev and Maki [5]). A function
Definition 2.4 (Dontchev and Maki [5]).A function f : Definition 2.5 (Noiri [7]).A function f : X → Y is said to be strongly θ-continuous provided that, for every x ∈ X and every open neighborhood V of f (x), there exists an open neighborhood U of x for which f (Cl(U)) ⊆ V .[5] proved that the θ-g-closed, continuous image of a θ-g-closed set is θ-gclosed.In this section, we strengthen this result by replacing both the θ-g-closed and continuous requirements with weaker conditions.Our replacement for the θ-g-closed condition uses the concept of a θ-c-open set from [2].Definition 3.1 (Baker [2]).A set A is said to be θ-c-closed provided there is a set B for which A = Cl θ (B).
We define a function
Since θ-c-closed sets are obviously closed, θ-g-closed implies θ-g-c-closed.The following example shows that the converse implication does not hold.
Example 3.2.Let X = {a, b, c} have the topology τ = {X, ∅, {a}, {a, b}, {a, c}} and let f : X → X be the identity mapping.Since the θ-closure of every nonempty set is X, f is obviously θ-g-c-closed.However, since f ({c}) fails to be θ-g-closed, f is not θ-g-closed.
Corollary 3.4 (Dontchev and Maki [5]).If f : X → Y is continuous and θ-g-closed, then f (A) is θ-g-closed in Y for every θ-g-closed subset A of X.
Theorem 3 .
3 can be strengthened further by replacing continuity with a weaker condition.Instead of requiring inverse images of open sets to be open, we require that the inverse images of open sets interact with θ-g-closed sets in the same way as open sets. | 793.8 | 2001-01-01T00:00:00.000 | [
"Mathematics"
] |
Heat Transport Driven by the Coupling of Polaritons and Phonons in a Polar Nanowire
: Heat transport guided by the combined dynamics of surface phonon-polaritons (SPhPs) and phonons propagating in a polar nanowire is theoretically modeled and analyzed. This is achieved by solving numerically and analytically the Boltzmann transport equation for SPhPs and the Fourier’s heat diffusion equation for phonons. An explicit expression for the SPhP thermal conductance is derived and its predictions are found to be in excellent agreement with its numerical counterparts obtained for a SiN nanowire at different lengths and temperatures. It is shown that the SPhP heat transport is characterized by two fingerprints: (i) The characteristic quantum of SPhP thermal conductance independent of the material properties. This quantization appears in SiN nanowires shorter than 1 µ m supporting the ballistic propagation of SPhPs. (ii) The deviation of the temperature profile from its typical linear behavior predicted by the Fourier’s law in absence of heat sources. For a 150 µ m-long SiN nanowire maintaining a quasi-ballistic SPhP propagation, this deviation can be as large as 1 K, which is measurable by the current state-of-the-art infrared thermometers.
Introduction
One-dimensional (1D) heat conduction at low temperatures has been extensively investigated due to the existence of a quantum of thermal conductance. This quantization is related to the heat flux carried by ballistic phonons or electrons in a single polarization and is given by G 0 = π 2 k 2 B T/3h, where k B and h are the respective Boltzmann and Planck constants, and T is the temperature [1][2][3][4][5]. This minimal and universal amount of heat, for a given T, holds for both electrons and phonons, as was theoretically predicted [6,7] and experimentally validated [8,9]. Given that the mean free paths of electrons and phonons are typically smaller than 1 µm at room temperature, with lower temperatures leading to longer mean free paths, the observation of this quantization in the ballistic regime typically requires the utilization of nanostructures at temperatures lower than 1 K [8,9].
The limitations of phonons and electrons to exhibit 1D ballistic heat conduction at temperatures comparable to room temperature, can be overcome with surface phononpolaritons (SPhPs), which are evanescent electromagnetic waves generated by the hybridization of photons and phonons at the interface of polar materials [10][11][12][13][14][15][16][17][18]. This ballistic behavior appears due to the huge SPhP propagation length that was found to be as long as 1 m [19][20][21][22] and is hence orders of magnitude longer than the typical mean free paths of electrons and phonons. The spectral values of this propagation length is mainly determined by the material permittivity, which is nearly independent of temperature, within a wide range of temperatures lower and higher than room temperature [23]. Therefore, the ballistic heat transport of SPhPs is not necessarily restricted to low temperatures, as is the case of electrons and phonons. On the other hand, the wavelength of SPhPs propagating along nanowires can be much longer than the nanowire diameter [21] and hence these energy carriers can be considered as a 1D quantum gas. As a result of these relatively long values of the propagation length and wavelength of SPhPs, their contribution to the axial heat transport was predicted to be comparable to or even higher than that of phonons. In fact, in the pure ballistic regime, the quantum of thermal conductance G 0 due to phonons and electrons in a nanowire at cryogenic temperature also holds for the SPhPs at room temperature [21]. Even though the phonon, electron, and SPhP quantum of thermal conductance of nanowires were already quantified separately, the heat transport driven by the simultaneous propagation of phonons and SPhPs along a polar dielectric nanowire has been not explored yet.
The purpose of this work is to theoretically study the temperature and heat flux profiles generated by the coupling of SPhPs and phonons along the surface of a polar nanowire at a temperature comparable to or lower than room temperature. This is achieved by solving, numerically and analytically, the Boltzmann transport Equation (BTE) and combining its prediction for the SPhP heat flux with the principle of energy conservation. An explicit expression for the SPhP thermal conductance valid for both the ballistic and diffusive regimes is derived and analyzed. The critical nanowire length at which the quantization of the thermal conductance appears is thus determined.
Theoretical Models
Let us consider a polar nanowire supporting the simultaneous propagation of SPhPs and phonons due to the temperature difference T h > T c set by two thermal baths, as shown in Figure 1. The resulting steady-state heat transport along the z axis is thus driven by the heat fluxes generated by these two types of energy carriers. Considering that the phonon heat conduction can be described by an effective thermal conductivity k ph [24], the principle of energy conservation along with the Fourier's law establishes that the temperature T inside the nanowire is given by where q is the SPhP heat flux and q t is the total heat flux, a constant independent of position z (i.e., ∂q t /∂z = 0), which yields the following heat diffusion equation: with S(z) = −∂q/∂z being an effective heat source term that stands for the coupling between SPhPs and phonons. Physically, S(z) > 0 (< 0) represents the heat source (sink) due to the thermal absorption (emission) of SPhPs at the nanowire surface. Taking into account that SPhPs can be treated like bosonic particles [20,25], q can be determined by means of the BTE under the relaxation time approximation in the intensity representation [26,27]. The validity of BTE for describing the energy transport by SPhPs still remains under debate as its predictions showed mixed results with respect to the fluctuational electrodynamic theory [28,29]. In thin films, the predictions of the BTE for the SPhP thermal conductivity showed a good agreement with the corresponding ones of this theory [28] and, therefore, in this work, we assume its validity for describing the propagation of SPhPs along a nanowire. For the steady-state heat transport along the z axis shown in Figure 1, the BTE for the 1D SPhP gas takes the two-component form: where the SPhP intensity and its equilibrium counterpart are defined by I ± = Vhω f ± D(ω)/2 and I 0 (T) = Vhω f 0 (T)D(ω)/2, respectively, the superscript "+(−)" stands for the SPhP propagation along +z(−z) direction, while the SPhP distribution function, group speed and propagation length are respectively denoted by f , V and Λ, with 2πh, f 0 , and D(ω) being the Planck constant, Bose-Einstein equilibrium distribution function and SPhP density of states per unit frequency interval per unit length, respectively. The group speed and propagation length are determined by the dispersion relation of SPhP and generally depends on frequency, as shown below. Since SPhPs propagate along the surface of the nanowire and span over its surface, their 1D density of states is given by [30]: D(ω) = 1/(πV). After solving Equation (3a,b) for the intensity distribution I ± , the SPhP heat flux can be determined by where a is the radius of the nanowire. According to Figure 1, Equations (1)-(3) are going to be solved either numerically or analytically under the following boundary conditions:
Numerical Approach
To numerically solve Equations (1)-(4), which are coupled, for the heat transport driven by SPhPs and phonons in a polar nanowire, the discrete-ordinate method (DOM) (see, for instance, [27,31]) and the finite difference method (FDM) are adopted for the SPhP BTE and the heat diffusion equation, respectively. This FDM scheme is exactly the same as that in our previous work [32]. The DOM scheme for the 1D SPhP BTE will be introduced here. Under this approach, the numerical integration for the SPhP heat flux in Equation (4) can be written as follows where the rectangular scheme is adopted with a uniform frequency interval ∆ω and the index of discrete frequency points n = 1, 2, ..., N m . The spectral discretization of the SPhP BTE in Equation (3) then takes the form The step scheme is adopted for the spatial discretization of the SPhP BTE to ensure both efficiency and accuracy. For the positive (+z) propagation, the forward difference scheme is applied to Equation (7a): where i = 1, 2, ..., N z denotes the index of spatial nodes, with the spatial step ∆z. For the negative (−z) propagation, on the other hand, the backward difference scheme is applied to Equation (7b): The evolution equations of the discrete SPhP intensity can then be obtained from Equations (8) and (9), as follows where M n ≡ Λ n /∆z is introduced for short notation. The positive component in Equation (10a) is updated from the left-hand hot (T h ) boundary, whereas the negative component in Equation (10b) is updated from the right-hand cold (T c ) boundary.
Once the discrete SPhP intensity distribution is resolved, the SPhP heat flux distribution is computed based on Equation (6). The temperature distribution is then calculated through a numerical solution of the heat diffusion Equation (2) by the FDM scheme. The equilibrium SPhP intensity is thus updated and the SPhP BTE is solved again. The solution of the coupled model is obtained through an iterative procedure until the solutions of the SPhP BTE and the heat diffusion equation are consistent with each other. More details of the solution procedure can be found in our previous work [32].
Analytical Approach
The analytical solutions of the BTE in Equation (3a,b) for the intensities I + and I − of the SPhPs leaving the surfaces z = 0 and z = l are given by where ξ = z/Λ, λ = l/Λ. In writing Equation (11a,b), we have used the boundary conditions in Equation (5): by the thermal equilibrium of the external surfaces ξ = 0 and ξ = λ set at the temperatures T h and T c , respectively. After inserting Equation (11a,b) into Equation (4), one obtains For simplicity, Equation (12) can be rewritten in terms of the normalized equilibrium intensity which indicates that the SPhP heat flux q results from the intensity difference I 0 (0) − I 0 (λ) driven by the temperature difference T h − T c , as expected. Considering that the nanowire undergoes small temperature gradients (T h − T c (T h + T c )/2 = T), the temperature dependence of the equilibrium intensity I 0 can be linearized. In addition, given that the temperature profile exhibits a nearly linear dependence on position, as shown below, the first-order approximation of the equilibrium intensity can be written as I 0 (ξ) ≈ α(β − ξ), with α and β being two parameters independent of position. Under this approximation, U(ξ) = 1 − ξ/λ and Equation (13) takes the form Note that the SPhP heat flux at two equidistant positions from the external nanowire surfaces (ξ = 0; λ) takes the same value (q(ξ) = q(λ − ξ)), such that its maximum appears at the middle of the nanowire (ξ = λ/2). This behavior arises from the non-local dependence of the heat flux on the temperature profile, as established by Equation (12). The integration of Equation (1) for the SPhP heat flux in Equation (14) yields the following temperature profile and total heat flux q t where ∆T = T h − T c , ψ(ξ) = e −ξ − e −(λ−ξ) and the spectral SPhP thermal conductivity k ω is defined in terms of its integrated counterpart k pol = k ω dω given by Equation (16) was derived by considering that the average temperature T = (T h + T c )/2 ∆T, such that f 0 (T h ) − f 0 (T c ) = ∆T∂ f 0 /∂T. According to Equation (15a), the deviation of the temperature profile from the usual linear dependence (first two terms) on position is driven by the ratio k pol /k ph between the SPhP and phonon thermal conductivities. Interestingly, regardless of the values of this ratio, the SPhP contribution to the temperature profile disappears at the middle of the nanowire (ξ = λ/2). This behavior is related to the symmetry of the SPhP heat flux around this position and is well confirmed by accurate numerical results, as shown below. As a result of this symmetry, the sum of temperatures at two equidistant points from the external nanowire surfaces is an invariant of heat conduction given by T(ξ) + T(λ − ξ) = T h − T c , as established by Equation (15a). This feature of temperature is generated by the non-local behavior of the heat conduction and is analogous to the characteristic temperature profiles found in radiative heat transfer [33].
As the heat transport in a polar nanowire is driven by both phonons and SPhPs, the total heat flux is determined by the sum of thermal conductivities related to these two energy carriers, as established by Equation (15b). This fact indicates that, as the nanowire radius a scales down, the usual reduction in k ph could be offset by the increasing values of k pol , due to the predominant surface effects driving the propagation of SPhPs. In the SPhP diffusive approximation (λ = l/Λ 1), the ratio ψ(0)/λ → 0 and Equation (16) becomes independent of the nanowire length l defining the parameter λ. In the ballistic limit (λ 1), on the other hand, 1 − ψ(0)/λ ≈ λ/2 and the SPhP thermal conductivity becomes independent of the propagation length Λ. For both cases, Equation (16) can conveniently be rewritten as the following Landauer formula for the SPhP thermal conductance G = πa 2 k pol /l of the nanowire where τ = 2[1 − ψ(0)/λ]/λ is the probability of SPhPs to transmit from one thermal bath to the other through the nanowire (Figure 1). For long nanowires (λ 1), the transmission probability goes to zero (τ → 0) and therefore G vanishes. By contrast, for short nanowires (λ 1), τ ≈ 1 − λ/3 ≈ 1 and Equation (17) reduces to the quantum of thermal conductance (G 0 ) of nanowires supporting the ballistic propagation of SPhPs [21], as expected. The ratio λ = l/Λ between the nanowire length and SPhP propagation length thus drives the SPhP thermal conductance G, which takes higher values for shorter wires.
Results and Discussions
The propagation and heat transport of the SPhPs along a SiN nanowire is quantified and analyzed in this section. SiN is a typical polar material able to support the propagation of SPhPs in a wide frequency range [23,34] and therefore can be considered as a good SPhP conductor. By solving the Maxwell equations under proper boundary conditions for the transverse magnetic polarization required for the existence of SPhPs [12,25], the following dispersion relation for the SPhP wavevector β along the wire axis is obtained [35] ε 0 p 0 where I n and K n are the modified Bessel functions, the prime ( ) indicates derivative with respect to their arguments, n = 1, 2, ... accounts for the contribution of the azimuthal modes, ε and ε 0 are the relative permittivity of the respective wire and its surrounding medium, and p 0 = β 2 − ε 0 k 2 0 and p = β 2 − εk 2 0 are the corresponding radial wavevectors, with k 0 = ω/c and c being the speed of light in vacuum. For thin enough wires (| p j | a << 1), which is of interest in this work to enhance the SPhP propagation along the wire, Equation (18) becomes independent of the radius a and branch n, as follows p 2 0 /ε 0 + p 2 /ε = 0. For nanowires of SiN, this condition is well satisfied for a ≤ 200 nm [21] and establishes that the azimuthal modes does not contribute to the thermal transport through nanowires. The solution of this symmetric relation for β is Equation (19) differs from the dispersion relation of the single plane interface [12] by just a factor of √ 2, due to the geometry effect. The frequency spectrum of the real (ε R ) and imaginary (ε I ) parts of the SiN relative permittivity are shown in Figure 2. The main resonance peak of ε I at 155 Trad/s indicates that SiN absorbs a significant amount of energy from the electromagnetic field and therefore limits the propagation of SPhPs, at that frequency. By contrast, the dip of ε R occurs at 175 Trad/s, which represents the frequency at which the SPhPs exhibit the strongest confinement to the interface [23]. The yellow zone (ε R < 0), on the other hand, stands for the Reststrahlen band determined by the frequency interval (167.0; 199.5) Trad/s that contains the range of frequencies (ε R < −ε 0 ) that would support the propagation of SPhPs in absence of absorption (ε I = 0), as established by Equation (18). However, given that SiN is an absorbing material (ε I > 0), SPhPs are expected to propagate with frequencies inside and outside of this band, as reported in the literature [34] for nanofilms and is shown in Figure 3 for a SiN nanowire.
The wavevector Re(β) and propagation length Λ =[2Im(β)] −1 of SPhPs propagating along the surface of a SiN nanowire suspended in air are shown in Figure 3, as functions of frequency. Note that Re(β) increases almost linearly with frequency, through values generally higher than those of the light line (k 0 = ω/c). The deviations from this behavior characterized by a SPhP group velocity V = ∂ω/∂Re(β) close to but smaller than c, show up around 200.2 Trad/s, which is close to the frequency (199.5 Trad/s) where ε R changes its sign. The relatively weak absorption of the thin nanowire (a < 300 nm) enables SPhPs to propagate distances as long as 2.7 cm at high frequency (500 Trad/s), as shown in Figure 3. The dip of Λ is related to the maximum of energy absorption driven by ε I and negligible value of ε R at 200.2 Trad/s, as shown in Figure 2. In addition, the fact that Λ > 1 µm, indicates that SPhPs propagate ballistically along a SiN nanowire shorter than 1 µm, which is a condition to reach the 1D quantum of thermal conductance G 0 reported in the literature [21]. Real and imaginary parts of the relative permittivity ε = ε R + iε I of SiN, as a function of frequency [23]. The yellow zone stands for the band in which ε R < 0. The temperature and heat flux profiles along a SiN nanowire supporting the simultaneous propagation of SPhPs and phonons are shown in Figure 4a and Figure 4b, respectively, for three nanowire lengths. For the shortest nanowire with a length (l =10 µm) much smaller than the propagation length of most SPhPs (see Figure 3), SPhPs propagate ballistically with weak adsorption and low energy exchange with phonons. The SPhP heat generation inside the nanowire is therefore small and T exhibits pretty much the same linear behavior predicted by the heat diffusion Equation (2), without a heat source term. This is confirmed by the relatively low SPhP heat flux shown in Figure 4b via the blue lines, which are nearly independent of position due to the independence of the phonon and SPhP heat transport. On the other hand, for longer nanowires with a length (l = 80 and 150 µm) comparable to the propagation length of some SPhPs, the quasi-ballistic propagation of SPhPs fosters their energy exchange with phonons, which generates a non-linear temperature profile similar to that predicted by the heat diffusion equation with a heat sink for z/l ≤ 0.5 and a heat source for z/l ≥ 0.5, as seen in Figure 4a. The apparent heat sink and heat source terms in the nanowire arise from the predominant emission and adsorption of SPhPs near its hot and cold sides, respectively. Therefore, the SPhP heat flux increases with position until z/l = 0.5 and decreases afterwards, while the phonon counterpart shows the opposite trend, as established by the principle of energy conservation in Equation (1). The increase in the SPhP heat flux with the nanowire length provides a pathway to enhance the heat transport along polar nanowires by means of the coupling of SPhPs and phonons, as is the case in polar nanofilms [32]. Furthermore, as the non-linearity of the temperature profile represents the fingerprints of SPhPs, its experimental observation can provide an intuitive and conclusive way to detect the SPhP heat transport. For instance, for the 150 µm-long SiN nanowire shown in Figure 4a, the largest temperature deviation from the linear profile is about 1 K, which is measurable by the current state-of-the-art infrared thermometers. The solid and dashed-dot lines in (b) represent the respective SPhP and phonon heat fluxes, whereas the dashed one stands for the total heat flux q t . Calculations were carried out for a SiN nanowire with a radius a = 50 nm and a typical phonon thermal conductivity of k ph = 1 W/m·K. Figure 5 shows the frequency spectrum of the SPhP transmission probability τ for four SiN nanowire lengths. Note that shorter nanowires exhibit a higher transmissivity, whose lowest value at 201.6 Trad/s is related to the minimum value of the SPhP propagation length shown in Figure 3. By contrast, for other sufficiently low and high frequencies, τ tends to unity as a result of the long propagation lengths of SPhPs. According to Equation (17), these lowest and highest values of the SPhP transmissivity drive the behavior of the thermal conductivity spectrum, which takes higher values for shorter nanowires, as shown in Figure 6a. At high enough frequencies, this spectrum becomes independent of the nanowire length and decays exponentially due to the insufficient thermal energy required to excite them, as established by the Bose-Einstein distribution function involved in Equation (17). At very low frequencies, on the other hand, the thermal conductance spectrum takes its highest values due to the high transmissivity of SPhPs. The integration of the spectra in Figure 6a yields the SPhP thermal conductance G shown in Figure 6b,c, as a function of the nanowire length and temperature, respectively. As a result of the predominance of ballistic regime characterized by a high transmissivity, shorter nanowires exhibit a higher G, whose values increase with temperature. The analytical (solid lines) and numerical (dots) predictions exhibit a very good agreement for the three temperatures and lengths, which confirms the high accuracy of Equation (17) for predicting the thermal conductance of SPhPs. More importantly, the upper bound of G, in the ballistic regime (l < 1 µm), is well confirmed by the analytical and numerical solutions and its values coincide with the quantum of thermal conductance G 0 . Even though the transmissivity of a 1 µm-long SiN nanowire is not unity over the full frequency spectrum (see Figure 5), the corresponding SPhP thermal conductance is pretty much equal to G 0 . The quantization of the SPhP thermal conductance is thus expected to be observed in SiN nanowires with a length comparable to or shorter than 1 µm.
Conclusions
Based on the Boltzmann transport equation, we have theoretically demonstrated that the heat transport by surface phonon-polaritons propagating along a nanowire is characterized by two fingerprints: (i) The characteristic quantum of thermal conductance independent of the material properties. This quantization appears in SiN nanowires shorter than 1 µm, supporting the ballistic propagation of polaritons. (ii) The deviation of the temperature profile from its typical linear behavior predicted by Fourier's law of heat conduction in the absence of heat sources. For a 150 µm-long SiN nanowire keeping up a quasi-ballistic polariton propagation, this deviation can be as large as 1 K, which can be observed by the current state-of-the-art infrared thermometers. Furthermore, we have derived an explicit formula for the polariton thermal conductance that is able to accurately predict the energy transport of polaritons for different lengths and temperatures of a polar nanowire. The obtained results can thus be useful for understanding and quantifying the thermal performance of surface phonon-polaritons in 1D structures. | 5,637.8 | 2021-08-19T00:00:00.000 | [
"Physics"
] |
An Exploration Algorithm for Stochastic Simulators Driven by Energy Gradients
In recent work, we have illustrated the construction of an exploration geometry on free energy surfaces: the adaptive computer-assisted discovery of an approximate low-dimensional manifold on which the effective dynamics of the system evolves. Constructing such an exploration geometry involves geometry-biased sampling (through both appropriately-initialized unbiased molecular dynamics and through restraining potentials) and, machine learning techniques to organize the intrinsic geometry of the data resulting from the sampling (in particular, diffusion maps, possibly enhanced through the appropriate Mahalanobis-type metric). In this contribution, we detail a method for exploring the conformational space of a stochastic gradient system whose effective free energy surface depends on a smaller number of degrees of freedom than the dimension of the phase space. Our approach comprises two steps. First, we study the local geometry of the free energy landscape using diffusion maps on samples computed through stochastic dynamics. This allows us to automatically identify the relevant coarse variables. Next, we use the information garnered in the previous step to construct a new set of initial conditions for subsequent trajectories. These initial conditions are computed so as to explore the accessible conformational space more efficiently than by continuing the previous, unbiased simulations. We showcase this method on a representative test system.
Introduction
In its most straightforward formulation, Molecular Dynamics (MD) consists of solving Newton's equations of motion for a molecular system described with atomic resolution.The goal of performing MD simulations is twofold: on the one hand, we want to gather samples from a given thermodynamic ensemble, while, on the other hand, we may seek to gain insight into time-dependent behavior.The first objective leads us to equilibrium properties.The second yields kinetic properties and is the reason why it is said that MD acts as a computational microscope.Recent success stories involving systems having more than one million atoms [1,2] attest to the ever-growing reach of MD simulations.
The possibility of using MD to study bigger bio-molecules at longer time scales is hindered by the problem of time scale separation.While the processes of interest (protein folding, permeation of cellular membranes, etc.) act on timescales of milliseconds to minutes, we are currently restricted by limitations in available computer capabilities and algorithms to simulations spanning timescales of microseconds.Moreover, to ensure stability when numerically integrating the equations of motion, we need to take steps of just a few femtoseconds.The reader interested in the numerical analysis of integration schemes in MD is referred to the excellent treatise [3] for more information.
It is often possible to identify a suitable set of so-called collective or coarse variables describing the progress of the process being studied (i.e., a "slow manifold").The simplest such "coarse variable" is perhaps the interatomic distance in the process of the dissociation of a diatomic molecule.In other cases, a subset of dihedral angles on the amino acids of a peptide proves to be a good choice.In practice, it is not always clear how to devise good coarse variables a priori, and it is necessary to rely on the expertise of computational chemists to postulate these variables with varying degrees of success.Of course, the quality of the coarse variables can be assessed a posteriori by methods such as the histogram test, etc. [30,[39][40][41][42][43].Ideally, the dynamics of the process mapped onto the coarse variables should be a diffusion on the potential of mean force (i.e., Smoluchowski equation) [44,45], but if the guessed variables are not good enough, they will be poor representations of the process of interest in that the relevant dynamics will be described instead by Generalized Langevin Equations (GLE) [46,47].The GLE incorporates a history-dependent term that complicates computations [48].
In this paper, we present a detailed account of the iMapD [49] method.This can be used as a basin-hopping [50] simulation technique that lends itself naturally to parallelization, and unlike most of the methods referenced above, it does not require a priori guesses on the nature of the coarse variables.The method works by (a) performing short simulations to obtain an ensemble of trajectories; (b) using data mining techniques (diffusion maps) to automatically obtain an optimal set of local coarse variables that describe the conformations sampled by these trajectories and (c) using that knowledge to generate a new set of conformations.The new conformations become initial conditions for a new batch of short simulations, which, by construction, are more likely to lead to the exploration of new, previously unexplored local free energy minima.Throughout these steps, the algorithm constructs a representation of the intrinsic geometry of the visited region of the conformational space and identifies the points from which a new trajectory may have more chances to exit the metastable basins already visited.It is worth stressing that, as opposed to our previous work [49], here, we use a non-linear scheme to lift into the ambient space the extended boundary points.Moreover (and importantly), preliminary results are also reported on an alternative manifold parameterization based on what we will call sine-diffusion maps.
The paper is organized as follows.Section 2 provides a brief introduction to Diffusion Maps (DMAPS) from the perspective of statistical mechanics, followed by an overview of the iMapD method, as well as an application of the algorithm to a model problem.Section 3 is an account of the required mathematical tools upon which the iMapD method is built; namely, we discuss some technical aspects of diffusion maps, boundary detection methods, out-of-sample extension using geometric harmonics, and the use of local principal component analysis as an alternative to diffusion maps.Finally, Section 3.6 contains a more in-depth treatment of the steps involved in the iMapD algorithm, describing how the previously introduced building blocks fit within the method and exploring factors affecting the implementation of the method.
Diffusion Maps in Statistical Mechanics
Consider a mechanical system whose conformational space is denoted by Ω.For the sake of simplicity, let us assume that Ω ⊂ R n is a bounded, simply-connected open set and that the system undergoes Brownian dynamics; that is, its time evolution is a solution of the Stochastic Differential Equation (SDE): where U = U(x) is the potential energy, β −1 > 0 is the inverse temperature and W is a standard n-dimensional Brownian motion [51,52].Potential energy functions in MD simulations are not smooth in general, but equilibrium trajectories almost never visit the singular points, so it is safe to assume that U is sufficiently smooth.Let: be the probability that a trajectory of (1) started at x ∈ Ω at time t = 0 belongs to the set A ⊂ Ω at time t ≥ 0. It is known that the time evolution of the probability density function p is governed by the Fokker-Planck equation [53], where ∂ ∂n denotes the derivative in the direction of the unit normal vector to the boundary ∂Ω of the conformational space Ω and δ x is a Dirac delta function centered at x.In the context of molecular simulation, there are other boundary conditions that are relevant such as periodic boundary conditions or prescribed decay at infinity (i.e., lim x →+∞ p(x, t) = 0 for all t ≥ 0, useful when Ω is unbounded).
We will refer to the operator on the right-hand side of the partial differential equation in (3) by the symbol L .That is, L p = ∇ • β −1 ∇p + p∇U .By the spectral properties of the operator L and its adjoint L, we know [15,54] that p admits a decomposition of the form: where λ 0 = 0 > −λ 1 ≥ −λ 2 ≥ • • • are the eigenvalues of L, the sequence of eigenvalues satisfies lim n→∞ λ n = ∞ and ψ i (x) are the corresponding eigenfunctions.Observe that ψ 0 (x) = 1 for all x ∈ Ω.
In Figure 1, we show the eigenfunctions of the operator L for a simple double well potential.For systems with time scale separation, there will arise a spectral gap; that is, λ k+1 λ k for some k ∈ N.Under such circumstances, (4) can be approximated as: and for a fixed value of ε ≥ λ k , we can construct the mapping: The components of Ψ ε are then, in effect, coarse variables that describe the state of the system.Therefore, the dimensionality reduction in diffusion maps stems from the existence of a spectral gap, and the effective dimension will be equal to k.These coarse variables are well suited to parameterize and study the free energy of the system.
Observe that the parameter ε > 0 plays the role of time in (4) and that events occurring at a rate smaller than ε −1 are ignored.This interpretation of ε suggests that one could use a priori knowledge of the dynamics of the system (e.g., frequency of bond vibrations, etc.) to set its value.Frequently, however, no such information is available.An optimal choice of ε was introduced in [56].The optimal ε depends on the dimension of the space of coarse variables and the geometry of the manifold, as well as on the number of samples available.
The explicit computation of the eigenfunctions ψ i is infeasible in practical applications, so our focus naturally shifts to the numerical estimation of these eigenfunctions up to a prescribed accuracy.Diffusion Maps (DMAPS) are a manifold learning technique that allows us to obtain these approximations to ψ i by studying sets of points sampled from the solution of (1) at different instants (e.g., we take y 1 = x(t 1 ), . . ., y m = x(t m ) for some t 1 , . . ., t m ≥ 0).The procedure is as follows: we first construct the m × m matrix: where • is a suitable norm in R m (the Euclidean norm or a "Mahalanobis-like" distance [57,58] are typical choices).The next step for the construction of the diffusion map is the definition of the matrix W with entries: , where By multiplying W by the inverse of the diagonal matrix D, with entries D ii = ∑ j Wij , we obtain a non-negative row-stochastic matrix, K = D −1 W. The matrix K gives us the transition probability of a Markov chain defined on the discrete state space {y 1 , . . ., y m } determined by the observed data.
The matrix L = K − I, where I is the m × m identity matrix, is known as the random walk Laplacian [59].It can be proven [60] that the eigenvectors of the random walk Laplacian L converge to the eigenfunctions of the operator L. Thus, the numerical solution of the eigenproblem Lψ = λψ yields an effective, data-driven approximation method to compute (5).For example, in the case of the double well potential that we considered before, we obtain the eigenvectors displayed in Figure 2.
Data-driven computation of the right eigenvectors of the random walk Laplacian L obtained using a value of ε = 1 4 and a set of m = 10 3 data points (with inverse temperature β −1 = 1).Compare with Figure 1.We used the BAOAB integrator [61] (this is a fourth-order accurate numerical scheme for solving Brownian dynamics) in the high friction limit with a time step length of 10 −4 to compute a numerical solution of (1) with initial condition x 0 = −1.The numerical integration was carried out for a total of 10 8 steps retaining one every 10 5 points, and it was verified that the samples yield a sufficiently good approximation of the exact stationary distribution by ensuring that the total variation distance between the empirical and the exact distributions was below a threshold of 0.025.Each subfigure corresponds to an eigenvalue: (a) As a more realistic example, we analyze a one microsecond-long simulation of the catalytic domain of the human tyrosine protein kinase ABL1 [62].This is a published dataset [63] that was generated on Folding@home [64] using OpenMM [65] 6.3.1 with the AMBER99SB-ILDNforce field [66], the TIP3Pwater model [67] and Cl and Na ions to neutralize the charge.To solve the Langevin dynamics equation, the stochastic position Verlet integrator [68,69] was used with a time step length of 2 fs at a temperature of 300 K with a collision rate (also known as the friction term) equal to 1 ps −1 .
To treat electrostatic interactions, the smooth particle-mesh Ewald method [70] was used with a cut off of 1 nm and a tolerance of 5 × 10 −4 .Pressure control was exerted by a molecular-scaling Monte Carlo barostat [71,72] using a 1-atm reference pressure attempting Monte Carlo moves every 50 steps.
We obtain the first two coarse variables, ψ 1 and ψ 2 , using the diffusion map method (see Figures 3 and 4 for the results).The previous considerations are motivated by/conform with statistical mechanics; however, it is important to emphasize that the DMAPS method will work, in the sense that it will provide a parameterization of the manifold, just as well with data points on the manifold not necessarily coming from sampling the solution of (3).What is important is the geometry of the manifold and not necessarily the dynamics of the process leading to the samples.Indeed, we have used the framework of statistical mechanics for didactic purposes, but practical applications need not rely on it.
Overview of the iMapD Method
As we stated in the Introduction, the iMapD method is aimed at enhancing the sampling of unexplored regions of the conformational space of a system.The method works by first running an ensemble of independent trajectories initialized from an initial configuration for a short time (e.g., a few nanoseconds).The points comprising the trajectories are actually samples of the local free energy minimum to which the initial configuration belongs.Next, we perform a diffusion map computation, giving us a set of coarse variables that parameterize the current basin of attraction, and we locate (in DMAP coordinates) the boundary of the region that our set of points has explored so far.By extending the boundary outwards in its normal direction, we get a new tentative boundary whose points we realize in the original, high-dimensional conformational space (typically by resorting to a suitable biasing potential).Finally, the new points are used as initial conditions in a new batch of simulations.By actively restarting simulations from the extrapolated points, we enhance the ability of the system to exit local free energy minima and to explore new regions of conformational space.
In order to illustrate the applicability of our method, we demonstrate how the algorithm works on a simple, yet non-trivial model system, which can be studied in-depth by numerically solving the stochastic differential equations involved. Let: and let: where b = −80, c = 20 and R = 4/π.Consider the system of stochastic differential equations (SDEs): where a = 200, D = 0.35, η = 1 × 10 −4 and W 1 , W 2 , W 3 are independent standard Brownian motions.
The above system of SDEs exhibits the most meaningful qualitative aspect of the type of problems that iMapD is designed for: a phase space with higher dimensionality than that of the manifold in which the effective dynamics occurs.Indeed, our system, despite being three-dimensional, has by construction a two-dimensional attractor located on the surface of a cylinder with radius R and axis y.There are two metastable states (as seen in Figure 5), and trajectories starting away from the attractor arrive at one of the metastable wells, where they remain for typically long periods of time.A trajectory "descends" from its initial condition onto the attracting manifold, the cylinder with radius R and axis y.On the manifold, the trajectory arrives at one of the metastable states that is near the middle of the cylinder at different values of θ.These metastable sets are depicted as the lightest colored areas.
In order to sample the conformational space of the system, we begin by running a single trajectory for enough time such that it gets trapped into one of the metastable sets.We process the trajectory so that the initial transient descent is removed, and points on the manifold have a more uniform distribution (e.g., by removing nearest neighbors that are closer than a fixed minimum distance).We then locate the boundary of the currently sampled area by running the alpha-shapes boundary detection method, which will be described in Section 3.3.This method is appropriate here, given that the manifold is two-dimensional and there is a correspondence between the points lying at the edge in the conformational space and the points at the edge in diffusion map space.Next, the boundary points in diffusion map space are extended using extrapolation and subsequently lifted up to the conformational space using geometric harmonics, which will be discussed in Section 3.5.Finally, the system is reinitialized, and the process starts over again, increasing the volume (here, the area) of explored conformational space and getting closer to the other metastable state.Figure 6 illustrates the first few steps in this process in conformational space and DMAP space, and Figure 7 shows how the extrapolated points approach the other basin as the algorithm marches on.
To create Figures 6 and 7, the first trajectory was started with an arbitrary initial condition of (−1.06, −0.05, 1.50) and run until t = 0.15 using the Euler-Maruyama scheme [73] with a time step length of 3 × 10 −7 .In each iteration of the algorithm, and therefore each run of the molecular simulator, the first 600 samples were discarded to increase the likelihood that the resulting cloud of points rested on the cylindrical manifold.To make the manifold sampling more homogeneous, points were removed such that a minimum distance of 0.04 existed between each pair of points.A maximum of 3000 points was stored in memory at any given time; this parameter was based on the available memory of the machine at hand and the particular implementation of the method.Points were randomly pruned if this maximum threshold was surpassed.Once the point cloud was properly conditioned, the manifold boundary was extended by a distance of 0.25 spatial units.To further illustrate the expansion of the point-cloud throughout the iterative process, we show in Table 1 the difference between the maximum and minimum angles of the set of points.This indicates how the iterative method explores the metastable sets on the cylinder.
Algorithmic Building Blocks
In this section we introduce several techniques on which the iMapD method relies.Section 3.1 continues the discussion of diffusion maps started in Section 2. Here, we study the convenience of using Neumann (reflecting) or Dirichlet (absorbing) boundary conditions in the formulation of the eigenvalue problem for DMAPS.In Section 3.2, we present Local Principal Component Analysis (LPCA), a simpler alternative to DMAPS that can be used in its place.Once we have charted the local geometry of the point-cloud associated with the current trajectory via DMAPS or LPCA, we need techniques to locate the boundary of the explored free energy basin.The purpose of Section 3.3 is to elaborate on the choice of boundary detection methods for this purpose.The outward extension of the current point-cloud is explained in Section 3.4.Finally, the extended points computed in DMAP space must be mapped into the conformational space of the system.We use geometric harmonics, as described in Section 3.5, to lift the points from the local representation to the original conformational space so that we can initialize new trajectories from the newly-extrapolated points.
Cosine and Sine-Diffusion Maps
As we previously mentioned, conventional diffusion maps are obtained by solving the eigenproblem corresponding to the Laplace-Beltrami operator on a domain with reflecting (Neumann) boundary conditions [58,74].Neumann boundary conditions are the default conditions in the (standard) formulation of DMAPS, as presented in Section 2. In this section, we will explore some of the implications of the choice of boundary conditions for the extension of sets of point-samples.We begin by considering a simple 2D strip, Ω = (0, L 1 ) × (0, L 2 ), on which DMAPS approximate the solution of: in Ω, where ∂ ∂n denotes the directional derivative in the direction of the unit vector normal to the boundary of Ω.Note that ( 8) is the eigenvalue problem associated with (3) with U constant and β = 1.The eigenfunctions of (8), with eigenvalues λ k 1 ,k 2 , are given by: The independent eigenfunctions, ϕ 1,0 and ϕ 0,1 , are one-to-one with x and y, respectively, and thereby parameterize the manifold Ω (see Figure 8).Note that the normal derivatives of the eigenfunctions vanish near the boundaries by construction [75].Recall that in iMapD, we need to be able to extend the current set of point-samples to obtain new initial conditions for running subsequent trajectories.We do so by using an appropriate extrapolation scheme (such as geometric harmonics, to be discussed in Section 3.5).
Extrapolating directly in cosine-diffusion map space presents some difficulties.This is because the parameterization near the edges of the currently explored region is flat, and extending functions in the diffusion map coordinates gives rise to ambiguities [75].One option to alleviate the potential zero-derivative issue of cosine-based diffusion maps is to move the singularity inside the manifold.This can be attained by extracting a sine-like parameterization (hence, "sine-diffusion maps").By solving (8) with absorbing (Dirichlet) boundary conditions instead of reflecting (Neumann) boundary conditions, the resulting eigenfunctions are: To approximate these eigenfunctions using the samples y 1 , . . ., y m ∈ R n , we again construct the matrix W as we did for cosine-diffusion maps.Boundary detection algorithms are then used to locate the edge points.Absorbing boundary conditions are now imposed on the rows of these points: if y i is a boundary point, then the corresponding entry in the matrix W becomes W ij = δ ij .Alternatively, the boundary points can be duplicated, the matrix W constructed as in (6) and the rows and columns corresponding to a single set of boundary points then removed before obtaining W using (7).The eigendecomposition of W results in the eigenvectors, or sine-diffusion map coordinates, and their corresponding eigenvalues.These coordinates approximate the eigenfunctions (10).We can see on our 2D strip example (Figure 9) how the strip is colored by the sine-coordinates.We make two observations.First, note that only the first nontrivial sine-coordinate is of importance: the subsequent eigenvectors are simply higher harmonics of the first.Because of this, the parameterization of a 2D nonlinear manifold can be accomplished with one sine-coordinate and one cosine-coordinate.Automatic detection of higher harmonics can be carried out in a variety of ways; here, we will just mention that we can accomplish this by studying the functional dependence between the eigenfunctions, and we refer the reader to the treatment in [76] (Section 2.1) for more details.In higher dimensions, the parameterization can be obtained by replacing the single cosine-coordinate (that is, the one that becomes almost constant around the point of interest) with a sine-based one.Second, for every sine-coordinate value and fixed x or y, there exist two potential data point candidates.This complicates the manifold parameterization and extrapolation scheme.Additionally, the data must be divided into groups, such that using the sine-and cosine-coordinates maintains a one-to-one relationship within the group.
To systematically determine which cosine-coordinate is poorly behaved for each boundary point, we examine the k-nearest neighbors of the point in question.The cosine-coordinate with the least variance among the neighbors is the one that should be replaced with the sine-coordinate.Parameterizing points using one sine-coordinate and one cosine-coordinate is not unique: for a fixed cosine-coordinate value, there are multiple points with the same sine-coordinate value.Therefore, care must be taken to maintain a one-to-one mapping throughout the entirety of the extrapolation.
Once the data are divided into groups based on which cosine-coordinate to replace and the sign of its eigenvector, the boundary points can be extended and mapped to the original conformational space using the same techniques as for cosine-diffusion maps.A sample manifold extended via sine-diffusion maps with geometric harmonics is shown in Figure 10.
Local Principal Component Analysis
Rather than using DMAPS coupled with geometric harmonics, one could also use LPCA to extend the manifold.LPCA is simpler than DMAPS, but it requires a local set of collective variables for each boundary point rather than a single, global set of collective variables for the entirety of the data.
LPCA is based on PCA, a widely-used dimensionality reduction technique [77], which aims to find the best (in the least-squares sense) linear manifold that approximates a dataset.The method finds an orthogonal basis such that the first basis vector points in the direction of greatest variance and all subsequent vectors maximize variance in orthogonal directions.The basis vectors are known as principal components and are the linear counterpart of nonlinear diffusion coordinates.The first principal component describes the line of best fit through the data, the first two the plane of best fit, and so on.
Given m samples of n-dimensional data arranged in an n × m matrix X, we can find the principal components by first considering the matrix X, formed by mean-centering the data, and then computing the eigendecomposition of its covariance matrix, Y.The eigenvalues, sorted in descending order, determine the importance of each of the principal components, which are eigenvectors of Y.In practice, the principal components are found through the singular value decomposition of XT [78,79].Indeed, XT = UΣV T , and we have: Since Y is a symmetric and positive definite matrix, the SVD is equivalent to the eigenvalue decomposition, so the columns of V are the eigenvectors of Y, and the square of the singular values of X are the eigenvalues of Y.Each data point in X can be assigned a set of n principal scores, representing the projection of the point onto each principal component.This change of basis is accomplished via X → V T X.
Dimensional reduction occurs when only the first k principal components are retained.The value of k is chosen by examining the interval spanned by the eigenvalues and locating the first spectral gap.Thus, the original high-dimensional, noisy data are mapped into k reduced dimensions via projection onto an appropriate linear subspace.While this technique works well for (almost) linear data, the attracting manifolds in the systems simulated with MD are typically nonlinear.Because of this, we restrict the use of PCA to small, local neighborhoods on the manifold that can be approximated as locally linear (provided that the potential of mean force is smooth).The combination of these local patches of PCA can serve as a form of nonlinear manifold learning, otherwise known as LPCA.
For use in the proposed exploration algorithm, we must first locate the edge points of the underlying manifold.Then, to obtain a reduced description, we can perform LPCA on small "patches" surrounding each boundary point [80,81].Consider a single boundary point found with an appropriate boundary detection algorithm.Its k-nearest neighbors form a small neighborhood near the edge of the n-dimensional manifold.The outward normal of the manifold at this location can be approximated by locating the center of mass and creating a unit vector u from this center towards the current boundary point.By projecting u onto the linear subspace formed by the first n local principal components found by executing PCA on the neighborhood, we reduce potential noise, skewing the outward normal.The boundary point can be extended outward a given distance on this de-noised normal, thereby yielding the new initial condition to be used in the simulator.This process is repeated for each boundary point.Extension of a sample manifold using LPCA is shown in Figure 11.
Note that extended points within the manifold of Figure 11 correspond to the extension of boundary points that do not cleanly fall on the manifold edge.This is a shortcoming of the boundary detection algorithm rather than a problem of LPCA.However, LPCA is not without its own limitations.The underlying linearity assumption implies that the extension should be relatively short because the assumption will only hold in small neighborhoods of the boundary points.Further, boundary detection must be done in the (high-dimensional) conformational space unless another nonlinear manifold learning technique, like DMAPS, is used to reduce the entirety of the manifold to a few coarse variables.Finally, as LPCA produces a set of local coarse variables for each boundary point, book-keeping becomes increasingly complicated, especially as the entire exploration algorithm repeats LPCA for each expansion of the explored region.See [82] for an approach on handling the local charts.
Boundary Detection
The success of our proposed algorithm is contingent on the ability to identify the boundary of the set of samples collected so far in the metastable state being currently visited.There exist at least two types of boundary detection algorithms: methods to find the concave hull around the sampled points, that is the tightest piecewise linear surface that contains all of the points; and more general methods that attempt to appropriately classify all of the data points so as to determine which samples belong to the boundaries.For a d-dimensional manifold embedded in a higher, n-dimensional space, the edge is d − 1 dimensional.Algorithms of the first type generate a d − 1 dimensional polytope for data that are d-dimensional.Therefore, for practical detection of the boundary, these procedures should be applied to low-dimensional manifolds.Note, however, that in some instances, the boundary of the manifold in conformational space may not always be the same as the boundary of the manifold in DMAP space; we assume here that this is not the case.Algorithms of the second type can be performed in either the d or n-dimensional space and provide a more robust way to determine which points lie on the boundary of the manifold.
The first set of algorithms construct the concave hull of the dataset (an optimal polytope that contains all points while minimizing volume) and include, e.g., the swinging arm [83] and the k-nearest neighbors approach [84].Both methods must be initialized at a point guaranteed to be on the boundary (such as the farthest point in a certain direction).In the 2D setting, the first method rotates a short line segment clockwise until a new point is hit, while the second method chooses from k-nearest neighbors the one that makes the widest angle.These procedures are then iterated until all of the boundary points in the dataset have been located.However, the produced concave hull can be different depending on which initial point is chosen.
In the alpha-shapes algorithm [85][86][87], two points are considered boundary points if there exists a disk (or sphere, in 3D) of user-specified radius α −1 in which (a) the points in question lie on the disk's perimeter and (b) the disk contains no other points.In practice, this method is executed by computing the Delaunay triangulation.The alpha-shape is then the union of triangles whose circumradius is less than α −1 and the boundary points that comprise the alpha-shape [88].Though this concave hull approach is computationally constrained to 3D, we utilize this method as MATLAB 2015 provides a built-in function.For higher dimensional manifolds, algorithms of the second class are appropriate.These methods iterate through each data point and use a set of parameters to determine whether on not they lie on the boundary [89][90][91][92].
Outward Extension across the Boundary of a Manifold
Let M be a smooth k-dimensional Riemannian manifold with a smooth boundary, ∂M.The manifold M is isometrically embedded [93] in R n via the smooth mapping ι : M → R n .We denote by ι the differential map (i.e., the Jacobian matrix at each point) associated with ι.It is well known [93] that ι maps tangent vectors of M into vectors in R n .In our case, ι is the embedding obtained via diffusion maps.
Consider the point x i ∈ ∂M and its image X i = ι(x i ) ∈ R n .The corresponding embedded tangent space ι T x i M has a natural basis ι ∂ 1 , . . ., ι ∂ k , which is the image by ι of the canonical basis ∂ 1 , . . ., ∂ k in a local chart around x i such that ι ∂ 1 is the inward normal at X i .This set of tangent vectors can be extended by an orthonormal frame e k+1 , . . ., e n ∈ R n such that ι ∂ 1 , . . ., ι ∂ k , e k+1 , . . ., e n is a basis of , where d(x, ∂M) denotes the geodesic distance from x ∈ M to the closest point in the boundary ∂M.Let x ∈ M ε be such that x i is the closest point to x lying in ∂M.Then, we define the reflective extension of X = ι(x) across the boundary of M, denoted by R(x) ∈ R p , as the vector: where •, • is the inner product associated with the Riemannian metric of M and II X is the second fundamental form [93] (Chapter 6), which describes how curved the embedded manifold is at a point X.Therefore, we can compute the outward extension of the point X as the new point X = X + δR(x) ∈ R p for some δ > 0 (see also Figure 12).
Geometric Harmonics
In this section, we review the construction of geometric harmonics introduced in [94].If we have a set of point-samples {y 1 , . . ., y m } ⊂ R n and a function f defined at those points, using geometric harmonics we can obtain an extension of f that is defined outside of the set of known samples.We will use geometric harmonics in Section 3.6 to fit a function to data and then extrapolate its value at new points.
Let us define the kernel: where x, y ∈ R n and ε 0 > 0. Consider the symmetric m × m matrix W with elements W ij = w(y i , y j ).
The matrix W is symmetric and, by Bochner's theorem [95] (Theorem 6.10), Positive Semi-Definite (PSD).This implies that W has a full set of orthonormal vectors ϕ 1 , . . ., ϕ m and its eigenvalues are real (due to W being symmetric) and non-negative (because W is PSD) For δ > 0, let us consider the set S δ = {α : λ α > δλ 1 } of indices of truncated eigenvalues.Let f be a function defined at some scattered points.We define the projection of f as: with •, • being the inner product.The extension of P δ f evaluated at a point x ∈ {y 1 , . . ., y m } is defined by: where ϕ i,α is the i-th component of the eigenvector ϕ α .The functions Φ α are called geometric harmonics.By projecting and subsequently extending the function f , we have an effective method to evaluate the function at points outside the set of known point samples.
The accuracy of the extrapolation method described above depends on the relative error between f and its projection P δ f being bounded by η ≥ 0 (that is, whether f − P δ f ≤ η f holds).In order to deal with functions where this condition is not satisfied, we use a multi-scale approach and project the residual f − P δ f onto a finer scale, ε 1 = 2 −1 ε 0 , by repeating the above procedure using a kernel w that uses ε 1 instead of ε 0 .This approach can be iterated by taking ε = 2 1− ε 0 for = 1, 2, . . .until the norm of the residual is sufficiently small.
A complete treatment of geometric harmonics can be found in [94], and an application to chemical kinetics appears in [76] (Section 3.2.5).This scheme is a crucial component of lifting from diffusion map coordinates to conformational space coordinates, which constitute the functions to be extended.
iMapD Algorithm
The algorithm we propose performs a systematic search for unknown metastable states on the attracting manifold of a high-dimensional molecular system without a priori knowledge of coarse variables.The method relies on an external molecular dynamics package to numerically solve the equations of motion in (typically short) simulations, starting from a single set of initial conditions as input.There is also a number of problem-dependent algorithmic parameters (e.g., alpha shape parameters, extrapolation step lengths, etc.); the ones germane to iMapD are reported.The steps in the algorithm are detailed below: 1. Collection of an initial set of samples: The molecular system is initialized and evolved long enough so that it arrives at some basin of attraction.After removing the initial points that quickly arrive at the attracting manifold, the remaining data points constitute the initial set of samples (point cloud) on the manifold.These samples will be used in the subsequent steps of the method.2. Parameterization of point cloud in lower dimensions: Using the set of samples from the previous step, we extract an optimal (and typically low-dimensional) set of coarse variables using DMAPS (for example, with cosine-diffusion maps).This process yields a parameterization of the local geometry of the free energy landscape around the region being currently visited by our system.All of our points are then mapped to the new set of coarse variables, thereby reducing the dimensionality of the system.3. Outward extrapolation in low-dimensional space: After identifying the current generation of boundary points in the space of coarse variables (for example, via the alpha-shapes algorithm), we obtain additional points by extrapolating in the direction normal to the boundary.4. Lifting of points from the (local) space of coarse variables to the conformational space: In order to continue the simulation, we must obtain a realization in conformational space of the newly-extended points in DMAP (or other reduced) space.In other words, we need a sufficient number of points in conformational space that are consistent with the DMAP (reduced) coordinates of the newly-extrapolated points.In the present paper, we use geometric harmonics, but in general, this task can be accomplished using biasing potentials, such as those available in PLUMED [96] or Colvars [97]. 5. Repetition until the landscape is sufficiently explored: The lifted points serve as guesses for regions of the manifold that are yet to be probed.The system is reinitialized at these points (usually by running new parallel simulations), and the unexplored space is progressively discovered.This process is then repeated, effectively growing the set of sampled points on the free energy landscape.
In practice, this process begins with the initial simulation.The outcome is a set of samples within some basin of attraction that are then used in order to identify a few coarse variables via DMAPS.Once the points are mapped to the coarse variables, we run a boundary detection algorithm to identify points at the edges of the dataset.Then, for each boundary point p in DMAP space, the center of mass of its k-nearest neighbors is found.Each point is extended outward along the vector u connecting the center of mass to p.The new DMAP coordinates are then converted back into the conformational space.Using a training set of diffusion coordinates and their corresponding coordinates in the conformational space, geometric harmonics is used to fit the relevant function (e.g., a dihedral angle), extrapolate it to the newly-extended point and return approximate coordinates in conformational space for this new point.For the training set, we supply the nearest neighbors of the boundary point.Once each boundary point is extended and lifted to the conformational space, new simulations are initialized from these points."Stitching" these new patches of explored regions together grows the approximation to the free energy landscape and explores it systematically without a priori knowledge of coarse variables.
In implementations of the algorithm, there arise various practical questions that affect the exploration of the attracting manifold, including: 1.
Simulation run time: Though system dependent, simulations should be run until (a) the trajectory enters a region already explored, or (b) a new basin is discovered, or (c) a reasonable amount of time has passed for the trajectory to have explored "new ground" within the current basin.These conditions can be tested by detecting if the trajectory remains within a certain radius for a given amount of time (it has most likely found a potential well) or if the trajectory has a nontrivial amount of nearest neighbors from already explored regions.
2.
Selection of trajectory points: Only "on manifold" points that belong to the basin of attraction should be collected.We implement this by removing a fixed number of points early in the trajectory that correspond to the initial approach to the attracting manifold.Discarding them will have the beneficial effect of preventing the exploration in directions orthogonal to the attractor.The exploration among the remaining points will lead to better sampling of basins and around saddle points within the attracting manifold.
3.
Memory storage of data points: Observe that the samples gathered throughout the exploration process need not be kept in memory and can instead be stored in the hard drive.In principle, the file system or an appropriate database can be used to keep the corresponding files, but if storage space becomes an issue, then it is possible to randomly prune points whenever a (user-specified) maximum number of data points is exceeded.Note that if, between random pruning and preprocessing the data, distinct patches of explored regions appear, each sample of the manifold must be expanded separately so as not to discard samples that may have potentially reached new metastable states.
Conclusions
We have presented, illustrated and discussed several components of an algorithm for the exploration of effective free energy surfaces.The algorithm links machine learning (manifold learning, in particular, diffusion maps) with established simulation tools (e.g., molecular dynamics).The main idea is to discover, in a data-driven fashion, coordinates that parametrize the intrinsic geometry of the free energy surface and that can help usefully bias the simulation so that it does not revisit already explored basins, but rather extends in new, unexplored regimes.Smoothness and low-dimensionality of the effective free energy surface are the two main underpinning features of the algorithm.Its implementation involves several components (like point-cloud edge detection) that are the subject of current computer science research and has led to the development of certain "twists" in data mining (like the sine-diffusion maps presented here).We believe that such a data-driven approach holds promise for the parsimonious exploration of effective free energy surfaces.The algorithm is (in its current implementation) based on the assumption that the effective free energy surface retains its dimension throughout the computation.The systematic recognition of points at which this dimensionality may change and the classification of the ways this can occur are some of the areas of current research that could expand the scope and applicability of this new tool.
Figure 1 .
Figure 1.First eigenvalues and the corresponding eigenfunctions (represented by continuous lines) of the operator L corresponding to the double well potential U(x) = (x 2 − 1) 2 (shown in the figure in dashed lines) at temperature β −1 = 1.Observe that ψ 1 (x) is approximately an indicator function that attains its maximum at one energy well, its minimum at the other, and is invertible throughout the interval.The eigenfunctions were computed by numerically solving the eigenvalue problem associated with (3), and the solution was obtained using the finite element method[55] with quadratic Lagrange elements and meshing the interval [−2, 2] with 10 4 domain elements.(a) λ 0 = 0; (b) −λ 1 ≈ −0.75; (c) −λ 2 ≈ −6.0;(d) −λ 3 ≈ −11.7.
2 Figure 3 .Figure 4 .
Figure 3. Joint density plot of visited points mapped onto the first two diffusion map coordinates, ψ 1 and ψ 2 , obtained using ε = 0.075 on a trajectory containing 4000 snapshots of a one microsecond-long simulation of the catalytic domain of the human tyrosine protein kinase ABL1.The distances between the data points were computed using the root mean square deviation among the alpha carbons of different snapshots.
Figure 5 .
Figure 5.A trajectory "descends" from its initial condition onto the attracting manifold, the cylinder with radius R and axis y.On the manifold, the trajectory arrives at one of the metastable states that is near the middle of the cylinder at different values of θ.These metastable sets are depicted as the lightest colored areas.
Figure 6 .
Figure 6.At each iteration, the algorithm extends the set of samples in the basin of attraction in order to better explore the underlying manifold and increase the likelihood of exiting the metastable state through one of the boundary points.The point cloud in conformational space is shown on the left, and the corresponding points in Diffusion Map (DMAP) space are displayed on the right.Green points represent the boundary of the so-far explored region.The system is reinitialized from the extended points, shown in magenta in both DMAP and conformational space.(a) The first iteration of the algorithm remains close to the basin of attraction.(b) The parameterization of the points formed by the first step in DMAP space.(c) The result of the third iteration of the algorithm in conformational space.(d) The result of the third iteration in DMAP space.(e) The result of the fifth iteration of the algorithm in conformational space.(f) The result of the fifth iteration in DMAP space.(g) By the seventh iteration, the point cloud escapes the initial basin of attraction.(h) The result of the seventh iteration in DMAP space.
Figure 7 .
Figure 7.The goal of reaching the second metastable state is attained here at Step 11.
Table 1 .
Difference between maximum and minimum values of the azimuthal angle θ(x, z) for the point-cloud at different iterations.Since the attracting set is a cylinder, this measure tells us how much the size of the point-cloud expands as iterations proceed for a generic run of the simulation.
Figure 8 .Figure 9 .
Figure 8. Cosine-diffusion maps on a 2D strip.(a,b) The first diffusion coordinate, ϕ 1 , parameterizes the x direction.(c,d) The second diffusion coordinate, ϕ 2 , parameterizes the y direction.Functions are cosine-like, and their normal derivative vanishes on the edges.These functions approximate ϕ 1,0 and ϕ 0,1 , the eigenfunctions of the 2D Laplace-Beltrami operator with reflecting boundary conditions, respectively.
Figure 10 .
Figure 10.Extending and lifting using one sine-coordinate and one cosine-coordinate.Geometric harmonics is used as the lifting technique.Blue points represent the original point cloud, while red points depict the newly extended points.
Figure 11 .
Figure 11.Extended manifolds using local PCA.Points extended into the manifold are a function of the boundary detection algorithm.Blue points represent the original point cloud, while red points depict the newly extended points.
Figure 12 .
Figure 12.An illustration of M embedded in R n via ι and its relationship with the tangent space, the normal direction and the curvature. | 10,802.4 | 2017-06-22T00:00:00.000 | [
"Computer Science",
"Physics"
] |
Asymptotic results for spatial causal ARMA models The of partial and
: The paper establishes a functional central limit theorem for the empirical distribution function of a stationary, causal, ARMA process given by X s,t = P i ≥ 0 P j ≥ 0 a i,j ξ s − i,t − j , ( s,t ) ∈ Z 2 , where the ξ i,j are independent and identically distributed, zero mean innovations. By judicious choice of σ − fields and element enumeration, one dimensional martingale arguments are employed to establish the result.
Introduction
The analysis of stationary random processes and random fields is a classic problem in mathematical statistics. The asymptotic behaviour of partial sums and empirical distributions is of particular interest, with the nature of the limit depending on whether the process has short or long memory. A stationary random field (X i,j : i, j ∈ Z) on the lattice is said to have short memory or to be shortrange dependent if and only if its covariance function is absolutely summable: i.e. i j |Cov(X 0,0 , X i,j )| < ∞; otherwise it is said to have long memory.
Many results are available for long memory fields; recent articles include [8,20] and [19], to which the reader is referred for thorough bibliographies. Although there is an extensive literature on asymptotics for random fields satisfying various types of conditions involving mixing or association (cf. [7,6] and [3] and the references therein), there are only a few papers available on short memory fields without explicit reference to mixing or association. For short memory processes (X i : i ∈ Z), such assumptions can often be avoided through the use of the elegant martingale methods developed by Gordin [13], but these techniques are not generally applicable in higher dimensions. Central limit theorems for partial sums of short memory stationary fields over sets have been investigated by Dedecker ([4] and [5]), but to date there seem to be no results on the behaviour of the empirical distribution of a short memory stationary random field without additional assumptions on mixing or association. We note that in [4] and [5], a projective criterion related to that of [13] is assumed, but martingale techniques are not used.
In this paper we will focus on the empirical distribution generated by a causal autoregressive moving average (ARMA) field in two dimensions: where {ξ u,v u, v ∈ Z} is an array of independent and identically distributed random variables. This model was first introduced by Tjøstheim in [24]; parameter estimation has been studied by a number of authors including [1,15,16,18,21] and [25]. In the case that only finitely many of the a i,j are non-zero, the field is strongly mixing and the behaviour of the empirical distribution is well understood (cf. [10], for example). Consequently, in what follows it will always be assumed that infinitely many of the a i,j are non-zero. Although the causal model may not seem as natural in two dimensions as it does in one, it is pointed out in [1] that the spatial causal model provides an appropriate representation of many general patterns for the covariance structure of a stationary random field. See [1] for a detailed discussion and bibliography, including references to applications of causal models to field trial data.
We will prove an invariance principle for the empirical distribution of the ARMA field when infinitely many of the a i,j in equation (1) are non-zero and illustrate some immediate consequences, including a functional central limit theorem for the quantile process. This model is of particular interest since its structure allows us to exploit a novel one-dimensional martingale argument which utilizes a certain total order on the plane. Significantly, we require no projective criteria nor do we make any assumptions about association or mixing properties. Indeed, although our model includes the short memory ARMA field, in the case of the invariance principle for the empirical process we do not even require that X i,j have a finite mean. We believe that our method is of independent interest and will be applicable to more general causal models in dimensions higher than one.
Invariance principles for the empirical distribution of a causal ARMA process on Z have been developed by Doukhan and Surgailis [9] and Ho and Hsing [14] under different assumptions. Our technique allows us to combine onedimensional martingale and two dimensional ergodicity arguments to produce an invariance principle for the empirical process generated by the spatial ARMA field. This is illustrated by following the development of Doukhan and Surgailis [9] to produce a two-dimensional result under conditions analogous to theirs.
Our main result and two applications are presented in Section 2; proofs appear in Section 3.
Results and applications
This paper will investigate the asymptotic behaviour of the ARMA model where {ξ u,v u, v ∈ Z} are independent and identically distributed random variables, If E[ξ 2 0,0 ] < ∞ and i j |a i,j | < ∞, we have a short memory field. We will proceed under the following more general assumptions.
Comments
• Note that the more general the moment condition, Assumptions 2.1.3 or 2.1.4, the more restrictive the summability condition Assumption 2.1.1.
• Assumption 2.1.2, like condition (4) of [9], implies that the distribution function of a partial sum of the a i,j ξ s−i,t−j terms is differentiable with density bounded by a constant provided a sufficiently large number of terms with nonzero a i,j are included in the sum. It also implies that the associated density satisfies a uniform Lipschitz condition provided sufficient terms are included in the moving average. See Giraitis and Surgailis, [12], for details.
We need to introduce some basic notation. The random variables X i,j and ξ i,j have distribution functions F and G respectively. Let Cov (R 0,0 (x), R i,j (x)) .
By applying the functional delta method, (for example, see van der Vaart and Wellner [26]), we obtain the following two corollaries as straightforward consequences of Theorem 2.3.
where W is the limiting Gaussian process in Theorem 2.3. In particular, the limit is a mean 0 normal random variable with variance σ 2 = ( i j a i,j ) 2 .
Comment: Convergence of √ mnX mn to the N (0, σ 2 ) distribution can be proven directly under Assumptions 2.1.1, and 2.1.3 with γ = 1. The method of proof for the ARMA field is virtually identical to that presented in [11] for the ARMA process.
Next recall Assumption 2.1.2 ensures that F is continuously differentiable. We can now state a functional central limit theorem for the empirical quantile process, H −1 m,n associated with X i,j , where H −1 m,n (p) = inf{x : H m,n (x) ≥ p}.
where W is the limiting Gaussian process in Theorem 2.3. In particular, the limit in (2) is a zero mean, Gaussian process with covariance function
Proofs
Let ≤ denote the usual partial order on The martingale argument will be based on the total order ≺ on R 2 defined as follows: To simplify the notation, C will denote a generic constant throughout the paper which may be different at each appearance.
A few observations.
1. Since the model is causal, X i,j is both F i,j and G i,j -measurable.
2. The ordering ≺ cannot be defined via an enumeration of Z 2 . It can if we are working on Z 2 + because we can start at (0, 0), move to (0, 1), then (1, 0) and progressively down each successive diagonal. Note that each diagonal is finite. We can also count backwards via ≺ order on (−∞, i] × (−∞, j], for any (i, j). Note that this is not true of the lexicographic order employed in [4] and [5].
6. Note that from (3) For all (i, j) and h, k ≥ 0 define (suppressing the dependence on x) For h, k fixed, the U i,j (h, k) are stationary in i, j. By referring to Figure 1 note that we can write for all i, j ≥ 1, h, k ≥ 0. The case k = 0 follows from equation (4) by setting u = h + 1. We use this unified formula in the sequel. Thus when we condition X i,j on G i−h−1,j+1 , it is the same as conditioning on G i,j−h−1 as the extra ξ u,v terms involved in defining G i−h−1,j+1 in addition to those generating G i,j−h−1 are independent of X i,j . As a result, via conditioning under the total order ≺ we are able to successively move over each diagonal in the quadrant to the left and below (i, j). Although many total orders can be defined on the plane, this procedure also enables us to maintain stationarity.
where the second line follows since the series collapses and the third line follows by (3).
Thus, almost surely, At this point, we observe that by (6) With this one-dimensional martingale structure in place we can now proceed with the proofs of Theorems 2.2 and 2.3 following an approach similar to [9].
We will show where the first limit is taken as m, n → ∞ and the second limit corresponds to N → ∞.
Proof of (a) Define Consequently, M N i,j are 1-d martingale differences in the total order ≺ on Z 2 + . Also, since U i,j (h, k) is stationary in (i, j) for each (h, k), we have that (M N i,j ) is stationary under horizontal and vertical shifts.
Henceforth, dependence on x will be suppressed in the notation when no ambiguity arises. Write We will apply a martingale central limit theorem to the first term and show that the second term converges to 0 in probability.
To show 1 √ mn Q N m,n p → 0, for fixed N , consider (9). For ℓ, h, j fixed we will This implies that (9) consists of a finite sum of terms, each of which converges to 0 in probability. The terms (10), (12), and (13) are similar, and the sums in (11) and (14) are bounded. Return to (15).
For j fixed, if i is increased then we move to a higher diagonal, i.e. G i,j ⊆ G i ′ ,j if i < i ′ . Therefore, the terms are all orthogonal and so where the second equality follows by stationarity and the third equality follows since E[U 0,0 (h, ℓ − h) U i,j (h ′ , ℓ ′ − h ′ )] = 0 unless the terms correspond to the same diagonal position, that is, We will now proceed with the proof of the central limit theorem for where N is fixed. The result follows from the four steps below.
1. {M N i,j , G i,j } is a martingale difference array in the total order, ≺ .
This completes the proof of (a).
To complete the proof of Theorem 2.2 we need the following two lemmas.
where C does not depend on i, j, h or k.
Proof. The proof follows as in [9] by writing Recalling the definition (5), we have Now observe that if ξ 0,0 ∼ G we have Substituting (18) and (19) into (17) we get Recall Assumption 2.1.2 implies that F u,v is differentiable with density bounded by a constant provided u + v > ℓ 0 for some ℓ 0 . By the mean value theorem Further, |U i,j (h, k)| ≤ 1 so (16) follows from the above and the fact that min(1, |x|) ≤ |x| γ , for 0 < γ ≤ 1. Proof.
From (16) and and i j b ′ i,j < ∞, by Assumption 2.1.1, since the number of terms in the sums above are finite. Now This completes the proof of Lemma 3.2.
Return to the Proof of Theorem 2.2. Proof of (b) Recall and and since the covariances are absolutely summable, by Lemma 3.2, we can exchange limits and summations to obtain (b).
Proof of Theorem 2.3. The finite dimensional convergence follows by using the Cramér Wold technique (see, for example, [17], Corollary 5.5) and arguing as in the proof of Theorem 2.2. Note we only need ξ 0,0 to have finite moments of order 2γ, that is, Assumption 2.1.3 holds, to obtain finite dimensional convergence.
To obtain the functional limit result we need to show that {W m.n } is tight in the sup norm topology on D[−∞, ∞]. As in Shao and Yu [23] it suffices to establish the following moment bound: there exist constants C < ∞ and δ > 0 such that for any x, y ∈ R, with |x − y| ≤ 1, For fixed x and y, with |x − y| ≤ 1, define, suppressing x and y in the notation, Tracking terms along the sth diagonal. .
is G t,s−t measurable and, V m,n (s, t) and V m,n (s ′ , t ′ ) are orthogonal unless s = s ′ and t = t ′ . By referring to Figure 2 we see the term preceding V m,n (s, t) in the total order, ≺, is V m,n (s, t − 1), where V m,n (s, s − n − 1) is defined to be V m,n (s − 1, m). Note V m,n (s, t) is measurable with respect to G t,s−t , which is a σ−field corresponding to a position on the diagonal passing through (0, s), (s, 0). We will use the procedure in [9] to establish (22). First we obtain an expression for the fourth moment like (13) in [9] by expressing the moment via sums in (s, t) and (s ′ , t ′ ), where (s ′ , t ′ ) is the term preceding (s, t) in the total order. We have where , a = 1, 2, 3, 4, where the last sum is 0 if t = s − n.
The term I 1 is 0 as V m,n (s, t) is a sum of martingale differences. For the other terms we will develop a deterministic bound, b Assumption 2.1.2 implies that X i,j has a bounded density which satisfies a uniform Lipschitz condition provided sufficient terms are included in the moving average. In our context this means that we include sufficient terms in the weighted sums by pulling back under the total order along a sufficient number of diagonals, ℓ 0 .
Let f h,k be the density associated with F h,k . For h+k ≥ ℓ 0 we have |f h,k (x)− f h,k (y)| ≤ C|x − y| and f h,k , is bounded by K for some constant K, so arguing as in the development of (20) Focussing on the h = 0 case, since the density f h,k is bounded and min(1, |x|) ≤ |x| γ for 0 < γ ≤ 1, Using the notation in the proof of Lemma 3.1, for clarity we will continue the proof of tightness assuming that g, the density of ξ 0,0 , is bounded and satisfies a Lipschitz condition. This implies the same for the density f h,k of X i,j (h, k) for all h and k. This simplifies the proof and allows us to use the fourth moment criterion given in [2] Theorem 12.3, refer to equation (12.51). However, tightness also holds under the weaker Assumption 2.1.2. The proof requires consideration of the cases s < −ℓ 0 and s ≥ ℓ 0 separately for each moment bound. The reader is referred to Doukhan and Surgailis [9] for details.
For I 3 , | 3,651.2 | 2010-01-01T00:00:00.000 | [
"Economics",
"Mathematics"
] |
On the Asymptotic Capacity of Information-Theoretic Privacy-Preserving Epidemiological Data Collection
The paradigm-shifting developments of cryptography and information theory have focused on the privacy of data-sharing systems, such as epidemiological studies, where agencies are collecting far more personal data than they need, causing intrusions on patients’ privacy. To study the capability of the data collection while protecting privacy from an information theory perspective, we formulate a new distributed multiparty computation problem called privacy-preserving epidemiological data collection. In our setting, a data collector requires a linear combination of K users’ data through a storage system consisting of N servers. Privacy needs to be protected when the users, servers, and data collector do not trust each other. For the users, any data are required to be protected from up to E colluding servers; for the servers, any more information than the desired linear combination cannot be leaked to the data collector; and for the data collector, any single server can not know anything about the coefficients of the linear combination. Our goal is to find the optimal collection rate, which is defined as the ratio of the size of the user’s message to the total size of downloads from N servers to the data collector. For achievability, we propose an asymptotic capacity-achieving scheme when E<N−1, by applying the cross-subspace alignment method to our construction; for the converse, we proved an upper bound of the asymptotic rate for all achievable schemes when E<N−1. Additionally, we show that a positive asymptotic capacity is not possible when E≥N−1. The results of the achievability and converse meet when the number of users goes to infinity, yielding the asymptotic capacity. Our work broadens current researches on data privacy in information theory and gives the best achievable asymptotic performance that any epidemiological data collector can obtain.
Introduction
During any prevention and control period in an epidemic, strengthening the protection of personal information is conducive not only to safeguarding personal interests, but also better controlling the development of the epidemic. Differently from the collection of other homogeneous data, such as the large-scale labeled sample obtained in machine learning, the characteristics of medical or epidemiological data collection are reflected in the following aspects: (1) In order to establish a surveillance system for a dynamical group of people to collect syndromic data, the sample size is always changing [1,2]; (2) Data sharing and early response are critical in containing the spread of highly infectious diseases, such as COVID-19. This requires the data stored in the database to be updated to track real-time changes in symptoms, severity, or other disease-related patterns [3,4]; (3) Some of the epidemiological data, such as the locations of infected individuals, the blood oxygen saturation levels of patients with respiratory diseases after medication, or the physical condition monitoring data after viral infection, are related to the user's privacy, so a "privacy-first" approach which uses dynamic identifiers and stores their data in a cryptographically secure manner is needed [5]. Hence, for these factors of epidemiological data collection, the key to ensuring the efficiency of information sharing and privacy protection is to maximize the balance between data privacy and collection rate in epidemic analysis.
While the data collection from public health authorities and the open-source access to researchers can provide convenience to epidemiologists, these strategies may also significantly intrude upon citizens' privacy. Some of these individuals were affected by unwanted privacy invasion, and the ubiquitous data surveillance devices certainly exacerbate those concerns. Therefore, the responsible use of shared data and algorithms, the compliance with data protection regulations, and the appropriate respect for privacy and confidentiality have become important topics in epidemiological data collection [6,7]. In 2014, the Global System for Mobile Communications (GSM) Association outlined some privacy standards for data-processing agencies regarding mobile phone data collection in response to the Ebola virus [8]. Some other methods that effectively guarantee user privacy include: encryption mechanisms [9], the privacy-aware energy-efficient framework (P-AEEF) protocol [10], the differential privacy-based classification algorithm [11], and the spatio-temporal trajectory method [12]. Moreover, unauthorized agencies, malicious hackers, and unidentified attacks, such as traffic analysis attacks, fake-node injection, and selective forwarding, may also eavesdrop on users' data under the current ambiguous and non-uniform collecting algorithms [13]. To avoid the leakage of information from malicious collecting servers or untrusted access, the privacy of data needs to be ensured during data storage and processing.
In line with ensuring the security and privacy of user data, epidemiological data collection also requires the protection of data collectors. In accessing public databases, various epidemiological investigation agencies have different requirements for data privacy. For example, many epidemiological surveys are conducted by governments, universities, research institutes, pharmaceutical companies, and private institutions. Access to public data may reveal these agencies' data preferences, resulting in information leakage. Therefore, the private-preserving epidemiological data collection includes the user's privacy regarding the storage and data collector, along with the data collector's privacy in data storage.
In epidemiological modeling, many recent studies have shown that various models have a good fitting effect on the nature of epidemics, such as the Bayesian model [14] and deep learning models, including multi-head attention, long short-term memory (LSTM), and the convolutional neural network (CNN) [15]. Additionally, when it comes to privacy and security concerns, some work conducted in computer science, cryptography, and information theory provides handy tools to model and solve such problems. The privacy leakage was modeled in differential privacy [16], k-anonymity [17], t-closeness [18], interval privacy [19], etc. With those concerns and analysis, several studies in cryptography and information theory have focused on the issue of sharing messages to untrusted agencies, such as distributed linear separable computation [20][21][22], secured matrix multiplication [23][24][25], secure aggregation [26], participatory sensing [27], and private information retrieval [28][29][30][31]. Specifically, a cryptographical epidemiological model with data security and privacy called RIPPLE was analyzed [32]. This model enables the execution of epidemiological models based on the most-recent real contact graph while keeping all the users' information private. As an extension to the model, the data collector uses the sum private information retrieval (PIR) schemes to obtain the statistical data, which is described as the sum of a set of elements from a database.
Inspired by the cryptographical epidemiological model in [32], we propose an information-theoretic privacy-preserving epidemiological-data-collection problem , described as follows. We have a large and changing number of users sharing their real-time epidemiological data to N servers. The server will update its database once new data are uploaded. The storage of those users' data is also open to all authorized data collectors. For any data collector who desires only some statistical feature, rather than all the data, it directly retrieves the statistic from N servers. We designed the protocol of the interaction between the N servers and the data collector so that when all N servers honestly answer the queries from the data collector, then the desired statistical data can be correctly decoded at the data collector. To simplify the problem, we assume the desired statistics to be the linear combinations of users' personal data. The privacy of this model is reflected in the following three aspects: (1) The privacy of users' data against the data collector: after downloading all answers from the servers, the data collector can decode the desired data without learning anything about the irrelevant details of the users' personal information.
(2) The privacy of users' data against servers: for any user successfully sharing the data to all N servers, the personal information of the user is still confidential, even if of any up to E(E < N) servers collude. (3) The privacy of the data collector's preference against servers: the protocol between data collector and servers should promise that any single server cannot know any preference of the desired statistical data from the query generated by the data collector. In our paper, we take the above privacy concerns into consideration and analyze the data collector's ability of privately receiving the shared data, with respect to the number of symbols it needs to download.
The remainder of the paper is organized as follows: In Section 2, we introduce an information-theoretic description of the privacy-preserving epidemiological-data-collection problem, and we define the communication rate and capacity of our problem. In Section 3, we give a closed-form expression for the asymptotic capacity, which is the main result of the paper. In Section 4, we derive a converse proof for E < N − 1, which provides an upper bound on the asymptotic capacity when the number of users tends to infinity. An asymptotically capacity-achieving scheme using the technique of cross-subspace alignment when E < N − 1 is given in Section 5, and in Section 6, we prove that the problem is not asymptotically achievable when E = N − 1. Finally, in Section 7, we summarize our results and suggest some open problems in this field.
System Model
We formulate the privacy-preserving epidemiological-data-collection problem over a typical distributed, secure computation system, in which there are K users, N servers, and a data collector; and the number of users (K ∈ N + ) is a large-enough integer. Here and throughout the paper, we assume that all of the random symbols in our system are generated by a large-enough finite field F q , and we standardize the entropy of any uniformly distributed symbol to be 1 by taking the term log in the entropy, conditional entropy, and mutual information to be base q. The model is depicted in Figure 1. Let W 1 , · · · , W K be K independent messages, where W k , k ∈ [1 : K] denotes the epidemiological data of user k and W k ∈ GF L×1 q , L ∈ N + is an L × 1 vector with L i.i.d. uniform symbols from the finite field GF q -i.e., The data-collection problem contains two phases: the upload phase and the computation phase. The upload phase starts when the user is required to update its data to each of the N servers. Before uploading, user k knows nothing about the contents of other users' epidemiological data. While uploading their personal data, the users would like to keep his/her message private against E (E ≤ N, E ∈ N) colluding servers; i.e., any of up to E servers will learn nothing about the messages uploaded by K users. For any n ∈ [1 : N], let D k,n ∈ D denote the uploaded message from the k-th user to the n-th server. We have the following equality called the privacy constraint of the users against E servers: For any k ∈ [1 : K], let Z k ∈ Z k denote a random variable privately generated by user k, and its realization is not known to any of the N servers. User k utilizes the user-side randomness Z k to encipher the message W k ; i.e., for any user k, there exist N functions {d k,n } n∈ [1:N] such that d k,n (W k , Z k ) = D k,n , where d k,n : GF L q × Z k → D is the encoding function from the user k to the server n. We have When the servers receive the updated data from users, the old contents of the server will be replaced with the new contents, and all servers will be ready for the computation phase and allow the access of data updated by data collectors.
The computation phase starts when a data collector would like to compute statistical data of the current epidemiological database. To simplify our problem, we only consider statistical data to be a linear combination of all messages W [K] . Let W f and f be the statistical data and the corresponding coefficient vector. Then, we have where W f ∈ GF L q has the same number of symbols with the message length, and f ∈ GF K q contains K elements in the finite field GF q . In our setting, the coefficient vector f only contains the preference of the data collector among K user's epidemiological data records. Therefore, the value of f does not depend on the users' messages W [1:K] or the storage of N servers Let Z ∈ Z denote a random variable privately generated by the data collector, and its realization is not available to any of the N servers and K users. In the computation phase, the data collector with its preference vector f utilizes the randomness Z to generate its queries to N servers. Assume that the query from the data collector to the n-th server is denoted as Q f n ∈ Q n . Then, the data collector uses the strategy g to map the randomness and the coefficient to the queries, such that where g : GF K q × Z → ∏ N n=1 Q n is the encoding function from the data collector to the servers. Hence, we have Since the randomness Z and queries Q f [1:N] are generated privately, and the user-side data and randomness W [1:K] , Z [1:K] are already known before the computation phase starts, the data collector has no knowledge of W [1:K] , Z [1:K] when the queries Q f [1:N] are generated. Thus, we have Upon receiving the query Q f n , the n-th server will send an answer A f n back to the data collector according to the storage of the n-th server. We assume that there is no drop-out in the model-i.e., each server n will successfully return its answer to the data collector. Let A f n ∈ A n be the answer from the n-th server to the data collector, and then for any n ∈ [1 : N], there exists a deterministic function a f n : We would like to design a scheme φ = {d k,n , g, a f n } k∈[1:K],n∈[1:N],f∈GF K q in the upload and computation phases so that the following three constraints can be achieved. Firstly, the data collector is able to reconstruct the desired message from all the information it has received, which we call the decodability constraint. Let ψ be the reconstruction function of the data collector, where ψ : We havê Let P e be the probability of decoding error achieved by a given scheme φ and decoding function ψ. We obtain According to Fano's inequality, the decodability constraint is equivalent to when P e → 0, where o(L) denotes any possible function h : The second constraint guarantees the data privacy of K users against the data collector. The privacy leakage to the data collector is unavoidable, as the data collector must learn some statistical data of the users. This constraint requires that the data collector can learn nothing about the information of the K users other than the desired data W f . We have To protect the privacy of data collector, the third constraint requires the coefficient vector f of the data collector to be indistinguishable from the perspective of each server; i.e., for any different (linearly independent) coefficient vectors f and f from the same scheme φ, the queries to every single server are identically distributed, so that any server cannot deduce f merely from the query and storage without communicating to other servers. Hence, we have , ∀f, f linear independent (11) where A ∼ B means that the random variables A and B have the same distribution. This constraint is called the privacy constraint of the data collector against non-colluding servers. The reason why in the upload phase, we consider up to E servers may collude, and in the computation phase, we consider non-colluding servers to be defined by the following: the upload phase and the computation phase do not always occur at the same time. For example, the users are required to upload their epidemiological data on a regular basis, and the data collector may start his/her queries of certain statistics at relatively random times. Due to the dynamic topology of the servers, the numbers of colluding servers may be different during the uploading phase and the computation phase. Our work assumes that the servers are non-colluding in the computation phase, since the servers may be more interested in the epidemiological data than the data collector's interest. If E = 1, then we have a model where the servers are non-colluding in both the upload phase and the computation phase.
For any scheme φ = {d k,n , g, a f n } k∈[1:K],n∈[1:N],f∈GF K q that satisfies the above decodability constraint, i.e., (9), and the privacy constraints, i.e., the privacy constraint of the users against E servers (2), the privacy constraint of the users against the data collector (10), and the privacy constraint of the data collector against the non-colluding servers (11), its communication rate is characterized by the number of symbols the data collector decodes per download symbol-i.e., It is worth noticing that R is not a function of f due to (11). A rate R is said to be ( -error) achievable if there exists a sequence of schemes indexed by L with their communication rate less than or equal to R where the probability of error P e goes to zero as L → ∞. The -error capacity of this random secure aggregation problem is defined as the supremum of all -error achievable rates, i.e., C := sup R, where the supremum is over all possible -error achievable schemes.
Main Result
For the information-theoretical framework of our privacy-preserving epidemiologicaldata-collection problem presented in Section 2, our main result is the characterization of the asymptotic capacity when K → ∞ for any N ∈ N + and E ∈ N.
To begin with, we show that the problem is infeasible when N = 1 or N = E, since in these cases, some constraints of our setting contradict each other, and no scheme can satisfy all the constraints. Firstly, when there is only one server, the privacy of users against the data collector and the privacy of data collector against servers will conflict with each other. The reason is as follows. First, according to (11), the answer A will be given that for two different f, f , the distribution of A is the same. Second, the decodability (9) guarantees that W f can be derived from A. Then, W f can be derived from A, which contradicts the privacy of users against the data collector.
Moreover, when E = N, the decodability constraint and the privacy of users against the servers will conflict with each other. The reason is as follows. First, the answers A f [1:N] from N servers are given by the queries Q f (6) and (2), which contradicts the decodability constraint as A f [1:N] is independent from the database W [1:K] . Therefore, no scheme can simultaneously satisfy all the constraints in a single-server or E = N scenario, and there does not exist a positive capacity.
The following theorem gives the asymptotic capacity of private-preserving epidemiological data collection for an infinitely large K, where we have N ≥ 2, E < N servers. Theorem 1. Consider E as a non-negative number, and there are N ≥ 2 servers. When E < N, and the number of users K → ∞, the asymptotic capacity of the secure privacy-preserving epidemiological-data-collection problem is When E < N − 1, the converse proof of Theorem 1 will be given in Section 4, and the achievability proof will be given in Section 5 for any finite K ∈ N + . When K → ∞, our scheme in Section 5 remains achievable at the same rate, and the performance of the achievability and converse will meet. When E = N − 1, the proof of the zero asymptotic capacity is given in Section 6.
Remark 1.
From Theorem 1, we can see a threshold in the asymptotic capacity on the number of the maximized possible colluding servers E. When E ≥ N − 1, there is no scheme with a positive asymptotic capacity; when E < N − 1, the asymptotic capacity is a decreasing function of E. When N approaches infinity while E is a constant, the asymptotic capacity approaches one.
Remark 2.
When the number of users K is a finite integer, the achievability and converse results do not always meet. From our converse proof in Section 4, the upper bound we give for finite K depends on the value of K. However, the performance (i.e., achievable rate) of our scheme in Section 5 is irrelevant to K, even though the scheme we propose is different for the finite K ∈ N + . How to close the gap between the upper and lower bounds when K is finite is still an open problem.
Proof of Theorem 1: Converse When
We give the converse proof of Theorem 1 when E < N − 1 in this section. The converse allows any feasible scheme φ, and we give an upper bound over the rates of all possible schemes. We start with the following lemma, which states an iterative relationship among the number of linear combinations of the users' messages. Lemma 1. Consider K linear independent vectors f 1 , f 2 , · · · , f K ∈ GF K q . Let E be a set and E ⊆ [1 : N], |E | = E. We have Proof. According to our problem setting, we have ≥H(A f where (15) holds because of the non-negativity of the following conditional entropy; i.e.,
H(A
where the first equality follows from (7), and the second equality follows from (9). Finally, (18) holds because W f is independent from the queries and randomness, the security constraint and that f, f ∈ GF K q are linear independent vectors.
The following lemma shows that any answers in a set are independent from any queries conditioned on the same set of queries to the same coefficient and any size of messages and randomnesses. This is the direct inference from the independence of message, queries, and randomnesses generated by the data collector (6).
Lemma 2.
Assume that f ∈ GF N q , N 1 , N 2 ∈ [1 : N], and K ∈ [1 : K]. Then, we have the following equality: Proof. The proof is the same as Section VI, Lemma 1, in [29], and the key to this proof is that A f N 1 is determined by W [1:K] , conditioned on Z and Q f N 1 . We omit the detailed proof here.
The lemma below has a similar form to Lemma 2, and it shows that any set of answers with size of E do not depend on the desired statistic, conditioned on the same set of queries and the randomnesses generated by the data collector.
Proof. We only need to show that I(A f E ; W f |Q f E , Z ) is less than or equal to 0 because of its non-negativity.
The following lemma shows that we can split the answers into two parts-one from E servers that cannot decode the database and the other from N − E servers: Proof. Based on the system model, we have ≥L where (24) (20), (6), and (7); (27) is due to (7); and (28) Now, we can get the lower bound on the asymptotic download size when L and K goes infinity by applying (14) to (23). We have where (30) Thus, for any possible scheme φ satisfying the constraints of the problem, the rate cannot be more than N−E−1 N when E < N − 1 and K → ∞.
Proof of Theorem 1: Achievability When
In this section, we give a cross-subspace alignment (CSA) scheme based on the coding of interference in the computation phase to reach the asymptotic capacity [33] for any integers N > E + 1 and K ≥ 2. Throughout the scheme, we choose the length of each personal message L = N − E − 1 ≥ 1, and we use the notation First, we specify the encoding functions {d k } k∈ [1:K] in the upload phase. Let W l k ∈ GF q be the l-th symbol of each W k , k ∈ [1 : K], l ∈ [1 : L], and W l ∈ GF 1×K q be the row vector of the l-th symbol of all K messages, i.e., W l = [W l 1 , · · · , W l K ]. Assume that α n , n ∈ [1 : N] are N distinct coefficients all belonging to the set {α ∈ GF q : α + i = 0, i ∈ [1 : L]}-i.e., for any i, j ∈ [1 : N], α i = α j . Note that the α n s are globally shared variables known to the users, servers, and the data collector. In order to protect the privacy of the users against the servers, each user k will generate L × E random noises Z k le uniformly from GF q . The uploaded information to the n-th server by the k-th user is given by . . .
For convenience of notation, we write the content stored at server n in a vector form as D n =[D 1 1,n , · · · , D 1 K,n , D 2 1,n , · · · , D 2 K,n , · · · , D L 1,n , · · · , D L K,n ] (34) where D n ∈ GF 1×KL q , and Z le is defined as Z le = [Z 1 le , · · · , Z K le ]. In the computation phase, the query to Server n is determined by the coefficient f and the randomness from the data collector Z . We design the query to Server n based on f as where Z 1 , · · · , Z L are L random column vectors of length K, whose elements are uniformly distributed on GF q , generated by the data collector. For any server n ∈ [1 : N], the answer to the data collector A f n ∈ A n = GF q is calculated by According to the expansion of the representation (38) in the descending power of α, we can see that l+α n W l · f and a polynomial of degree E in α n . We can rewrite (38) as where I e is the coefficient of α e n for any e ∈ [0 : E]. We can clearly see from (38) and (39) that I e is not a function of n. If we write the answers to the data collector from all the N servers together, we can get the following formula in a matrix form: Now, we prove that this scheme satisfies the decodability constraint, i.e., (9), and the privacy constraints-i.e., the privacy constraint of the users against E servers (2), the privacy constraint of the users against the data collector (10), and the privacy constraint of the data collector against the non-colluding servers (11).
Recall that in our scheme, we let L = N − E − 1. The decodability constraint is satisfied because the matrix in (40) is an N × N full-rank matrix when the α n s are distinct Lemma 5 in [33]. Hence, W 1 · f, · · · , W L · f can be fully recovered from (4) is obtained by The privacy constraint of the users against E colluding servers is satisfied due to the sharing strategy of the users. In (33), we know that the k-th user shares its l-th symbol to the n-th server in a form where D l k,n denotes the storage in server n that W l k shares. The security needs to guarantee that any E out of N servers do not know W k for any k ∈ [1 : K]. For any set E := {o 1 , · · · , o E } such that E ∈ [1 : N] and |E | = E, we choose the E servers to be in E . We can write the storage of these servers with respect to what W l k shares in a matrix form: Notice that the Vandermonde matrix in (43), denoted by V E , is invertible for distinct {1 + α e : α e ∈ GF q , e ∈ E }, so the second term of (43) contains E symbols that are linearly independent. The privacy constraint of the users against E colluding servers can be guaranteed as the E additional random symbols protect the shared message. We have where (44) comes from (43), and (45) holds because when i < j, we have and when i > j, we have so the remaining items are those (i, j) such that i = j = l.
To prove that the privacy constraint of the data collector against the non-colluding servers is satisfied, we notice that the query to each server is composed of the desired coefficient f and independent additional randomness Z [1:L] . Consider two linear independent vectors, f, f ∈ GF K q . For any l ∈ [1 : L], the l-th entries of Q f n and Q f n are ∆ n l+α n (f + (l + α n )Z l ) and ∆ n l+α n (f + (l + α n )Z l ), respectively. Notice that Z l (thus ∆ n l+α n · Z l ) is chosen uniformly from GF K q , and that ∆ n l+α n · f and ∆ n l+α n · f are two deterministic vectors in GF K q . The l-th symbol of Q f n or Q f n has the same distribution. Therefore, any single server can not distinguish queries from the data collector with one coefficient f. Furthermore, if we assume the desired coefficient t is a random variable with some distribution known only to the data collector, and f is an implementation of t, we can prove that the mutual information between t and (Q t n , A t n , W where (46) is from (38), (47) is from (10), and (48) is from (6).
Finally, to prove that the privacy constraint of the users against the data collector is satisfied, we construct a basis of GF K q containing the desired f. Assume that the vectors in the basis is denoted by {f 1 , f 2 , · · · , f K } where f 1 = f. We then have Thus, we prove that the scheme satisfies all the constraints. As the answer from any server contains one symbol (the inner product) from GF q , the rate of our proposed scheme is It can be seen that the scheme we construct by (33), (36), and (38) is achievable with the rate (54) invariant with K by rearranging the data W [1:K] to W [1:L] . We notice that the achievable rate meets the asymptotic upper bound for any K ∈ N + , so the scheme is then proved to be asymptotically optimal, by letting K → ∞.
Converse Result When
In this section, we prove that the asymptotic capacity is zero when N = E + 1. First, the inequality (23) also holds when N = E + 1 because the inequality in (15) becomes an equality. Hence, we have Thus, for any linear independent vectors f 1 , f 2 , · · · , f K ∈ GF K q , we have
=0.
The upper bound of C indicates that it is unfeasible to construct a scheme that has a positive communication rate when K → ∞. However, differently from the N = E scenario, our proof of the zero asymptotic capacity does not mean that there does not exist any scheme that satisfies all the constraints of our problem. In other words, there may be schemes that can satisfy all the constraints of the problem, albeit with an asymptotic capacity of zero. The detailed construction of a feasible scheme for E = N − 1 and finite K is still an open problem.
Conclusions
Thanks to the research on data privacy and modeling of infectious diseases, the privacy-preserving epidemiological-data-collection problem was proposed, which aims to maximize the collection rate while protecting the privacy of all users' data and the data collector's preferences. We have found the asymptotic capacity of this problem, and the result shows that when there is more than one remaining server that not colluding with the other servers to decode the users' data, the asymptotic capacity exists. The objective of this work was to find the best performance for the privacy-preserving epidemiologicaldata-collection problem, and we partly achieved this goal by giving the construction and proof of the optimal scheme when K is infinitely large. The achievability for N ≥ E + 2 was given by the cross-subspace alignment method, and the infeasibility of N = 1 or N = E was also proved. Our findings not only extend the research on secure multi-party computing systems in information theory, but also provide information-theoretic frame-works, implementations, and capacity bounds for the study of privacy epidemiological modeling. Although we characterized the asymptotic capacity for this problem, the exact capacity is still unknown. Some future directions include finding the exact capacity for finite K, the construction of a scheme when N = E + 1, and the performance of asymptotic capacity under irregular colluding patterns. In general, our result of asymptotic capacity for this problem will provide useful insights for further studies in data both privacy and epidemiological modeling.
Institutional Review Board Statement: Not applicable.
Data Availability Statement: Data sharing is not applicable to this article as no new data were created or analyzed in this study.
Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.
Abbreviations
The following abbreviations are used in this manuscript: | 8,022 | 2022-12-12T00:00:00.000 | [
"Computer Science"
] |
A Parsec-Scale Catalog of Molecular Clouds in the Solar Neighborhood Based on 3D Dust Mapping: Implications for the Mass-Size Relation
We dendrogram the Leike et al. 2020 3D dust map, leveraging its $\sim 1$ pc spatial resolution to produce a uniform catalog of molecular clouds in the solar neighborhood. Using accurate distances, we measure the properties of 65 clouds in true 3D space, eliminating much of the uncertainty in mass, size, and density. Clouds in the catalog contain a total of $1.1 \times 10^5 \; \rm M_{\odot}$, span distances of $116-440$ pc, and include a dozen well-studied clouds in the literature. In addition to deriving cloud properties in 3D volume density space, we create 2D dust extinction maps from the 3D data by projecting the 3D clouds onto a 2D"Sky"view. We measure the properties of the 2D clouds separately from the 3D clouds. We compare the scaling relation between the masses and sizes of clouds following Larson 1981. We find that our 2D projected mass-size relation, $M \propto r^{2.1}$, agrees with Larson's Third Relation, but our 3D derived properties lead to a scaling relation of about one order larger: $M \propto r^{2.9}$. Validating predictions from theory and numerical simulations, our results indicate that the mass-size relation is sensitive to whether column or volume density is used to define clouds, since mass scales with area in 2D ($M \propto r^{2}$) and with volume in 3D ($M \propto r^{3}$). Our results imply a roughly constant column and volume density in 2D and 3D, respectively, for molecular clouds, as would be expected for clouds where the lower density, larger volume-filling gas dominates the cloud mass budget.
INTRODUCTION
Star formation takes place in molecular clouds, which are associated with the densest and coldest phase of the interstellar medium (ISM).Studying the properties of molecular clouds has thus long been the focus of star formation research, as the structure of these clouds has a direct impact on the location, number, size, and mass of newly formed stars (Rosolowsky et al. 2008).
Maps of the extinction or emission from dust trace out the interstellar medium (ISM) in "position-position" or "p-p" space, on the 2D plane of the sky (Lombardi 2009;Lada et al. 2009).Spectral-line observations of the ISM can add a third dimension, owing to the Doppler effect, which allows for conversion of wavelength or frequency to velocity.The resulting so-called "postion-position-velocity" or "p-p-v " cubes, can be analyzed as 2D maps (integrating over velocity) or as pseudo-3D maps, where velocity is treated as a non-spatial third dimension.
Catalogs of molecular clouds have previously been derived using both p-p and p-p-v data.Rice et al. (2016) use the dendrogram technique (Rosolowsky et al. 2008) to extract and analyze molecular clouds from the CO p-p-v survey of Dame et al. (2001), identifying over a thousand clouds across the full Galactic plane.Miville-Deschênes et al. (2016) apply a hierarchical cluster identification method to a Gaussian decomposition of Dame et al. (2001) and produce a catalog of 8,107 clouds covering the entire Galactic plane.Using 2D extinction maps derived from the NICEST color excess method (Lombardi 2009), Dobashi (2011) identify over 7,000 dark clouds in the Galactic plane using a fixed extinction threshold.
Numerical simulations show that projection effects intrinsic to p-p and p-p-v space impact the study of cloud structures (e.g.Shetty et al. 2010;Ballesteros-Paredes & Mac Low 2002a).Comparing simulated p-p-p-and pp-v-derived clouds' overlap, Beaumont et al. (2013) find that studying clouds in p-p-v space (rather than in true physical 3D space) can induce approximately 40% scatter in their masses, sizes, and velocity dispersions.Moreover, Beaumont et al. (2013) demonstrate that many pp-v structures can be fictitious, especially in "crowded" regions.Thus, accurate estimates of cloud properties depend critically on studying clouds in position-positionposition space, which requires knowledge of clouds' distances.
In the past few years, distance estimates to molecular clouds have improved dramatically.Using so-called 3D dust mapping, Schlafly et al. (2014) produce one of the first uniform catalogs of accurate distances to nearby molecular clouds, with typical distance uncertainties of ≈ 10%.Specifically, Schlafly et al. (2014) use multiband photometry from Pan-STARRS1 (Chambers et al. 2019) to infer self-consistent distances and extinctions for a large number of stars across the solar neighborhood, the key ingredients necessary for constructing a 3D dust map (see also Green et al. 2015).The advent of the Gaia mission (Gaia Collaboration et al. 2016), and especially the results from its second and third data releases, Gaia DR2 and DR3 (Brown et al. 2018;Lindegren et al. 2021), has made it possible to construct evermore-accurate 3D-dust-based distances to clouds, owing to stellar parallax measurements for millions of stars in the solar vicinity.Zucker & Speagle et al. (2019) utilize the Gaia DR2 data release to produce an accurate catalog of distance estimates to molecular clouds, with uncertainties on the order of 5% − 6% (see also Zucker et al. 2020;Yan et al. 2019) Building on the accurate distances enabled in the Gaia era, there have only been two molecular cloud catalogs based on true three-dimensional "p-p-p" data obtained from 3D dust mapping, as presented in Chen et al. (2020) and Dharmawardena et al. (2023).Chen et al. (2020) obtain a catalog of 567 molecular clouds using the 3D dust map of Chen et al. (2018).However, the molecular clouds are typically resolved in distance on ≈ hundreds of parsec scales, so key cloud properties, including the sizes of clouds, are still derived using 2D projections.Dharmawardena et al. (2023) also derive a catalog of molecular cloud properties towards sixteen complexes within 1 − 2 kpc from the Sun using their 3D dust mapping algorithm DUSTRIBUTION, which leverages stellar distance and extinction estimates from Fouesneau et al. (2022).Applying the astrodendro package (Robitaille et al. 2019) to 3D dust cutouts around each complex, Dharmawardena et al. (2023) obtain estimates of e.g. the volume, mass, and density for each cloud and its myriad of substructure in "p-p-p" space (see also Dharmawardena et al. 2022).
However, one of the highest resolution 3D dust maps over appreciable volumes of the solar neighborhood is the Leike et al. (2020) map, which traces the structure of the local interstellar medium at ∼ 1 pc distance resolution.Leveraging distance and extinction estimates from the StarHorse catalog (Anders et al. 2019), Leike et al. (2020) utilize a combination of Gaussian Processes and Information Field Theory to produce a highly resolved 3D dust map that charts molecular clouds out to a distance of d ≈ 400 pc with distance uncertainties lower than 1%.Such accurate distance uncertainties enable the extraction and characterization of molecular clouds in true 3D p-p-p space.
In this work, we dendrogram the Leike et al. (2020) 3D dust map and uniformly analyze the properties of resolved molecular clouds derived in p-p-p space.We produce a catalog of 65 distinct local molecular clouds, including a dozen well-studied clouds in the literature, and compare our results to extant literature derived primarily from p-p-v and p-p space.In §2 we present the Leike et al. (2020) data used to create the catalog.In §3 we present the dendrogram technique applied to the data to derive the properties of our molecular clouds in real 3D space.We then describe how we project our data into 2D space following Zucker et al. (2021), in order to measure the 2D properties of clouds.In §4 we summarize our cloud property results and characterize Larson's mass-size relation in both 2D and 3D space.In §5 we hypothesize what could be driving differences in the 3D-and 2D-derived mass-size relations, and discuss our mass-size results in the context of existing literature, including previous exploration of the mass-size relation using analytic theory and mathematical modeling (c.f.Ballesteros-Paredes et al. 2012).Finally, we conclude in §6 2. DATA Leike et al. (2020) reconstruct the 3D dust distribution in a Heliocentric Galactic Cartesian reference frame out to a distance of ≈ 400 pc (−370 pc < xy < 370 pc, −270 pc < z < 270 pc).This distance range includes about a dozen well-studied star-forming regions, including Taurus, Perseus, and Orion.We convert from the native units of the Leike et al. (2020) map (optical depth in the Gaia G band per 1 pc) to volume density of hydrogen nuclei (n H ) following Zucker et al. (2021) and Bialy et al. (2021).We derive all results in this work using the total volume density of hydrogen nuclei, including contributions from both atomic and molecular hydrogen gas.
Generating 3D Dendrogram
After converting the 3D dust map of Leike et al. (2020) to total volume density of hydrogen nuclei, we segment the Leike et al. (2020) 3D dust map into a set of molecular cloud features and measure their properties using the dendrogram algorithm.To do so, we build upon the existing functionality for dendrogramming 3D p-p-v data in the astrodendro package.Abstractly, the dendrogram algorithm constructs a tree starting from the highest density point in N-dimensional density (volume density in this work) data, moving to the next largest value and connecting along isosurfaces of constant density.A leaf is defined to be a feature without any descendants.Each time a local maximum point is found (i.e. a leaf), the algorithm determines, based on neighboring maxima and the behavior of the contour levels between maxima, whether to join the pixel to an existing structure, or to create a new structure.Once a local minimum point between the two structures is found, it is classified as a branch that connects the two structures.Iterations of this procedure will eventually either merge all values into a single tree or create multiple trees.Moreover, once the data are contoured with levels, the algorithm searches through every contour level, starting from the top, and records how many local maxima are above each contour level.When the surface around two local maxima merge together, that density level is recorded as a branch.If more than two local maxima merge together between two successive contour levels, the algorithm will continue to search with better tuned contour levels such that every merger includes up to two leaves.The dendrogram algorithm depends on three user-defined parameters set in the astrodendro package, n min , ∆ n , and # voxels : 1. n min : the minimum absolute volume density threshold for a structure to be included as part of the dendrogram.
2. ∆ n : how significant a leaf must be in order to be considered an independent entity.The significance is measured from the difference between its peak density and the density value at which it is being merged into the tree.
3. # voxels : the minimum number of voxels needed for a leaf to be considered an independent entity.If a leaf is about to be joined onto a branch or another leaf, the algorithm checks the leaf's number of voxels.If the leaf's number of voxels is lower than # voxels , the algorithm combines it with the branch or leaf it is being merged with, so that it is no longer considered a separate entity.
The dendrogram is most sensitive to changes in n min , as this value determines the minimum volume density value required to classify local maxima as meaningful.Setting a high n min can lead to multiple isolated singleleaf trees, especially when dealing with 3D dust maps.
To determine what values to adopt for these parameters, we created a set of different combinations of values and compared the subsequent masses computed using these values to a benchmark sample of about a dozen wellstudied clouds in p-p space from Lada et al. (2010) and p-p-p space from Zucker et al. (2021).We tailored the parameters to reproduce similar results to the benchmarked cloud samples.After testing multiple values for the parameters, we ultimately settled on a fixed threshold of: n min = 25 cm −3 , ∆ n = 25 cm −3 , # voxels = 150 voxels.The result of this procedure is a hierarchy of cloud emission, where each structure in the dendrogram corresponds to a contiguous, resolved feature in 3D Heliocentric Galactic Cartesian xyz coordinates, bounded by a surface of constant volume density.In the next section, we filter the dendrogram to extract clouds and their properties.
Filtering 3D Features
After generating a hierarchy of cloud structure using the dendrogram approach, we need to convert the dendrogram tree into a meaningful set of molecular cloud features for analysis.In order to avoid both spurious features (with relatively low mass) and double counting of nested clouds (i.e.counting a branch and its leaves as separate structures), we introduce a filtering scheme.
Our filtering scheme is based on the adoption of a minimum cloud mass, M min , and cloud radius, r min , required for a feature to be included in the catalog.The mass is computed for all features as described in §3.1.2below.We define M min = 500 M ⊙ and r min = 2 pc.By using this definition, the algorithm only includes structures that correspond to trunks in the dendrogram that are above M min and r min .All other structures are removed to avoid counting nested clouds, which by definition are not trunks.
Given that most dendrograms computed from 3D dust maps are composed of an ensemble of single structure trees, retaining only the trunk feature means retaining the structures defined by isosurfaces near n min = 25 cm −3 .The filtered molecular cloud features extracted using this approach are highlighted and overlaid on the underlying Leike et al. (2020) 3D dust map in Figure 1.The implication of this filtering method is that we are removing most of the cloud hierarchy and limiting the extracted clouds to a narrow range in mean cloud density.In theory, we could achieve a similar catalog by thresholding the Leike et al. (2020) volume above a density of n min = 25 cm −3 .However, we choose to dendrogram both to utilize the existing functionality of the astrodendro package (Robitaille et al. 2019) and to enable further follow-up studies of the full hierarchy.
In Figure 2, we show the full dendrogram, and highlight the cloud features that survive filtering.The combined mass of the filtered out structures is 3.7 × 10 4 M ⊙ and are shown in black in Figure 2. The remaining, surviving clouds are color-coded by the mean density, with the clouds possessing mean densities between n average = 33 − 92 cm −3 .As we will discuss further in §5, the narrow range in density of extracted clouds will pre-ordain the mass-size results we obtain in §4 due to the large filling factor of low density gas near the chosen n min (see e.g.further discussion in Beaumont et al. 2012).
Finally, we also recognize that a relatively low volume density isosurface is defining the 3D cloud boundaries.However, it is not possible to define clouds using significantly higher volume density thresholds because the Leike et al. (2020) 3D dust map is not sensitive to the highest volume density regions within molecular clouds, due to the map's reliance on optical stellar photometry and astrometry from Gaia (Brown et al. 2018).Despite not being sensitive to very high volume densities, Zucker et al. (2021) show that the Leike et al. (2020) is still recovering cloud properties based on 2D integrated approaches, as determined for a benchmark sample of well- 1), with filtered out structures shown in black (totaling 3.7 × 10 4 M⊙).A constant isosurface density of nmin = 25 cm −3 (dashed horizontal line) is used to define cloud boundaries and will pre-ordain the narrow range of mean cloud volume densities (33 cm −3 ≤ naverage ≤ 92 cm −3 ) seen in our sample.
studied clouds.Thus, the low isosurface levels defining cloud boundaries should not have a significant effect on our mass results.
Measuring Cloud Properties in 3D
To calculate the properties of clouds in p-p-p space, we again build on existing infrastructure for computing cloud properties in p-p and p-p-v space using the astrodendro package (Robitaille et al. 2019).In order to calculate cloud properties, we take as input the dendrogrammed cloud structure, where each cloud structure consists of a set of contiguous volume density voxels bounded by a surface of constant volume density.We first calculate physical properties for all structures, and subsequently define the final cloud catalog through filtering as explained in §3.1.1.Our catalog includes the following properties for every cloud (see Table 1).
The total mass is the sum of the mass in each individual voxel dM i , computed by multiplying the volume density in the ith voxel (n i ) by the mean molecular weight of hydrogen (1.37 × m p , correcting for the helium abundance) and its volume (1 pc 3 ) 6. n peak (cm −3 ): maximum volume density within the cloud 7. A (pc 2 ): surface area of the cloud, calculated by assuming a spherical geometry with a radius of r and determining the cross-sectional area (πr 2 ) 8. Σ ( M⊙ pc 2 ): the mass surface density of the cloud, given as the cloud's mass divided by its surface area 9. n average (cm −3 ): average volume density of the cloud 3.2.2D Methods
Converting 3D Dust Data into 2D Extinction Maps
Once a catalog of cloud features is defined and characterized in 3D, we create a 2D projected map of each 3D cloud following the methodology of Zucker et al. (2021) (see their §3.3 for full details).Briefly, that work uses the yt package (Turk et al. 2011) to integrate 3D volume density cubes (containing the 3D cloud of interest) along the line of sight and produce 2D maps of the total hydrogen column density.For each cloud, we obtain a 3D volume density sub-region suitable for projection by extracting a cutout of the Leike et al. (2020) 3D dust map using the minimum and maximum extent of the cloud boundaries along x, y, and z.Once we obtain the projected 2D column density maps, we convert from total hydrogen column density to visual extinction in the K band using a relation from Lada et al. (2009) of N (HI)+2N (H2) A K = 1.67 × 10 22 cm −2 mag −1 to produce a map of K-band extinction, A K .Converting to A K allows us to compare to previous 2D cloud catalogs built on similar maps of integrated dust extinction from Lada et al. (2009).
To analyze the 2D maps, we extract clouds on the plane of the sky using the existing p-p dendramming functionality of the astrodendro package.In order to understand how 3D clouds map to 2D projected space we use Zucker et al. (2021) as a guide, who analyze the 3D cartesian space (x, y, z) and Galactic (l, b, d) coordinates of a sample of famous nearby clouds.Identifying the relevant plane of the sky features from the 3D projected famous cloud data, we then use Lada et al. (2009) as a benchmark to determine the optimal A Kmin , ∆ A K , and # pixels parameters (where A Kmin , ∆ A K , and # pixels are the 2D analogs of the n min , ∆ n , and # voxels 3D input parameters described in §3.1) for computing the dendrogram, with the goal of obtaining similar cloud sizes as derived in Lada et al. (2009).With the intention of also having a single 2D structure representing each 3D cloud feature, we settle on A Kmin = 0.05 mag, ∆ A K = 0.05 mag, and # pixels = 300 pixels as the dendrogram input parameters.
In Figure 3, we show an example of the 3D to 2D projection for a single feature in the catalog (the Perseus Molecular Cloud).We emphasize that due to the imperfect mapping from 3D to 2D space -stemming from the complex geometries of individual clouds (Zucker et al. 2021) -a few 3D features do not have a 2D counterpart, largely because they were sub-divided into multiple components and failed to produce a cloud feature with the same mass and/or size minima adopted for the 3D catalog.Our goal in this work is not to measure the most accurate 2D-based properties of molecular clouds.Rather, we seek to understand how defining features in 3D versus 2D projected space (given the same underlying 3D data) affects cloud properties in aggregate.
Nevertheless, for clouds that have a 2D counterpart meeting these criteria (61/65 clouds, or ≈ 94% of the 3D sample), the morphological matching between 3D and 2D cloud shapes is clear.We show and discuss the correspondence between 3D and 2D further in Appendix §B After creating the dendrogram based on the A K maps, we filter the features in our 2D catalog by implementing the same minimum mass threshold (M min = 500 M ⊙ ) and radius threshold (r min = 2 pc) as our 3D data.In 2D space we measure the following properties: 2016) and the distance of the cloud originally detected in 3D:
Calculating Properties for 2D Projected Structures
2 Retrieved from the 3D cloud structure before projecting.
6. r (pc): Radius calculated using the exact area of the structure in p-p space A π assuming a spherical geometry 7. Σ ( M⊙ pc 2 ): the mass surface density of the cloud, given as the cloud's mass divided by its surface area 4. RESULTS
Summary of 3D and 2D Cloud Properties
In Table 1, we present a summary of the properties of molecular clouds derived in 3D space following §3.1.2.A machine readable version of Table 1 and its associated astrodendro dendrogram file is available online at the Harvard Dataverse (DOI:10.7910/DVN/BFYDG8).The 3D catalog contains a total mass of 1.1 × 10 5 M ⊙ across the 65 cloud features identified in 3D volume density space, with an average cloud mass of M = 1.7 × 10 3 M ⊙ .The distance range of the clouds spans d = 116 − 440 pc.The typical average density of clouds in the 3D catalog is n average = 47 cm −3 , while the typical peak density is about an order of magnitude higher (n peak = 414 cm −3 ).We find an average cloud volume of V = 1220 pc 3 and an average equivalent radius assuming a spherical geometry of r = 6 pc, though we emphasize that some of the clouds show more complex, extended geometries.While every 3D cloud feature is assigned a unique identifier, the catalog includes a number of well-studied clouds in the literature, including Perseus, Taurus, Lupus, Chamaeleon, Cepheus, and the Orion complex (Orion A, Orion B, and λ Orion) which have been denoted as such in a separate column in Table 1 to aid comparison with existing studies.
In Table 2 we present the corresponding catalog of 2D cloud properties derived from the projected 3D data following §3.2.2.A machine readable version of Table 2 is likewise available online at the Harvard Dataverse (DOI:10.7910/DVN/BFYDG8).The 2D catalog contains a total mass of 2 × 10 5 M ⊙ across the 61 cloud features derived from the projection of the 3D cloud data.One of these 61 clouds, feature 7, is broken into two components, leading to a total of 62 clouds in Table 2.Moreover, in Table 2 we use the same cloud identifiers as Table 1, which specifies how each 2D cloud feature maps to its 3D counterpart.In the case a cloud in Table 1 has no corresponding cloud identifier in Table 2, the cloud was filtered for not meeting our minimum mass threshold of 500 M ⊙ .The typical radius of clouds in the 2D catalog is marginally larger than the 3D catalog, averaging r = 7 pc, and the average cloud mass is about a factor of two higher, at M = 3.2 × 10 3 M ⊙ .
Considering the ensemble of clouds, the total mass of the entire 2D-derived catalog is approximately ≈ 1.9× higher than the total mass of the 3D-derived catalog.The discrepancy suggests that projecting 3D gas density into 2D can alter the perceived shape of molecular clouds enough to bear significantly on their derived mass.This effect likely stems from the complications of projecting a non-spherical 3D cloud geometry onto the plane of the sky, resulting in a different cloud boundary definition.However, diffuse emission in the vicinity of the cloud also likely plays a major role.
As a testament to the impact of diffuse intervening gas, recall that we create 2D dust maps by projecting 3D dust cutouts which were extracted using a bounding box corresponding to the the minimum and maximum extents of the 3D cloud features in xyz space.Over the sample of 3D cutouts, we compute the ratio of the mass inside the 3D features to the mass outside the feature but within the bounding box used for 2D projections.We find that, over the full sample, there is 2× as much mass outside the 3D dendrogrammed features as within them.Thus, if even half of this excess mass in the vicinity of each cloud is incorporated into the 2D cloud definitions, this contamination would be enough to account for the discrepancy in total mass between the 3D-and 2D-derived catalogs that we observe.
Fitting the Mass-Size Relation
We use the masses and sizes in Table 1 and 2 to explore the mass-size relation, first proposed by Larson (1981).Larson (1981) conclude that the mass M contained within a cloud of radius r obeys a power-law of the form: Larson (1981) obtain the relation that M (r) = 460 M ⊙ × ( r pc ) 1.9 or more generally, that the mass of a cloud is proportional to its area, implying constant column density.This law of constant column density has come to be known as one of the fundamental properties of molecular cloud structure (McKee & Ostriker 2007).Recently, a similar relationship between the masses and lengths L of filaments (M ∝ L 2 ) has also been found (Hacar et al. 2022) and attributed to turbulent fragmentation.With the goal of testing whether the dimensionality used to define clouds affects our results, we fit the mass-size relation in both 3D and 2D space.Fitting the relation in log-log space, we use a linear-least-squares fitter to obtain a, b and their associated uncertainties.For the 3D results we obtain log M = 2.9 × log r(±0.1)+ 0.86(±0.3)such that: And for the 2D results, we obtain log M = 2.1 × log r(±0.2) + 1.59(±0.4),such that: Moreover, we have included in the Appendix (see §A) another version of the 2D catalog with a minimum extinction threshold when defining the dendrogram of A Kmin = 0.1 mag.This test yielded fewer features, as expected, but maintained a similar mass-size relation of M (r) = 83 M ⊙ × ( r pc ) 1.9 , confirming that the scaling of the mass-size relation does not depend on the threshold used to define cloud boundaries.We also repeat both fits using only the subset of the clouds which are wellstudied in the literature (e.g.Perseus, Taurus, Lupus, Chamaeleon, Cepheus, and the Orion complex), finding that the results agree with the full catalog fits within our reported uncertainties.
In Figure 4, we plot mass versus size for our 3D and 2D catalogs with the best-fits overlaid and four lines of constant volume density (n = 15, 30, 100, 300 cm −3 ), assuming purely spherical geometries.Figure 4 shows that the clouds in the 3D catalog lay between n = 30 cm −3 and n = 100 cm −3 lines of constant volume density, which we will argue in §5 is a consequence of our dendrogramming procedure and the narrow volume density range probed by the Leike et al. (2020) 3D dust map.6) Mass ( 7) Radius (8) Exact area (9) Surface mass density.A small fraction of the 3D clouds did not have a 2D counterpart that met our cloud definition, which accounts for the fact that there are 62 structures identified in 2D after projecting our 65 3D structures from Table 1 on to plane of the sky.
Note-A machine readable version of this table is available at https://doi.org/10.7910/DVN/BFYDG8.
Note-Projecting feature 7 from 3D into 2D with A K min = 0.05 mag yields two components, 70 and 71.
Note-A version of this table with a higher minimum threshold for cloud boundary definition, A K,min = 0.1 mag, is available in Appendix §A.* The Orion Clouds lie at the very edge of the Leike et al. (2020) 3D dust grid, thus adding more uncertainty to their derived properties and should be treated with caution.
DISCUSSION
Here we compare our results for the 3D and 2D masssize relation with extant results from the literature.We base our comparison on the work of Lada & Dame (2020), which analyzes both dust-based cloud catalogs and CO-based cloud catalogs to investigate the nature of the mass-size relation in the Milky Way.Specifically, we consider the original cloud sample of Larson (1981) We also include a comparison to Dharmawardena et al. (2023), which is the only other study to extract cloud properties in p-p-p space.For consistency, we compare to the Dharmawardena et al. (2023) primary trunks only catalog (see Table 2 in their work).
In Figure 5, we plot our mass-size results in context.Following Lada & Dame (2020) 2020) are all consistent with b = 2 (M ∼ r 2 ), implying constant surface (column) density across molecular clouds.While some of the clouds in these catalogs may have originally been identified using 3D position-position-velocity data (Rice et al. 2016;Miville-Deschênes et al. 2016) or even 3D position-positionposition data (Chen et al. 2020), the masses and/or sizes of these clouds have all been measured in 2D by projecting the 3D data on to the plane of the sky (Chen et al. 2020;Rice et al. 2016;Miville-Deschênes et al. 2016).
By measuring the masses and sizes of fully-resolved molecular clouds directly in 3D volume density space, we find a larger power law slope of approximately three, or b = 2.9.This discrepancy suggests that the power law slope is directly dependent on the number of dimensions used to measure mass and area, with the power law slope consistent with b = 2 when measuring cloud properties in column density space and b = 3 when measuring cloud properties in volume density space.We directly test this hypothesis by projecting the 3D volume density data into 2D, re-defining the cloud boundaries in column In 3D, M ∝ r 2.9 , while in 2D, M ∝ r 2.1 .We demarcate the 95% confidence interval with the thin semi-transparent band around each best-fit line.We include four lines of constant volume density (n = 15, 30, 100, 300 cm −3 ) in dashed semi-transparent black lines.The gray triangles represent the inaccessible volume and column densities, either due to the minimum volume and extinction thresholds required for inclusion in the 3D and 2D dendrograms (n < 25 cm −3 and AK < 0.05 mag) or the inability of the 3D dust map to probe higher densities due to the map's reliance on optical stellar photometry (n ≳ 100 cm −3 or AK ≳ 0.2 − 0.3 mag).density space and re-measuring their masses and areas.We find that despite stemming from the same underlying 3D dust data, the projected results are consistent with a shallower power law slope of b = 2.1.
While Dharmawardena et al. (2023) argue that their p-p-p-based mass-size results are consistent with Larson's b = 1.9 relationship, Figure 4 suggests that the Dharmawardena et al. (2023) results may be closer to b = 3, albeit with an order of magnitude higher cloud masses.We attribute the difference in 3D-derived cloud masses to the existence of more extended cloud substructure along the line of sight in Dharmawardena et al. (2023), which is not observed in Leike et al. (2020).This claim is supported by Figure 6, which shows that the Taurus molecular cloud -one of the sixteen cloud complexes in the Dharmawardena et al. (2023) samplespans distances of d = 93 − 342 pc, about a factor of five more extended than we find in this work (d = 127 − 170 pc; based on Leike et al. 2020).
The higher power law slope for the 3D catalogs observationally validates previous predictions for the scaling of the mass-size relation based on a combination of extant 2D observational results, numerical simulations, and analytic theory.2012) argument stems from the fact that for clouds with similar boundary definitions, the filling factor of dense structures is small while the filling factor of fluffier structures used to define the cloud boundaries is high, implying that mass should scale with the area in 2D and with volume in 3D (see also e.g.Ballesteros-Paredes & Mac Low 2002b;Ballesteros-Paredes et al. 2019).When clouds are defined as isocontours or isosurfaces above a particular threshold, the average column or volume density of the cloud is similar to the adopted threshold, because a large fraction of pixels or voxels in the cloud lie close to the threshold value.
As an observational counterpart to the investigations of Shetty et al. (2010) and Ballesteros-Paredes et al. (2012), Beaumont et al. (2012) examines the mass-size relationship in terms of the column density PDF and its possible variation within and between clouds.Leveraging 2D dust extinction maps from Lombardi et al. (2010), Beaumont et al. (2012) find that for structures defined with a constant extinction threshold, the mean of the column density PDF within each structure varies less than the region-to-region dispersion in area, naturally yielding M ∝ A ∝ r 2 In our work, the thresholds used to define cloud boundaries lie close to the minimum volume density (n min ) or extinction (A Kmin ) threshold required for a feature to be included in the dendrogram, and are roughly constant across the sample.As seen in Figure 4, on the lower mass end, the clouds all lie above the n = 25 cm −3 line of constant volume density and N = 8 × 10 20 cm −2 line of constant column density, which is pre-determined by the minimum volume density (n min = 25 cm −3 ) and extinction threshold (A Kmin = 0.05 mag) required for inclusion in the 3D and 2D catalogs, respectively.On the higher mass end, the clouds lie below n ≈ 100 cm −3 and N ≈ 4 × 10 21 cm −2 which is also pre-determined by the fact that the Leike et al. (2020) 3D dust map is not sensitive to the densest, most extinguished regions in molecular clouds (A K ≳ 0.3 mag) due to their reliance on optical photometry (see e.g.discussion in §4.4 of Zucker et al. 2021).Thus, following Ballesteros-Paredes et al. ( 2019), Beaumont et al. (2012), andShetty et al. (2010), mass should scale with area in 2D and volume in 3D given the narrow range of column and volume density probed, which we validate here for the first time using the same underlying observational data.
CONCLUSIONS
Using the Leike et al. (2020) 3D dust map with a distance resolution of 1 pc, we extend the dendrogram technique to position-position-position space to extract and measure the properties of clouds in 3D physical space, including their 3D positions, masses, sizes, and volume densities.To compare with extant results, we also create synthetic 2D dust extinction maps from the 3D dust distributions and derive similar properties for the same clouds defined on the plane of the sky.Given the masses and sizes of clouds obtained in 2D and 3D space, we fit the mass-size relation following Larson (1981).Consistent with predictions from extant observational studies and numerical simulations (see e.g.Beaumont et al. 2012;Ballesteros-Paredes et al. 2019), we find that our 2D projected mass-size relation, M ∝ r 2.1 , agrees with the original Larson (1981) results (M ∝ r 2 ), where mass scales according to the cloud's area.However, we obtain a steeper power-law slope for the 3D results, M ∝ r 2.9 , where the mass scales according to the cloud's volume.This difference in scaling is a natural consequence of the roughly constant thresholds used to define cloud boundaries, in combination with the fact that the PDF of column and volume density do not systematically scale Software: Astropy (Astropy Collaboration et al. 2013, 2018), glue (Beaumont et al. 2015), Unity 3D (Technologies 2015), Astrodendro (Robitaille et al. 2019) APPENDIX
A. DEPENDENCE OF 2D CATALOG PROPERTIES ON MINIMUM EXTINCTION THRESHOLD
To confirm that the 2D mass-size relation is robust to the choice of boundary definition we repeat the cloud extraction procedure described in §3.2.2 but using a higher minimum extinction threshold of A Kmin = 0.1 mag (in comparison to A Kmin = 0.05 mag whose results are described in §4).As expected, this higher-extinction-threshold version yields fewer features, as well as divided several of the clouds into multiple components 3 .Nevertheless, the catalog maintains a similar mass-size relation of log M = 1.9 × log r(±0.2) + 1.92(±0.4),such that M (r) = 83 M ⊙ × ( r pc ) 1.9 , confirming that the scaling of the mass-size relation does not depend on the threshold used to define cloud boundaries.
B. MORPHOLOGICAL MATCHING BETWEEN 3D PROJECTED AND 2D CLOUD FEATURES
After projecting the 3D data on to the plane of the sky to derive the 2D Cloud features, we compare the morphological agreement between each 3D projected feature and its corresponding 2D cloud counterpart.As seen in Figure 7 for a subset of the sample, we overall find good morphological agreement between the 3D and 2D clouds.The remainder of the morphological maps can be accessed at https://doi.org/10.7910/DVN/BFYDG8.3,4,9,12,15).The semi-transparent red on the 2D cloud panels denote 2D projected cloud components that are filtered out from the catalog, since they did not meet our minimum mass or radius requirements.
3D 2D Maps Comparison
Figure 1.3D spatial map of the local interstellar medium, showing all gas with density n > 5 cm −3 (gray) and clouds identified in this work (blue).The Sun is shown at center in yellow.An interactive version of this figure is available here.
Figure 2. Dendrogram of the Leike et al. (2020) 3D dust map.Structures that survive the cloud filtering scheme summarized in §3.1.1 are color-coded by their mean density (naverage in the context of Table1), with filtered out structures shown in black (totaling 3.7 × 10 4 M⊙).A constant isosurface density of nmin = 25 cm −3 (dashed horizontal line) is used to define cloud boundaries and will pre-ordain the narrow range of mean cloud volume densities (33 cm −3 ≤ naverage ≤ 92 cm −3 ) seen in our sample. 1 1. V (pc 3 ): Exact volume of the structure in p-p-p space 2. r (pc): Equivalent radius of the sphere occupying the same volume as the volume exact V 3. x, y, z (pc): Central x, y, and z position of the cloud in Heliocentric Galactic Cartesian coordinates 4. l ( • ), b ( • ), and d (pc).The cloud's Galactic coordinates (longitude, latitude, and distance), computed from the mean x, y, and z position of the cloud in Heliocentric Galactic Cartesian coordinates 1 We adapted and extended a version of the astrodendro package written by Dario Colombo and Ana-Duarte Cabral.The software is available here: https://github.com/dendrograms/astrodendro/pull/147/files 5. M (M ⊙ ): the mass of the cloud, calculated as follows:
Figure 3 .
Figure 3.Comparison between the 3D and projected 2D dust data for the Perseus Molecular Cloud.The feature corresponding to the Perseus Molecular Cloud in 3D volume density space is shown in blue.The 3D dust has been projected onto the plane of the sky and shown via an AK extinction map in the background, where the 2D feature corresponding to the Perseus Molecular Cloud is shown in red.
1. l ( • ): Central longitude of the cloud 2. b ( • ): Central latitude of the cloud 3. d (pc): The distance of the cloud 2 4. A (pc 2 ): Exact surface area of the structure in p-p space 5. M (M ⊙ ): Mass of the cloud, derived using the following mass surface density relation from Zari et al. ( , alongside more recent cloud catalogs re-analyzed in Lada & Dame (2020), including: the Rice et al. (2016) catalog based on a dendrogram decomposition of the Dame et al. (2001) 12 CO survey; the Miville-Deschênes et al. (2016) catalog based on a hierarchical clustering algorithm applied to Gaussian fits of the same Dame et al. (2001) 12 CO survey; and the Chen et al. (2020) catalog based on the 3D dust map of Chen et al. (2018).
Figure 4 .
Figure 4. Comparison of the mass-size relation derived from our 3D catalog (blue points) and 2D catalog (red points) of molecular cloud properties.In 3D, M ∝ r 2.9 , while in 2D, M ∝ r 2.1 .We demarcate the 95% confidence interval with the thin semi-transparent band around each best-fit line.We include four lines of constant volume density (n = 15, 30, 100, 300 cm −3 ) in dashed semi-transparent black lines.The gray triangles represent the inaccessible volume and column densities, either due to the minimum volume and extinction thresholds required for inclusion in the 3D and 2D dendrograms (n < 25 cm −3 and AK < 0.05 mag) or the inability of the 3D dust map to probe higher densities due to the map's reliance on optical stellar photometry (n ≳ 100 cm −3 or AK ≳ 0.2 − 0.3 mag).
For example, Shetty et al. (2010) measure masses and sizes of clouds in both volume and column density space based on hydrodynamical simulations, finding b = 3.03 ± 0.02 in 3D and b = 1.95 ± 0.03 in 2D.Likewise, Ballesteros-Paredes et al. (2012) argue that the mass-size relation depends on cloud boundary definition, with column density definitions yielding a power-law slope b = 2 and volume density definitions yielding b = 3.The Ballesteros-Paredes et al. (
Figure 6 .
Figure 6.A bird's eye comparison between the Taurus molecular cloud complex as analyzed in Dharmawardena et al. (2023) (orange) and in this work (blue), based on the 3D dust map from Leike et al. (2020).Both 3D dust cutouts have been integrated over the same range in z.Dharmawardena et al. (2023) find roughly an order of magnitude higher cloud masses across their sample of sixteen local clouds compared to this work, likely due to the presence of cloud substructure at farther distances along the line of sight, which is largely not detected in Leike et al. (2020).withstructure size.Future work connecting these highresolution 3D cloud results to complementary tracers of a cloud's CO kinematics should enable further constraints not only on Larson's other relations (see also e.g.Kainulainen et al. 2021, for insight into the Kennicutt-Schmidt relation) but also on the physical conditions of star formation within molecular clouds.
exploration, and interpretation of data presented in this work were made possible using the glue visualization software, supported under NSF grant numbers OAC-1739657 and CDS&E:AAG-1908419.AG and CZ acknowledge support by NASA ADAP grant 80NSSC21K0634 "Knitting Together the Milky Way: An Integrated Model of the Galaxy's Stars, Gas, and Dust."CZ acknowledges that support for this work was provided by NASA through the NASA Hubble Fellowship grant #HST-HF2-51498.001awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555.The authors acknowledge Thomas Dame and Andreas Burkert for helpful discussions that contributed to this work.We also thank Thavisha Dharmawardena for help with Figure 6.
Figure 7 .
Figure 7. Morphological matching between 3D projected and 2D cloud features for a subset of six clouds in the catalog (Clouds 0,3, 4, 9, 12, 15).The semi-transparent red on the 2D cloud panels denote 2D projected cloud components that are filtered out from the catalog, since they did not meet our minimum mass or radius requirements. | 10,141.6 | 2023-08-28T00:00:00.000 | [
"Environmental Science",
"Physics"
] |
A multi channel coupling based approach for the prediction of the channel capacity of MIMO-systems
When installing Multiple Input Multiple Output (MIMO)-systems, the antenna positioning has a major influence upon the achievable transmission quality. To determine those antenna positions, which maximize the transmission quality, in adequate time, a computer based prediction of the channel capacity is imperative. In this paper, we will show that Ray Tracing, which is a very popular prediction method and well suited for the prediction of transfer functions or power delay profiles, produces unacceptable errors when predicting the channel capacity of MIMO-systems. Furthermore we identify the source of the prediction errors and present a new algorithm, based on an approach known as Multi Channel Coupling (MCC), which avoids this error source. Finally a comparison of the prediction results of our algorithm with prediction results gained with an Image Ray Tracer as well as with measured results is used to show the formidable increasement of prediction accuracy which can be gained by using our algorithm.
Introduction
In Foschini and Gans (1998) it was shown, that MIMOsystems using spatial multiplexing increase the channel capacity to such an extent, that an immensely higher spectral efficiency becomes possible.
When installing such MIMO-systems the count of positions, where antennas can be placed, is usually higher than the number of antennas, which are to be placed.Being aware of the fact, that the antenna positioning has a big impact on the spatial multiplexing capabilities of the MIMO-system and thereby the achievable transmission quality, a lot of effort Correspondence to: F. Hagebölling<EMAIL_ADDRESS>has already been taken to find antenna positionings which maximize transmission quality.
A lot publications concentrate on measuring channel capacities for different positionings in certain scenarios, Tang and Mohan (2005) and Fügen et al. (2002) shall be mentioned exemplarily.But measuring based approaches are always limited by the fact, that the number of possible MIMOsystems increases very fast with the number of possible antenna positions.
To be able to compare several thousand or more possible systems, computer based simulation is needed.In Talbi (2001) and Ziri-Castro et al. (2005) and a lot of other publications the received power was predicted and compared with measurements.
Though the results presented in those publications accord very well with measurements, the received power is, in our opinion, not a sufficient quantity to judge the transmission quality of MIMO-systems, because it doesn't contain any information about the linear independence of the Multiple Input Single Output (MISO)-systems contained in each MIMO-system.The latter is important, because in a spatial multiplexing MIMO-system the received signals can only be decoded properly, if the MISO-systems are linearly independent.
Though the channel capacity contains this important information only a comparatively small amount of publications deals with the prediction of this quantity.And most of the publications, which do so, don't present measurements as comparison for the prediction results.Elnaggar et al. (2004) may be named as example.
In the following we will briefly summarize some fundamentals in Sect.2, compare results of a ray tracing based prediction algorithm with measurements and point out the disadvantages of this approach in Sect.3, present our new algorithm in Sect. 4 and verify the better performace of our algorithm with more measurements in Sect. 5. A summary and conclusion marks can be found in Sect.6.
Published by Copernicus Publications on behalf of the URSI Landesausschuss in der Bundesrepublik Deutschland e.V.
gle Output (SISO) impulse response between every transmit antenna m and every receive antenna n (see Fig. 1).Assuming the same order L for each of these impulse re- T the frequency selective MIMO channel can be described by L + 1 complex channel matrices H(k) with k = 0,...,L: (1)
Channel Capacity
Assuming that no power allocation strategy is used, the transmitted power P T is uniformly distributed over the bandwidth B and the Channel Capacity of a frequency selective MIMO system can be written as (Palomar et al., 2000) with S nn (f ) being the power spectral density matrix of the noise, m = min(n T ,n R ) and Discretizing this equation, assuming additive white noise and normalizing channel energy according to (Bauch and Al-Dhahir, 2002) leads to the formula ity of different MIMO systems.To maintain the differences and to enable a comparison of N M MIMO systems the condition has to be relaxed to be (Hagebölling et al., 2006)
IMAGE RAY TRACING
In (Hagebölling et al., 2006) we presented a prediction algorithm based on the very popular method of Image Ray Tracing (IRT).The algorithm determines all possible paths between each pair of transmit and receive antennas in a given scenario and with a given number of maximal reflections per path.It then identifies the points, where rays following these paths interact with the surrounding and calculates the impact of these interactions upon the electromagnetic field.We showed that the prediction of the channel capacity using this algorithm is in general very accurate but produces certain discrepancies for some scenarios.
Figure 2 shows some actual predictions of this algorithm for 27 indoor scenarios.The measurement of the channel capacity of this scenarios has been done using our laboritory MIMO system presented in (Weikert and Zölzer, 2005).In all scenarios there are n T = 4 transmit antennas and n R = 4 receive antennas, the carrier frequency is 2.49 GHz and the SNR amounts 30dB.Especially for the systems In order to find the reason for the erroneous prediction of this scenarios, we prospected the propagation paths, which were used during the Ray Tracing process and those which were not used due to a too high number of reflections.It turned out that in all of this scenarios there are paths with a very low damping but with a very high number of reflections, mostly
Channel description
The MIMO Channel with n T transmit antennas and n R receive antennas consists of one complex Single Input Single Output (SISO) impulse response between every transmit antenna m and every receive antenna n (see Fig. 1).
Assuming the same order L for each of these impulse responses h n,m = h n,m (0) h n,m (1) ... h n,m (L n,m ) T the frequency selective MIMO channel can be described by L + 1 complex channel matrices H(k) with k = 0,...,L: (1)
Channel capacity
Assuming that no power allocation strategy is used, the transmitted power P T is uniformly distributed over the bandwidth B and the Channel Capacity of a frequency selective MIMO system can be written as (Palomar et al., 2000) with S nn (f ) being the power spectral density matrix of the noise, m = min(n T ,n R ) and Discretizing this equation, assuming additive white noise and normalizing channel energy according to Bauch and Al-Dhahir ( 2002) leads to the formula with N F being the number of discrete frequencies and ρ being the mean Signal to Noise Ratio (SNR).
Channel Capacity
Assuming that no power allocation strategy is used, the transmitted power P T is uniformly distributed over the bandwidth B and the Channel Capacity of a frequency selective MIMO system can be written as (Palomar et al., 2000) with S nn (f ) being the power spectral density matrix of the noise, m = min(n T ,n R ) and Discretizing this equation, assuming additive white noise and normalizing channel energy according to (Bauch and Al-Dhahir, 2002) leads to the formula boritory MIMO system presented in (Weikert and Zölzer, 2005).In all scenarios there are n T = 4 transmit antennas and n R = 4 receive antennas, the carrier frequency is 2.49 GHz and the SNR amounts 30dB.Especially for the systems In order to find the reason for the erroneous prediction of this scenarios, we prospected the propagation paths, which were used during the Ray Tracing process and those which were not used due to a too high number of reflections.It turned out that in all of this scenarios there are paths with a very low damping but with a very high number of reflections, mostly The normalization according to Eq. ( 4) is needed to replace the term P T /(n T •B) S nn (f ) by ρ, but it abolishes differences in the path loss of the SISO-channels and reduces the comparability of different MIMO systems.To maintain the differences and to enable a comparison of N M MIMO systems the condition has to be relaxed to be (Hagebölling et al., 2006)
Image Ray Tracing
In Hagebölling et al. (2006) we presented a prediction algorithm based on the very popular method of Image Ray Tracing (IRT).The algorithm determines all possible paths between each pair of transmit and receive antennas in a given scenario and with a given number of maximal reflections per path.It then identifies the points, where rays following these paths interact with the surrounding and calculates the impact of these interactions upon the electromagnetic field.We showed that the prediction of the channel capacity using this algorithm is in general very accurate but produces certain discrepancies for some scenarios.
Figure 2 shows some actual predictions of this algorithm for 27 indoor scenarios.The measurement of the channel capacity of this scenarios has been done using our laboritory MIMO system presented in Weikert and Zölzer (2005).In all scenarios there are n T = 4 transmit antennas and n R = 4 receive antennas, the carrier frequency is 2.49 GHz and the SNR amounts 30 dB.
Especially for the systems number 4, 5, 13, 14 and 15 the prediction error is very high.
In order to find the reason for the erroneous prediction of this scenarios, we prospected the propagation paths, which were used during the Ray Tracing process and those which were not used due to a too high number of reflections.It turned out that in all of this scenarios there are paths with a very low damping but with a very high number of reflections, mostly at metallic materials.
Due to their low damping those paths imperatively have to be considered when calculating the impulse response, but because of their high number of reflections they were not considered by the algorithm.This error source is inherent for ray tracing based algorithms and can only be bated by increasing the maximum number of reflections per path.
However this measure does not solve the problem generally and is very expensive in terms of computation time and needed memory, because the complexity of Ray Tracing is of the order w R for w walls and a maximal number of reflections per path R.
Multi Channel Coupling
Multi Channel Coupling (MCC) is a prediction algorithm, which takes an infinite number of interactions per path into account.It thereby avoids the mentioned error source, which is inherent for Ray Tracing based algorithms.MCC was first presented as algorithm to predict the transmission of power in 2-D-scenarios in Liebendorfer and Dersch (1997).This algorithm is based upon the following considerations: -For every pair of walls there are two channels, one in each direction.
-Transmit antennas couple a certain percentage of their transmitted power into each channel.
-Each channel couples a certain percentage of the present power into each other channel.
-Each channel couples a certain percentage of the present power into each receive antenna.
Each coupling of transmit antennas into channels includes one reflection at or transmission through the start wall of the channel and each coupling from a channel into another channel is a reflection or transmission.Every coupling is described by a coupling factor between 0 and 1 and the coupling factors are organized in matrices: a (n C × n T ) matrix T for the coupling factors of the n T transmit antennas into the n C channels, a (n C × n C ) matrix C for the coupling factors of channels into each other and a (n R × n C ) matrix R for the coupling factors of the channels into the n R receive antennas.Assuming no direct component and considering an infinite number of couplings from channels into channels, i.e. an infinite count of reflections and transmissions, the power transfer matrix from the transmit antennas to the receive antennas can then be calulated by the equation Thus MCC considers an infinite number of reflections and transmissions with the computation time being finite.Moreover the most computation time is needed for the calculation -For every pair of walls there are two channels, one in each direction.
-Transmit antennas couple a certain percentage of their transmitted power into each channel.
-Each channel couples a certain percentage of the present power into each other channel.
-Each channel couples a certain percentage of the present power into each receive antenna.
Each coupling of transmit antennas into channels includes one reflection at or transmission through the start wall of the channel and each coupling from a channel into another channel is a reflection or transmission.Every coupling is described by a coupling factor between 0 and 1 and the coupling factors are organized in matrices: a (n C × n T ) matrix T for the coupling factors of the n T transmit antennas into the n C channels, a (n C ×n C ) matrix C for the coupling factors of channels into each other and a (n R × n C ) matrix R for the coupling factors of the channels into the n R receive antennas.
Assuming no direct component and considering an infinite number of couplings from channels into channels, i.e. an infinite count of reflections and transmissions, the power transfer matrix from the transmit antennas to the receive antennas can then be calulated by the equation 4.1 THE ELEMENTS OF THE MATRIX T(f ) The element T ij describes, how an impulse at the transmit antenna j is coupled into channel i.To calculate T ij , the end Fig. 3. Comparison of MCC and IRT wall of channel i is discretized.Then for each ray p from the transmit antenna T j through one of the discrete wallelements with the area A c it is calculated, how the amplitude and the phase of an impulse transmitted by the antenna is altered by the coupling.Only rays, which intersect with the start wall of the channel and are not disturbed by other walls can contribute to the coupling factor.The impact on the amplitude is represented by τ p and calculated using the portion of the solid angle, under which the wallelement is seen from the position of the transmit antenna, the antenna gain G j and the absolute directional characteristic |C j,p | of the antenna at path p and of the matrix (I − C) −1 , which only depends on the location and the material parameters of walls in the surrounding.Thus MCC is very effective, when calculating the same scenario several times with different antenna positions.
It was already shown, that the MCC method can also be used to predict other values than power.In Karthaus (2001) it was used to predict power delay profiles in 3-D-scenarios.
To be able to predict the channel capacity of frequency selective MIMO systems with and without line of sight using the MCC method, we write Eq. ( 7) as with f being the frequency, H(f ) being the complex transfer function in the frequency domain and the (n R × n T ) matrix D(f ) containing the coupling factors of the direct paths between each pair of transmit and receive antennas.
In the following we will present our formulas for the prediction of the channel capacity with Eq. 8.
The elements of the matrix T(f )
The element T ij describes, how an impulse at the transmit antenna j is coupled into channel i.
To calculate T ij , the end wall of channel i is discretized.Then for each ray p from the transmit antenna T j through one of the discrete wallelements with the area A c it is calculated, how the amplitude and the phase of an impulse transmitted by the antenna is altered by the coupling.
Only rays, which intersect with the start wall of the channel and are not disturbed by other walls can contribute to the coupling factor.The impact on the amplitude is represented by τ p and calculated using the portion of the solid angle, under which the wallelement is seen from the position of the transmit antenna, the antenna gain G j and the absolute directional characteristic C j,p of the antenna at path p and the transmission / reflection coefficient r p (f ) at the start wall of the channel.The superposition of all rays yields the absolute value of the coupling coefficient.
The impact on the phase is the sum of the phase of the transmission / reflection coefficient r p (f ) and the phase shift The element C ij describes the coupling from channel j into channel i and is the expectation value of the ratio between the transfer function in channel i and that one in channel j.
For the calculation, the start and the end wall of channel j are discretized.Of all rays p α from a discrete wall element of the start wall a of channel j through a discrete wall element α of the end wall b of channel j, only those, which hit the end wall of channel i and are not disturbed by other walls, contribute to the coupling.Again the absolute value of the coupling factor is obtained by the superposition of all contributing rays and its phase is the average of the weighted phases of the rays.
The wall element at wall a has the area A a and is thought solid angle, under which the wallelement of wall c is seen from the position x a and the transmission / reflection coefficient r p (f ) at wall b are used to calculate the coupling factor:
THE ELEMENTS OF THE MATRIX R(f )
The element R ij describes how the signal is coupled from channel j into the receive antenna i.The coupling factor is unequal to zero for all non disturbed rays P α from a discrete wall element of the start wall a of channel j through the position of the receive antenna and a discrete wall element α of the end wall b of channel j.Every ray is thought of as representing a subchannel of channel j, having the cross section area A a at wall a, A R at the receive antenna and A b at wall b.The discrete wall element at wall a is again thought of as full radiator.The coupling factor is further determined by the portion of the solid angle, under which the wallelement of wall b is seen from the position x a and the ratio between the cross section area A R and the aperture of receive antenna , where G i ist the antenna gain and C i,p is the directional characteristic of antenna i at path p. ϕ 0 caused by the free space propagation from the antenna to the wallelement.The phase of each ray p is weighted with the according value τ p and the mean value of all weighted phases is the phase of the coupling coefficient: 1 if ray from T j through A c and b is not interrupted 0 else (10)
The elements of the matrix C(f )
The element C ij describes the coupling from channel j into channel i and is the expectation value of the ratio between the transfer function in channel i and that one in channel j .
For the calculation, the start and the end wall of channel j are discretized.Of all rays p α from a discrete wall element of the start wall a of channel j through a discrete wall element α of the end wall b of channel j , only those, which hit the end wall of channel i and are not disturbed by other walls, contribute to the coupling.Again the absolute value of the coupling factor is obtained by the superposition of all contributing rays and its phase is the average of the weighted phases of the rays.
The wall element at wall a has the area A a and is thought of as full radiator, which transmits in every direction proportional to A a cos(ϑ a ).The remaining, the coupling coeficcient defining quantities are the portion of the solid angle, under which the wallelement of wall b is seen from the position x a and the transmission / reflection coefficient r p (f ) at wall b.For the calculation of all transmission or reflexion coefficients the wave matrix method (Layer, 2001) is used, which allows the definition of walls with layers of different materials.
If the points x b and x a are equal, which is possible, if the walls a and b do intersect each other, only the portion of the solid angle, under which the wallelement of wall c is seen from the position x a and the number N c of rays starting at x a , which hit wall c are used to calculate the coupling factor.χ p then is χ p = 1 and
The elements of the matrix R(f )
The element R ij describes how the signal is coupled from channel j into the receive antenna i.The coupling factor is unequal to zero for all non disturbed rays P α from a discrete wall element of the start wall a of channel j through the position of the receive antenna and a discrete wall element α of the end wall b of channel j .Every ray is thought of as representing a subchannel of channel j , having the cross section area A a at wall a, A R at the receive antenna and A b at wall b.The discrete wall element at wall a is again thought of as full radiator.The coupling factor is further determined by the portion of the solid angle, under which the wallelement of wall b is seen from the position x a and the ratio between the cross section area A R and the aperture of receive antenna , where G i ist the antenna gain and C i,p is the directional characteristic of antenna i at path p.
Using the intercept theorem one can show that and that leads to a formula for R i j which needs only one summation over all rays r from the discrete wall elements of wall a to the receive antenna: with and ρ, ∆ 1 and ∆ 2 remaining the same as in Eq. ( 15).
THE ELEMENTS OF THE MATRIX D(f )
The element D ij describes the free space distribution between transmit antenna j and receive antenna i.It is calculated as with r being the distance between the antennas r 0 = λ(4π) −1 .If the first fresnel zone is not free of obstacles, D ij is proportional to r −2 instead of r −1 , which is known as double regression model.
APPRAISAL OF PREDICTION RESULTS
Figure 6 shows the results of the prediction of the 27 scenarios mentioned in Sect. 3 using the new algorithm.For comparison with the results of the Ray Tracing based algorithm and the measurements, this data is also shown in the figure .One can see, that the prediction using MCC does not produce the same big errors as that using IRT.By avoiding the errors, which are inherent to measures, which can only handle a finite count of interactions, Multi Channel Coupling outperforms Image Ray Tracing in terms of the root mean square error (RMSE).While the RMSE of the Ray Tracing based prediction amounts up to 10.8 bits Hz•s , MCC has a RMSE of only 3.8 bits Hz•s , which is approximately a third of the first one.To further support the thesis above, Fig. 5 shows the absolute deviations of MCC and IRT from measurements for 108 indoor scenarios, 54 with line of sight (LOS) and 54 without one.In a scenario with a line of sight, usually the LOS is the path, where the most power is transfered to the receiver.Concomitantly, the LOS is always taken into recognition while the Ray Tracing based prediction, because the number of reflections on that path is zero.Because of that and as the Ray Tracing based approach fails only when paths with a lot of interactions transfer a big part of the received power, one would expect the Ray Tracing based approach, to perform as good as MCC when the predicted scenario contains a line of sight.The results of the 54 systems with LOS confirm this expectation and that of the 54 systems without LOS show again, that MCC avoids the big errors, which cannot be avoided using Ray Tracing.
Using the intercept theorem one can show that and that leads to a formula for R i j which needs only one summation over all rays r from the discrete wall elements of wall a to the receive antenna: with and ρ, 1 and 2 remaining the same as in Eq. ( 15).
The elements of the matrix D(f )
The element D ij describes the free space distribution between transmit antenna j and receive antenna i.It is calculated as Using the intercept theorem one can show that and that leads to a formula for R i j which needs only one summation over all rays r from the discrete wall elements of wall a to the receive antenna: and ρ, ∆ 1 and ∆ 2 remaining the same as in Eq. ( 15).
THE ELEMENTS OF THE MATRIX D(f )
The element D ij describes the free space distribution between transmit antenna j and receive antenna i.It is calculated as comparison with the results of the Ray Tracing based algorithm and the measurements, this data is also shown in the figure .One can see, that the prediction using MCC does not produce the same big errors as that using IRT.By avoiding the errors, which are inherent to measures, which can only handle a finite count of interactions, Multi Channel Coupling outperforms Image Ray Tracing in terms of the root mean square error (RMSE).While the RMSE of the Ray Tracing based prediction amounts up to 10.8 bits Hz•s , MCC has a RMSE of only 3.8 bits Hz•s , which is approximately a third of the first one.To further support the thesis above, Fig. 5 shows the absolute deviations of MCC and IRT from measurements for 108 indoor scenarios, 54 with line of sight (LOS) and 54 without one.In a scenario with a line of sight, usually the LOS is the path, where the most power is transfered to the receiver.Concomitantly, the LOS is always taken into recognition while the Ray Tracing based prediction, because the number of reflections on that path is zero.Because of that and as the Ray Tracing based approach fails only when paths with a lot of interactions transfer a big part of the received power, one would expect the Ray Tracing based approach, to perform as good as MCC when the predicted scenario contains a line of sight.The results of the 54 systems with LOS confirm this expectation and that of the 54 systems without LOS show again, that MCC avoids the big errors, which cannot be avoided using Ray Tracing.with r being the distance between the antennas and r 0 = λ(4π ) −1 .If the first fresnel zone is not free of obstacles, D ij is proportional to r −2 instead of r −1 , which is known as double regression model.
Appraisal of prediction results
Figure 6 shows the results of the prediction of the 27 scenarios mentioned in Sect. 3 using the new algorithm.For comparison with the results of the Ray Tracing based algorithm and the measurements, this data is also shown in the figure.One can see, that the prediction using MCC does not produce the same big errors as that using IRT.
By avoiding the errors, which are inherent to measures, which can only handle a finite count of interactions, Multi Channel Coupling outperforms Image Ray Tracing in terms of the root mean square error (RMSE).While the RMSE of the Ray Tracing based prediction amounts up to 10.8 bits (Hz s) −1 , MCC has a RMSE of only 3.8 bits (Hz s) −1 , which is approximately a third of the first one.To further support the thesis above, Fig. 5 shows the absolute deviations of MCC and IRT from measurements for 108 indoor scenarios, 54 with line of sight (LOS) and 54 without one.In a scenario with a line of sight, usually the LOS is the path, where the most power is transfered to the receiver.Concomitantly, the LOS is always taken into recognition while the Ray Tracing based prediction, because the number of reflections on that path is zero.
Because of that and as the Ray Tracing based approach fails only when paths with a lot of interactions transfer a big part of the received power, one would expect the Ray Tracing based approach, to perform as good as MCC when the predicted scenario contains a line of sight.The results of the 54 systems with LOS confirm this expectation and that of the 54 systems without LOS show again, that MCC avoids the big errors, which cannot be avoided using Ray Tracing.We explained, why in our opinion only the channel capacity is an adequate quantity to judge the transmission quality of MIMO systems and showed, that Ray Tracing under certain circumstances produces big prediction errors when predicting the channel capacity of scenarios without a line of sight.Those errors can not be excluded in general as long as one uses Ray Tracing as prediction measure.We then presented a new algorithm based upon the concept of Multi Channel Coupling, which accounts for an infinite number of interactions of the rays with the surrounding and thereby avoids the identified error source.The new algorithm was validated against a Ray Tracing based algorithm and against measurements.For scenarios with line of sight, the prediction results using our approach were as good as with Image Ray Tracing, for scenarios without a line of sight, our approach outperformed the Ray Tracing based algorithm remarkably.
Conclusions
We explained, why in our opinion only the channel capacity is an adequate quantity to judge the transmission quality of MIMO systems and showed, that Ray Tracing under certain circumstances produces big prediction errors when predicting the channel capacity of scenarios without a line of sight.Those errors can not be excluded in general as long as one uses Ray Tracing as prediction measure.
We then presented a new algorithm based upon the concept of Multi Channel Coupling, which accounts for an infinite number of interactions of the rays with the surrounding and thereby avoids the identified error source.The new algorithm was validated against a Ray Tracing based algorithm and against measurements.
For scenarios with line of sight, the prediction results using our approach were as good as with Image Ray Tracing, for scenarios without a line of sight, our approach outperformed the Ray Tracing based algorithm remarkably.
Fig. 3 .
Fig. 3.Coupling from antenna j into channel i; green rays contribute to the coupling factor.
Fig. 4 .
Fig. 4. Coupling from channel j into channel i; green contribute to the coupling factor.
Fig. 5 .
Fig. 5. Coupling from channel j into antenna i; green rays contribute to the coupling factor. | 7,301 | 2011-07-29T00:00:00.000 | [
"Computer Science"
] |
Patient Engagement With a Game-Based Digital Therapeutic for the Treatment of Opioid Use Disorder: Protocol for a Randomized Controlled Open-Label, Decentralized Trial
Background: Prescription digital therapeutics are software-based disease treatments that are regulated by the US Food and Drug Administration; the reSET-O prescription digital therapeutic was authorized in 2018 and delivers behavioral treatment for individuals receiving buprenorphine for opioid use disorder. Although reSET-O improves outcomes for individuals with opioid use disorder, most of the therapeutic content is delivered as narrative text. PEAR-008 is an investigational device based on reSET-O that uses an interactive, game-based platform to deliver similar therapeutic content designed to enhance patient engagement, which may further improve treatment outcomes. Objective: We aim to investigate how participants interact with the prescription digital therapeutic’s new content delivery format. Secondary objectives include evaluating treatment success, symptoms of co-occurring mental health disorders, recovery capital, and skill development. Methods: Due to the COVID-19 pandemic, this study was redesigned using a decentralized model because it was not possible to conduct medication initiation and study visits in person, as initially intended. A decentralized, randomized controlled trial design will be utilized to compare patient engagement with PEAR-008 and that with reSET-O using both subjective and objective assessments. The study population will consist of approximately 130 individuals with opioid use disorder (based on Diagnostic and Statistical Manual of Mental Disorders 5 criteria
Background and Rationale
The United States is in the midst of an opioid overdose epidemic [1,2]. Underlying opioid use disorder is a key driver of this epidemic, and approximately 1.6 million people in the United States met criteria for opioid use disorder in 2019 [3]. Opioid use disorder is a chronic disease with a range of physical, psychological, and personal consequences, including high mortality. Opioids are particularly hazardous due to the rising prevalence of potent illicit opioids (predominantly fentanyl) with high risk of lethality [4]. During the COVID-19 pandemic, overdose deaths surged to an all-time high of 92,183 in the United States, driven primarily by synthetic opioids [1]. Maximizing the impact of effective therapies that are easily accessible during the pandemic and beyond is critical to helping individuals with opioid use disorder receive optimal and necessary care.
Pharmacologic treatments, such as US Food and Drug Administration (FDA)-approved medications (for example, buprenorphine, naltrexone, and methadone), are the first line of treatment for opioid use disorder, in conjunction with evidence-based behavioral therapies, but the majority of individuals in need of treatment (80% to 90% [2,5,6]) for substance use disorders do not receive care. There are a variety of contributing factors, including refusal to seek treatment, high cost of care, stigma associated with care, homogeneity of treatments offered, and lack of or limited access to treatment [7,8]. For individuals with opioid use disorder who do seek treatment, there is significant variability in quality and utilization of evidence-based therapies across providers [9,10]. Significant training, time, and clinical oversight are required to ensure proper face-to face delivery of behavioral therapy [11]. Digitizing and offering evidence-based therapies on mobile devices can standardize care, ease the burden on clinical staff, and expand access to behavioral treatment.
Prescription digital therapeutics are software-based treatments that have been evaluated for safety and effectiveness in randomized clinical trials and authorized by the FDA. Prescription digital therapeutics have the potential to safely expand access to evidence-based interventions because they are delivered on mobile devices and are prescribed and initiated by treatment providers.
Two prescription digital therapeutics are currently available-reSET and reSET-O-to deliver digitized behavioral therapy for substance use disorder and opioid use disorder, respectively [12,13]. Both prescription digital therapeutics deliver therapy modeled on the community reinforcement approach, which is an evidence-based treatment that promotes behavioral change [14]. Although studies indicate prescription digital therapeutics hold promise in treating substance use disorder and opioid use disorder [15][16][17][18][19][20], the current content delivery method used by these prescription digital therapeutics is largely didactic, with the majority of content delivered as narrative text. PEAR-008 is an investigational device that delivers therapeutic content similar to reSET-O via an interactive game-like environment designed to maximize patient engagement and satisfaction-factors that are critical in retaining patients in opioid use disorder treatment [21][22][23][24][25][26]. We hypothesize that the use of a more interactive and engaging platform to deliver similar therapeutic content will enhance patient engagement with a digital therapeutic.
Overview
We will compare reSET-O to PEAR-008 and evaluate objective differences in participant engagement with each digital therapeutic. Secondary outcomes include subjective differences in engagement, opioid use disorder treatment outcomes (ie, retention in treatment and abstinence from opioids), symptoms of common comorbid mental health conditions, including anxiety and depression, recovery supports (eg, recovery capital and resilience), and participant satisfaction with their assigned digital therapeutic. Exploratory aims include evaluating development of cognitive behavioral therapy skills and buprenorphine adherence.
Study Design
This is a 2-arm, randomized controlled, open-label, outpatient-based study to be conducted virtually by 2 recruitment sites: the New York State Psychiatric Institute's Substance Treatment and Research Services (STARS) program at Columbia University Irving Medical Center and the Addiction Research and Education Foundation (AREF). Study participants will be recruited from outpatient addiction specialty treatment programs and individual providers in the United States.
Study Population and Sample Size
The trial will include 130 adults aged 18 to 60 years with opioid use disorder who are already receiving buprenorphine treatment, with no criteria regarding gender identity, race, or ethnicity.
Inclusion criteria are having the ability to provide informed consent, age 18 to 60 years, having adequate English proficiency, being within the first 120 days of starting buprenorphine, receiving buprenorphine pharmacotherapy under the care of a licensed health care provider and being willing to provide the name of the provider or practice, being capable of using common software apps on a smartphone, and having access to an internet-enabled smartphone that meets minimal operating system requirements for the duration of the study. Exclusion criteria are having a history of reSET-O use, having participated in user-testing of PEAR-008 or any investigational drug trials within 30 days of trial enrollment, or currently receiving methadone or naltrexone pharmacotherapy.
The sample size and power were based on the primary engagement outcome, determined by frequency of interaction with the intervention, percentage of module completion, and approval ratings. A sample size of 130, α=.05, and power=0.80 will allow for detection of a moderate effect size (d=0.50).
Study Settings and Recruitment Procedures
All study sessions will be conducted virtually by study staff at 2 participating organizations: New York State Psychiatric Institute's STARS and AREF.
Since its establishment in 1997, the STARS clinic of Columbia University has served as the center for clinical trial operations within the Division on Substance Use Disorders. Recruitment will be directed to individuals who live in New York, New Jersey, and Pennsylvania. Participants may be recruited via flyers in office spaces or intake packets (as allowed; flyers will be disseminated electronically to providers and opioid treatment programs) or via word of mouth by providers. In addition, potential participants may be referred to this study after screening procedures conducted in concurrent research studies taking place at STARS (eg, if they are ineligible for concurrent studies, they may be referred to this study for screening).
AREF is a research foundation that conducts and disseminates research related to addiction medicine to advance the science surrounding the treatment of individuals with a substance use disorder. AREF conducts research activities with patients recruited from a multistate network offering guideline-driven outpatient treatment with buprenorphine for individuals with opioid use disorder in a group practice setting. When possible, flyers will be posted in the waiting room at treatment locations (where patients are being seen face-to-face, which is dependent on local regulations related to COVID-19). Flyers will be included in patient packets that are emailed or distributed to new patients. Additional participants may also be recruited via online advertisements (eg, Craigslist).
Participant flyers will provide the URL for the study website as well as a QR code to access the website. On the study website individuals will find information about the study and a form to express interest in participating in the study. Data entered on the website are sent to an encrypted database housed by Formstack, a Health insurance Portability and Profitability Act-compliant platform and to the sites via PGP-encrypted emails.
Randomization and Blinding
Following informed consent, the baseline assessment and confirmation of eligibility, participants will be randomly assigned to 1 of 2 treatment groups: reSET-O or PEAR-008. Randomization lists will be prepared by the study sponsor (Pear Therapeutics) prior to the start of the study. Randomization will be 1:1 and stratified by site and gender with a block size of 10. An electronic list of IDs, access codes, and credentials will be securely provided to the sites. There will be no blinding; this is an open-label study.
reSET-O
reSET-O is a prescription digital therapeutic for opioid use disorder delivered concurrently with standard buprenorphine treatment [13]. reSET-O delivers therapy in the form of a series of 67 interactive lessons via a patient-facing mobile software app. A typical therapy lesson comprises a behavioral therapy component and skill-building exercises. The therapeutic content is based on the community reinforcement approach, an intensive addiction-specific form of cognitive behavioral therapy that has been validated for opioid use disorder [14]. Therapy lesson content is delivered primarily via written text but may include videos, animations, and graphics. After most therapy lessons, the user undergoes fluency training, which is a method of questioning that has been demonstrated to promote learning and improve both short-term and long-term retention of material [27].
reSET-O also includes contingency management delivered via a virtual rewards wheel. Contingency management rewards are either virtual (thumbs up icon) or tangible rewards (gift card with value range US $5 to $100) that can be earned for completion of therapy lessons. Studies [28] have consistently demonstrated that contingency management interventions, particularly abstinence-based incentives, can support treatment and recovery in individuals with a wide range of substance use disorders. The odds of winning a tangible reward are 50% each time a reward is possible (wheel spin or mystery box), with higher-value rewards occurring less often. The odds of receiving a $100 gift card are 0.2%, whereas the odds of receiving a $5 gift card are 41.8%. The value of the rewards is commensurate with the amount of time users typically spend with the prescription digital therapeutic over the 12 weeks of treatment. Users are also prompted to report substance use, cravings, and triggers every 72 hours. A user can self-initiate reports of substance use, cravings, and triggers at any time. reSET-O contains an optional daily medication reminder that can be set to enhance adherence to buprenorphine for opioid use disorder.
PEAR-008
PEAR-008 is an investigational device with therapeutic content and a contingency management reward system that are similar to those in reSET-O; however, clinical content enhancements have been made, and the therapy has been reformatted as a game with mechanics designed to promote engagement. Content enhancements include use of person-centered language and lowering the reading level to make it more accessible. In PEAR-008, the reSET-O therapy lessons were divided into a tiered structure of shorter chapters with the intent of providing small, achievable goals to help keep users motivated and engaged. Each chapter has an associated quiz based on the fluency training approach.
The PEAR-008 home screen shows a nature scene that transitions from winter to summer as the patient progresses through therapy (Figure 1). The game economy of PEAR-008 is variable, consisting of the ability to earn stars that unlock virtual rewards such as birds and home-screen upgrades, as well as Mystery Boxes. The Mystery Boxes replace the contingency management rewards wheel in reSET-O and contain either virtual (stars) or tangible rewards (gift card with value ranges from $5 to $100) with the same odds of winning a tangible reward at each level of value as those in reSET-O. Similar to reSET-O users, PEAR-008 users earn the opportunity for contingency management rewards by completing fluency training quizzes (ie, therapy lessons). Engagement is also incentivized: a user can earn rewards by repeating a chapter and by engaging at least once daily with PEAR-008. The user is required to complete a daily check-in the first time they open the app each day. The check-in consists of a series of questions related to substance use, medication use, general recovery status, and recovery-specific questions regarding cravings, triggers, and problems the user is managing.
Overview
All study visits will be conducted remotely. Each prospective participant will complete a short screening assessment, and if basic eligibility is confirmed, complete informed consent procedures and sign an electronic informed consent form prior to completing the baseline assessment. After baseline assessments, participants will be randomly assigned to either reSET-O or PEAR-008 groups. Study staff will assist each participant with installation of their assigned digital therapeutic on their mobile device. Staff will provide training on the app's use. Study participants will be enrolled for 12 weeks, with weekly virtual sessions during weeks 1-8 and a final visit at week 12, to evaluate the impact of reSET-O and PEAR-008 on participant engagement and treatment outcomes. Participants will also complete slightly longer assessments at weeks 4 and 8.
Weekly study assessments completed during the first 8 weeks of treatment include saliva drug screening (participants will receive drug screening equipment on a regular basis by mail; urine drug screen results may be retrieved from the electronic medical record for AREF participants), timeline followback [29], and adverse event reporting. Additional self-report assessments will be delivered at week 4 and week 8.
Participants will attend a virtual end of treatment study session at 12 weeks to complete the following: saliva drug screening, timeline followback, and adverse event reporting assessment. Additional measures will be assessed at the 12-week follow-up visit (Table 1).
Primary
Number of active sessions with PEAR-008 or reSET-O per week To evaluate participant engagement with PEAR-008 compared to that with reSET-O. The hypothesis is that PEAR-008 group will have significantly greater participant engagement than the reSET-O group.
Secondary
Time to dropout (last contact with a participant) To evaluate the impact of PEAR-008 compared to reSET-O on treatment retention Abstinence will be defined as abstinence on patient self-reports (via timeline followback) and the absence of nonbuprenorphine opioids on saliva drug screens. Abstinence (binary outcome: yes or no) will be determined 9 times, weekly during weeks 1-8 and at week 12.
To evaluate the impact of PEAR-008 compared to reSET-O on abstinence from illicit opioids To evaluate a more global measure of engagement by combining data from secondary endpoints 3-6
Exploratory
Daily and weekly use patterns; saliva (or urine drug screen for AREF a participants only) and self-report; time to dropout To evaluate the association between engagement with PEAR-008 compared to reSET-O and treatment outcomes (abstinence and retention)
Demographics
Demographic information will be collected at the baseline session. Variables to be collected will include age at time of consent, sex assigned at birth, race and predominant self-reported ethnicity, level of education, marital status, employment status, occupation, and legal status.
Medical and Medication History
Medical history and current medical conditions, with current or prior treatment received, such as mental health disorders, hepatitis C virus, human immunodeficiency virus, and chronic pain syndromes, will be collected at the baseline session. Participant-reported history of substance use will be collected for the following substance categories: opioids, cocaine, stimulants (other than cocaine), alcohol, marijuana, benzodiazepines, other. Data to be collected regarding each substance include age at onset of use, number of years used regularly, amount used, type used (eg, pill vs powder), route of administration, history of overdose, and longest period of abstinence. Participant-reported history of substance use treatment will be collected, including present and prior treatment, type of treatment facility, number of treatment episodes, and current recovery activities. Nicotine use history will also be collected, including type, route, quantity, duration of use, and prior use. Medication history will include the name, dose, frequency, start and stop dates of the medication, and the indication for use. Prior or current medication for substance use disorder and opioid use disorder will also be recorded.
Abstinence From Opioids and Buprenorphine Adherence
Participant self-report of substance use and medication adherence will be collected within the reSET-O and PEAR-008 apps. In PEAR-008, participants are prompted to report use or abstinence each time they open the app as part of the check-in feature. In reSET-O, participants are prompted to report substance use or abstinence every 72 hours and can choose to self-initiate responses anytime.
Timeline followback will be completed at each virtual study session to assess patient-reported substance use since the time of the last assessment. The timeline followback is a validated calendar-based assessment used to obtain self-reports of amount and frequency of substance use retrospectively, using memory aids to enhance recall (eg, patterns of use, key dates).
Participants will self-administer a 12-panel saliva drug test during video sessions with study staff, who can assist in proper administration in addition to providing high-fidelity confirmatory testing. The 12-panel tests detect the presence of the following drugs: amphetamines, cocaine, cannabis, opioids, methamphetamine, barbiturates, benzodiazepines, buprenorphine, oxycodone, methadone, fentanyl, and alcohol. Saliva drug testing will be performed at the baseline session, once weekly during weeks 1-8 of the treatment phase and at the week 12 follow-up session. Participants will receive drug screening equipment regularly by mail.
When available, results of urine drug screening collected as part of routine care at participating treatment centers will also be used for participants recruited by AREF. All urine drug screen data are collected for clinical purposes and not as a study procedure. Urine drug screen results will be exported from the electronic medical record for inclusion in the study database. These data will be used to evaluate buprenorphine adherence and drug use. Results from additional urine drug screen confirmatory analyses for buprenorphine and norbuprenorphine may be available for some participants. When available, these data will be used to evaluate buprenorphine adherence.
Psychiatric Symptoms
Individuals with substance use disorders often experience psychiatric comorbidities, such as depression and anxiety. To evaluate the change in severity of co-occurring depression and anxiety symptoms, Patient Health Questionnaire-8 and Generalized Anxiety Disorder Questionnaire assessments will be delivered at baseline, week 4, week 8, and week 12.
The Patient Health Questionnaire-8 is an 8-item multipurpose instrument for screening and monitoring changes in depression [30]. The Generalized Anxiety Disorder Questionnaire-7 is a 7-item questionnaire for screening and monitoring changes in symptoms related to generalized anxiety disorder [31].
Recovery Status, Resilience, and Cognitive Behavioral Therapy Skills
The Substance Abuse and Mental Health Services Administration developed a working definition of recovery that includes 4 major dimensions: Health, Home, Purpose, and Community [32]. This definition highlights the importance of including measures of recovery across these dimensions in addition to substance use outcomes such as abstinence.
The Brief Assessment of Recovery Capital-10 is a 10-item assessment that will be used to measure participants' level of recovery capital [33]. Recovery capital consists of a variety of resources and strengths that patients can use to support their recovery. The 4 major dimensions of recovery are thought to be strengthened as an individual builds recovery capital and may indicate an individual's likelihood of remaining in remission [34]. The Connor-Davidson Resilience Scale-10 is a 10-item self-rating scale developed to assess resilience [35]. The measure is an abbreviated version of the 25-item version and was established on the basis of a factor analysis in a community sample. The questionnaire asks individuals to indicate how much they agree with a series of statements on a 5-point Likert scale. Resilience is a multidimensional trait characterized by an individual's capacity to maintain normal functioning and resist the development of psychiatric symptoms and disorders in response to stress and adversity. The Connor-Davidson Resilience Scale will be used to evaluate the malleability and stability of trait resilience over courses of treatment with reSET-O and PEAR-008.
The Cognitive Behavioral Therapy Skills Questionnaire is a 16-item assessment that measures the use and acquisition of cognitive behavioral therapy skills during treatment [36] and is a validated measure of behavioral activation and cognitive restructuring. Development of skills that support behavior change is a key goal of cognitive behavioral therapy. This scale will be used to assess the development of cognitive behavioral therapy skills and whether there is a difference in skill development between individuals treated with reSET-O versus those treated with PEAR-008.
These scales will be administered at baseline, week 4, week 8, and week 12.
COVID-19 Impact
Two exploratory assessments will be used to evaluate the impact of the COVID pandemic on participants. The CAIR Pandemic Impact Questionnaire [37] is a 5-item assessment that measures how the COVID-19 pandemic is impacting participants, using a 5-point Likert scale to evaluate whether the respondent has experienced any growth changes related to COVID-19 in the past 2 weeks. A modified version of the Coronavirus Perinatal Experiences-Impact Survey asks participants how they are coping with stress related to COVID-19 from a list. The respondent is provided with a list of coping strategies and asked to select all strategies they have employed. Both assessments were selected from the PhenX Toolkit [38] and will be administered at baseline, week 4, week 8, and week 12.
Participant Motivation and Satisfaction
Participant motivation and satisfaction will be evaluated via surveys and qualitative interviews. Surveys will be administered at baseline, week 4, week 8, and week 12, with a range of questions designed to evaluate participant motivation (baseline only) and satisfaction with their assigned intervention (eg, ease of use, relevance, satisfaction).
A subset of participants (approximately 10 per treatment arm) will be asked to participate in a 1-on-1 qualitative interview to evaluate their respective experiences with each therapeutic, particularly ease of use and acceptability. Interviews will last approximately 60 minutes, be conducted by study staff, and will be performed remotely via video or phone. Interview transcripts will be coded and analyzed using grounded theory methodology to identify key themes. An inductive, open coding approach will be used to assign emerging categories. Emerging categories will be grouped to arrive at high-level themes during axial coding, and their properties and dimensions will be identified and described in a codebook.
Data Management, Study Oversight, and Monitoring
Oversight of data management, including data collection, storage, export, security, tracking, data analysis, and quality assurance will be the responsibility of the study monitor designated by the study sponsor. Trial data will be managed with an electronic data capture system (Captivate, ClinCapture). Sites have access to this software as does the sponsor data monitor. Data collected by PEAR-008 and reSET-O are stored in the cloud. A data and safety monitoring board will provide additional oversight regarding the safety of study participants.
Adverse Events and Safety Monitoring
The investigator or designee and research site staff will be responsible for the detection, documentation, classification, reporting, and follow-up of events that meet the definition of an adverse event or serious adverse event. Spontaneously reported or observed adverse events will be recorded throughout the study from the time of consent until the end of the last study visit. Adverse events will be elicited using a nonleading question at designated time points. Regardless of seriousness, intensity, or presumed relationship to reSET-O or PEAR-008, all adverse events will be recorded. The site investigator will monitor the occurrence of adverse events during the study.
Adverse events and serious adverse events will be collected and reported using the methods and definitions of the Office for Human Research Protections and National Institutes of Health (NIH) requirements for human participant protection. The investigator or designee is responsible for making an assessment as to the seriousness, intensity, causality, and outcome of an adverse event. The investigator will determine causality as related, possible, unlikely, or unrelated to reSET-O or PEAR-008.
Confidentiality
Procedures to assure confidentiality will be strictly observed. All participant personal information will be kept confidential and will not be released without written permission, except as required by law. All study information will be kept separately from identifying information on consent forms and locator forms.
Data collected by the reSET-O and PEAR-008 system are securely transferred using industry standard encryption to a cloud-based infrastructure that serves and communicates with the patient facing mobile app; the backend services contain all data and analytics for reSET-O, PEAR-008, and clients (participants and clinicians). All data stored by the device are hosted and stored with a cloud-computing service (Amazon Web Services), which follows a variety of internationally recognized security standards, such as National Institute of Standards and Technology SP800-53 [39] and Health Insurance Portability and Accountability Act [40]. All patient information is automatically encrypted when it is entered into the system, which allows for secure data transfer (from patient device to clinician device) and storage.
In accordance with the 21st Century Cures Act [41], all ongoing or new research funded by NIH as of December 13, 2016 that collects or uses identifiable, sensitive information is automatically issued a Certificate of Confidentiality, which protects participants against disclosure of any sensitive information or illicit behavior (eg, drug use).
Statistical Analysis
All statistical methods will be consistent with the International Conference on Harmonization E9 Guidance [42]. Data will be summarized by treatment group. For baseline, safety, and efficacy outputs a total population will combine both groups. Where appropriate, the data will be summarized by session in addition to treatment group. Baseline, demographic, and efficacy output data will be summarized by intended treatment. Safety output will be summarized by the treatment received. Every effort will be made to obtain required data at each scheduled evaluation. Missing data will not be imputed. Sensitivity analyses incorporating various imputation assumptions may be performed if missing data exceed 5% of the total possible observations. Descriptive statistics will be used to describe the population of study participants at the beginning of the study (mean, standard deviation, minimum, 25th percentile, median, 75th percentile, and maximum for continuous data; frequencies and percentages for categorical data). Differences in continuous variables will be summarized with Hedges g effect size; differences in categorical variables will be summarized with odds ratios.
Primary Endpoint Analysis
Engagement with PEAR-008 and reSET-O will be defined as the number of active sessions per week. A session is defined as a set of in-app events with the same session ID. An active session is any session that contains some active participation in the app such as navigating to a different screen, engaging with a learning module, or responding to a notification. This endpoint was selected to allow a 1:1 comparison of content delivery method (eg, brief chapters vs longer lessons). The number of active sessions per week will be evaluated with a repeated measures mixed model of the form: Number of Sessions in a Week = Week + Treatment + Week × Treatment + Subject Error + Random Error. To evaluate the impact of treatment, this repeated measures mixed model will be compared to another of the form: Number of Sessions in a Week = Week + Subject Error + Random Error with a likelihood ratio test. The likelihood ratio test will be evaluated using model fit to maximize the log-likelihood.
Secondary Endpoint Analysis
Abstinence will be self-reported by patients via timeline followback and assessed as the absence of opioids (except buprenorphine) on saliva drug screens. Data on abstinence (binary yes and no) will be evaluated with the 9 possible saliva drug screens and urine drug screen and timeline followback data at weeks 1-8 and week 12. Differences between the treatment arms in abstinence will be assessed with a generalized estimating equation analysis using the binomial abstinence outcome as the dependent variable, assessment time, treatment, and the interaction between assessment time and treatment as fixed effects and subject as a random factor. This generalized estimating equation will be compared to a second generalized estimating equation without a treatment term using a likelihood ratio test to evaluate the impact of treatment. A treatment responder analysis will also be conducted, with a treatment responder defined as someone with ≥80% of all saliva drug screens and urine drug screens and timeline followback reports negative for all nonprescribed opioids over the course of the trial.
Treatment retention will be measured as time to dropout (number of days from baseline to last face to face contact) and analyzed using the Kaplan Meier method followed by a log rank test to compare treatment groups.
Patient assessments of recovery capital (Brief Assessment of Recovery Capital-10) resilience (Connor-Davidson Resilience Scale-10) and severity of co-occurring psychiatric symptoms (Patient Health Questionnaire-8 and Generalized Anxiety Disorder Questionnaire-7) will be evaluated with a repeated measures mixed model in a manner consistent with the primary endpoint.
Participants' use patterns with PEAR-008 and reSET-O will include total time engaged, number of lessons and chapters completed, number of lessons and chapters repeated, number of completed self-report assessments, and response to notifications. Descriptive statistics of each treatment arm will be summarized and differences between PEAR-008 and reSET-O will be assessed with a t test (or its nonparametric alternative if the distributional assumptions are violated).
Treatment motivation and satisfaction will be evaluated based on individual participants' rating of interest in using (baseline only), ease of use, satisfaction, perceived helpfulness, and likelihood of recommending reSET-O or PEAR-008. Descriptive statistics (mean, median, standard deviation) will be performed on Likert scale and multiple choice items that assess user satisfaction and attitudes about the patient mobile app. Analyses will be conducted on data collected at each assessment point throughout the study, ratings over the course of the study, and for overall user satisfaction as measured at the end of the study.
Exploratory Endpoint Analysis
Data on abstinence (binary-yes and no) will be evaluated at 9 saliva drug screen and timeline followback time points at weeks 1-8 and week 12. The association between abstinence and engagement will be evaluated using a generalized estimating equation model. A given week will be considered negative if a participant has no indication of opioid use on the saliva drug screens or timeline followback. Missing data will be ignored if saliva drug screens or a timeline followback is available for a given time point. In the case where saliva drug screens and timeline followback methods yield data that do not agree, the week will be considered positive.
The relationship between engagement and retention will be assessed using a Cox proportional hazards model with time to dropout as the dependent variable and the number of active sessions as an independent variable. This analysis will be performed separately for each treatment arm.
Patient assessment of skill acquisition (Cognitive Behavioral Therapy Skills Questionnaire) will be evaluated with repeated measures mixed model analysis consistent with the primary endpoint. Results will be presented for the total Cognitive Behavioral Therapy Skills Questionnaire score, the Behavioral Activation Score, and the Cognitive Restructuring score.
Medication adherence will be evaluated using saliva drug screens and, when possible, confirmed by urine drug screen (positive result for buprenorphine and norbuprenorphine). Differences between the treatment arms in medication adherence will be assessed with a generalized estimating equation analysis consistent with the abstinence analysis.
Ethics Approval
This study protocol has been reviewed and approved by the New York State Psychiatric Institute Institutional Review Board. The study is registered on ClinicalTrials.gov (NCT04542642).
Results
Recruitment for this study was active as of February 2021 and will continue until the projected sample size is met.
Discussion
While initially designed as a standard, site-based clinical trial, this study was redesigned as a decentralized study to circumvent challenges in conducting in-person visits that arose as a result of the COVID-19 pandemic. Standard in-person procedures for this patient population that were planned for the study, such as initiation of buprenorphine medication in-clinic or on-site urine drug screening, were no longer feasible. The decentralized study model aligns with a shift in health care delivery observed during the pandemic, as many substance use disorder treatment providers were able to transition to telemedicine for care delivery, including initiation onto buprenorphine and maintenance treatment [43,44]. Digital therapeutics lend themselves to remote therapy delivery models, presenting a unique opportunity to evaluate their use along with existing technology and tools such as videoconferencing, electronic signatures for documenting consent, and video-observed, self-administered saliva drug test kits.
Several challenges arose with the shift in study design. One of the sites, a research clinic, typically manages buprenorphine medication during studies of this patient population. Without in-clinic participant visits, it became necessary for the site to confirm that participants were receiving buprenorphine under the care of a licensed prescriber. This was accomplished by obtaining release of medical information waivers from prospective participants, allowing the site to reach out directly to the individual's treatment provider for confirmation of eligibility. This pivot allowed the research clinic to recruit a broader geographic sample of individuals than is typical for similar studies [45] conducted on-site. Another challenge was ensuring that all assessments could be conducted remotely. While most self-report assessments were easy to transition to virtual delivery, it is challenging to conduct urine drug screening virtually. Saliva drug screening kits were selected as an alternative that allowed participants to self-administer the test during video sessions and under supervision by study staff. Finally, participant recruitment methods shifted toward a strategy focused on digital media and treatment programs using telemedicine.
Several questions about decentralized studies in this patient population will be addressed by this study. For example, it is not yet clear whether it will be easier to recruit and retain individuals with opioid use disorder in a virtual study than in a standard face-to-face study. Providing a more convenient mechanism for conducting study sessions may increase retention, which can be challenging in this patient population. Evaluating the utility of self-administered saliva drug screening may also be beneficial to other investigators who are considering this method of evaluating substance use. Challenges that arise over the course of the study will help elucidate the limitations of this study design. This example of a decentralized clinical trial may provide a useful model for conducting future virtual studies with people with opioid use disorder. | 7,907.2 | 2021-08-09T00:00:00.000 | [
"Medicine",
"Computer Science"
] |
Ionic Liquids-Based Nanocolloids—A Review of Progress and Prospects in Convective Heat Transfer Applications
Ionic liquids are a new and challenging class of fluids with great and tunable properties, having the capability of an extensive area of real-life applications, from chemistry, biology, medicine to heat transfer. These fluids are often considered as green solvents. Several properties of these fluids can be enhanced by adding nanoparticles following the idea of nanofluids. These ionic liquids-based nanocolloids are also termed in the literature as ionanofluids or nanoparticles-enhanced ionic liquids. This review summarizes the findings in both areas of ionic liquids and ionic liquids nanocolloids (i.e., ionic liquids with nanoparticles in suspension) with direct applicability in convective heat transfer applications. The review presents in a unified manner the progress and prospects of ionic liquids and their nanocolloids from preparation, thermophysical properties and equally experimental and numerical works. As the heat transfer enhancement requires innovative fluids, this new class of ionic liquids-based nanocolloids is certainly a viable option, despite the noticed drawbacks. Nevertheless, experimental studies are very limited, and thus, extensive experiments are needed to elucidate ionic liquids interaction with nanoparticles, as well as their behavior in convective heat transfer.
Introduction
Ionic liquids (ILs) are considered as a candidate for heat transfer applications particularly when nanoparticles are dispersed into them making a new class of fluids (known as ionanofluids) with improved thermal performance. Thus, it is important to briefly highlight thermophysical properties of ILs such as density, viscosity, thermal conductivity and specific heat and how these properties are influenced by temperature and pressure, which are particularly crucial for convective heat transfer application. Similar to common molecular liquids, density of ILs slightly decreases (mostly linearly) with increasing temperature. For instance, at atmospheric pressure, an increase in temperature from 288 to 363 K decreases the density of [BMIM][NTf 2 ] from 1446 to 1375.7 kg/m 3 (4.86%) [1,2]. Density of ILs also changes with pressure, and it increases with increasing pressure. For example, at 298 K density of [BMIM][NTf 2 ] increased from 1436 to 1561.5 kg/m 3 (8.74%) due to increasing pressure from 0.1 (atmospheric) to 249.6 MPa [1]. Although viscosity of ILs is generally higher than those of common heat transfer fluids such as ethylene glycol similar to any other liquids' viscosity of ILs also decrease considerably (non-linearly) with increasing temperature (e.g., Ferreira et al. [3]). Such a decrease in viscosity of IL is particularly important for the convection applications at elevated temperature, as it can significantly reduce the pumping power. However, unlike conventional liquids, thermal conductivity of ILs was found to decrease slightly (for some ILs almost independent of temperature) with increasing temperature [3,4]. However, specific heat of ILs shows behavior similar to common viscous fluids such as ethylene glycol, as this property increases mostly linearly with temperature [5], which is good for thermal energy storage.
Apart from above properties and their dependent on temperature and pressure, ILs are thermally stable up to considerably high temperature (e.g., 450 • C). Because of interesting characteristics and properties as well as potential applications some special types of ILs such as imidazolium-based ILs are widely used and studied types. Based on application as for convective heat transfer, the properties and features of ILs play an important role for their own performance as well as their nanofluids (INF).
Adding nanoparticles to ionic liquids came as a logical step to increase their thermal conductivity, which is rather low if compared to several well-known heat transfer fluids. A comprehensive discussion on this topic was attained by Minea [6], where the advantages and disadvantages of using ionic liquids for different applications based on the ionic liquids description at molecular level can clearly be noticed. Additionally, Minea [6] discusses thermophysical properties of ionic liquids in comparison with regular heat transfer fluids, outlining both their benefits and drawbacks, concluding that ionic liquids are superior to basic heat transfer fluids mostly in relation of stability, low vapor pressure and environmental safety. The most important feature of ILs is their easy-to-design properties by merging anions and cations, and the most significant feature that distinguishes ionic liquids among regular commercial heat transfer fluids is the extraordinarily low saturated vapor pressure at high temperature. From the state-of-the-art literature, it is obvious that the thermal conductivity is increasing by adding solid nanoparticles to ionic liquid, and the phenomenon occurring is similar with the one observed for nanofluids. In regard to viscosity, a general conclusion is that the viscosity is increasing by adding nanoparticles and is decreasing at heating. More details about this behavior and the changes in thermophysical properties of a number of ionic liquids studied in the open literature can be found in a previous work published by these authors (Minea and Murshed [7]).
One of the first reviews on ionic liquids-based nanocolloids came from Marsh et al. [8] who presented the net advantages of adding nanoparticles to ionic liquids and also discussed their possible applications.
Many papers discuss heat transfer applications: For example, a study performed by França et al. [9] demonstrated that these new fluids, due to high thermal conductivity and specific heat, are suitable candidates for heat transfer applications in a shell and tube heat exchanger. The same conclusion was also reached by other authors (see, for example, [7,[10][11][12][13][14][15]) that performed mainly numerical studies on heat transfer performance. Anyhow, it was noticed from the archived literature that, at least by these authors' knowledge, the number of experimental studies are scarce.
This review came as a continuation of our work, and it summarized and discussed comparatively recent research performed both in the area of ionic liquids and ionic liquidsbased nanocolloids, with emphasis on both of these fluids' thermophysical properties in relation to their convection heat transfer. Nevertheless, the last parts are dedicated to numerical studies performed until now as well as proposed analytical and numerical correlations on heat transfer behavior.
Selection of ILs and Preparation of INF
For heat transfer-based applications, ILs are mainly selected based on their thermophysical properties particularly of high thermal conductivity and low viscosity. Another important factor is their miscibility in water due to improving their thermal properties such as thermal conductivity, heat capacity and reducing viscosity.
Preparation of ionanofluids is the first key step, as their properties, performance and suitability in application highly depend on it. The preparation methodology of ionanofluids is similar to those of conventional nanofluids where nanoparticles are either directly synthesized inside the base fluid or mixed in base fluid [16]. While the first route is known as the one-step method, the latter is called the two-step method. For ionanofluids, the one-step method, which is direct synthesis of nanoparticles in base ionic liquid, is rarely used. Whereas, ionanofluids are commonly prepared using the two-step method where dry nanoparticles (purchased or synthesized) are dispersed in base IL and then they are homogenized (better dispersed) mainly using ultra sonication. Schematic of ionanofluids preparation methodology (two-step) is shown in Figure 1, which also highlights different techniques of stable dispersion of nanoparticles in base IL. as the one-step method, the latter is called the two-step method. For ionanofluids, the onestep method, which is direct synthesis of nanoparticles in base ionic liquid, is rarely used. Whereas, ionanofluids are commonly prepared using the two-step method where dry nanoparticles (purchased or synthesized) are dispersed in base IL and then they are homogenized (better dispersed) mainly using ultra sonication. Schematic of ionanofluids preparation methodology (two-step) is shown in Figure 1, which also highlights different techniques of stable dispersion of nanoparticles in base IL. Various types of nanoparticles such as Al2O3, carbon nanotubes, graphene, SiC and graphene oxide are used for the preparation of ionanofluids; whereas, among ionic liquids, imidazolium-based ionic liquids are widely used. While selecting ionic liquid as base fluids for heat transfer-based applications, it is important to choose those with high thermal properties such as thermal conductivity and heat capacity. Although the preparation procedure is quite straight forward, it is very challenging to ensure proper/homogenous dispersion of nanoparticles and long-term stability of prepared ionanofluids. Thus, besides sonication, surfactants are also added to improve stability of prepared ionanofluids. Another way to improve stability is by nanoparticles' surface treatment or modification. However, the latter option is rarely employed in ionanofluids preparation. It is important to note that special attention must be given while ultrasonicating ionanofluids, as excessive sonication (long time and at high amplitude) can deteriorate the sample in both chemical and physical condition (such as destroying structure and surface of nanoparticles such as CNT). Due to prolong ultrasonication (especially probe type) the sample ionanofluids can be evaporated, and the concentration of nanoparticle can be changed. It is also advisable not to use surfactant, as they can also deteriorate or can become inactive at moderate to high temperature conditions. Nevertheless, it is important to assess the degree of stability of prepared ionanofluids by performing a stability study, which includes determining zeta potential, UV-Vis absorbance, size distribution using dynamic light scattering as well as TEM or SEM analysis. The stability assessments of ionanofluids are the same as commonly used for nanofluids [16][17][18].
Ionic Liquids Thermophysical Properties
Thermophysical properties of base ILs are crucial for their own as well as their INFs' heat transfer performance, particularly for convective heat transfer applications. Thus, important thermophysical properties including viscosity, density, thermal conductivity and heat capacity of commonly considered ILs are presented in Tables 1 and 2. Reference temperature (mainly room temperature condition) of the property value and corresponding references are also provided. It is noted that the values of these properties can be different in other sources that are not used in these tables. As the focus of this study is not ionic Various types of nanoparticles such as Al 2 O 3 , carbon nanotubes, graphene, SiC and graphene oxide are used for the preparation of ionanofluids; whereas, among ionic liquids, imidazolium-based ionic liquids are widely used. While selecting ionic liquid as base fluids for heat transfer-based applications, it is important to choose those with high thermal properties such as thermal conductivity and heat capacity. Although the preparation procedure is quite straight forward, it is very challenging to ensure proper/homogenous dispersion of nanoparticles and long-term stability of prepared ionanofluids. Thus, besides sonication, surfactants are also added to improve stability of prepared ionanofluids. Another way to improve stability is by nanoparticles' surface treatment or modification. However, the latter option is rarely employed in ionanofluids preparation. It is important to note that special attention must be given while ultrasonicating ionanofluids, as excessive sonication (long time and at high amplitude) can deteriorate the sample in both chemical and physical condition (such as destroying structure and surface of nanoparticles such as CNT). Due to prolong ultrasonication (especially probe type) the sample ionanofluids can be evaporated, and the concentration of nanoparticle can be changed. It is also advisable not to use surfactant, as they can also deteriorate or can become inactive at moderate to high temperature conditions. Nevertheless, it is important to assess the degree of stability of prepared ionanofluids by performing a stability study, which includes determining zeta potential, UV-Vis absorbance, size distribution using dynamic light scattering as well as TEM or SEM analysis. The stability assessments of ionanofluids are the same as commonly used for nanofluids [16][17][18].
Ionic Liquids Thermophysical Properties
Thermophysical properties of base ILs are crucial for their own as well as their INFs' heat transfer performance, particularly for convective heat transfer applications. Thus, important thermophysical properties including viscosity, density, thermal conductivity and heat capacity of commonly considered ILs are presented in Tables 1 and 2. Reference temperature (mainly room temperature condition) of the property value and corresponding references are also provided. It is noted that the values of these properties can be different in other sources that are not used in these tables. As the focus of this study is not ionic liquid, no analysis of results from individual studies from the literature on these properties of ionic liquid will be provided here. However, a detailed review on ILs thermophysical properties and on ILs as heat transfer fluids can be found elsewhere in the literature (e.g., Chernikova Nanomaterials 2021, 11, 1039 4 of 23 et al. [19]). The data presented in these tables (Tables 1 and 2) will help to identify suitable ILs for INFs as well as for their applications, particularly in thermal applications. Unlike conventional heat transfer fluids, Figure 2 reveals that temperature does not have noticeable influence on thermal conductivity of ILs. However, as can be seen from Table 2 as well as Figure 2, changing the anion or cation type resulted in a larger variation in thermal conductivity. Varying the alkyl chain length, n, of the [Cnmim][NTf 2 ] ionic liquids had no significant effect on the thermal conductivity.
Ionic liquids commonly exhibit high viscosity and, thus, are not very suitable in convection application. However, similar to common heat transfer fluids, the viscosity of ILs is strongly influenced by temperature, as can be seen from Figure 3 where the viscosity of representative ILs decreases exponentially with the temperature, which is good for their cooling application at high temperature conditions. Ionic liquids commonly exhibit high viscosity and, thus, are not very suitable in convection application. However, similar to common heat transfer fluids, the viscosity of ILs is strongly influenced by temperature, as can be seen from Figure 3 where the viscosity of representative ILs decreases exponentially with the temperature, which is good for their cooling application at high temperature conditions. Nanomaterials 2021, 11, x FOR PEER REVIEW 5 of 24 Ionic liquids commonly exhibit high viscosity and, thus, are not very suitable in convection application. However, similar to common heat transfer fluids, the viscosity of ILs is strongly influenced by temperature, as can be seen from Figure 3 where the viscosity of representative ILs decreases exponentially with the temperature, which is good for their cooling application at high temperature conditions. Usually, reduction in viscosity and increase in specific heat capacity of ILs are commonly used by mixing with water. For binary mixture of IL and water, the heat capacity of the mixture increases by increasing the mole fraction of water [58]. Heat capacity of IL also increases with temperature [58]. Although there are many immiscible ILs, binary mixture of ILs with water is better as a base fluid for ionanofluids than a heat transfer medium.
Thermophysical Properties of Ionic Liquids-Based Nanocolloids
This section attempts a comprehensive review on thermophysical properties of ionic liquid-based nanocolloids with emphasis on relevant properties for convective heat transfer.
Thermal Conductivity
Thermal conductivity is one of the most important property of fluids when it talks about heat transfer capability of a certain fluid. Table 3 shows experimental data on ionic liquids-based nanocolloids thermal conductivity. [47,65], Hosseinghorbani et al. [68]). As for base fluids, several ionic liquids were considered and few authors, such as, for example, Xie et al. [37] and Chereches et al. [47,60], made mixtures between water and ILs.
If we consider experimental results on thermal conductivity, all of the authors noticed an increase in thermal conductivity values when nanoparticles are added to the ionic liquids. Nevertheless, the temperature influence was little, as was shown in Table 3. Overall, the enhancement in thermal conductivity is up to 10% at low percentages of nanoparticles.
Nevertheless, Ribeiro et al. [59] found an increase of up to 30% when 1%wt. MWCNT are added to several ILs.
For instance, thermal conductivity was found almost constant with temperature variation of several ionic liquids with nanoparticles measured by Franca [26]. The same phenomenon was noticed also by other researchers (see, for example, Ribeiro et al. [59], Patil et al. [60], Ferreira et al. [3] and Ribeiro et al. [4]) concluding that the thermal conductivity of ionic liquids with nanoparticles is following the same trend as that found in the literature for molecular liquids [69] and other ionic liquids [24,53,[70][71][72].
Furthermore, a comparison is performed in terms of nanoparticles and/or ionic liquid influence on the thermal conductivity values. From Table 3, we can conclude that the experimental data are scattered and a large variety of combinations were considered. First, the influence of base ionic liquid was checked using two kinds of the most considered nanoparticles: MWCNTs and alumina.
Figures 4 and 5 synthetize some data from the literature in regard to nanoparticles' influence on thermal conductivity enhancement if compared with the ionic liquid thermal conductivity. If we look to Figure 4, we can conclude that the enhancement of conductivity is decreasing when a mixture of ionic liquid + water is considered as the base fluid (see the results from Xie et al. [37]). Plus, if we compare data from Franca [26] and Xie et al. [37], we can see that, for the same quantity of nanoparticles, the ionic liquid slightly impacts the experimental values. On the other hand, Wang et al. [34] obtained larger increases with very low quantities of nanoparticles (of 0.03% and 0.06% wt. MWCNT). [47,62,63,65]. Results concluded that, for 1%wt. alumina, the thermal conductivity enhancement varies from 0-10%, thus there is a relatively strong influence of the base fluid.
Furthermore, in Figure 6, the thermal conductivity values of [HMIM][BF 4 ] and of several nanoparticles-enhanced ionic liquids are plotted with the addition of graphene, MWCNT and SiC. Results clearly show that the nanoparticle type influences the experimental conductivity of the fluid. For example, adding 0.03%wt. of graphene, the augmentation is 9%, which is larger than that if SiC or MWCNT are added (i.e., 3.6%). Furthermore, a comparison is performed in terms of nanoparticles and/or ionic liquid influence on the thermal conductivity values. From Table 3, we can conclude that the experimental data are scattered and a large variety of combinations were considered. First, the influence of base ionic liquid was checked using two kinds of the most considered nanoparticles: MWCNTs and alumina.
Figures 4 and 5 synthetize some data from the literature in regard to nanoparticles' influence on thermal conductivity enhancement if compared with the ionic liquid thermal conductivity. If we look to Figure 4, we can conclude that the enhancement of conductivity is decreasing when a mixture of ionic liquid + water is considered as the base fluid (see the results from Xie et al. [37]). Plus, if we compare data from Franca [26] and Xie et al. [37], we can see that, for the same quantity of nanoparticles, the ionic liquid slightly impacts the experimental values. On the other hand, Wang et al. [34] obtained larger increases with very low quantities of nanoparticles (of 0.03% and 0.06% wt. MWCNT). Furthermore, in Figure 6, the thermal conductivity values of [HMIM][BF4] and of several nanoparticles-enhanced ionic liquids are plotted with the addition of graphene, MWCNT and SiC. Results clearly show that the nanoparticle type influences the experimental conductivity of the fluid. For example, adding 0.03%wt. of graphene, the augmentation is 9%, which is larger than that if SiC or MWCNT are added (i.e., 3.6%).
Concluding, the phenomenon behind the thermal conductivity augmentation is similar with that noticed for regular nanofluids with water or ethylene glycol. Brownian motion seems to be accepted by most of the researchers, while several other mechanisms are discussed in the open literature (for example: thermal boundary resistance, clustering and layering phenomenon), but a number of questions are still unanswered in regard to the main cause for this phenomenon. Another aspect that has to be clarified in the next steps Concluding, the phenomenon behind the thermal conductivity augmentation is similar with that noticed for regular nanofluids with water or ethylene glycol. Brownian motion seems to be accepted by most of the researchers, while several other mechanisms are discussed in the open literature (for example: thermal boundary resistance, clustering and layering phenomenon), but a number of questions are still unanswered in regard to the main cause for this phenomenon. Another aspect that has to be clarified in the next steps of research is the influence of the base ionic liquid and of the nanoparticle type/shape in order to tailor a better new heat transfer fluid.
Viscosity
While most of nanofluid research has been devoted to thermal conductivity, viscosity has received little attention. Viscosity is a critical parameter when a new fluid for heat trans-fer applications is developed. This is relevant in the majority of heat transfer applications, where a pumping power is employed to pump the fluids in a certain application.
Most of the experimental studies, as can be seen from Table 4, noticed an increase in viscosity when nanoparticles were added to the ionic liquids, depending on nanoparticles mass concentration (see, for example, Paul et al. [62], Fox et al. [72]). Besides that, several authors (see Patil et al. [60], Ferreira et al. [3], Zhang et al. [68]) found a decrease in viscosity when nanoparticles were added and explained this phenomenon relying on the low density and lubricating properties of nanoparticles, on the interactions between the ions of ILs and the MWCNT, which can hardly be acceptable without a scientific explanation. Additionally, a comparison is shown in Figures 7 and 8 in terms of nanoparticles and/or ionic liquid influence on viscosity values. From Table 4, it can easily be noticed that the experimental data are scattered. Additionally, a comparison is shown in Figures 7 and 8 in terms of nanoparticles and/or ionic liquid influence on viscosity values. From Table 4, it can easily be noticed that the experimental data are scattered. Figure 7 shows the influence of base ionic liquid using MWCNTs as a base of comparison, and we can conclude that the viscosity is decreasing when a mixture of ionic liquid + water is considered as the base fluid (see the results from Xie et al. [37]). Figure 7 depicts an increase of up to 38% at a small fraction of MWCNTs (i.e., 0.005). Most of the authors found an increase in viscosity when nanoparticles were added to the ionic liquid, and several authors (see, for example, Wang et al. [34]) obtained a decrease. Nevertheless, the decrease in viscosity is a phenomenon rarely noticed and insufficiently described in the literature. Viscosity increase mechanisms are to be elucidated, and several authors attributed this growth to strong interactions between graphene sheets and IL molecules (see Pamies et al. [26]). Plus, Pamies et al. [38] discussed the increase in concentration based on increases in the internal shear stress, with the subsequent viscosity increase. Figure 7 shows the influence of base ionic liquid using MWCNTs as a base of comparison, and we can conclude that the viscosity is decreasing when a mixture of ionic liquid + water is considered as the base fluid (see the results from Xie et al. [37]). Figure 7 depicts an increase of up to 38% at a small fraction of MWCNTs (i.e., 0.005). Most of the authors found an increase in viscosity when nanoparticles were added to the ionic liquid, and several authors (see, for example, Wang et al. [34]) obtained a decrease. Nevertheless, the decrease in viscosity is a phenomenon rarely noticed and insufficiently described in the literature.
In Figure 8, a comparison for alumina and different base ionic liquid is depicted. A smaller upsurge in viscosity was observed for base fluids from ionic liquids and water mixtures, but the actual influence of the base fluid seems larger at higher nanoparticles' mass concentrations.
Viscosity increase mechanisms are to be elucidated, and several authors attributed this growth to strong interactions between graphene sheets and IL molecules (see Pamies et al. [26]). Plus, Pamies et al. [38] discussed the increase in concentration based on increases in the internal shear stress, with the subsequent viscosity increase.
Even though in the literature, there are numerous models for viscosity estimation, no theoretical correlation was found acceptable to estimate both nanofluids or other nanoparticle-enhanced fluids' viscosity behavior. However, a number of papers are proposing the Krieger-Dougherty or Pastorizza-Galllego models (see, for example, the work of Chereches et al. [65] and Pastorizza-Galllego et al. [76]), which seems to describe well the experimental results.
Specific Heat
Specific heat results are also contradictory, as can be clearly seen from Table 5, and it is concluded that the experimental values may greatly depend on the chemical structure of the ionic liquid and of its molecules interaction with nanoparticles.
Based on the previous reports on the simple molecular solvents-based nanofluids, the mechanism of the heat capacity enhancement of ionanofluids is probably driven by the existing interfacial nanolayering occurring on the surface of nanoparticles [45].
Zhang et al. [68] found that the decreases noticed for the GNPs-dispersed nanofluids are less than those reached by the SWCNT and GE; the explanation came from the fact that the zero dimensional GNPs has higher thermal energy density than the two-dimensional GE and the one-dimensional SWCNTs.
Some other studies reported the possibility of mesolayers overlapping, as a mechanism of variation of specific heat for nanofluids also extended to the ionic liquids with nanoparticles (see Oster et al. [45]).
In the case of specific heat, since the results are scattered, it is hard to make a good comparison on nanoparticles or ionic liquid influence on the actual variation of the experimental values. Based on the previous reports on the simple molecular solvents-based nanofluids, the mechanism of the heat capacity enhancement of ionanofluids is probably driven by the existing interfacial nanolayering occurring on the surface of nanoparticles [45].
Zhang et al. [68] found that the decreases noticed for the GNPs-dispersed nanofluids are less than those reached by the SWCNT and GE; the explanation came from the fact that the zero dimensional GNPs has higher thermal energy density than the two-dimensional GE and the one-dimensional SWCNTs.
Some other studies reported the possibility of mesolayers overlapping, as a mechanism of variation of specific heat for nanofluids also extended to the ionic liquids with nanoparticles (see Oster et al. [45]).
In the case of specific heat, since the results are scattered, it is hard to make a good comparison on nanoparticles or ionic liquid influence on the actual variation of the experimental values.
Density
Patil [40] performed some experiments to evaluate the density of several ILs with Ru nanoparticles and noticed a slight decrease in density due to Ru addition, as per Table 6. Overall, the density is the less studied parameter, and all authors concluded that density variation is in line with existing equations, meaning that it increases with nanoparticle addition and decreases with temperature rise.
Experimental Works on Convective Heat Transfer (for Both ILs and INFs)
Only a handful of experimental works from a single research group on convective heat transfer of ILs and their nanofluids (INFs) are reported in the literature [62,[77][78][79][80]. The findings of those works are summarized in Table 7. It can be seen from Table 7 ]), and their convective heat transfer coefficient was determined in forced and natural convection conditions. For laminar flow conditions, they reported a maximum enhancement of heat transfer coefficient of 20% for 1 %wt. loading of spherical shaped Al 2 O 3 nanoparticle [79]. A natural convection study from the same group [80] showed that whiskers shaped nanoparticles had slightly higher Nu compared to spherical one at the same Ra. However, both nanoparticles actually degraded the natural convection heat transfer. Apart from direct convective heat transfer experimentation, Huminic and Huminic [15] Compared to a relatively large number of numerical works on convection heat transfer of ILs and INFs, such a handful of experimental works was performed due to several reasons among, which are the high price of ILs and nanoparticles as well as ILs and INFs having very high viscosity. Thus, despite showing some enhancement in convection heat transfer of INFs [79,80], based on large pressure drop (leading to high pumping power) and high cost, no conclusions can be made on the suitability of these INFs as advanced heat transfer fluids for convection applications.
Numerical Works on Convective Heat Transfer of ILs and INFs (for Both ILs and INFs)
One of the first numerical studies performed on ionic liquids and their colloids is from Minea and Murshed [7], who implemented simple geometry into several fully described ionic liquids (i.e., [C 4 Table 8. One of these authors' main conclusions is that with increasing flow, the heat transfer coefficient increases considerably, and it appears that the thermal conductivity plays a superior role in laminar convection, while viscosity is of reduced relevance. Plus, heat transfer seems to be greatly influenced by both ionic liquid and nanoparticle type and concentration. The explanations behind these results are attributed to several phenomenon, such as the increase in viscosity when nanoparticles are added to the ionic liquid; the dominant role of convection over conduction heat transfer when it comes to ionic liquid nanocolloids; the formation of polar molecules (i.e., water molecules) around ionic liquids ions associated with the decrease in bonds between ionic components of the IL when water is added. Furthermore, alumina nanoparticles' addition marginally drops the ions mobility by substituting water molecules with nanoparticles in the ions vicinity [10,[80][81][82].
It may underline here that all the fluids were modelled as single-phase fluids with known thermophysical properties. This is a good approach, especially in the case of experimentally determined properties, as was demonstrated for nanofluids in the only numerical benchmark study, as can be seen from Minea et al. [85]. Of course, other techniques are available, as multiphase model, but no relevant studies were identified in the open literature, where most of the simulations involve calculated properties, based on the nanofluids' empirical models.
Theoretical Development and Correlations
In regard to theoretical development of correlations, the literature review revealed little information. Work was performed mostly on simulation and results will be discussed further.
Chereches et al. (1) The correlation, with a ±7% data precision, is valid under the laminar flow regime with 500 < Re < 2000 and total weight concentration ranging from ϕ = 0 to 2.5%. Based on these results, Chereches et al. [10] found an increase in heat transfer performance and Nu number with the increase in nanoparticle addition, as can also be noticed from Table 8.
Another interesting analysis was performed by El-Maghlany and Minea [11] in a tube subjected to heat flux, with direct application to solar energy. The aforementioned study considered [C 4 mim][NTf 2 ] ionic liquid enriched by adding alumina nanoparticles with 0.5, 1 and 2.5% volume concentration. The simulation geometry was similar to the one for the solar collectors, modelling the real application as accurate as possible, and the correlations are (with a deviation of up to 5.5%): Nu = 0.558 (Re Pr D/L) 0.376 -valid for the ionic liquid, Nu = 0.6 (Re Pr D/L) 0.372 -valid for ϕ = 0.5% alumina, Another correlation that involves the thermal diffusivity (α) was also proposed by El-Maghlany and Minea [11] as follows: Authors explained that the equation reveals the relevant role of thermal diffusivity in evaluating the performance of the heat transfer and concluded that the outcomes show that adding nanoparticles to ionic liquids improves the convection heat transfer, corroborated with low pressure drop consequence.
Another approach comes from studying the ionic liquids and its derivatives in natural convection in a squared enclosure. In this regard, Minea and El-Maghlany [12] performed a study of [C 4 mim][NTf 2 ] ionic liquid with small volume concentrations of alumina nanoparticles at Ra = 10 4 -10 6 .
The numerical results are correlated as a function of both Ra and ϕ, and the results in terms of Nu number are: Ansarpoura et al. [13] studied [EMIM][EtSO 4 ] ionic liquid with small concentrations of alumina nanoparticles in laminar flow and determined a correlation for Nu number using Gauss Newton algorithm using 143 data points and it writes: The correlation is valid for 500 < Re < 2000, 278.15 < T < 323.15 and for volume concentrations less than 2.5% wt.
Huminic and Huminic [15] performed a very interesting theoretical study on performance evaluation of [Hmim][BF 4 ] ionic liquid and several suspensions with nanoparticles (silicon carbide and graphene), using the experimental properties available on the literature. Authors evaluated several figures of merit in laminar and turbulent flows. The conclusion pointed out that ionanofluids can enhance the thermal performance, particularly in laminar flow.
Conclusions and Future Works
Developing a new heat transfer fluid as well as improving thermal properties of existing ones has become extremely important nowadays due to the necessity of reducing energy consumption in many applications.
Ionic liquids have major advantages, especially as medium temperature heat transfer fluid, and by adding nanoparticles, the thermal conductivity is augmented resulting in better convective heat transfer coefficients.
Here, an extensive review was performed in terms of properties and thermal convection applications of ionic liquids and their suspensions with nanoparticles. The following conclusions are drawn from this state-of-the-art review:
•
Although thermal conductivity of ionic liquids are mostly independent of temperature, viscosity follows the common fluids nature with temperature, as they decrease with temperature; • Thermal conductivity increases by adding nanoparticles and slowly decreases with temperature; • Viscosity upsurge depends on nanoparticle addition and type and decreases drastically with increasing temperature; • Specific heat variation is determined by the type of nanoparticles, while it increases with temperature; • Density increases with nanoparticle addition and decreases with rising temperature; • Heat transfer seems to be greatly influenced by both ionic liquid and nanoparticle type and concentration.
Nevertheless, an important drawback of the studies published by now is the lack of insight at a molecular level, such as intermolecular interaction between nanoparticles and the solvent. The phenomenological approach needs to be further developed. Furthermore, the application of artificial intelligence-based predictive methods in ionic liquid studies is at its very beginnings and requires further insights. The first step was noticed in the open literature (see Yusuf et al. [86]), and a number of machine-learning applications in the prediction of several ionic liquids' properties are carefully reviewed. These predictive methods can also be further extended for the ionic liquids-based nanocolloids; however, a more coordinated approach is recommended.
As a conclusion of this review, it can be inferred that ionic liquids-based nanocolloids can be seen as an efficient method for convective heat transfer enhancement. However, tremendous studies are needed in order to better understand and to elucidate their heat transfer mechanisms together with the interactions between anions, cations and nanoparticles.
Conflicts of Interest:
The authors declare no conflict of interest. | 7,984.2 | 2021-04-01T00:00:00.000 | [
"Chemistry",
"Physics"
] |
Analysis of Shape Memory Behavior and Mechanical Properties of Shape Memory Polymer Composites Using Thermal Conductive Fillers
Shape memory polymers (SMPs) are attracting attention for their use in wearable displays and biomedical materials due to their good biocompatibility and excellent moldability. SMPs also have the advantage of being lightweight with excellent shape recovery due to their low density. However, they have not yet been applied to a wide range of engineering fields because of their inferior physical properties as compared to those of shape memory alloys (SMAs). In this study, we attempt to find optimized shape memory polymer composites. We also investigate the shape memory performance and physical properties according to the filler type and amount of hardener. The shape memory composite was manufactured by adding nanocarbon materials of graphite and non-carbon additives of Cu. The shape-recovery mechanism was compared, according to the type and content of the filler. The shape fixation and recovery properties were analyzed, and the physical properties of the shape recovery composite were obtained through mechanical strength, thermal conductivity and differential scanning calorimetry analysis.
Introduction
Shape memory materials have the property of remembering and returning to their original form in response to specific external stimuli such as heat, light, current and magnetic fields; heat is the main external stimulus [1][2][3][4][5][6][7]. Shape memory materials are transformed by applying an external force at a high temperature, and the shape is temporarily fixed when they are cooled. Later, they return to their original, permanent shape, which they remembered, at temperatures above the glass transition [8][9][10]. The shape memory effects of materials have been studied extensively since they were first discovered in Ni-Ti alloy at the U.S. Naval Ordnance Laboratory in 1963, and by the 1980s, they had been put into practical use. Since then, the Nippon Zeon Company developed the first shape memory polymer polynorbornene in the early 1980s, the second discovery, a trans-isopolypremebased feature shape memory polymer, was developed in Kuray, and later a shape-memory polymer based on styrene butadiene, was developed by Asahi [11,12].
SMPs have the following property: if they attain a rubbery state at a temperature above the glass transition temperature, the elastic modulus lowers rapidly. Subsequently, when the surrounding temperature cools down, they display a temporary shape. If the surrounding temperature rises above the glass transition temperature again, they return to the glassy state and the elastic modulus increases, thereby resulting in the original shape [13]. Recently, the development of composite materials that exploit these characteristics of shape-memory materials, has attracted much attention. Shape memory alloys (SMAs) have advantages such as biocompatibility and a bidirectional shape memory capability, but they also have disadvantages such as limited rigidity and processing conditions. Shape memory polymers (SMPs) have a lower density than shape memory alloys and can thus be easily realized with lightweight characteristics. They also have excellent shape memory characteristics and excellent biocompatibility. In addition, SMPs can be applied in various fields due to their low price and good formability; they have attracted attention for use in wearable displays and biomedical materials due to their excellent biocompatibility. Nevertheless, because of their polymer properties, pure SMPs have inferior mechanical properties relative to SMAs, and the use of SMPs in a wider range of engineering applications has remained limited. Studies to reinforce the physical properties, such as the tensile strength of SMPs have thus been carried out. At present, most of the research on shape memory materials are mainly conducted in academia and on metal-based alloys; moreover, it is in the early stages of research.
In this study, we have attempted to find optimized curing conditions of shape memory polymer composites and have also analyzed shape memory performance and their physical properties according to the types of fillers and hardener amount. In addition, by adding graphite, we investigated the mechanical properties of the composites with improved shape memory performance.
Materials and Preparation
The SMP sample was prepared using an epoxy resin and hardener (Struers, Korea). The following reinforcements were added: graphite (Sigma Aldrich, USA), Cu (Yeeyoung Cerachem, Korea), Al (Yeeyoung Cerachem, Korea) and 60 µm and 100 µm carbon fiber (Fiberman, Korea). Figure 1 indicates the epoxy resin and hardener used in this work. The SMP sample preparation procedure is shown in Figure 2. First, the epoxy resin and curing agent were placed in a clean bottle in a 10:1 weight ratio and hand shaken until completely mixed. Subsequently, the various reinforcements were added to the mixture, which was mixed with a mechanical stirrer. The mixing ratios of the reinforcements are shown in Table 1. The SMP composite was cured in a mold of 100 mm × 20 mm × 1 mm for 2 h at 80 • C. The mold and the resulting samples are shown in Figure 2. The shape fixation rate and recovery rate tests were conducted on samples with ratios of epoxy resin to hardener of 8:1, 9:1 and 10:1, respectively. The shape fixation rate was the highest and the recovery time was the fastest for sample 3, for which the ratio of epoxy resin to hardener was 10:1. Therefore, the hardener ratio was fixed at 10:1, and the fillers were added. The shape recovery test was conducted with 40 wt% and 50 wt% fillers. However, because fractures occurred during deformation to the temporary shape, the maximum ratio of the additive was fixed at 30 wt%. DSC thermal analysis of the shape memory polymer sample was performed on a DSC250 thermal analyzer (TA instrument, USA) to determine the glass transition temperature (T g ) for the type and amount of the filler. The samples were heated from 30 • C to 180 • C in a protective atmosphere of N 2 at a heating rate of 10 • C/min.
Tensile Test
Tensile tests were carried out at room temperature using a universal testing machine (Instron 3382, USA) with the ASTM D638 standard. The gauge length was 50 mm, and the crosshead speed was 1 mm/min.
Shape Memory Test
Samples of 100 mm × 20 mm × 1 mm were heated to 100 • C and then modified to fit a 20 mm thick mold by applying an appropriate force. The maximum bending angle recorded was θ max . The fixed mold is illustrated in Figure 3. The modified sample was cooled to room temperature under constant external force. The mold and force were removed after the sample was fixed, and the sample then kept at room temperature until it was fully fixed.
The fixed bending angle is denoted as θ fixed . Finally, we maintained a constant temperature of 100 • C and recorded the bending angle (θ i ), every 10 s. The process is illustrated in Figure 4.
Shape fixation ratio : Shape recovery ratio :
Thermal Conductivity
The thermal conductivity was measured using a Hot Disk (TPS 2500 S, Sweden) equipment to measure the change and improvement of the thermal conductivity according to the type and content of the filler.
Differential Scanning Calorimetry (DSC)
The results of DSC for the three ratios of epoxy resin to hardener are shown in Figure 5. The glass transition temperatures (T g ) obtained from the DSC analysis are summarized in Table 2. Polymer segments are assumed to be locked into a glassy state when the polymer segmental motion is limited at temperatures below T g . In this work, the midpoint of the temperature range of the DSC curve was defined as T g . The value of T g was found to be between 59 • C and 73 • C, and the T g values tended to decrease with a relative decrease in the amount of hardener. The results of DSC according to the filler type and amount are shown in Figure 6, and the T g values obtained from the DSC analysis are summarized in Table 3. This result shows that all samples with Graphite and Cu fillers, have a distinctive T g, ranging from 46.41 • C to 58.37 • C and their T g value decreases as the amount of filler increases. It is expected that the overall transition temperature can be tuned by adding fillers. The fillers make the thermal conductivity of SMP composites relatively higher. The typical segments of these SMP composite added fillers would respond faster than SMPs without filler for the same amount of heat. Thus, the transition temperature of composites shift to a lower value by adding filler [14].
Tensile Strength Test
The tensile strength according to the ratio of the epoxy resin to the hardener and the type of filler is shown in Figure 7. The tensile strength of the specimen with a curing agent to resin ratio of 8/1 was 127% higher than that of the 10/1 specimen. As the ratio of the curing agent increased, the mechanical strength improved, but the shape-recovery ability tended to decrease. As the hardening agent ratio increases, the tensile strength of compo- Figure 6. Results of DSC according to filler type and amount with Epoxy 10/1.
Tensile Strength Test
The tensile strength according to the ratio of the epoxy resin to the hardener and the type of filler is shown in Figure 7. The tensile strength of the specimen with a curing agent to resin ratio of 8/1 was 127% higher than that of the 10/1 specimen. As the ratio of the curing agent increased, the mechanical strength improved, but the shape-recovery ability tended to decrease. As the hardening agent ratio increases, the tensile strength of composites also increases, which is due to the larger number of 3D cross-linking networks during the curing process of epoxy. Generally, because fillers play important roles in enhancing mechanical properties, the tensile strength of composites may also vary according to the amount and shape of fillers. Generally, by using nanofillers such as graphite, copper and carbon fiber, the tensile strength of composites can be improved by adding appropriate amounts of fillers. However, the reported mechanical properties do not reflect the expected level of improvement, which can be attributed to the poor dispersion effect of the filler, agglomerates that act as crack initiation and weak interfacial interactions.
Shape Fixation Ratio
The fixation rate tended to decrease as the additive content increased, but the fixation rate was maintained above 90%. A shape fixation ratio graph according to type and amount of filler is shown in Figure 8 and Table 4. Generally, the use of Cu as fillers yield a high fixation rate. When carbon-based filler graphite flake of average 20 µm size was used, the fixation rate tended to be substantially lower. For Cu, the 1 µm diameter particles were spherical and did not affect the fixation rate, whereas the plate-like graphite was considered to affect the shape fixation rate. SEM images of the fillers are shown in Figure 9.
Evaluation of Shape Recovery Rate
The shape recovery ability was tested according to the filler type and content. Eventually every samples with filler show the permanent shape is fully recovered regardless of time. Thus, the comparative analysis by type filler was conducted on the capability of shape recovery over a specific period of time. A graph of the shape recovery ratio versus time, is shown in Figure 10. The recovery rate from the tests are shown in Tables 5 and 6. Samples reinforced with nanocarbon materials such as graphite tended to have an increased recovery rate as the filler amount increased, whereas in the samples containing Cu, the recovery rate decreased as the filler amount increased. Figure 11 shows snap shot images of measuring the shape recovery ratio according to the type and filler content. Figure 11. Snap shots of shape recovery performance by type of filler.
Thermal Conductivity of SMP Composites
The thermal conductivity was measured to investigate the changes in thermal conductivity according to the filler type and content, and to examine the correlation between the thermal conductivity and shape recovery capability. A graph of the thermal conductivity according to the filler type and amount, is shown in Figure 12. For comparison, a pure SMP sample without additives was prepared and measured: it exhibited a low thermal conductivity of 0.2296 W/mK. By adding only 10 wt% of graphite, the thermal conductivity was doubled. In addition, it was also observed that, the higher the amount of fillers, the higher the thermal conductivity. The highest thermal conductivity was 0.898 W/mK for 30 wt% graphite composites. However, for the copper filler, the effect of filler amounts was not as significant. The highest thermal conductivity for copper filler was 0.2776 W/mK for 10 wt% amount. For this reason, graphite, which has higher thermal conductivity, shows better shape recovery performance. This indicates that graphite is a more effective filler than Cu for SMPs in terms of thermal conductivity and the thermal reaction of shape recovery. This is because the volume of graphite filler is much larger than that of copper for the same weight, so the dispersibility of graphite in SMP composites may be higher than that of copper. Figure 13 shows the volume comparison of graphite and copper for the same amount.
Conclusions
SMPs have poor shape recovery performance such as rate and time to full recovery for without fillers, so their applicability is low. The thermal conductivity plays an essential role in the improvement of shape recovery capability. Therefore, in this study, commonly available fillers with the highest thermal conductivity were considered to enhance their applicability and supplement their thermal conductivity and shape recovery performance. DSC results were also provided. On comparing the shape recovery ability according to the filler type under the same conditions, the specimens with graphite additives exhibited a tendency of increased thermal conductivity, as the filler content increased. For the specimens with non-carbon-based Cu additives, the higher the filler content was, the lower was the directional recovery ability. Nevertheless, for all specimens, the final recovery rate exceeded 90%.
Author Contributions: D.C. designed the research; M.K., S.J., S.C., J.Y., J.K. and D.C. performed the experiments and analyzed the data; M.K. and D.C. wrote the manuscript; all authors discussed and commented on the manuscript. All authors have read and agreed to the published version of the manuscript.
Funding:
The authors acknowledge the support of this research by Korea Institute of Industrial Technology (KITECH). | 3,320.8 | 2021-09-01T00:00:00.000 | [
"Materials Science"
] |
Reconciling the Cretaceous breakup and demise of the Phoenix
s (Vol. 21, No. 10, pp. 793-813). Elsevier. 1459 Wobbe, F., Gohl, K., Chambord, A., & Sutherland, R. (2012). Structure and breakup history of the 1460 rifted margin of West Antarctica in relation to Cretaceous separation from Zealandia and 1461 Bellingshausen plate motion. Geochemistry, Geophysics, Geosystems, 13(4). 1462 https://doi.org/10.1029/2011GC003742 1463 Wortel, M.J.R. and Spakman, W., 2000. Subduction and slab detachment in the Mediterranean1464 Carpathian region. Science, 290(5498): 1910-1917. 1465 Worthington, T. J., Hekinian, R., Stoffers, P., Kuhn, T., & Hauff, F. (2006). Osbourn Trough: 1466 Structure, geochemistry and implications of a mid-Cretaceous paleospreading ridge in the 1467 South Pacific. Earth and Planetary Science Letters, 245(3-4), 685-701. 1468 Wright, N. M., Seton, M., Williams, S. E., & Mueller, R. D. (2016). The Late Cretaceous to recent 1469 tectonic history of the Pacific Ocean basin. Earth-Science Reviews, 154, 138-173. 1470 https://doi.org/10.1016/j.earscirev.2015.11.015 1471 Yan, C. Y., & Kroenke, L. W. (1993). A plate tectonic reconstruction of the Southwest Pacific, 01472 100 Ma. Oceanic Drilling Program, Scientific Results, 130, 697–709. 1473 Yang, T., Liu, S., Guo, P., Leng, W., & Yang, A. (2020). Yanshanian orogeny during North China's 1474 drifting away from the trench: Implications of numerical models. Tectonics, 39(12), 1475 e2020TC006350. 1476 Zhang, G. L., & Li, C. (2016). Interactions of the Greater Ontong Java mantle plume component 1477 with the Osbourn Trough. Scientific Reports, 6(1), 1-8. 1478 Zhao, X. F., Zhou, M. F., Li, J. W., & Wu, F. Y. (2008). Association of Neoproterozoic A-and I-type 1479 granites in South China: implications for generation of A-type granites in a subduction1480 related environment. Chemical Geology, 257(1-2), 1-15. 1481 1482 This manuscript has been submitted to Earth-Science Reviews
153
The southern boundary of the Pacific Plate is the Pacific-Antarctic Ridge (Fig. 1B). This Phoenix Plate's daughters, the Aluk Plate (Herron and Tucholke, 1976), is ongoing below the 166 northern part of the Antarctic Peninsula ( Fig. 1) (e.g. Eagles, 2004). The Aluk Plate is often also 167 referred to as Phoenix Plate, but we prefer the name Aluk Plate to make the distinction with the
234
This manuscript has been submitted to Earth-Science Reviews 8 We restore spreading along the different mid-ocean ridges that existed in the southern 235 Panthalassa realm based on published marine magnetic anomaly data of ocean floor presently 236 underlying the south Pacific Ocean (Fig. 4), reviewed in section 4. The ages of the polarity 237 chrons in our reconstruction are updated to the timescale of Ogg (2020). We incorporate all 238 rotation poles as published, even though on short time intervals (<1 Myr) these are likely 239 subject to some noise (Iaffaldano et al., 2012). Our conclusions, however, are not affected by the 240 short time-scale noise and we prefer to see the effect of all interpreted isochrons rather than an 241 arbitrary selection of these. Peninsula, the Aluk Plate, is therefore thought to be a descendent of the Phoenix Plate ( Fig. 1; 392 e.g., Barker, 1982;Eagles, 2004). Interestingly, however, for much of the Cenozoic, and until the 393 cessation of spreading around 3.3 Ma, the Aluk Plate has not been spreading relative to the 394 Pacific Plate, but relative to oceanic lithosphere of West Antarctica (Eagles, 2004). Marine
597
We reconstruct the start of spreading in both basins at 120 Ma (Fig. 6B)
689
Rotation poles of the Chasca Plate relative to the Manihiki Plate are calculated in GPlates. In our 690 reconstruction, we ensure that early motion of the Chasca Plate follows the trend of the curved 691 rift structures at the NE Manihiki margin (Fig. 8). In addition, we assume that the Pacific- Pacific, convergence and subduction continue today (Fig. 1). Conversely, convergence ceased 733 along the southern and western margins in the Late Cretaceous, which was followed by re-
738
It is well agreed upon that a subduction zone was present along the entire East
739
Gondwana margin, from the Antarctic Peninsula to New Caledonia, until 105 Ma (Bradshaw,
768
The Hikurangi-Pacific ridge formed a triple junction with the subduction zone located 769 along the margin of East Gondwana, in the vicinity of the Norfolk Ridge ( Fig. 6 and 7). North of Plate, for which there is no evidence, and which is two orders of magnitude faster than typical 796 hotspot motions (e.g., Doubrovine et al., 2012). In addition, we tested whether the latest and
818
The first often-cited argument for subduction cessation at 105-100 Ma is the timing of 819 the onset of extension that is recognized in the geology of New Zealand (Bradshaw, 1989; predicts that this spreading ridge subducted around 100 Ma below New Zealand ( Fig. 7 and 11).
853
The progressive arrival of successively younger oceanic crust before arrival of the spreading 854 ridge may then explain the 128-105 Ma adakitic magmatism, which is often related to the 855 subduction of young oceanic crust (Tulloch and Rabone, 1993).
856
In summary, geological and geochemical interpretations made for New Zealand do not 857 require that subduction ended during c. 105-100 Ma ( Fig. 7 and 11). Alternative structural and 858 stratigraphic arguments for the forearc region of New Zealand (Mazengarb and Harris, 1994; 859 Kamp, 1999Kamp, , 2000
865
Explanations for this cessation have so far mostly focused on regional geological features, such 866 as the arrival of a mid-ocean ridge in the trench (Luyendyk, 1995;Bradshaw, 1989 | 1,255.8 | 2022-12-01T00:00:00.000 | [
"Geology"
] |
Evaluation of an Environmental Transport Medium for Legionella pneumophila Recovery
The collection and storage of water-related matrices such as biofilm from collection to processing are critical for the detection of Legionella pneumophila by cultural and molecular tests. SRK™ is a liquid medium that acts both as an antimicrobial neutralizing agent and a transport medium for bacterial culture enumeration and is useful to maintain the stability of the sample from collection to analysis. The aims of this study were to evaluate Legionella pneumophila viability and bacterial nucleic acids’ stability in SRK™ medium over time at different storage conditions. Artificial bacterial inoculates with an approximate concentration of 104, 103 and 102 CFU/mL were made using Legionella pneumophila certified reference material suspended in SRK™ medium. Bacteria recovery was analyzed by cultural and molecular methods at time 0, 24 and 48 h at room temperature and at 0, 24, 48 and 72 h at 2–8 °C, respectively. SRK™ medium supported Legionella pneumophila culture viability with CFU counts within the expected range. The recovery after 72 h at 2–8 °C was 83–100% and 75–95% after 48 h at room temperature. Real-time PCR appropriately detected Legionella pneumophila DNA at each temperature condition, dilution and time point. Results demonstrated a good performance of SRK™ medium for the reliable recovery of environmental Legionella.
Introduction
Legionella spp. are aquatic bacteria that are ubiquitously found in nature, in both anthropogenic structures and in environmental waters [1]. The most common pathogenic species is Legionella pneumophila (Lp) serogroup 1 and is responsible for up to 80% of Legionnaires disease (LD) cases [2]. The exact incidence of LD worldwide is unknown because countries differ greatly in the methods used to ascertain whether someone has the infection and in reporting known cases [3]. In 2019, the incidence of LD in Italy was equal to 52.9 cases per million inhabitants [4].
Environmental sampling for the detection of Lp represents an important tool to obtain data of epidemic risk assessment and to provide remedial interventions. Monitoring water systems involves choosing sampling sites, and the number and type of samples to be obtained (water and/or biofilm), as well as the sampling method to be used [5]. Environmental sample storage and transport can be critical for the culture and nucleic acid detection of Lp, especially from biofilm samples. Italian guidelines for LD prevention and control suggest the collection of biofilm samples from a specific surface area using a sterile swab subsequently stored in a tube containing 2-5 mL of Ringer, Page or saline solution [6]. These solutions contain different concentration of salts that help to maintain the osmotic balance and allow bacterial enumeration. However, these solutions do not contain components able to inactivate the presence of antibacterial agents that may be present in samples which could interfere with bacterial quantification, such as ammonium, alcohol, and oxidizing and phenolic compounds used for sanitation procedures. SRK™ (Copan Italia SpA, Brescia, Italy) is an alternative liquid medium that acts both as a neutralizing agent of antimicrobial substances and as a transport medium for bacterial culture enumeration. De Filippis and colleagues previously described the use of this medium to evaluate the prevalence of Legionella in retirement homes and group homes' water distribution systems [7]. Another study conducted in Italy evaluated the use of biofilm samples to monitor Legionella spp. in hot water systems using 2 mL of Page's solution for specimen resuspension [8]. Casini and colleagues chose to rinse biofilm samples into 2 mL of water for the investigation of non-culturable Legionella spp. in hot water systems [9]. The standardization of biofilm sampling and related analytical practices is still far from being optimized [10], although reference documents [11,12] consider biofilm sampling an essential as part of Legionella environmental surveillance [13].
Conventional culture methods represent the gold standard for the detection and enumeration of Legionella spp. in water samples, although it can take up to 14 days to obtain a result. Moreover, culture methods are often hampered by the presence of viable but nonculturable (VBNC) Legionella and/or by the presence of fast-growing microorganisms that can inhibit the growth of Legionella, reducing the sensitivity of the method. Molecular detection, such as quantitative polymerase chain reaction (qPCR), represents an alternative tool for the rapid identification and quantification of Legionella in environmental water samples. The main advantages of this technique are the ability to detect Legionella contamination at very low levels, the rapid acquisition of results and the easier handling of large sample volumes. However, the interpretation of the results has been largely controversial [14][15][16].
The aim of this study was to evaluate the use of SRK™ medium for the recovery of Lp in terms of viability to culture and nucleic acid stability for qPCR detection over time and in different temperature conditions.
Nine lenticules were dissolved into 7.5 mL of SRK™ medium to obtain an Lp bacterial suspension of 10 5 CFU/mL (6.9 × 10 5 and 2.3 × 10 5 CFU/mL considering BCYE and GVPC agar, respectively). Two further serial dilutions (10 4 and 10 3 CFU/mL, respectively) were obtained using 0.75 mL of the bacterial suspension and 6.75 mL of SRK™ medium. These 3 starting bacterial suspensions were further diluted (0.25 mL of each bacterial dilution was added to a further volume of 2.50 mL of SRK™ medium in order to achieve a bacterial suspension of approximately 10 4 , 10 3 and 10 2 CFU/mL) in a set of 12 tubes for each concentration, in order to store the bacterial suspensions at different temperatures for recovery at different time points using both culture and molecular methods (tube A and B). The samples preparation procedure is summarized in Figure 1. To evaluate the ability of SRK™ medium to maintain Lp viability and nucleic acid stability, bacterial inoculates were stored in two different temperature conditions: room temperature (20-25 • C) and refrigerated temperature (2-8 • C). Bacterial recovery was evaluated by cultural and molecular methods at time 0, 24 and 48 h (T0, T24, T48) at room temperature and at time 0, 24, 48 and 72 (T0, T24, T48, T72) hours at 2-8 • C, respectively.
Culture Method
Culture media (BCYE and GVPC) inoculate volumes were used as indicated in ISO 11731:2017 [17]. The agar plates were inoculated with 0.1 mL of each dilution and incubated aerobically in presence of 5% CO 2 at 37 • C for 7 days in a humid atmosphere. Colony counts were performed in triplicate for each bacterial inoculum.
Molecular Methods
Nucleic acid stability in inoculated SRK™ medium was evaluated using both quantitative and qualitative real-time PCR detection assays associated with their nucleic acid extraction kits following manufacturer's instructions.
Two different commercial kits were used: iQ-Check ® Quanti Legionella spp. in association with AQUADIEN™ KIT for DNA extraction (Bio-Rad, Hercules, CA, USA); and qualyfast ® Legionella qPCR detection Kit with qualyfast ® DNA Extraction kit I (Bioside, Brescia, Italy). A total of 500 µL of each bacterial dilution was centrifuged for 5 min at 15,000 rpm to obtain a bacterial cell pellet, which was then resuspended using specific buffers, according to the manufacturer's instruction, respectively. Extracted DNA was eluted in 100 µL of R2 solution of AQUADIEN™ KIT and in 200 µL of qualyfast ® Legionella buffers (Bioside, Brescia, Italy).
The iQ-Check™ Quanti Legionella spp. (Bio-Rad, Hercules, CA, USA) is NF VALIDA-TION certified (certificate numbers BRD07/15-12/15), and it contains reagents to amplify and quantify Legionella spp. Each amplification was performed using 45 µL of reaction mix and 5 µL of samples or controls, according to manufacturer's instructions. The detection limit of this qPCR method is 5 Genomic Units (GU) per well, corresponding to 80 GU/L. The quantification limit of the method is 608 GU/L.
The qualyfast ® Legionella product is a kit for detection, discrimination, and quantification of Legionella spp. and L. pneumophila from water. All the reagents are pre-dosed and lyophilized in the reaction tubes, allowing storage at room temperature. A total of 15 µL of extracted DNA was added to each tube containing lyophilized reagents. A total of 15 µL of DNA free solution was added to positive and negative controls and to calibration scale (external standard). Limits of determination and quantification of this assay are 5 GU and 25 GU per reaction, respectively.
Real-time PCR assays were performed on CFX96 Touch Real-Time PCR Detection System (Bio-Rad, Hercules, CA, USA) following technical sheet. Amplification results were analyzed using CFX Manager™ Software (Bio-Rad, Hercules, CA, USA).
Data Analysis
Data regarding Lp growth on agar plates were reported as CFU mean values of plate counts performed in triplicates. Recovery rate was calculated as: (mean CFU at 48 h or 72 h/mean CFU at T0) × 100 for both GVPC and BCYE plates. Expected colonies were evaluated starting from CFU values reported on lenticule certificate and considering the number of lenticules used to prepare each bacterial suspension and volumes used for each dilution (Figure 1). This calculation was performed for both GVPC and BCYE agar plates.
Legionella quantification by qPCR method was reported as log 10 Genome Units (GU)/ sample values. Legionella GU/sample was obtained following calculation according to the two specific detection kits used.
Culture Methods
Results obtained from 10 4 (expected colonies: 2100 and 6300 on GVPC and BCYE, respectively) and 10 3 (expected colonies: 210 and 630 on GVPC and BCYE, respectively) dilutions showed an uncountable growth on both types of agar plates (not shown). Only the bacterial suspension of approximately 10 2 CFU/mL allowed for Lp bacterial colonies' enumeration at all tested conditions. In general, the recovery after 72 h at 2-8 • C storage was 83-100% and after 48 h at 20-25 • C was 75-95% based on the expected number of colonies. Results are reported in Table 1.
Molecular Methods
Real-time PCR detection showed a detection signal in keeping with bacterial inocula up to 72 h at 2-8 • C and up to 48 h at room temperature (20-25 • C), indicating bacterial nucleic acid stability in SRK™ medium. Molecular methods allowed the quantification of all three bacterial suspensions in SRK™ medium (10 4 , 10 3 and 10 2 CFU/mL) as genomic units (GU).
iQ-Check ® Quanti Legionella Spp. Real-Time Assay
Results obtained using iQ-Check ® Quanti Legionella spp. Real-Time detection assay showed the genomic units remaining stable over time at all three concentrations at both temperatures, as shown in Figure 2. The Legionella spp. DNA recovery was almost 99-100% considering all studied dilutions, after 72 h at 2-8 • C storage and after 48 h at 20-25 • C.
Qualyfast ® Legionella qPCR Detection Kit
Results obtained using qualyfast ® Legionella qPCR detection kit showed genomic units to be stable over time at all three bacterial concentrations at both temperatures, as shown in Figure 3. An optimal recovery ranging from 95% to 100% was observed using this quantitative real-time PCR kit. Furthermore, this kit also allowed the correct identification of L. pneumophila by the use of a second set of primers/probe specific for this bacterial species.
Discussion
Environmental monitoring represents an important tool to evaluate Legionella pneumophila contamination of water systems in order to prevent possible LD outbreaks. Quantification in water samples using culture examination is the gold standard for Legionella detection and it is performed according to the International Organization for Standardization [17]. To identify potential Legionella presence in water distribution systems, large amounts of water (0.5-1 L) must be collected, and the analysis must be performed within 24 h to ensure that the pathogen remains viable for culture analysis. An alternative way to detect environmental Legionella could be the analysis of biofilm samples. It is well known that this pathogen survives as an intracellular parasite of amoebae and protozoa that are found in naturally occurring microbial communities that form biofilms [18,19]. Storage and transport can be critical for Legionella culture and nucleic acid detection for both types of specimens.
The aim of this study was to evaluate the bacterial viability by culture and the stability of the nucleic acid detection by PCR of Legionella pneumophila in SRK ™ , a liquid medium that acts both as a neutralizing agent for antimicrobial substances and as a transport medium for bacterial culture enumeration.
Regarding culture results, the average number obtained from the bacterial colony counts showed an excellent viability of Legionella pneumophila at all tested conditions both by means of growth in the non-selective BCYE medium and in the selective GVPC medium. The colony count averages, resulting from the inoculation of 0.1 mL/plate of the 10 2 CFU/mL suspension, fell within the CFU/mL count expected for GVPC plates (21 CFU); a slightly higher value was shown in BCYE plates. The inoculation of the same volume from bacterial suspensions at concentrations 10 4 and 10 3 CFU/mL showed the growth of uncountable confluent colonies. Cell viability after 72 h at 2-8 • C of storage was found to be between 83 and 100%; after 48 h at room temperature, it was 75-95% as compared to the expected certified lenticule CFU counts. These results indicated that the SRK ™ conservation medium maintains Lp viability over time and at different temperature conditions. Comparing the two different growth media used, a higher number of CFU was observed in the non-selective BCYE medium compared to the selective GVPC medium, in accordance with the lenticule enumeration certificate. This difference in L. pneumophila growth is related to the highly selective GVPC composition-a medium enriched with glycine (able to weaken the bacterial wall and favor the action of antibiotics) and with polymyxin B (antibiotic acting against Gram negative bacteria) that could have interfered with the growth of L. pneumophila colonies [19].
Even if traditional culture represents the gold standard method to detect Lp in water, it can take up to 14 days to obtain a definite result, which is often variable with poor bacterial recovery. The availability of more reliable Legionella detection methods could be of great value to rapidly identify contaminated water systems. Molecular biology testing could be a good alternative to the standard culture method due to the high sensitivity and specificity of the results obtained in a shorter time. Several commercial assays that allow the extraction of bacterial DNA and subsequent detection by real-time PCR are currently commercially available. The results of this study demonstrated the high sensitivity and reproducibility of both molecular methods investigated in this study, indicating that the composition of the SRK ™ medium does not affect the stability and conservation of bacterial nucleic acids and does not interfere with the amplification reagents used in the assays.
Considering the different dilutions made, real-time PCR showed higher values of Lp quantification when compared to the culture method on the same samples. Different reasons need to be considered. Real-time PCR cannot distinguish viable from non-viable organisms, although it is able to detect viable but non-culturable (VBNC) Legionella. Moreover, the PCR measurement expressed in genomic units per liter cannot be considered equivalent to the unit of measurement for culture methods, expressed in colony-forming units per liter. Despite the clear advantages of molecular methods over culture, the limit of discriminating between live and dead microorganisms remains. Another issue, related to the determination of quantitative Legionella GU cutoffs, is to assess the risk of LD. Furthermore, different assays have different sensitivities and different limits of detection; therefore, standardizing molecular method quantification is necessary [20][21][22][23].
Recently, techniques able to inhibit DNA amplification of non-viable cells have been developed to overcome this issue. For example, some studies reported the use of molecules that intercalate into free bacterial DNA or enter membrane-compromised cells, inhibiting qPCR amplification. Propidium monoazide (PMA) is a molecule capable of covalently binding to the non-viable bacterial genome, preventing its amplification [24,25]. However, their use at certain concentrations may have a cytotoxic effect for some bacterial species, such as Lp [24]. Another solution, projected to discriminate the viable from the nonviable Lp in environmental water samples, is the use of DNase enzymes, able to enter the membranes of dead cells and degrade the nucleic acid of dead bacteria cells. In the future, these innovative approaches could allow the application of molecular biology not only as a screening technique, but also as a confirmation method for the presence of Legionella spp. recognized at the level of technical standardization.
Conclusions
The data obtained in this study showed a good performance of the SRK™ medium, supporting both bacterial viability and nucleic acid stability up to 48 h at room temperature and 72 h at 2-8 • C. SRK™ represents a good collection and transport device for the detection of environmental Legionella spp. iQ-Check ® Quanti Legionella spp. (Bio-Rad, Hercules, CA, USA) and qualyfast ® Legionella qPCR (Bioside, Brescia, Italy) also showed excellent recovery of Lp in artificially contaminated water samples.
The use of a transport medium such as SRK™ could improve the standardization of both culture and molecular detection of Lp from water or water-related matrices, useful for Legionella risk assessment evaluation. The water samples' concentrates, according to ISO 11731:2017, can be tested up to 2 days in the case of epidemic events and with high concentrations of interfering flora. This additional time, by extension, is also applicable to water-related matrices. The good recovery of Legionella pneumophila obtained by SRK™ up to 72 h following bacterial inoculation could be taken into consideration for the future updating of ISO 11731:2017.
Further experiments using both Legionella not pneumophila species and real water and biofilm samples collected from different water systems will be useful in the future in order to confirm the reliability of SRK™ in maintaining Lp viability and DNA recovery. | 4,083.8 | 2021-08-01T00:00:00.000 | [
"Biology"
] |
Investigating the Effective Factors on the Occurrence of Smuggled Goods in Iran
This study aims to examine the economic and social factors affecting emergence of smuggling goods and government's approach toward it. The crime of smuggling goods is one of the most important economic crime factors causing irreparable damage to the country’s economic system and also is seriously threatened social and cultural principles and values that govern the society. Other studies have determined the emergence of smuggling goods due to multiple factors of economic, social, and cultural, which are surveyed in this research as the most important effective factors on occurrence of smuggling goods. The aim of this research is to focus on economic and cultural factors existing in this field. In this study, we will conclude how cultural factors and consumption patterns cause the phenomenon of smuggled goods.
Introduction
Smuggling of goods is part of the country economy aiming to take advantage from the illegal trade agents.Iranian custom statistics of seizures of smuggled goods indicate the increasing number of trafficking cases, in recent years.According to the statistics, the total number of cases has increased from 28829 cases in 1995 to 77,829 counts in 2003.Due to the hidden nature of trafficking itself, the real statistics of smuggling goods is not recorded in official statistics and subsequently, it would cause being the hidden part of the country's economic performance, this fact in practice can encounter with the difficulties function of allocation and distributive policies of government.However, with the knowledge of the trafficking process or its volume with using of the strategies, it can be lead to, into the formal economic activities recorded in the national accounts other than activities in the informal economy simultaneously (Bahrami and Ghasemi, 2007).It is important to know the size of smuggling in Iran inevitability.This article tries to answer the following questions. 1) How the smuggling procedure has been in Iran during the last three decades?2) What are the factors that affect the size of smuggling?3) What are the consequences of changes in the volume of traffic?4) What ways is suggested to reduce the size of trafficking?Methods of survey in this study is based on literature related to hidden variables as a special case of Model 1, where the use of indicators and general multiple causes (MIMIC) is linear structural relations (Lisrel), the size of smuggling in Iran is estimated.2 One of the main drawbacks to empirical studies in the literature of hidden variables is lack of theoretical basis consistent with the planed modeling of Lisrel model, 1. Multiple-Indicators Multiple-Causes 2 .Linear Structural Relationships www.SID.irArchive of SID Economic Bulletin 46, in this economic research, the study for the first time at the level of foreign and domestic studies, not only this weakness was offset and introduce a theoretical model for trafficking, the empirical modeling is done consistent with it for estimating the size of the smuggling in a time series.
The Relative Desirability of Foreign Goods
The desirability of foreign goods is one of the main factors of demand for these products in the domestic market and hence the factors of trafficking with identification of taste and demand of domestic consumers, and type and extent of available demand with the aim of gaining more profit from illegal trade de facto carry out supplying goods from the unofficial route (Sheikh, 1974).There are several factors of interest for foreign goods consumption that the most important of them can be named as follows: 1.1.2Beauty and Innovation in Design and Color of Products Because of the being diversity and being interested to beauty is including of the inherent characteristics in every human, hence big companies manufacturing consumer products in order to attract customers and selling more products and ultimately gaining more earn, have considered innovation and invention in the design of its industrial as the main core of its activities and constantly try to create diversity and attractiveness according to consumer's tastes and nature in its industrial production .And this despite the fact that domestic production of country in terms of diversity and attractiveness and customer-friendly don't have ability to compete with foreign trafficking products and does not provide the available demand for consumption of these kind of goods and of course the smuggling of foreign goods is placed in the basket of consumer goods of compatriots (Gassin, 1992).
Desirability of Quality and Quantity of Foreign Goods
Desirability of commodity is among the features of a product both in terms of quality and quantity and the price that make the product to be requested and has been sold, Product quality is important for all consumers So that with the same conditions of access and price often consumers prefer to buy quality products rather than inferior and undesirable goods and to the assumption in accordance with the popular saying that "we do not have much money to buy inexpensive goods (cheap))" (Bakhshinejad, 2001).Buy quality goods, even if they have high prices.Lack of after-sales service or guarantee of related to product quality; provide grounds caused losses to consumers.
Unreasonable Tariffs for Import and Export of Goods
In the literature of international trade, tariff to be remembered is the second best policy.Custom tariffs can be a kind of tax on imports (and often exports) that cause increasing in the prices of goods for consumers and the domestic producers.Economists believe that the enacting of tariffs from the direction of undeveloped countries cause increasing prices of imported goods, reducing domestic consumption, increase domestic inefficient production, reduce imports, generate revenue for the government, redistribution of income and create inefficiency (which are known to support costs) (Lovely and Nelson, 1995;Seif, 1999).However, developing countries to implement of support policies have specific reasons, such as: protection of infant industries, the problem of external balance of payments, government income and the like this.Basically, trade restrictions and adopted support procedures resulted from the government's desire for change in the volume and pattern of trade that is determined by free competition.Tools used for protection of domestic products of developing and developed countries are very diverse.In general, these tools divided into two parts of precious and non-precious.Precious tools are including tariff policy, foreign policy and manufactured subsidies (Fausti, 1991).Non-precious tools include import licenses (permits), quotas, import restrictions, administrative barriers and technical barriers exception of tariffs of other protectionist instruments is part of tariff barriers.In our country, thus tariffs are applied on imported goods.Applied tariff rates in our country is illogical and more than other countries in the region and this is one of the main reasons for the being favorable background of smuggling goods into the country.Because the price of imported goods rises inefficiently from legal bases with obtaining further tariff and importers to reduce these costs and being earning more profit of smuggling turn to illicit crime.In our country in addition to obtaining the tariffs, other amounts with different titles (like-tariffs) are taken from imports.These amounts include all additional costs and other import taxes, is not the title customs duties and commercial benefit.Raising the rate of custom protections in the country and existence of smuggled goods on a massive scale indicates that the amount of this support should be amended to reduce the incentive for smuggling of goods.Obviously, if artificial barriers (tariff and non-tariff) be in the normal course of business, the illegal trade of smuggling goods is exacerbated and this case cause smuggling.Research suggests that there is direct link between trade policy and informal market.Rahmdel (2007) in his study entitled "smuggling of goods and currency in the Iranian criminal law" examined the effect of the extent of customs protection and its links with smuggling of goods and the results of his studies show that commodity imports with lower tariff rates will lead to reduce import and lower smuggling of goods.Based on the results of this research, tariffs should not be over 20 percent otherwise it would lead to underground activities.On the other hand, unconditional release of the goods import into the country, cause irreparable damages to production and economy of the country .In May 2006, according to suggestion of the Minister of Industry and Mines of country (time) increased import tariffs for mobile phone.Because of support of domestic products and create incentives for investors, import tariffs of mobile phones increased from 4% to 60% so artisans can maximum use from requirement of phone market that was about 10 million units alone in last year.Import tariff policy of the government in import of mobile phone with reducing import of formal borders lead to economic boom and profit in smuggling.Therefore it can be seen in action that government protection policies of some local products not only have not a positive impact on domestic products but also has increased the smuggling of these goods.Therefore, reduction of custom tariffs to prevent of trafficking is of solutions that Enrico Ferri deals with to it in the discussion of "the punishment currencies".He advised the government to prevent of the smuggling of goods do not need to use punishment or repressed leverage.Reduction of government revenue, the importer will lead to the adoption of the law rather than take the risk."Trafficking, turned into resistance against severe and terrible punishments like amputation of the hand, and death for centuries and in our time, prison and shot the offending of different Customs officers also failed to prevent the smuggling of goods.The reduction of customs rates in France, traffic declined in that country.Adam Smith (1790-1723) was right in his book "The Wealth of Nations", to declare: legislation that stimulates People to trafficking and then due to commitment of trafficking punish them to justice and cusses factor of stimulation be stronger and intensification of punishment, is a law, contrary to all the principles of legal justice."So if custom tariffs reduce and the importer of goods feels that there is a common interest despite of payment of tariff costs, he will continue to pay the customs fees rather than acceptation of smuggling risk and with paying the custom fees, deal with to the import of goods (Bhagwati and Hansen, 1973).
Trading Rules
Trade and customs laws alone are not effective in the incidence of smuggling and not to improvement and revision of the structure of trade rules and regulations, Trafficking can be eradicated forever.Trafficking resulted from many factors that contribute to the commercial and customs laws.But some of the contributions should not be underestimated in terms of impact although in terms of the number of cases seem less than other factors, Because business and customs laws is effective in outbreak, escalation or reduction of smuggling (Johnson, 1974).These factors include: 1) The structure of the rules (trade, customs) has the following problems: 3) Regulatory restrictions 4) There are numerous legal requirements, including establishment of import or export licenses, requirements related to the use of internal transportation in import, insurance of imported goods to Iranian insurer, duty payment before the entrance that underlying cost and being expensive of the price of imported goods, Financial standards, health and safety considerations of the product, process order goods at the Ministry of Commerce and Bank, foreign exchange obligations, etc. 5) Tariff barriers and para-tariffs, including diversity, and numbers of tariffs as well as being unreasonable, 6) The complexity of the calculations to import or export duties paid, 7) Excise on imports, 8) Direct taxes from the importer, domestic producer, domestic products, as well as production or sales duties.
1.1.6Giving Subsidies to Some Domestic Goods Subsidy refers to a variety of government transfer payments in order to raise consumer welfare.In other words subsidizing is part of the price of goods or services in order to increase purchasing power of consumer or increase selling power of producer.In order to make economic and social justice and benefiting all segments of society, from a minimum of amenities and livelihood feasibilities, the government pays subsidies for some goods and for subsidizing usually three aims, which include ; optimum allocation of resources, economic stability and fair income distribution.Allocation of subsidies on basic commodities will lead to differences between domestic and international prices (Norton, 1988).The difference between the prices is incentive to create demand and smuggling of goods from countries with lower domestic prices than world prices for another country.Domestic prices of some commodities, including energy carriers such as oil, gasoline and other commodities such as flour, medicines because of the government pays subsidies to them, in domestic markets of Iran is far less than the market of neighboring countries (Firuzjaee, 2003).The difference between the prices is raised exit of such goods by traffickers and even ordinary people for the supply of their foreign currency needs in abroad.So as long as the subsidies payments are not targeted in the country and the differences in price caused by the subsidies remain in place, traffic will be profitable (ibid).The present Subsidy system in the economy of Iran has been one of the affecting factors on trafficking of the exported goods.Because subsidies payment on some basic goods, cause differences of prices of these goods in the domestic market to the foreign markets of neighboring countries on the one hand and the creation of informal market of buying and selling of such goods in the actual price on the other hand.With consideration of difference in price from subsidies on some goods, gross profit from trafficking also increased in these goods, So long as the subsidies allocation for goods not to be targeted and this difference of price from subsidizing remain in place, trafficking also will be profitable, and full and proper implementation of targeted subsidies law of 2010 came into force, can be effective in reducing the illicit of export of domestic goods.
Official Paperwork and Lengthy Process of Formal Import and Export
According to regulations of import and export, import of goods and customs clearance some of imported goods subject to the authorization of some ministries and agencies, including, Ministry of Industry, Mine and Trade, Agriculture, Health and Medical Education, ICT, oil, Culture, Defence and Armed Forces Logistics, Science, Research and Technology, Roads and Urban Development, Environmental Protection Agency, Atomic Energy Agency, the country's forests, the General Directorate of Civil Aviation, the Central Bank and ... As well as several other ministries and organizations under the terms of export and import laws, export certificates related to allow clearance of imported goods or exported goods, Which can be noted :Standard Institute, Ministry of Agriculture, Ministry of Health and Medical Education, Ministry of Islamic Culture, Ministry of Communications and Information Technology, Ministry of Defense and Armed Forces Logistics, Oil Ministry, Central Bank and other institutions .Official paperwork for export and import of goods also result in a long and costly legal procedures and stagnating of exporter and importer capital as well as the deterioration of their goods.For this reason, some traders are forced to ignore the rules and t export or import their goods through illegal route.The result is the widespread smuggling of goods.Being prolong of trade and customs provisions and procedures is the effect of the following factors: Not Transparency of decisions, instructions and regulations related to a commercial, banking, tax, health, safety, and financial performance to be delivered to Customs.
Being allowed to apply different rates to each other creates problems and prolong customs formalities between the owners of goods and custom that.
The multiplicity of import licenses the multiplicity of certification organization.
The complexity, scope and long duration of the administrative process of official imports is of reasons of trafficking increase in the country and has caused some importers apply to trafficking imports, to acceleration the importation.In fact, it seems that the group did not engage on contraband imports for tax evasion on import, but the length of the import process has affected on decision.
Unemployment, Underdevelopment and Deprivation Residents of Border Areas
Reduce of the rate of formal employment is both justifying and reason of increase the employment rate in the informal economy and smuggled goods.Increase of labor supply and decrease of demand for labor in the formal sector could increase employment in the informal sector.Therefore, the reduction of employment rate in the formal economy is justifying of trafficking increase, particularly in border areas.Unemployment in addition to cut income and increase of the unemployed has social consequences, and it can be increasing factor or origin of great social corruptions and in the most optimistic state could lead to the development of mediation and trafficking.In other words it can be said that the decline in employment in the formal economy, increase the rate of employment in the informal economy and smuggling.Therefore, unemployment rate in the formal economy has direct connection with increase of smuggled goods.11 According to the magazine of "tomorrow industry" in Hormozgan province, 200 thousand people named: "paratroopers" are engaged in the smuggling of goods.
The unemployment rate in the country not only in the past decade was significantly high, but it has increase procedure.Lack of productive jobs in the border regions has caused that young people become hired workers to earn more income for smuggling networks because they don't have enough capital themselves, to work.While the average unemployment rate was declared 18 percent in 2007, the provinces of Ardebil, Bushehr, Khuzestan, Sistan and Baluchestan, Kordestan, Kermanshah, Golestan, Gilan, and Hormozgan are with unemployment rates higher than the average of country.However, rural areas of the borders have higher rate of unemployment.Check the status of border provinces shows that, despite of actions taken in order to deprivation over the past two decades; these provinces are still heavily in the economic and cultural deprivation.This means that on the one hand due to weather patterns, soil types and lack of capital possibilities, there is no basis for employment in agriculture and on the other hand for various reasons, industrial activities in these areas is lagging (Cheraghi and Heidari, 2016).Anti-smuggling law passed in 2014 to strengthen of border livelihood and development of economic activities of border areas and eventually reduce the rate of smuggling in the border areas of the country the Ministry of country (Interior) is mandated to cooperate with the headquarters (central staff) of the Anti-smuggling, and prepare the bill currency of development and sustainable security of the border areas to and submit for approval to the Council of Ministers, that Until the formulation of this thesis, action has not been taken in this regard (ibid).
Changing Consumption Patterns of the Society toward Foreign Luxury Goods
Extension of telecommunications, being satellites TV, foreign travel, a variety of advertising of foreign goods in stores and locations across the country, seeing the use of this product to acquaintances, quick access to information related to the present of new products and their quality and like this, have cause to consumers receive update information in the level of world.Now, according to those in respect of quality, price and variety of foreign goods mentioned, this factor is increased demand for foreign goods.In the field of goods consumption has been considered three approaches theoretically: The first approach, assumes a passive consumer and consumption assumes a kind of manipulation on the behalf of power.In the second approach, look to consumption is assumed as a medium for communication.Consumption in the view is a kind of rivalry, competition and communication.And the third approach, its consumption is assumed to be a secondary production.Consumer with consumption behavior, starts innovations as a result of, oh his it will be brought down power.Factors such as increased income, advertising, quality weakness of internal productions and other factors, has caused the consumption pattern of society changes toward foreign luxury and consumed goods in recent years (Fausti, 1991).And these despite the fact that major of the goods have not the possibility of business entry into the country.More importantly, is that the consumption types of luxury goods and foreign consumed goods have become an almost stable consumption patterns for households in high-income and part of middle-income families.This pattern of consumption has shown its conflict as undermine the culture of consumption pattern of Iranian goods.High demand for consumption of foreign goods and substantial income that through obtained illegal importers and sellers of goods smuggled, have increased significantly scope and volume of the arrival of the goods.Unfortunately, consumer culture to motivate people to consume foreign goods has caused even some domestic manufacturers to present their products with abroad.
Conversion of Smuggling into the Local Culture
Social -cultural components in formation of trafficking phenomenon linked mainly with social justice.Social justice is commitment to justice in the social relations and the elimination of discrimination between social groups, social classes, ethnic groups and races and between different regions.In fact, social justice is presence of equal opportunities for getting education and, skill of access to physical and financial capital through the appropriate markets.If there is damage in the area, form abnormal social phenomenon that one of the most important of them are the prevalence of smuggling and the loss of its social evil.Residents of border areas since ancient times have economic relations by the inhabitants of cross-border and always estimated level of transactions has been authorized by the government between them, but after the applying severe restrictions of trade and exchange controls and profitable smuggling of goods, the practice was more widespread among residents of border areas.After the cancellation of non-pecuniary penalties for shipments of less than a million dollar, contraband cargo shifted with worth of less than one million dollars and increased volume of illegal employment and a significant proportion of residents of border areas resorted to smuggling over the past years so opposition to it, is difficult.Smuggling has been affected of how to make and enforce rules in the community and more people due to the current situation, suppose trade laws are unfair and justify their violations in the field (Johnson, 1974).The lack of a legal ban on informal trade and smuggling on behalf of elders and religious scholars of Sunni in border areas has led to the employment of labor smuggling become as a way of promoting of income and employment of people convert to a subculture and social value and those who are active in the field by denying their violation of social norms and obligations without any concern and unscrupulous do smuggling and in most cases also benefit from the cultural support and popular support.Remarkably, even in terms of some Sunni scholars in the border areas in the seizure of smuggled goods into the country, police seized evidence and its buying and selling, is prohibited and the property must be returned to their original owners.Therefore, people of the some areas avoid of purchasing and consumption of such goods that sometimes are being sold through customs or respective departments (since seized).
Conclusion
Based on research into the affecting factors on the occurrence of trafficking of goods in Iran the following results were obtained: 1) One of the main causes of smuggling in border cities is poverty and unemployment due to the increase in labor supply and decrease of demand for labor in the formal sector is causing it.
2) Cultural issues and the desire of people to use of foreign products because of better quality make appeal to consumers.
3) According to regulations of import and export, import of good and customs clearance some of the imported goods are subject to catching license some of the various ministries and agencies that this long process has led to smuggling.4) Unreasonable tariffs for import and export of goods are one of the factors that cause the economic issue and rationalizing this situation can help to improve smuggling problem.
-
Conform with present reality -Not connecting the rules to the needs of society, Volatility or instability, -Providing field of monopolies and loss of healthy competition, in business -being inaccurate and incomprehensive rules, -Irrational tendencies laws to protect domestic production regardless of quality, price, and... -Interfering with other laws -Frequent changes in laws -The number of rules 2) Statutory prohibition | 5,541.2 | 2017-10-09T00:00:00.000 | [
"Political Science",
"Economics",
"Law"
] |
Multigear Bubble Propulsion of Transient Micromotors
Transient, chemically powered micromotors are promising biocompatible engines for microrobots. We propose a framework to investigate in detail the dynamics and the underlying mechanisms of bubble propulsion for transient chemically powered micromotors. Our observations on the variations of the micromotor active material and geometry over its lifetime, from initial activation to the final inactive state, indicate different bubble growth and ejection mechanisms that occur stochastically, resulting in time-varying micromotor velocity. We identify three processes of bubble growth and ejection, and in analogy with macroscopic multigear machines, we call each process a gear. Gear 1 refers to bubbles that grow on the micromotor surface before detachment while in Gear 2 bubbles hop out of the micromotor. Gear 3 is similar in nature to Gear 2, but the bubbles are too small to contribute to micromotor motion. We study the characteristics of these gears in terms of bubble size and ejection time, and how they contribute to micromotor displacement. The ability to tailor the shell polarity and hence the bubble growth and ejection and the surrounding fluid flow is demonstrated. Such understanding of the complex multigear bubble propulsion of transient chemical micromotors should guide their future design principles and serve for fine tuning the performance of these micromotors.
Additionally, external fields such as magnetic field have been employed to successfully guide and control the motion of micromotors [9]. The engines in the early generations of bubble-propelled micromotors employed catalytic degradation of fuels, such as hydrogen peroxide and sodium borohydride by materials such as platinum, palladium, or manganese oxide [10][11][12][13][14]. While these micromotors offered proof of concept for microscale self-locomotion, their widespread use is restricted by the incompatibility of their fuels with biological environments. Another obstacle was the retrieval of the micromotor, made of nondegradable materials, upon completion of its task. Transient, chemically powered micromotors-a new microengine generation-address these challenges. In an attempt to move away from toxic fuels, expensive catalysts, and nondegradable leftovers, a push towards biofriendly materials has begun in recent years in the micromotor community [15,16]. To incorporate biodegradability for in vitro and in vivo applications, these micromotors are powered by the consumption of active metals, such as magnesium (Mg), zinc, and iron, which react with biofluids or seawater [17][18][19][20][21][22]. These micromotors self-propel via single replacement reactions in gastric acid, or via reaction with water in intestinal fluid, salty buffer solutions, or basic buffer solutions where the counter ions aid in removing the passivating byproduct layer of magnesium hydroxide [16].
The ability of Mg-based micromotors to propel in biological fluids with minimal risk has enabled their use for important applications, such as drug delivery, where micromotors outperform passive diffusion-based methods [17][18][19][20]23]. To fine tune the performance of these micromotors and provide design principles, it is crucial to understand their dynamics and the underlying mechanisms of motion.
Unfortunately, the transient nature of these Mg-based micromotors and the variation of their active material over their lifetime make them a more complicated system to study compared to chemically propelled hollow shell micromotors with constant active area [24][25][26][27]. Moreover, while a hollow tubular microrocket has an opening for fluid entrance and another opening for bubble ejection [28][29][30], these Mg-based transient micromotors have only one opening that serves for both purposes. Additionally, time-dependent depletion of the active metal inside a transient micromotor increases the complexity of the bubble-propulsion mechanisms. Therefore, current theoretical models for bubble-propelled catalytic micromotors cannot address the dynamics of transient micromotors, and a new framework is needed to understand their distinct time-varying propulsion behavior.
In this paper, we investigate the mechanisms of bubble propulsion for transient chemically powered micromotors and identify the elements of micromotors' powered motion and stochastic dynamics. We investigate self-locomotion over the lifetime of micromotors and analyze the different processes involved in their motion. Our study identifies distinct patterns in the formation and ejection of bubbles, calling each pattern a gear, in analogy with macroscopic multigear machines. We also investigate the distinct behavior emerging from the effect of hydrophobic and hydrophilic shell surfaces upon the bubble propulsion and motion of such transient micromotors. Finally, we discuss the fluid flow around the stationary and motile microengines. We hope that our multigear framework described here, along with the new understanding of the bubble growth and ejection and influence of the shell polarity, could give insight into the future design and engineering of a wide range of highperformance transient chemical micromotors.
Results and Discussion
We studied the behavior of Mg-based transient micromotor with hydrophilic (titanium dioxide) and hydrophobic (parylene) insulating shells [31]. A typical micromotor is fabricated by coating an Mg microparticle (diameter 20-25 μm) with an insulating material using atomic layer deposition (Fig. S1). The thickness of a titanium dioxide (TiO 2 ) shell is~170 nm for the majority of our analysis, and the thickness of parylene is~500 nm. One area of the Mg particle (facing the substrate) is not covered by the insulating material and serves as an "opening," through which Mg is exposed to the reactive solution, in our case simulated gastric acid (pH~1-2). The reaction of Mg with the acid results in the production of hydrogen molecules, leading to nucleation, growth, and ejection of bubbles (Figure 1(a)). Micrographs of a typical Mg-TiO 2 micromotor propelling in simulated gastric acid illustrate the bubble production and parallel depletion of the Mg core over time (Figure 1(b)). Scanning electron microscopy (SEM) (Figure 1(c)) and energydispersive X-ray spectroscopy (EDX) (Figure 1(d)) images at different stages of micromotor lifetime demonstrate such gradual depletion of the Mg core over time. Throughout this depletion, the speed of the micromotor undergoes a large variation. Figure 1(e) shows a typical micromotor's instan-taneous speed (dots) alongside a local average fit (solid line). Figure S2 demonstrates an alternative version of Figure 1(e) with a jagged line representing the speed profile of the micromotor. The fluctuations in the speed suggest that random processes and stochastic dynamics are involved in the micromotor dynamics during its lifetime, until complete Mg depletion and, hence, the stop of micromotor motion at~250 s. To understand the underlying mechanism behind these phenomena, we study the dynamics of these micromotors at shorter time scales. Figure 2 demonstrates how these micromotors move by both bubble push (Video S1) and fluid jet (Video S2) mechanisms at short time scales. In case of an axisymmetric micromotor (including perfectly spherical Mg particle, no shell defects, and an axisymmetric circular opening), a Mg-TiO 2 micromotor and the ejected bubbles move rectilinearly along the symmetry axis. Figure 2(a) shows an experimental realization of an axisymmetric micromotor with an almost uniform distribution of bubble size. Upon formation and growth, each bubble pushes the micromotor forward by exerting force on the micromotor and the bubbles in the tail. Such bubble-push process is the main mechanism during the initial stages of the micromotor lifetime. Thus, as shown in Figure 2(a), iii, the micromotor's net displacement (the distance from micromotor's initial position at t = 0) consists of discrete steps. Since there is no significant backward motion upon bubble ejection, the length (solid red line) of the micromotor travel path almost coincides with the net displacement (dashed blue line).
The structural and dynamic symmetries have a significant influence on the operation of micromotors. While structural asymmetries [13,32] appear in typical transient micromotors ( Figure 2(b)) as a result of imperfections in materials and fabrication process, dynamic asymmetries can occur during the operation of both axisymmetric and typical micromotors. The structural asymmetries in a typical micromotor may result from nonisotropic Mg particles, defects and nonuniformity in the shell, or asymmetry in the opening as artifacts of the fabrication process ( Figure 2(b), ii). On the other hand, the dynamical asymmetries appear as a result of random nucleation of bubbles with different sizes at several locations inside the micromotor (after significant depletion of the Mg core) and their interactions, coupled with their ejection at various angles or extended growth while attached to the micromotor. Additionally, environmental noise, fluid convection, and buoyancy force affect the motion of these micromotor. Thus, the length of the micromotor trajectory will differ greatly from its displacement. (Figure 2(b), iii). The asymmetry effects become more pronounced once a portion of the Mg core is depleted and a cavity is formed inside the micromotor. The bubbles can nucleate and grow at different locations inside the cavity before being ejected. Upon the sudden formation of each bubble inside the cavity, a corresponding volume of the fluid is ejected out from the opening. This sudden fluid jet results in hopping of the micromotor (Figure 2(c) and Video S2). The intensity of the fluid jet and the hopping distance depends on the bubble size inside the cavity and the size of the micromotor's opening. As illustrated in Figure 2(c) upon bubble nucleation inside the cavity, the micromotor hops forward, the bubble is ejected joining to the train of bubbles, and the micromotor is stationary until the next bubble is nucleated inside the cavity.
The majority of the micromotors behave similarly to the typical micromotor shown in Figure 2(b). There are usually structural and dynamic asymmetries involved whose effect may vary over the lifetime of the micromotor, and sequences of bubbles with random sizes and ejection times are formed.
To find order in this complex system, we aimed to identify the elements of motion upon which the dynamics of a micromotor is built. We looked closely at how bubbles form and where the bubble size variation comes from. In all of the experiments, we used a solution containing a surfactant (0.2% of Triton X-100) to stabilize the bubbles; yet, it is useful to examine how different amounts of surfactant will change the overall bubble size. The dependence of the bubble size Data Fit upon the surfactant concentration is presented in Figure S3. As expected, higher surfactant concentration resulted in smaller bubble diameter while averaging over all gears. To build a framework for quantitative analysis, we categorized the bubble formation mechanism into three bubble ejection processes which contribute to the propulsion differently. Thus, in analogy with a macroscopic multigear machines, we call each process a gear.
At the early stages of micromotor operation, bubbles nucleate on the Mg surface and grow on the micromotor surface before detachment. At later times, upon cavity formation inside the micromotor, some bubbles grow first inside the cavity and then continue to grow while a portion of them is outside of the micromotor (Figure 3(a)). We call this process "Gear 1." Some of the bubbles only grow inside the cavity and suddenly hop out of the micromotor. We call these "Gear 2" (Figure 3(b)). Due to the extended growth period, on average a Gear 1 bubble grows to a larger size than a Gear 2 bubble. We also observed the ejection of very small bubble, which usually does not contribute strongly to propulsion (Figure 3(c)). We call this small bubble ejection Gear 3. This gear can result from many nucleation events taking place at the same time inside the cavity, forcing some small bubbles to hop out before having enough time to grow. In summary, Gear 2 is more prevalent in the early stage of a micromotor's life while all gears are prevalent in the middle of the lifetime as the cavity inside has expanded with depleted Mg. Finally, at the end, we see sporadic Gears 1 and 3 bubbles before the motion stops.
To illustrate the differences between Gear 1 and Gear 2, we present in Figure 3(d) a micromotor showcasing both modes of bubble production (Video S3). During the first 10 ms of the time lapse, we see the nucleation of a bubble (highlighted in blue). By the 20 ms mark, the bubble is already outside the motor but has not detached and is continuing to grow until about 80 ms at which point it has grown to a size comparable to the size of the micromotor. Finally, the bubble detaches, and the micromotor moves forward. The displacement between the bubble and micromotor at 90 ms is due to the fluid jet caused by the nucleation of other bubbles inside the micromotor. The growth phase for the next bubbles (Gear 2, highlighted by red) is much shorter (30 ms). The bubble nucleates and grows inside the micromotor structure and is ejected out. While the bubbles of Gear 1 have time to grow on the surface, the Gear 2 bubbles are limited in size to the space inside the cavity and are thus expected to be smaller.
We analyzed the micromotor in Figure 3(d) for a longer period of 8.5 s to quantify the behavior of Gear 1 and Gear 2 bubbles and their contribution to motion. The micromotor did not eject a Gear 3 bubble during the time interval of our analysis. We observed that the sequence of gear occurrence is random which we attribute to the stochastic processes involved in bubble nucleation and ejection. Therefore, we statistically quantified the significance of each gear. The micromotor speed varies over time (Figure 3(e)). There are periods of inactivity in displacement mostly during the growth phases of Gear 1 bubbles followed by large spikes in speed due to the large displacement from bubble push or fluid jetting. To differentiate the behavior of the gears quantitatively, for each bubble, we extracted the time required to eject the bubble, the bubble size, and the micromotor displacement due to each bubble formation and ejection. The time it takes to eject a bubble from the micromotor (Figure 3(f)) ranges around 0:2 ± 0:06 s for Gear 2 bubbles while Gear 1 bubbles take more than three times longer with an average of 0:64 ± 0:34 s. A similar trend is observed in the bubble size (Figure 3(g)). Gear 2 bubbles are smaller with an average size of 12:1 ± 0:85 μm while Gear 1 bubbles grow up to 20:3 ± 7:25 μm. Finally, Gear 2 bubbles result in a smaller displacement of 1:6 ± 0:86 μm (Figure 3(h)) compared to Gear 1 bubbles with average displacement of 4 ± 1:96 μm.
Having established a multigear dynamics framework, an important design question may arise: can we engineer the micromotor structure such that we can have more control over the bubble propulsion process and the occurrence of gears with fine-tuned bubble properties? A comprehensive answer to this question requires exploring the design parameter space of the micromotor with different material properties and symmetry considerations, and this will be the scope of our future work. However, within the scope of the current study, we demonstrate qualitatively the effect of material selection on multigear bubble propulsion. The presented results so far have been based on a hydrophilic TiO 2 shell. Changing the shell to hydrophobic parylene significantly affects the bubble nucleation, growth, and ejection, and thus the overall micromotor propulsion (as shown in Figure 4(a) and Video S4). During the first one minute of a micromotor's lifetime, a typical Mg-TiO 2 micromotor (Figure 4(a)) shows higher average speed and displacement than a typical Mg-parylene micromotor. A micromotor with a parylene shell has a lower bubble generation frequency than a Mg-TiO 2 one and longer bubble growth periods, both accompanied by diminished displacement over time. The speed spikes of an Mg-parylene micromotor are much smaller than that of a Mg-TiO 2 micromotor (Figure 4(b)). Figure 2(c) shows the formation of a bubble by an Mg-parylene micromotor halfway through its lifetime. The bubble grows in the middle, part of it extends out of the opening, whereby it continues to grow for a very long time until finally detaching from the micromotor (Video S4). This is a clear demonstration of Gear 1 and here the bubble grows up to a size larger than the micromotor itself (Figure 4(c)). The time of Gear 1 bubble growth and ejection for a micromotor with hydrophobic shell is more than 30 times longer than compared to a micromotor with a hydrophilic shell (Figure 3(f), B).
Halfway through the micromotor lifetime, while the majority of bubbles for hydrophobic shell micromotors are Gear 1, hydrophilic shell micromotors produce a random train of Gears 1, 2, and 3 at a much higher rate and smaller bubble size. We observed a major structural distinction in the curvature of Mg inside a micromotor after the formation of the cavity. As shown in Figure S4, for a hydrophilic shell micromotor, the Mg core becomes slightly convex in shape, with the Mg core being dissolved most rapidly at the edges. We speculate that as gastric acid enters the micromotor, it preferentially wets the sides of the micromotor, thus consuming faster the Mg at the sides. Additionally, it is easier to nucleate a bubble on the side adjacent to a TiO 2 wall as opposed to the middle of the Mg core. Conversely, as schematically presented in Figure 4(d), i, it is our understanding that the Mg surface in a hydrophobic shell micromotor is concave. While we do not have a way to observe the curvature inside the micromotor directly, we deduced from the circle fitting and the angle between the bubble and the equator line created by Mg that the metal surface is concave (Figure 4(e)). As such, the bubble has space to grow to a larger size inside the cavity which supports and keeps the part of the bubble inside the cavity while a portion of the bubble grows on the micromotor surface. As a result, the outside part has more time to grow before the surface tension at the water-bubble interface, the pressure inside the bubble, and the curvature of the bubble around the opening pull the inside part out (Figure 4(d), ii).
The effect of gear type and occurrence frequency on bubble propulsion, at more fundamental level, is manifested in the pattern of the reactive fluid flow inside and around the micromotor. A detailed analysis of the effects of gears on fluid dynamics is beyond the scope of our current study. Here, we provide general discussion on the pattern of fluid flow generated by bubble production mechanism. Figure 5 and Video S5 demonstrate the operation of a stationary and a motile Mg-TiO 2 microengine. The bubble ejection of a stationary microengine near a substrate induces a pattern of circular flow (Figure 5(a)) similar in shape but opposite in direction to a puller microorganism under confinement [33]. These filter feeder microorganisms mix their local environment by circular flow and bring food to their mouth. The similar biomimetic flow pattern of transient micromotors can serve the same purpose by enhancing the transport of reactive materials in the fluid toward the opening of the microengine which provides efficient local mixing. The biomimetic flow pattern changes when the stationary microengine turns into a motile micromotor. Instead of circular flow, the translocation of freely moving microengines generates disordered open streamlines. (Figure 5(b)). The remarkably enhanced fluid dynamic resulting from the transient micromotor platform offers considerable promise for increasing the efficiency of a variety of medical and decontamination processes.
Conclusion
In conclusion, we have established a multigear bubble propulsion framework to analyze the stochastic sequence of bubbles generated during the motion of transient micromotors. We identified three modes of bubble ejection. The bubbles that continue to grow outside the micromotor tend to be larger and take more time for ejection but present larger micromotor displacement. We investigated the distinct effects of hydrophobic and hydrophilic shell on the operation of micromotors including bubble nucleation rate, bubble size, and the bubble ejection processes. A more detailed investigation of the effect of material selection upon multigear dynamics and discovering design principles for fine tuning the dynamics of multigear bubble propulsion micromotors will be the subject of our future studies. Our analysis of the fluid flow pattern around the microengines and its similarities to flow around filter feeder microorganisms suggest new possibilities aligned with our previous studies [33] for exploiting the transient micromotors for enhanced local mixing and environmental remediation. Our analysis framework provides a pragmatic guideline to quantitatively study the complex system of multigear bubble propulsion and investigate the effect of the material and environmental parameters (including additional parameters involved in other biological media such as serum or interstitial fluid) on elements of motion. Our analysis framework provides new insights and understanding of the bubble propulsion of chemical micromotors and can be extended to other transient micromotor structures where multiple bubble production mechanisms may change with time. Our study guides future design principles of transient micromotors and serves for fine tuning the performance of these micromotors. | 4,771.2 | 2020-02-21T00:00:00.000 | [
"Engineering"
] |
A PI3K p110β–Rac signalling loop mediates Pten-loss-induced perturbation of haematopoiesis and leukaemogenesis
The tumour suppressor PTEN, which antagonizes PI3K signalling, is frequently inactivated in haematologic malignancies. In mice, deletion of PTEN in haematopoietic stem cells (HSCs) causes perturbed haematopoiesis, myeloproliferative neoplasia (MPN) and leukaemia. Although the roles of the PI3K isoforms have been studied in PTEN-deficient tumours, their individual roles in PTEN-deficient HSCs are unknown. Here we show that when we delete PTEN in HSCs using the Mx1–Cre system, p110β ablation prevents MPN, improves HSC function and suppresses leukaemia initiation. Pharmacologic inhibition of p110β in PTEN-deficient mice recapitulates these genetic findings, but suggests involvement of both Akt-dependent and -independent pathways. Further investigation reveals that a p110β–Rac signalling loop plays a critical role in PTEN-deficient HSCs. Together, these data suggest that myeloid neoplasia driven by PTEN loss is dependent on p110β via p110β–Rac-positive-feedback loop, and that disruption of this loop may offer a new and effective therapeutic strategy for PTEN-deficient leukaemia.
D ysregulation of the molecular pathways involved in the self-renewal, differentiation and proliferation of haematopoietic stem cells (HSCs) can cause leukaemia. Notably, the serine/threonine kinase Akt, which acts downstream of PI3 kinase (PI3K), is hyper-phosphorylated in up to 80% of acute myeloid leukaemia (AML) cases 1 . This is unlikely to be due to mutations in upstream receptor tyrosine kinases alone. In chronic myelogenous leukaemia, PI3K/Akt signalling can also be activated through downregulation of the phosphatase and tensin homologue (PTEN) by BCR-ABL 2 . PTEN is a lipid phosphatase that counteracts PI3K signalling by dephosphorylating phosphatidylinositol-3,4,5-trisphosphate (PIP3). PTEN is frequently inactivated in haematological malignancies 3,4 , including in AML and T cell acute lymphoblastic leukemia (T-ALL) 5 . Notably, PTEN expression is often reduced in the disease through several other modes of PTEN regulation, for example, microRNAs, epigenetic modifications and ubiquitination [6][7][8][9] , which likely contribute to the high frequency of Akt phosphorylation in myeloid leukaemia.
In mice, genetic ablation of PTEN in the haematopoietic system leads to HSC depletion in the bone marrow (BM), myeloproliferative neoplasia (MPN) and transplantable acute leukaemia (myeloid or T-cell leukaemia) [10][11][12] . In patients, MPNs such as chronic myelogenous leukaemia or myelofibrosis can progress to AML 13 .
Class I PI3Ks are heterodimeric lipid kinases that produce the lipid second messenger PIP3 on stimulation of cells by many growth factors. Class I PI3Ks are divided into class IA (p110a, p110b and p110d) and class IB (p110g) enzymes; of these, the p110a and p110b isoforms are ubiquitously expressed, while p110d and p110g are enriched in leukocytes. Work in several different murine models has documented distinct requirements for different PI3K isoforms in particular tumour types 14,15 . For example, p110a is essential in a model of mutant Kras-induced lung adenocarcinoma 16 . Recently, we showed that Ras-mutated myeloid leukaemia is also dependent on the p110a isoform, and combined pharmacologic inhibition of p110a and mitogenactivated protein kinase kinase (MEK) could be an effective therapeutic strategy for Ras-mutated myeloid malignancies 17 . Although p110b plays a less prominent role in receptor tyrosine kinase (RTK) signalling, it mediates G protein-coupled receptor (GPCR) and integrin signalling [18][19][20] , and has been shown to interact specifically with Rho family GTPases Rac1 and CDC42 (ref. 21). Several recent studies demonstrated that p110b is required in many, but not all, PTEN-deficient solid tumours 20,22,23 . However, it is not known which PI3K isoforms are most important for myeloid neoplastic transformation driven by PTEN loss.
A number of pan-class I PI3K and dual class I/mTOR inhibitors are now in clinical trials for cancer, including leukaemia. However, targeting PI3K with these inhibitors could potentially lead to severe toxicity, which could be prevented by targeting single PI3K isoforms. To this end, numerous isoform-selective compounds are currently under development with some already in clinical trials 14 . The p110d-selective inhibitor idelalisib (referred to here as GS1101) has been remarkably effective in treating indolent B-cell malignancies, and is now approved by the FDA for the treatment of chronic lymphocytic leukaemia 24 . In the case of solid tumours, p110a-selective inhibitors have shown great promise in early-phase trials for patients with tumours bearing PIK3CA mutations 14 .
Notably, selective inhibitors of p110b are in clinical trials as anticancer reagents for advanced solid tumours with PTEN deficiency (NCT01458067). Thus, unravelling the role of each PI3K isoform, and its contribution to leukaemic transformation driven by PTEN loss, would inform rational approaches in targeting the PI3K pathway with a better therapeutic window.
In the present study, we used genetically engineered mouse models to determine which of the class IA PI3K isoforms are most important in mediating the effects of Pten loss in HSCs. We show that, in the setting of Pten loss, p110b is the main PI3K isoform responsible for MPN development and HSC depletion in the BM. Furthermore, we show that isoform-selective PI3K inhibitors recapitulate our genetic findings. We also found that a signalling loop featuring p110b and Rac plays an important role in the absence of Pten. Our results suggest that targeting p110b and/or Rac may lead to an effective therapeutic strategy for PTEN-deficient myeloid leukaemia.
Consistent with previous studies 10,11 , all Pten D/D mice developed MPN and reached the survival end point 20-40 days post injection (DPI; Fig. 1a). Pten D/D ;p110a D/D and Pten D/D ; p110d À / À mice also developed MPN with slightly extended survival (Fig. 1a). Notably, Pten D/D ;p110b D/D mice lived the longest, with median survival significantly longer than that of any other group (Fig. 1a). Further observation revealed that, whereas control, Pten D/D , Pten D/D ;p110a D/D and Pten D/D ;p110d À / À animals developed MPN, six out of nine Pten D/D ;p110b D/D mice succumbed to T-ALL (Fig. 1b). BM from the three Pten D/D ; p110b D/D mice that did develop MPN was analysed for excision of the pik3cb allele. Notably, we found that BM of these mice had incomplete deletion of Pik3cb alleles suggesting that p110b is critical for the development of MPN in this model ( Supplementary Fig. 1b). Deletion of p110b in HSCs using Mx1-Cre in animals that are wild-type (WT) for Pten does not significantly affect blood counts ( Supplementary Fig. 1c).
Histopathological analysis of moribund animals of Pten D/D , Pten D/D ;p110a D/D and Pten D/D ;p110d À / À mice at 20-40 days post pIpC showed that they developed massive splenomegaly with a marked increase in cells expressing myeloperoxidase, a marker used to detect leukaemic cells of the myeloid lineage, in both the spleen and liver ( Supplementary Fig. 2a), confirming MPN development in these mice. Notably, thymuses in these moribund mice appeared normal ( Supplementary Fig. 2b). However, most Pten D/D ;p110b D/D animals became moribund at 50-70 days post pIpC with markedly increased thymus weights ( Supplementary Fig. 2b), infiltration of terminal deoxynucleotidyl transferasepositive T lymphoblasts (CD4 þ or CD4 and CD8 double-positive T-cell blasts) in the thymus and BM and increased white blood cell counts ( Supplementary Fig. 2a,c-e), all of which are manifestations of T-ALL. These results suggest that the p110b isoform of PI3K plays a uniquely important role in driving myeloid neoplastic transformation in mice with Pten-deficient HSCs, but does not contribute to the development of T-ALL in this murine model.
Previous studies have shown that Pten deletion in T-cell progenitors causes malignant transformation in the thymus and leads to T-cell lymphoma/T-ALL within 50-150 days 28,29 . Mice with Mx1-Cre-mediated deletion of Pten D/D , Pten D/D ;p110a D/D or Pten D/D ;p110d À / À showed infiltrating MPN disease and became moribund within 20-40 days after pIpC, earlier than the disease latency for T-cell disease development. Since Pten D/D ;p110b D/D mice did not develop MPN, they survived longer and developed T-cell lymphoma/T-ALL B50-70 days post pIpC injection, a timeline consistent with previous reports on T-cell lymphoma/ T-ALL formation in models of Pten loss in T-cell progenitors 28,29 .
This suggests that p110b ablation does not prevent T-ALL formation driven by Pten loss.
To examine further the PI3K isoform dependence in T-ALL induced by Pten loss, we investigated the roles of p110a and p110b in a different T-ALL model driven by Pten ablation in T-cell progenitors using Lck-Cre 30 . Interestingly, deletion of either p110a or p110b had no effect on T-ALL in this model 3 ( Supplementary Fig. 2f). These results underscore the distinct roles of p110b in myeloid and lymphoid neoplasia induced by Pten deletion in haematopoietic cells. p110b mediates myeloid expansion induced by Pten loss. To further characterize disease in the Pten D/D ;p110 D/D mice, we killed mice of each genotype at 26 DPI, the time point at which the Pten D/D mice become moribund. Similar to previous reports, all animals in the Pten D/D group displayed massive splenomegaly, increased spleen cellularity and loss of spleen architecture at this time point (Fig. 1c,d). Both Pten D/D ;p110a D/D and Pten D/D ; p110d À / À mice showed evidence of MPN similar to that of Pten D/D mice, suggesting that ablation of p110a or p110d failed to rescue this disease phenotype. Notably, Pten D/D ;p110b D/D mice had significantly reduced spleen cellularity and size, compared with Pten D/D mice (Fig. 1c,d). Consistently, pathological analysis of the spleen and liver revealed infiltration of myeloid cells in Pten D/D , Pten D/D ;p110a D/D and Pten D/D ;p110d À / À animals, but not in Pten D/D ;p110b D/D mice (Fig. 1c). Flow cytometric analysis confirmed an increased population of myeloid cells (Mac1 þ Gr1 þ ) in the BM, spleen and peripheral blood of Pten D/D animals ( Fig. 1e; Supplementary Fig. 3). Again, the numbers of Mac1 þ Gr1 þ cells in these organs in Pten D/D ;p110b D/D but not in Pten D/D ;p110a D/D and Pten D/D ;p110d À / À animals were consistently reduced compared with those of Pten D/D mice ( Fig. 1e; Supplementary Fig. 3), suggesting that ablation of p110b suppressed myeloid cell expansion on Pten loss.
To further validate the role of p110b in the myeloid expansion caused by Pten loss, we performed colony assays in methylcellulose supplemented with myeloid growth factors. Compared with wild-type controls, both BM and spleen cells from Pten D/D animals generated an increased number of colonies, which was significantly reduced in Pten D/D ;p110b D/D mice (Fig. 2a). Together, these results demonstrate that p110b is required for MPN development in the absence of Pten.
To determine whether the contribution of p110b to myeloid neoplasia in the absence of Pten is a cell-autonomous or indirect effect, we transplanted whole BM cells from Pten D/D , Pten D/D ; p110b D/D or control mice into recipient mice (Fig. 2b). Four weeks after transplantation, all groups were treated with pIpC, and the relative frequency of CD45.2 þ donor-derived Mac1 þ Gr1 þ cells was monitored over 16 weeks. The proportion of Pten D/D donor-derived myeloid cells expanded significantly 4 weeks after pIpC and remained elevated during the course of the experiment. In contrast, the Pten D/D ;p110b D/D donor-derived myeloid population remained stable during the entire experiment, with levels much comparable to that of wild-type control mice (Fig. 2c). There were no significant differences in the percentage of donor-derived CD3-positive T cells among any of the groups tested ( Supplementary Fig. 4a). The percentage of donor-derived B220-positive B cells was reduced after Pten deletion, and deletion of p110b did not alter B-cell chimaerism ( Supplementary Fig. 4b). These data suggest that p110b mediates the expansion of myeloid cells in a cell-autonomous manner.
p110b perturbs HSC homeostasis on loss of Pten. Earlier studies showed that HSC-specific deletion of Pten leads to the exhaustion of HSCs in the BM, their accumulation in the periphery and extramedullary haematopoiesis 10,11 . Hence, we wanted to test whether p110b ablation could rescue HSCs. In Pten D/D mice, the numbers of both the Lin À Sca-1 þ c-kit þ (LSK) cells, containing HSCs and the CD150 þ CD48 À Lin À Sca-1 þ c-kit þ population, which is enriched for long-term HSCs (LT-HSCs) were significantly reduced at 26 DPI, consistent with previous findings 11 ( Fig. 3a; Supplementary Fig. 5a). Ablation of p110b was able to partially rescue LSK cells and restore LT-HSCs in Pten-null BM (Fig. 3a). Loss of Pten did not change the total number of myeloid progenitors, or the frequencies of the common myeloid progenitors and granulocyte macrophage progenitors or megakaryocyte-erythroid progenitors, but led to a significant decrease in the number of common lymphoid progenitors consistent with original reports 11 To determine whether p110b is responsible for the increased extramedullary haematopoiesis in the spleen seen after Pten loss, we measured the frequency and absolute numbers of HSCs and progenitors in the spleens of Pten D/D and Pten D/D ;p110b D/D animals. Pten deficiency led to a significant increase in the number of LSK cells, as well as LT-HSCs, short-term HSCs (ST-HSCs) and progenitors in the spleens of Pten D/D animals ( Fig. 3b; Supplementary Fig. 5c,d) 11,31 , which was partially suppressed in the spleens of Pten D/D ;p110b D/D animals ( Fig. 3b; Supplementary Fig. 5c,d). These results suggest that deletion of p110b normalizes the distribution of phenotypic LSK cells between the BM and extramedullary tissues in Pten D/D ;p110b D/D animals compared with Pten D/D controls. Thus, our findings are consistent with the idea that p110b contributes to the perturbed HSC homeostasis observed in the absence of Pten leading to extramedullary haematopoiesis and the development of MPN.
p110b mediates leukaemia initiation in the absence of Pten. It has been reported that Pten loss in the BM leads to the depletion of HSCs and the generation of leukaemia-initiating cells 10,11 . To determine whether the p110b isoform also uniquely plays critical roles in these processes in the Pten-loss setting, we performed competitive multi-lineage repopulation assays to compare the contribution of marked (CD45.2) Pten D/D , Pten D/D ;p110a D/D , Pten D/D ;p110b D/D donor BM cells to that of wild-type competitor cells (CD45.1) following transplantation into lethally irradiated mice. Consistent with earlier reports, the contribution of donorderived cells to the peripheral blood was progressively decreased and eventually depleted for Pten D/D donors, but not for control donors 10,11 (Fig. 4a). HSCs derived from Pten D/D ;p110a D/D mice also failed to sustain long-term reconstitution. In striking contrast, ARTICLE HSCs derived from Pten D/D ;p110b D/D mice were able to reconstitute recipient animals for more than 20 weeks (Fig. 4a). In addition, the majority of Pten D/D and Pten D/D ;p110a D/D -recipient mice developed T-ALL as evidenced by the abundance of donor-derived CD45.2 þ CD3 þ ;CD4 þ or CD3 þ CD4 À T lymphoblasts at the experimental end point of 20 weeks in these mice ( Fig. 4b; Supplementary Fig. 6).
In contrast, recipients of BM from wild-type control mice and from the majority of Pten D/D ;p110b D/D animals remained leukaemia free with few CD45.2 þ CD3 þ cells at the experimental end point ( Fig. 4b; Supplementary Fig. 6). Furthermore, analysis of the BM at week 20 showed that the donor chimaerism in the LSK, ST-HSC and LT-HSC compartments was significantly improved in the Pten D/D and Pten D/D ;p110a D/D groups (Fig. 4c). These data suggest that, in the absence of Pten, p110b is the major PI3K isoform critical for the loss of HSCs and for leukaemia initiation.
To determine the cellular mechanism underlying the improved reconstitution of Pten-null BM cells on loss of p110b, we examined the cell cycle status, senescence, apoptosis and homing properties of HSCs. As reported earlier, we also found that loss of Pten led to increased cycling of HSCs and reduced the number of quiescent HSCs (Supplementary Fig. 7a) 11 . Although ablation of p110b resulted in a tendency towards rescuing these effects, the results did not reach statistical significance ( Supplementary Fig. 7a). Moreover, we did not observe any change in the proportion of whole BM or LSK cells expressing senescenceassociated b-gal activity or undergoing apoptosis in any of the groups tested ( Supplementary Fig. 7b,c). We then performed homing assays, in which fluorescently labelled BM cells were transplanted into irradiated wild-type hosts, and donor-derived cells were quantified after 24 h. We found that Pten deficiency significantly reduced the homing capacity of transplanted cells to the BM, and p110b ablation could partially rescue the homing potential (Fig. 4d). We also found that p110b ablation does not affect homing in Pten-wild-type BM cells (Fig. 4d). Thus, we conclude that p110b is responsible, at least in part, for the reduced homing activity of Pten-deficient HSCs.
Inhibition of p110b suppresses myeloid leukaemogenesis.
To determine whether our findings using a genetic method could be recapitulated by pharmacologic approaches utilizing PI3K isoform-selective inhibitors at effective doses as published in earlier studies, we first examined the effects of PI3K isoform inhibition on myeloid progenitor function. We cultured BM cells and splenocytes from Pten D/D animals in methylcellulose supplemented with myeloid growth factors in the presence of PI3K inhibitors. As reported in previous studies 10 , the pan-PI3K inhibitor GDC0941 and the mTOR inhibitor RAD001 significantly suppressed the increased colony formation arising from Pten deletion in a dosedependent manner (Fig. 5a). Consistent with our genetic findings, inhibition of p110a with BYL719 (a p110a-selective inhibitor) 32 and p110d with GS1101 (ref. 33) had a modest effect on the expansion of myeloid cells in the context of Pten loss (Fig. 5a). Since p110g is also expressed in leukocytes, we tested the p110g inhibitor NVSPI35 (ref. 34). Interestingly, inhibition of p110g with NVSPI35 showed some effect on BM cells, but not on splenocytes (Fig. 5a). Notably, inhibition of p110b with KIN193 (a p110bselective inhibitor, also known as AZD6482) 14,22 significantly reduced formation of both BM-and spleen-derived myeloid colonies in methylcellulose in a dose-dependent manner (Fig. 5a) suggesting that pharmacologic inhibition of p110b is highly effective in suppressing myeloid cell expansion driven by Pten loss.
To further determine the effects of pharmacologic inhibition of PI3K isoforms in vivo, we treated a group of pIpC-induced Pten D/D animals with BYL719, KIN193, IC87114 (a p110dselective inhibitor in the same class as GS1101, but with better bioavailability in mice) 35 , AS605240 (p110g-selective inhibitor suitable for in vivo studies) 36 or a vehicle control 10 days after induction (Fig. 5b). All the inhibitors were used at the effective doses in vivo as published in earlier studies [36][37][38] . Treatment with BYL719 (ref. 37), IC87114 (ref. 38) or AS605240 (ref. 36) resulted in a minimal survival benefit compared with vehicle-treated animals (Fig. 5c). Notably, mice treated with KIN193 had a significantly longer survival as compared with mice in any other group (Fig. 5c). Moreover, KIN193-treated animals appeared healthy and had significantly reduced spleen weights and normallooking spleen architecture compared with vehicle-treated mice ( Fig. 5d; Supplementary Fig. 8), consistent with our genetic data that ablation of p110b largely prevented myeloid leukaemia in Pten-deficient mice.
Next, we examined PI3K/Akt signalling in Pten-null BM cells in response to isoform-selective inhibition. As expected, vehicletreated Pten-null BM cells from Pten D/D animals showed markedly increased Akt phosphorylation compared with wild-type BM cells (Fig. 5e). Interestingly, inhibition of either p110a, p110b or p110d led to a significant reduction of p-Akt, compared with the controls (Fig. 5e). We also examined Akt activation by measuring basal p-Akt levels in LSK cells by intracellular phosopho-flow cytometry after Pten deletion and short-term isoform-selective inhibitor treatment of lineagenegative cells from Pten D/D BM. We detected significantly higher basal levels of p-Akt in Pten D/D LSK cells compared with WT LSKs, and again inhibition of p110a, p110b, p110d or p110g led to a significant reduction of p-Akt compared with the vehicle group (Fig. 5f). Since p110b is not the only isoform responsible for mediating Akt signalling in Pten-deficient BM and HSCs, Akt signalling alone is not sufficient to explain the specific biological effects of p110b ablation or inhibition observed in our study.
Pten-deficient HSCs depend on the p110b-Rac axis. Recent data suggested that p110a, p110d and p110g bind to and are activated by the Ras subfamily of GTPases, while p110b instead binds to and is activated by the Rho subfamily GTPases, Rac1 and CDC42 via its 'Ras-binding domain' (RBD) 17,21 . Previous studies also reported that an intact RBD was required for signalling and oncogenic transformation by wild-type p110b, suggesting a potential role for the interaction of Rho GTPase with p110b in transformation 39,40 . Notably, Rac1 and CDC42 can also be activated downstream of PI3K by PIP3-dependent guaninenucleotide exchange factors 41,42 . It has been previously reported that Rac plays important roles in the homing and survival of HSCs 43,44 . Given the significant rescue of HSCs in Pten D/D ; p110b D/D mice, we hypothesized that a unique positive-feedback signalling loop might exist between p110b and Rac, in which p110b is activated by Rac and Rac could in turn be activated by the phosphoinoside products of p110b in the setting of Pten-null haematopoietic cells.
Notably, we detected higher levels of Rac-GTP in the BM of Pten D/D mice, which could be suppressed by deletion of p110b but not p110a (Fig. 6a). To investigate whether the binding of p110b to Rac is important in mediating p110b activity in Ptendeleted BM cells, we mutated the two highly conserved key residues within the p110b RBD to generate a p110b-S205D/ K224A double mutant lacking the binding activity to Rac1 (ref. 21), and performed an add-back experiment with either wild-type or RBD-mutant p110b in BM cells derived from Pten D/D ;p110b D/ D mice ( Fig. 6b; Supplementary Fig. 10). Colony-forming assays revealed that, while adding back a wild-type p110b in Pten D/ D ;p110b D/D BM cells restored myeloid colony numbers comparable to those of Pten D/D BM cells, the RBD-mutant p110b failed to rescue colony formation (Fig. 6c). To determine whether p110b affects Rac-GTP levels in HSCs/progenitor cells (HSPCs), we performed the Rac-GTP assay either on Lin-negative Pten D/D BM cells or Pten D/D ;p110b D/D cells expressing wild-type p110b and RBD-mutant p110b. We detected higher levels of Rac-GTP in the Pten-deficient cells compared with WT control cells, and these levels were significantly reduced in Pten D/D ;p110b D/D cells. Adding back wild-type p110b to Pten D/D ;p110b D/D HSC/P cells, partially rescued Rac-GTP levels but adding back RBD-mutant p110b failed to rescue Rac activity ( Fig. 6d; Supplementary Fig. 10) Together, these data suggest that the interaction of p110b with Rac plays an important role in mediating the myeloid clonogenic activity driven by Pten loss.
To further investigate the functional dependency of Pten-deleted leukaemic cells on the p110b-Rac axis, we utilized NSC23766, a potent Rac inhibitor 45 in our Pten-null model (Fig. 7a). We found that treatment of these mice for 10 days led to a reduced disease burden, as demonstrated by reduced spleen size and cellularity ( Fig. 7a; Supplementary Fig. 9). Similarly, treatment of Pten D/D mice with NSC23766 resulted in a significant reduction of HSC and myeloid progenitor numbers in the spleen compared with vehicle controls (Fig. 7b; Supplementary Fig. 9). Treatment with NSC23766 also led to a significantly prolonged survival of Pten D/D mice (Fig. 7c), recapitulating the findings for genetic ablation or pharmacological inhibition of p110b in Pten-null animals.
Since Rac is required for p110b activation downstream of GPCRs 21 , we assessed the functional importance of the Rac-p110b signalling axis in HSPC function in response to activation of CXCR4, a GPCR important in the regulation of HSPCs. We used Transwell migration assays with CXCL12, a NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9501 ARTICLE potent chemo-attractant of stem cells that signals through CXCR4. Lineage-negative BM cells from Pten D/D mice showed increased migration towards CXCL12 compared with WT control cells (Fig. 7d). This migration was abolished by the GPCR inhibitor pertussis toxin (PTX; Fig. 7d). Interestingly, we observed significantly reduced migration of Pten D/D ;p110b D/D cells, and of Pten D/D cells treated with either KIN193 or NSC23766, compared with Pten D/D and Pten D/D ;p110a D/D cells (Fig. 7d). This suggests that deletion of p110b, or pharmacologic inhibition of either p110b or Rac, partially interferes with the migration of Pten D/D Freshly isolated lineage-negative BM cells were treated with inhibitors as in (e) and subjected to flow cytometry for LSK staining and intracellular P-Akt staining (n ¼ 3) for each, and median fluorescence intensities were normalized to control. cells towards a CXCL12 gradient, likely through perturbed GPCR signalling.
Because murine models of haematopoietic-specific Rac1 and Rac2 deficiency have revealed differential roles of Rac proteins in terms of HSPC function, we wanted to understand which Rac isoform is more important in the absence of Pten. To this end, we used siRNA to knockdown either Rac1 or Rac2, or both, and performed colony assays on Pten D/D and Pten D/D ;p110b D/D BM cells (Fig. 7e,f; Supplementary Fig. 10). We also tested the Rac inhibitor NSC23766, which targets both Rac1 and Rac2 (ref. 46). Knockdown of either Rac1 or Rac2, or their combined knockdown or pharmacological inhibition significantly reduced colony formation by Pten D/D cells to levels obtained with Pten D/D ; p110b D/D BM cells (Fig. 7f). However, knockdown of Rac1 or Rac2, the combination, or NSC23766 treatment did not further suppress colony formation beyond the effects of p110b deletion (Fig. 7f), suggesting that there is no additive or synergistic effect of Rac inhibition with p110b deficiency in Pten D/D cells. Together, these results suggest that p110b-Rac1/2 work in concert to mediate the effects of Pten loss in promoting myeloid neoplasia.
Discussion
We and others have reported that Pten-deficient solid tumours frequently rely on p110b (refs 20,23,47). In this study, we report for the first time an essential role for p110b in promoting haematologic neoplasia driven by Pten deletion in HSCs despite the expression of four different PI3K isoforms in haematopoietic cells. We have also found that p110b contributes to HSC depletion in the BM after Pten deletion. Interestingly, we found that Mx1-Cre-mediated deletion of p110b in HSPCs of animals that are WT for Pten does not significantly affect blood counts. In fact, these animals appear healthy for many months after excision, suggesting that targeting p110b may lead to an effective therapy for myeloid leukaemia with little toxicity to normal HSCs.
Despite the marked impact of genetic deletion or pharmacologic inhibition of p110b on MPN, and the significantly delayed onset of leukaemia, a fraction of Pten D/D ;p110b D/D animals succumbed to T-ALL at a later time. Berenjeno et al. 48 showed that in Pten þ /animals, inactivation of p110b led to reduced PIP3 generation in lymphoma tissues, but had little impact on lymphoma formation. It is possible that these tumours become p110b independent through the acquisition of secondary alterations. In fact, Yilmaz et al. 10 have documented the presence of cytogenetic alterations in leukaemic blasts from Pten D/D animals. Alternatively, isoform dependency may shift with cell differentiation. For example, the isoform dependency in the skin hamartoma driven by Pten loss changed from a p110b dependency in the basal layer of the epidermis to a p110a dependency in the suprabasal cells as the basal cells underwent stepwise differentiation to become suprabasal cells 37 . In this study, we also provide evidence that neither p110a nor p110b has any effect on T-ALL driven by T lymphocyte-specific deletion of Pten using Lck-Cre. In this system, it has been shown that p110d and p110g contribute to T-ALL induced by Pten loss in T cells 28 . These studies provide additional data that accentuate the distinct roles of p110b in the HSCs and in myeloid and lymphoid tumour initiation in the absence of Pten. Interestingly, we found that inhibition of p110b, p110a or p110d could similarly reduce p-Akt in Pten-deficient BM and HSCs, suggesting an Akt-independent pathway specific to p110b is important in Pten-deficient HSCs in promoting myeloid neoplasia. We report a new mechanistic insight that may explain the unique role of p110b in this setting. Since p110b binds to Rac rather than to Ras via its RBD, unlike the other class I PI3K isoforms 21 , we investigated the role of the p110b-Rac axis in the setting of myeloid neoplasia induced by Pten loss in HSCs. Notably, Rac signalling is not only important for the activation of p110b but it itself is also activated by PIP3 via PIP3-activated guanine-nucleotide exchange factors, forming a potential signalling loop (Fig. 7g) 14,49 . We found strong evidence that this loop is indeed active in our Pten-deficient model. We show that Rac was activated in Pten-null BM cells, and this activation was suppressed in Pten/p110b double KOs, but not in Pten/p110a double KOs. This hypothesis was further supported by our finding that only wild-type p110b, but not the RBD mutant of p110b, rescued colony formation in Pten/p110bdeficient BM cells. Notably, the effect of the RBD-mutant p110b on inhibiting colony formation in Pten-null BM cells is comparable to that of p110b deletion. An intact RBD was reported to be required for membrane localization of p110b for both signalling and oncogenic transformation by wild-type p110b in cultured cells 40 . Our data suggest that the interaction of p110b-Rac may play an important role in mediating p110b activity downstream of GPCRs and tyrosine kinases in the context of Pten deficiency. Moreover, pharmacologic inhibition of p110b or Rac in Pten-deficient mice resulted in a strikingly similar functional rescue in vivo, with a reduction in extramedullary haematopoiesis in the spleen and improved survival.
Of the three isoforms of Rac family GTPases, Rac2 is expressed specifically in haematopoietic cells, while Rac1 and Rac3 are ubiquitously expressed 44,50 . The Rac inhibitor NSC23766 targets all three Rac members: Rac1, 2 and 3 (ref. 46). Both Rac1 and CDC42 have been shown to bind p110b in a recent study 21 . Binding to Rac2/3 was not tested, but might also be expected, based on the homology of their effector domains with that of Rac1. Previous studies have suggested that Rac1 and Rac2 play both distinct and overlapping roles in HSCs and progenitor cells, while the role of Rac3 in haematopoiesis has not been defined 44,51 . It also has been shown that targeting both Rac1 and Rac2 was effective in a mouse model of BCR-ABL-induced MPN, as well as in a mouse model of MLL-AF9 AML 46,52 . Interestingly, our data show that the effect of knockdown of Rac2 is comparable to that of combined knockdown of both Rac1 and Rac2, or a pan-Rac inhibitor NSC23766. Since Rac2 is primarily expressed in haematopoietic cells, our data suggest that Rac2 could potentially be a better pharmacologic target with reduced toxicity.
Yilmaz et al. have shown that the mTOR inhibitor rapamycin can rescue HSC depletion and can suppress the development of leukaemia in vivo. More recently, the Armstrong and Morrison groups reported that mTORC1 and mTORC2 play critical roles in haematopoiesis and Pten-loss-driven leukaemogenesis, respectively 53,54 . By ablation or inhibition of p110b, we obtained similar results suggesting that the activation of mTOR in HSCs by Pten loss may be mediated largely by p110b. A recent study demonstrated that Rac1 regulates the activity of both mTORC1 and mTORC2 (ref. 55), providing a potential Akt-independent link between p110b-Rac and mTOR. Together, these data suggest that p110b-Rac acts upstream of Akt and mTOR. We feel that our data are most consistent with the working model shown in Fig. 7g, in which p110b works in a signalling loop with Rac to generate the key signals arising from Pten loss. Notably, these signals include both Akt-dependent and Akt-independent pathways leading to cell proliferation and migration.
In summary, our results provide the first evidence that PI3K-p110b plays an essential role in controlling HSC function in the setting of Pten loss 56 . We have also uncovered a specific role for p110b in myeloid leukaemia induced by Pten deficiency. In contrast, we found that p110b is dispensable for T-ALL induced by Pten loss. Most importantly, our data show that a p110b-Rac signalling loop is important for the induction of myeloid neoplasia in the absence of Pten. Thus, secondgeneration p110b-or Rac-selective inhibitors may interrupt this loop, thereby providing a promising new therapeutic strategy for Pten-deficient myeloid leukaemias while preserving normal haematopoiesis.
Colony-forming assays. BM and spleen cells were collected, subjected to red-cell lysis and resuspended in Iscove's modified Dulbecco's medium/10% fetal bovine serum/5% penicillin-streptomycin. Cells were plated in the presence of inhibitors in duplicate in M3434 methylcellulose media (Stemcell Technologies) at 1 Â 10 4 cells per dish for BM and 5 Â 10 4 cells per dish for spleen cells. Colonies were scored after 7 days.
Rac activation assay. BM cells from corresponding mice at 7 DPI of pIpC were collected and immediately subjected to Rac1 activation assay with the Rac1 activation assay kit (Millipore) according to the manufacturer's instructions.
Histology. Recipient mice were killed at the indicated time points, or when they began to show signs of disease. Organs were fixed in formalin, and histology slides were prepared and stained at the Brigham and Women's Rodent Histology Core Facility. Digital images were acquired on a Nikon Eclipse E400 microscope equipped with a digital camera and analysed using Spot Advanced software.
Immunohistochemistry. For histological analyses, formalin-fixed tissue sections were embedded in paraffin, sectioned and stained with haematoxylin and eosin by the Dana-Farber/Harvard Cancer Center Rodent Histopathology Core. P-Akt flow cytometry analysis of LSK cells. Phospho-flow cytometry was performed as previously described 56 , with the following modifications: lineagenegative BM cells from mutant animals were isolated using lineage depletion kit (Miltenyi Biotec) and serum starved for 1 h, and treated for 2 h with 1 mM of BYL719, KIN193, GS1101 and NVSPI3. Cells were then fixed with 4% paraformaldehyde, and permeabilized with cold 100% acetone. Cells were than stained simultaneously with c-kit, Sca-1 and anti-mouse P-Akt (Alexa 647; 1:100 dilution, cat. no. 2337, Cell Signaling). All data acquisition was performed on a LSRII (BD) flow cytometer, and results were analysed and basal level of P-Akt was calculated as normalized to WT cells by calculating median fluorescent intensity using FlowJo v.8.8.7 (Tree Star).
Long-term competitive repopulation assays. Recipient mice (4-6 weeks old female mice; B6.SJL strain) received two doses of 540 rads each, delivered 3 h apart. Nucleated BM cells from control and Pten D/D mice (C57 Bl/6) or from compound mutant mice (Pten D/D ; p110a D/D , Pten D/D ;p110b D/D and Pten D/D ;p110d À / À ) were mixed with wild-type competitor BM-nucleated cells (B6.SJL), and were injected into the retro-orbital venous sinus of irradiated recipients. Peripheral blood was obtained retro-orbitally every 4 weeks, subjected to red-cell lysis and analysed by flow cytometry to assess donor cell engraftment for up to 20 weeks after transplantation. Pilot experiments showed that Pten-mutant animals had a greatly reduced repopulation capacity; therefore, an excess of mutant cells over control cells was used. Each recipient mouse received 1 Â 10 6 Pten mutant, ctrl or compound mutant BM-nucleated cells plus 2 Â 10 5 competitor cells. Tissues from recipient mice were collected and stained for pathological examination.
Plasmid constructs. Mutations were generated in the pBabe-HA wild-type P110b by site-directed mutagenesis to obtain p110b-S205D/K224A double mutant to obtain Ras-binding mutant P110b. This plasmid was used to transduce Pten D/D ; p110b D/D BM cells and for colony-forming experiments. | 8,212.4 | 2015-10-07T00:00:00.000 | [
"Medicine",
"Biology"
] |
New constraints on the linear growth rate using cosmic voids in the SDSS DR12 datasets
We present a new analysis of the inferred growth rate of cosmic structure measured around voids, using the LOWZ and the CMASS samples in the twelfth data release (DR12) of SDSS. Using a simple multipole analysis we recover a value consistent with $\Lambda$CDM for the inferred linear growth rate normalized by the linear bias: the $\beta$ parameter. This is true in both the mock catalogues and the data, where we find $\beta=0.33\pm0.06$ for the LOWZ sample and $\beta=0.36\pm0.05$ for the CMASS sample. This work demonstrates that we can expect redshift-space distortions around voids to provide unbiased and accurate constraints on the growth rate, complementary to galaxy clustering, using simple linear modelling.
I. INTRODUCTION
The growth rate of cosmic structure f tells us how fast density fluctuations ∆ grow with respect to the scale factor of the Universe a: Its measurement as a function of time and scale is a key cosmological probe, very sensitive to the nature of gravity (e.g. [26,32]). To infer the growth rate, we can measure redshift-space distortions (RSD) in the galaxy clustering signal. These distortions are due to the peculiar motions of galaxies, which on large scales have a coherent motion sourced by the gravitational potential of cosmic structures. This gravitational potential is itself proportional to the growth rate, in the linear regime. For standard General Relativity (GR) and isotropic cosmologies, the linear growth rate does not depend on the comoving spatial scale [36] and can be approximated by f ∼ Ω m (z) γ where Ω m is the matter density parameter at redshift z, and γ is a constant. For a ΛCDM Universe γ ∼ 0.55 [26,32], independently of the environment. Constraints on the linear growth rate made with galaxy-galaxy correlation function measurements in redshift-space are well known, e.g. [9,10,18,35,40,43] . These measurements have shown a general consistency with the ΛCDM cosmological model, up to a 2.5% precision, albeit in some cases showing tension with the predictions of the latest Cosmic Microwave Background measurements [37].
On the other hand, it was only recently that the growth rate has been inferred using the RSD pattern around cosmic voids. There are at least two reasons to perform this consistency test of the linear growth rate. First, certain models of modified gravity, such as f (R) [25], rely on the the chameleon screening mechanism [29] which suppresses the 5th force in high density regions, while in under-dense regions the total gravitational force is enhanced (due to the presence of the 5th force), resulting in specific imprints on void abundance and density profiles around underdense regions (e.g. [1,3,6,11,15,45]). These theories would naturally lead to an environmentally-dependent growth rate. In fact, in the non-linear regime, the linear growth rate is also sensitive to the underlying density, as shown in [5]. For very large under-dense regions, the effective cosmological parameters are expected to be different to the globally-averaged parameters, but the quantification of this critical scale can also serve as an interesting test for departures from Einstein gravity. Second, the formation and evolution of cosmic voids is non-linear and reduced compared to the dynamics of dark matter halos or the evolution of overdense regions with ∆(r) 1. This is why we can expect that quasi-linear or linear models can describe the RSD around voids relatively well, although recent works have shown the limitation of this assumption [2,5,12,33]. The first studies that have tested the growth rate measurements using RSD around cosmic voids in galaxy surveys, have used a Gaussian Streaming Model (GSM) [12,19,22,30,36] to model the 2D galaxy-void correlation function in redshift space.
The analyses that first constraints the growth rate around voids from galaxy surveys are [21], where the authors used the CMASS sample of the Sloan Digital Sky Survey (SDSS), [4], where we used the low redshift 6-degree Field Galaxy Survey (6dFGS) [27], and [24], where the authors used the high redshift VIPERS survey datasets. While these analyses have shown an overall consistency with the ΛCDM expectation of the linear growth rate, the GSM does assume a knowledge of the real space density profiles around voids, which may induce a bias in the analysis 1 . In [20] the authors took advantage of the approximated linear behavior of cosmic void evolution to perform a multipole analysis of the RSD around voids using both the CMASS and the LOWZ galaxy samples of SDSS DR12. Such a mutlipole analysis allows to derive the growth rate purely from the data measurement, assuming a linear relationship between the monopole and the quadrupole (see also the recent work of [16] for a complementary approach). With this assumption they have derived a linear growth rate consistent with ΛCDM in the CMASS sample, but at a ∼ 2-3σ deviation from it in the LOWZ sample.
In this work we perform an independent analysis from [20] using a different void finder and a different treatment of the errors which enter into the likelihood analysis. Using the 500 mocks from the publicly available mock galaxy catalogues produced with the Quick Particle Mesh (QPM) method [44], we test the validity of the mutlipole decomposition and use them to compute the covariance matrix that enters into the likelihood. We will show that in our case, we observe no deviation from ΛCDM when we disregard the mutlipole measurements at small scales (< 10 h −1 Mpc). This paper is organized as follows: in section II we describe the data and the mocks we use to perform our analysis, in section III we explain how we obtain our void catalogues, in section IV we introduce the model we use to derive the linear growth rate, in sections V, VI we test our approach using the QPM mock catalogues and in the CMASS and LOWZ dataset. In section VII we present our conclusion.
II. DATA & MOCK CATALOGUES
We use the publicly available data of SDSS-III [8] Data Release 12 (DR12) which contains two datasets of galaxy catalogues from the Baryon Oscillation Spectroscopic Survey (BOSS) 2 : the LOWZ and the CMASS samples. Both map the southern and the northern hemispheres. The LOWZ north/south sample contains ∼ 248/114×10 3 galaxies in redshift range 0.15 < z < 0.43 and a median z = 0.32 while the CMASS north/south sample contains ∼ 569/208×10 3 galaxies in redshift range 0.43 < z < 0.70 withz = 0.54.
To identify the voids in the galaxy samples and to compute the multipoles, we use the two random catalogues generated by the BOSS collaboration (for each sample e.g. LOWZ north/south and CMASS north/south), featuring the redshift distribution. Each of these catalogues are referred to as RAN and RAN2. These random catalogues are also publicly available and contain about 50 times more points than the observed galaxies. To compute the covariance matrix and to test our analysis, we use the publicly available SDSS-III DR12 mocks, generated with the Quick Particle Mesh (QPM) algorithm [44]. They were generated assuming a flat ΛCDM cosmology (Ω Λ = 0.71, Ω m = 0.29, Ω b = 0.0458, σ 8 = 0.80, h = 0.7, n s = 0.97) [14]. We note that in these mocks, the linear galaxy bias is b = 2.2 while in both CMASS and LOWZ it was estimated to be b = 1.85 [14].
III. VOID CATALOGUE
To identify the cosmic voids in both the galaxy dataset and the QPM mocks, we use the void finder developed by [1], that was used in the 6dF Galaxy Survey analysis [4] to infer the growth rate. This void finder uses a sample of RAN2 to identify candidate voids with an effective radius r v that satisfies the following density constrains: where the binning is given in steps of dr = 3 h −1 Mpc, r 0 = 1.5 h −1 Mpc and δ(r) is approximated by counting the number of galaxies around each random position we select from RAN2, divided by the number of randoms we compute from the RAN catalogues. The first 3 conditions ensure that the centre of the voids is underdense while the conditions around r = r v ensure that the selected voids have a ridge. We then perform two loops over these void candidates that satisfy the density conditions: the first loop to smooth the individual void profiles by requiring that δ(r + 3dr < R < r v /2) < −0.3, The second to remove overlapping voids, keeping the largest.
We use between 5 to 8 times the number of candidate positions as tracers, which is a good compromise between numerical computing power and having a convergence in the number of identified voids. Indeed, given that we remove overlapping voids, increasing the number of candidates can increase the number of identified voids up to a limited number. Keeping the same criteria for the data samples and the mocks, we end up with a selection of voids distributed in redshift as displayed in Fig. 1.
We repeat the same procedure using 500 QPM mocks for LOWZ North/South and CMASS North/South. Finally, we introduce a cut in the minimum size of the voids for the RSD analysis r min v = 25 h −1 Mpc. The motivation for this cut is that (i) small voids identified with galaxy tracers do not necessarily correspond to underdensities in the matter density field. They also show a stronger deviation from linear evolution, and the galaxy bias around small voids can be amplified compared to the large-scale average bias [38,39,42]. (ii) we found that the overall void size distribution matches the mean value of the QPM mocks distribution when r > r min v . Although we are not interested in testing for void abundance in this work, having a mismatch in the void size distribution could introduce an offset between the mean void density profiles measured in the data and in the mocks, which could possibly introduce a bias in the derivation of our cosmological parameters. After applying this threshold, we found a total of 5986 voids identified in the LOWZ sample and 6373 in the CMASS sample. The normalized number of voids as a function of radius is displayed in Fig.2. The blue/red histograms correspond to the LOWZ/CMASS samples while the blue/red dashed curves correspond to 5 randomly selected samples from LOWZ/CMASS mocks, respectively. The mean void radius in the LOWZ/CMASS samples are, respectively, r v = 38.5 and 38 h −1 Mpc.
A. Multipole decomposition
The peculiar velocities of galaxies, v, that are due to the local gravitational potential result, on small scales, in random motions of galaxies within virialized halos. In principle this effect is not present within voids, which are generally empty of galaxies in their centre. On large scales however, the coherent bulk flow pointing outwards from centres of voids is responsible for an overall coherent distortion known as the 'Kaiser effect' [28]. It is this coherent outflow that carries information of the linear growth rate. Indeed, the galaxy peculiar velocities sourced by the underlying mass distribution of a void can be expressed in the linear regime as ( [12,20,22,36]): where f (z) is the linear growth rate, H(z) is the Hubble rate, r ≡ x − X is the separation between the comoving coordinate of the void centre X, and a galaxy at position x. We also assume that on average the void density profiles are spherical and can be described by the density contrast ∆(r) where r ≡ | r |. To relate the averaged galaxy density contract,ξ(r), to the matter density contrast, we generally assume a linear bias b such that ξ(r) = b∆(r) andξ where ξ(r) is equivalent to the galaxy density contrast at a scale r (i.e. the galaxy-void cross-correlation function).
The peculiar velocity of a galaxy gives a contribution to the redshift space separation between the galaxy and the void centre, and in the limit where | r | X, whereX is the unitary vector along the line of sight to our void centre.
Performing a Jacobian transformation between the coordinate s and r, at linear order, the redshift-space 2D correlation function can be described by ([12, 20, 23, 28]): where µ ≡ cos(θ) =X.r is the cosine of the angle between the line-of-sight direction and the separation vector while ξ 0 , ξ 2 are the monopole and the quadrupole respectively, computed using the Legendre polynomials P l (µ) via In the linear regime [28], where β = f /b and ξ(r) is the real-space galaxy-void correlation function. These expressions lead to a simple relationship between monopole and quadrupole: This is the key equation that [20] have used to probe β solely by measuring the monopole and the quadrupole. We will also use this equation in what follows, but we will introduce a cut at the scale r cut below which this approximation is no longer valid.
B. Measurement of the galaxy-void correlation function
To perform the mutlipole decomposition we start by measuring the void-tracer cross-correlation functions using the Landy-Szalay estimator: where D v D g is the number of data void-galaxy pairs, R v R g the random void-galaxy pairs and D g/v R g/v the number of galaxy/void data-random pairs, in bins at separation r and µ. The total number of galaxies, voids, galaxy-randoms and void-randoms are N g , N v , N rg and N rv , respectively. In all cases we use a sample of the first random catalogues provided by the BOSS collaboration, having 10 times the number of galaxies/voids than our data samples.
C. The likelihood analysis
To infer the linear growth rate from the measurement of the monopole and quadrupole, we solve for the value of β which satisfies Eq. 7, performing a Gaussian likelihood where the sum is in radial bins r 2β is the left hand side of Eq. 7 and C is the covariance matrix C ij = ε i ε j which depends explicitly on β. Hence the normalization of the likelihood needs to be taken into account. Unlike the analysis performed in [20], which uses a jackknife method to estimate the covariance matrix, in what follows we compute the covariance matrix using 500 QPM mocks.
In Fig. 3 we show the correlation matrix (covariance matrix of the residuals after normalization by its diagonal) FIG. 4: Multipole measurements in the mocks (grey curves) and in the data (blue curves) we obtained from Eq. 6. The data multipoles are qualitatively in good agreement with the ones we obtain in the mocks. which can be compared to Fig. 4 in [20]. The correlations between our bins follow the same qualitative trend as [20]: in the inner part of the voids, r/r v < 1, the bins seem less correlated while for r/r v > 1 we see some off diagonal correlations. We also note that in order to compute the galaxy-void correlation function we employ the Landy-Szalay (LS) estimator, while [20] use the approximation ξ l (r)
V. ANALYSIS
We start by using Eq. 8 to measure the galaxy-void correlation function in the data and the mocks, and then we apply Eq. 6 to compute the monopole (l=0), quadrupole (l=2) and hexadecapole (l=4).The resulting multipoles are shown in Fig. 4, where the grey curves correspond to the mocks measurements (1000 in total for CMASS and LOWZ) and the blue curves to the data. First we observe that the multipoles computed from the data and the mocks are qualitatively in good agreement with one another. Second we observe that for r/r v ≤ 0.3, which corresponds to a radius below r ∼ 10 h −1 Mpc, the slope of the monopole changes, and ξ 0 → −1 while |ξ 4 | > 0. These behaviours could indicate a breakdown of the linear assumptions and/or ill-defined regions due to the lack of particle counts at the core of the voids. In any case, these low scales can not be used within our current linear model hypothesis. Hence in what follows we define a cut-off scale r cut below which we disregard our measurements when performing the likelihood analysis.
Finally, we also show the measurement of the 2D galaxy-void correlation function in both LOWZ/CMASS samples in Fig. 5, that we have measured parallel (π) and perpendicular (σ) to the the line of sight, using a binning of 4 h −1 Mpc. This is just to illustrate the asymmetry due to the peculiar velocities of galaxies that have a coherent outflow due to the gravitational potential of the void. This measurement could be used to extract the growth rate using a quasi-linear modelling (e.g. Gaussian Streaming Model), as it was done in [4,21,24]. However it would require assumptions on the real space density profiles around the voids, which we know are sensitive to the underlying cosmology and to the void finder algorithm. Hence we do not explore further these 2D measurements.
VI. RESULTS
In what follows, we set r cut = 10 h −1 Mpc and we use our measurement in bins of dr = 4 h −1 Mpc up to r max = 78 h −1 Mpc. We have verified that the results we present in this section remain unchanged via the transformation r cut → r cut ±dr or r max → r max ±dr. We also tested that the inferred value of β is insensitive to the fiducial size of our voids r v , nor to the hemisphere (splitting voids in large vs. small, separating north vs. south datasets). Thus for this analysis, we combined all the void sizes to obtain better statistical errors. To obtain the best fit value for β, we use a large prior of β = [−0.1, 1.2] in steps of dβ = 0.0024. We have verified that our results remain unchanged by increasing the prior range.
A. Mocks
We start our analysis by inferring the value of β on each individual mock catalogue, using the Likelihood computation given in Eq. 9 in order to evaluate the uncertainties on the β measurement. In Fig. 6 we show the histogram of the best fit values we have found in the CMASS, LOWZ mocks as well as the mean values and the standard deviation:β = 0.36 ± 0.06 for the CMASS mocks andβ = 0.21±0.05 for the LOWZ mocks. It is not trivial to compare these values to the mock expectations. Indeed, given the fiducial cosmology of the QPM mocks [44] we can easily compute the expected value for the growth rate but the linear bias is not explicitly given at the mean redshift of the mocks. At z = 0.5 the linear bias is expected to be b = 2.2 for the QPM mocks [8]. In such case, we can extrapolate the value β(z = 0.5) = 0.34. This value can be compared to the CMASS mocks because in these mocks the redshift is z ∼ 0.54. If we neglect the redshift dependence of the linear bias and keep b = 2.2 but use the growth rate at the redshift of the LOWZ mocks then we can expect a value of β = 0.30. Both theoretical values are within 2-σ deviation from the mean of β we obtain. Finally before performing the data analysis, we should make a few critical remarks: • Galaxies around voids may be more biased compared to the average galaxies in the full simulation.
In which case we can expect the fiducial value of β to be lower than the one computed from b = 2.2. We note however that in [4] the value of the linear bias we have inferred in mocks using the galaxyvoid and the galaxy-galaxy correlation functions were consistent with one another. This must depend on the fiducial void size and the characteristics of the void profiles (e.g amplitude at the void ridge).
• We note that if we would have inferred β from the mocks mean measurement of the multipole, the systematic errors due to the linear assumptions would most likely dominate: in the LOWZ sample we have found the mean of the β best fit values to be in agreement with the fiducial cosmology at 2-, but not 1-σ. This may be an issue for upcoming surveys such as TAIPAN which will probe a larger volume, with a higher density of galaxies and voids [17] at low redshift.
• We also point out the limitation of using QPM mocks [44] to test for the validity of the growth rate at low redshift. Indeed, unlike in full N-body simulations, efficient algorithms such as [44] have not yet fully investigated the validity of their approach to reproduce the statistical description of the undersense matter density field.
Overall, apart from these remarks, we find that the mean of β from the best fit values of the mocks are within 2-σ deviation of the expected fiducial cosmology, which validate our approach given the statistical errors we have.
B. Data
Following the same procedure but for the data sample, we find a best fit β = 0.33 ± 0.06 and β = 0.36 ± 0.05 for the LOWZ and CMASS samples, respectively, with a reduced χ 2 /d.o.f. of 22.6/16 = 1.41 and 21.8/16 = 1.36. The posterior distribution is shown in Fig. 7. We note that our errors on β are consistent with what we found using the standard deviation of the best fit values from the mocks and that the best fit values correspond to the mean value of the likelihood PDF.
Once again we can compare these results with the expected values of β in the case of a ΛCDM cosmology (see sec. II for cosmological parameter values). With a linear bias b = 1.85 (as inferred in [14]), the theoretical values for LOWZ/CMASS are β = 0.37, 0.41 respectively. These are the same reference values that [20] have used to compare with their results. In Fig. 7 they correspond to the long dashed lines. Unlike what the authors in [20] have found, we obtain a 1-σ agreement with respect to ΛCDM, both for the LOWZ and the CMASS samples. We also show in Fig. 7 the fiducial values of β for b = 2.2 (motivated by the discussion in sec. VI A). The latter is also consistent at 1-σ with our best fitting values.
VII. CONCLUSION
In this work we have probed the parameter β = f /b, using the public galaxy catalogues released by the BOSS collaboration and an RSD mutlipole analysis of the galaxy-void cross-correlation function. The model we used to infer the growth rate is derived from linear theory and was initially used in [20] to perform a similar analysis. However, in this work we find that our derived values for the growth rate are consistent with a ΛCDM cosmology within 1-σ. The main differences in this analysis compared to the one presented in [20] are: • Our void catalogues are completely independent and based on different criteria (density criteria [1] vs. watershed transform [41]). While the peak of the void size distribution is relatively similar in both studies, we have better statistics on the number of voids in the LOWZ sample. As a result, our errors on β are similar in both the LOWZ ∆β = 0.06 and CMASS sample ∆β = 0.05.
• Motivated by our analysis with the mocks, we introduce a cut in scale to disregard our measurement at the centre of the voids where |δ| → −1, which corresponds to the non-linear regime where Eq. 7 does not hold in principle, as we discuss in sec. V.
• The treatment of the covariance matrix is different: in this work we used the mocks to compute the covariance while in [20] they used a jackknife method. We also provide in this work a complete study of the inferred values of β within the mocks in order to check the validity of our model (sec. VI A).
Overall, this work has provided some interesting results: • Using mock catalogues, we have shown that β can be extracted using no theoretical modelling of the void-galaxy correlation function in real space. This is particularly interesting to avoid assuming a fiducial cosmology in order to predict the void density profiles, which could lead to potential bias of the growth rate value (the void density profiles carry the imprints of the cosmology e.g. [3,7,13,31,34]), or to avoid parametrizing the real space density profile and/or marginalising over the profile parameters, which would introduce potentially weaker constraints on the growth rate.
• The values of β that we obtain in the LOWZ/CMASS datasets are consistent with the value probed in [14]. However in [14] the scale range used to derive β is [40 − 180] h −1 Mpc, while we used the information contained within ranges [10 − 78] h −1 Mpc. This illustrates again the complementarity of using cosmic voids to perform cosmological analysis: we have access to additional information, and the systematic errors are different.
Finally we can emphasise on the fact that that the value of β we obtained in this analysis is in good agreement with the ΛCDM linear prediction. It would be interesting to probe the information contained in smaller scales (e.g. below 10 h −1 Mpc) where the non-linearities can carry more information. For instance, in [5] we have shown how the growth rate of cosmic structure can vary considerably when the underlying matter density |∆| ≥ 1. We hope to perform such analysis in future work. | 5,941.6 | 2019-03-13T00:00:00.000 | [
"Physics"
] |
Ultimate Osmosis Engineered by the Pore Geometry and Functionalization of Carbon Nanostructures
Osmosis is the key process in establishing versatile functions of cellular systems and enabling clean-water harvesting technologies. Membranes with single-atom thickness not only hold great promises in approaching the ultimate limit of these functions, but also offer an ideal test-bed to explore the underlying physical mechanisms. In this work, we explore diffusive and osmotic transport of water and ions through carbon nanotube and porous graphene based membranes by performing molecular dynamics simulations. Our comparative study shows that the cylindrical confinement in carbon nanotubes offers much higher salt rejection at similar permeability in osmosis compared to porous graphene. Moreover, chemical functionalization of the pores modulates the membrane performance by its steric and electrostatic nature, especially at small-size pores due to the fact that the optimal transport is achieved by ordered water transport near pore edges. These findings lay the ground for the ultimate design of forward osmosis membranes with optimized performance trade-off, given the capability of nano-engineering nanostructures by their geometry and chemistry.
Scientific RepoRts | 5:10597 | DOi: 10.1038/srep10597 From the viewpoint of thermodynamics, the osmotic process across a semi-permeable membrane can be formulated through the van't Hoff equation at the low-concentration limit, i.e. Δ P = k B Tc s , where Δ P is the osmotic pressure across the semi-permeable membrane and c s is the concentration of solute 22 . Notably, this simplified description of osmotic flux does not account for the atomistic details such as types of solutes and solvents, structures of the membrane and pores, as well as their interactions. These factors could be very critical for the osmotic performance and can be clarified by performing atomistic simulations. For example, recent work has shown that the driving force of osmotic flux could be the pulling of solvent molecules across the membrane in the wake of solute-membrane collisions 10 . In thermodynamic equilibrium, solvent molecules close to the pore and in contact with the solution experience a net force towards the solvent, which is balanced by a diffusive flux of solvent particles into the solution 22 . This hopping picture of osmosis has much in common with the classic colloidal sedimentation equilibrium where an inhomogeneous colloidal density profile is maintained by the balance of a downward flux in the gravitational field and an upward diffusive flux. These concepts elucidate the molecular-level dynamics of osmotic processes in natural and synthetic systems, and pave the way for optimal design of FO applications. However, from a material design point of view, one would ask what would be the ultimate membrane for FO applications. Due to the facts we introduce above, porous carbon nanostructures are the promising candidates for this question and thus it would be interesting to explore their optimized performance by engineering their structures and chemistry.
To this end, we perform molecular dynamics (MD) simulations for a comparative study of diffusive and osmotic transport through membranes composed of porous graphene and CNTs (Fig. 1). We identify the effects of pore size for simultaneous optimization of osmotic flux and ion rejection, or so-called the performance trade-off. The role of chemical functionalization is then investigated by modifying the atomic structures and charge distribution of the pores, which exhibits notable effect on the osmotic process. The optimization is achieved by enabling ordered water transport in nanopores with specific sizes, which makes a transition to disordered flow in larger pores, where the effects of pore geometry and pore edge functionalization become insignificant. The performance of FO applications based on these membranes is discussed in this work, which is demonstrated to outperform most of conventional membranes reported in the literature.
Results and Discussion
Trans-membrane diffusion of water molecules. Across a semi-permeable membrane, the osmotic flux is determined by the osmotic strength (or pressure) and the permeability of solvents across the membrane. The process of water permeation depends on pore structures in the membrane, as well as the interaction between water molecules and the pore. According to the hopping picture of osmosis introduced earlier, understanding the self-diffusion of water molecules could offer some insights into the osmotic transport and is thus discussed here. We first consider slabs with width h next to the semi-permeable membrane. Water molecules in the slab of solvent compartment with solvent density ρ solution hop into the solvent compartment with solvent density ρ solvent , and experience an energy penalty hf at the same time. Here f is the outward force on the water molecules in the solution arising from the fact that the total density in the solution is higher than the solvent. f can be related to the osmotic pressure as Δ P = f/a, where a is the slab area per solvent particle 22 . The steady-state of osmosis can be settled by the balance between diffusive fluxes across the membrane, i.e. ρ solvent = ρ solution exp(-fh/k B T). Consequently, the osmotic flow rate is closely tied to the rate of water diffusion.
To quantify the diffusivity of water molecules across the membrane, we carry out MD simulations with two salt water chambers interfaced by the graphene or CNT membrane. We set the concentration c of NaCl in the solution compartment as 5 mol/L, which is comparable with the room-temperature solubility of NaCl in water (6.14 mol/L at 25 °C) 23 . We then analyze the correlation between the pore structure and diffusive flux of water j W in thermal equilibrium, which is obtained by counting the numbers of exchanged water molecules across the membrane in both directions. We plot the diffusive fluxes as a function of the pore size in Fig. 2. Here the definition of pore size is geometrical and thus sensitive to the detailed atomic structures for small pores. Specifically, for porous graphene sheets the pore area is defined as A pore = n × A c , where n is the number of atoms removed from the pore region and A c is the area per atom in crystalline graphene. While for armchair (n, n) CNTs, the pore size is defined as A pore = π d 2 /4, where the diameter d is calculated as √3na/π and the lattice constant of graphene a is 0.246 nm. It should be remarked here that for practical consideration, a depletion length of a few angstroms from the graphene edge or CNT walls should be excluded from these definitions. Our simulation results show that the diffusive water flux in activated with pore sizes of 0.052 and 0.231 nm 2 through the porous graphene and CNT membranes by these definitions. The amplitudes of fluxes feature peak values of 4922.472 and 1978.263 L cm −2 per day at A pore = 0.627 and 1.445 nm 2 , respectively. Here we evaluate the flux by referring to the area of pores, and the values should be divided by a factor of porosity for comparison with the conventional definition using the area of membranes. The water fluxes across these two types of membranes converge at large pore size above 4 nm 2 , indicating the insensitivity of the atomic structures of pores and their interaction with the water molecules at this limit.
The peaks in the diffusive flux originate from the ordered nature of water transport through the pores. To see this effect in porous graphene, we plot radial density profiles of water molecules inside the pores, which shows that for water diffusion through very small pores, the molecule has to get through a pore with comparable size with it, which results in a considerable energy barrier. As can be seen from the density profile of oxygen atoms in the water molecules (Figs. 3a and S1, S2), we find that starting from A pore = 0.31 nm 2 , the pore is open for the lateral motion of water molecules in the pore, so the nature of single-file transport through the center of pores is broken. At a larger pore of 0.63 nm 2 , the diffusion path close to the pore edges is favored, corresponding to the peak flux measured. This result also indicates potential strong effect by functionalizing the pore edges, which could direct the order in the water transport path, and modulate the permeability as well as selectivity. As the pore size continues to increase, more paths for the water diffusion are activated, but with less ordered structures and inefficient use of the space inside the pore. As a result, the diffusive flux is reduced. For water diffusion through CNTs, similar phenomena are characterized (Fig. 3a). For CNTs with pore size below a specific value between 0.92 and 1.44 nm 2 , ordered water chain in transport is identified in the region close to the CNT walls, which results in a maximum water flux in this range. For smaller pores, the water molecules are driven through the center of CNTs that leads to significant energy penalty, while for larger pores, the atomic structures of water flow turns to be more and more disordered, as have been discussed before in the study of forced water transport through carbon nanotubes 8,9,24 . These arguments can also be clearly demonstrated from the simulation snapshots summarized in Fig. 3b.
Comparing the simulation results for porous graphene and CNTs concludes that the peak diffusive flux across porous graphene membrane is ~2.5 times higher than that across CNT membranes. To understand this, we perform steered molecular dynamics (SMD) simulations to explore the free energy profile for the diffusion of a water molecule across the membrane. The potential of mean force (PMF) data ( Fig. 4a) shows that the free energy barrier Δ G for diffusion across graphene with a pore size of 1.10 nm 2 is lowered by 62.2% in comparison to the CNT with a pore size of 1.44 nm 2 . This can be explained by the change in the nature of hydrogen bond (H-bond) network between water molecules during the diffusion process. Specifically, for a water molecule diffusing across porous graphene, the average number of H-bonds for each water molecule decreases slightly from the bulk value of n HB = 3.487 to 3.137 for the pore with size of 1.10 nm 2 , while n HB decreases significantly to 2.751 for a CNT pore of 1.44 nm 2 ( Fig. 4b and 4c). That is to say, the H-bond network remains more intact for water transport across porous graphene compared to the CNT, because the water molecules inside the pore could form contact with other molecules in both the compartments. While for molecules transport through the CNT with a pore size comparable to the length scale of the H-bond, the H-bond network has to be reconstructed or even broken due to the one-dimensional cylindrical confinement. The analysis on the H-bond network agrees with the observation that the diffusive flux is higher through porous graphene with similar pore sizes.
Trans-membrane diffusion of ions. The diffusion of salt ions (Na + and Cl − ) is also analyzed from the MD simulation results (Fig. 2b). The diffusion of ions is initialized at larger pore sizes compared to that for the water molecules. Similarly, peaks are identified in the relation between diffusive flux j I and the pore size. Because in our simulations both Na + and Cl − diffuse and the charge neutrality is maintained, so we here focus on the flux of Na + ions only without the loss of generality. From the results we can conclude that the salt flux across graphene membranes is significantly higher than that for CNT membranes with the same pore size due to the different steric effects. The values of fluxes are expected to converge at a larger pore size, indicating the insensitivity to the atomic details of membranes.
The difference in the ionic diffusivity arising from the geometry of pores can be quantitatively concluded from the free energy profile of a single ion diffusing across the membrane (Fig. 4a). In bulk solvent, the ions are usually surrounded by a solvation shell, with sizes typically of 0.60 nm for Na + and 0.66 nm for Cl − , known as the hydrated diameter, although the sizes of naked Na + and Cl − ions are much smaller (their crystal diameter 0.23 and 0.39 nm, respectively) 25 . As a result, when a salt ion diffuses through nano-sized pores, the hydration shells surrounding it have to be reduced because of the spatial constriction. Specifically for porous graphene, the ion should detach from the water molecules ahead of it to approach the pore. However, the contact between the ion and a new solvation shell on the other side of the membrane could be immediately established when the ion diffuse through the pore. In contrast, for ions diffusing through the CNTs with a cylindrical nanoconfinement, their solvation shell must be reduced as they enters the CNT and the dehydrated state needs to be well maintained before they diffuse across the whole nanotube and take the exit into the solution again. As a result, the free energy cost for the ions to transport through the CNTs is much higher than that for porous graphene. We analyze the pair distribution function (RDF) between the ion and water molecules based on the MD simulation trajectories. We find that the coordination number defined as the number of water molecules under the first peak of RDF curve is 6.21 for Na + and 7.51 and Cl − in bulk solvent. The values are reduced to 6.06, 6.85 respectivly for ions transport across porous graphene, and more significantly to 5.46, 6.62 for ions across CNTs, which are consistent with our previous discussions. It could be inferred from Fig. 2b that the threshold pore sizes for porous graphene and CNTs are 0.313 and 0.925 nm 2 , respectively, which are close to the size of hydrated ions. Specifically, for graphene pores, the cross-section areas of the hydrated ions S ion are 0.34 nm 2 for Cl − and 0.28 nm 2 for Na + by considering them as spherical particles. While for CNT pores, the values of S ion are 1.323 nm 2 for Cl − and 1.204 nm 2 for Na + by taking the van der Waals radius r vdW = 0.319 nm into account, as the size of CNT pores are defined by the positions of carbon atoms.
Osmotic flux and salt rejection.
With the understanding of water and ionic transport across porous graphene and CNTs, we now turn to discuss the osmotic transport. We calculate the osmotic water flux from a pure water compartment towards the sodium chlorite (NaCl) solution. The concentration of NaCl in the solution compartment, 5 mol/L, is high enough to drive an osmotic flow over the fluctuating flux of diffusion. The measured osmotic water fluxes are summarized in Fig. 5a, which show similar peak features as in the diffusive processes. Here we define an osmotic flux J O as the net flux directed from the pure water chamber to the solution by subtracting the diffusive backflow. Compared to the results for diffusion in Fig. 2a, the amplitudes of peak osmotic fluxes are comparable, but the characteristic pore sizes corresponding to the peak fluxes now shift to larger values for both porous graphene and CNT because of the presence of a finite osmotic pressure. As the pore size increases, the CNT membrane outperforms porous graphene as it is more resistant to the ions, which leads to a higher osmotic strength and less mixing between osmotic water flow and the ionic transport.
The salt ions start to permeate into the pure water chamber as the pore size keeps increasing. Here we quantify the ionic flow by defining a salt rejection ratio as r S = n P /n S , where n P is the number of salt ions permeated through the membrane and n S is the total number of salt ions initially solved in the solution. In our work, the simulation data within a specific time interval of 20 ns are analyzed before the osmotic strength decays significantly and the equilibrium is established between the two compartments. The final values of c in the simulations range from ~5 molL −1 for nearly impermeable pores to 3 molL −1 for highly permeable pores. The results summarized in Fig. 5b show that the salt rejection of CNT membranes is much higher than porous graphene, similarly as in the situation of diffusive ion transport. The threshold pore sizes are 0.627 and 1.445 nm 2 for porous graphene and CNT membranes, respectively. Based on these results, we could conclude that although the CNT channel is much longer than the one-atom thickness of porous graphene membrane, the osmotic strength still can drive similar osmotic flow across the whole membrane, while the ultralow flow resistance by the graphitic wall does not reduce the performance. With the same density of pores in the membrane, the CNTs are thus better candidates for FO applications compared to porous graphene. However, there are some practical issues to create well-aligned and dispersed, high-density CNT arrays in the membrane. In contrast, the porous graphene could be easily created by exotic treatment such as irradiation and chemical functionalization, and controls could be made for specific size and density of pores 11,12 . Functionalization of the nanopores. One of the additional promising features of carbon nanostructures such as graphene and CNTs is the opportunities to modify their structures at the molecular level. In addition to tailoring the pore size as we have discussed, chemical functionalization is also investigated in this study, aiming at elevating the performance of aforementioned nanoporous membranes. Here we explore the roles of chemical functionalization on the osmotic transport by considering hydrogenated, fluorinated and hydroxylized functionalization with similar sizes but different atomic charges (Fig. 1). Our MD simulation results ( Fig. 6a and 6b) demonstrate notable functionalization effects for both CNT and porous graphene membranes, with strong dependence on the type of functional groups. Here the pore size is redefined by subtracting the size of functional groups. For hydrogen-terminated edges, the osmotic flux does not show significant changes compared to the pore with bare edges. The peak flux is higher through graphene pores but slightly slower in the CNT. Although charged negatively, the fluorine-termination does not change the permeability of both graphene and CNT pores as well, due to its electrostatic repulsion with the oxygen atoms in water molecules. As the bare edges of porous graphene with dangling bonds are not chemically stable in solution, and thus our findings indicate Hor F-termination provides a good protection of the edges without the loss of the performance and even higher flux at small pore sizes. In contrast, the hydroxyl group that features a similar size as F − strongly prohibits the permeability because of their dipole interaction with water molecules and the formation of H-bond network. This functionalization-enabled selectivity is easy to be understood for water osmosis through pores in the single-atom-thick graphene, but not so straightforward for the CNTs as the functionalization is only available at the entrance and exit of the CNT and the whole channel in between remains intact. Moreover, we do not find notable difference in the density profile of water molecules inside the CNT channel. These facts indicate a remarkable end-functionalization effect, which could be feasibly established in experiment, as the inner walls of CNTs are difficult to be modified. We also find that the excellent salt rejection is well preserved (Figure S3), which shows very gentle dependence on the functionalization at small pore sizes.
Assessment of FO applications. Based our simulation results, the optimized pore size can be determined by balancing the osmotic flow rate and salt rejection in practical FO applications. Considering a typical setup with pore density of 10%, we compare the performance of CNT and porous graphene with various desalination techniques including both forward and reverse osmosis applications, using carbon nanostructures, aquaporin water channels, polymeric membranes 4,26-29 . The results plotted in the chart (Fig. 7) show that both nanoporous graphene and CNT based FO membranes are quite promising, which actually set a limit for related applications due to their extremely simple atomic structures and potential for functionalization based nanoengineering as addressed in this work. Practical issues such as fouling may be solved by combining electrochemical or thermal treatment of the membranes by utilizing the outstanding electrical thermal transport performance of carbon nanostructures, and structural failure can also be avoided by design the membrane architecture by efficiently utilize their outstanding mechanical resistance 17,30 .
In brief, we assess the performance of single-atom-thick membranes, made of embedded carbon nanotube arrays and porous graphene, in the applications of forward osmosis. We identify the peak flux that corresponds to an ordered edge-aligned water transport mechanism and the critical size to prohibit ion transport through the pores, which is much different between the CNT channel and porous graphene sheet due to a prominent steric effect. Chemical functionalization serves as a further control of the performance and hydrogen-or fluorine-termination protects the bare graphene edges for better stability in the harsh environment. The simulation results show that these membranes hold great promises in FO applications, with a balanced performance between the permeability and salt rejection that outperforms most of the conventional membranes. The simplicity of carbon nanostructures and the understandings we obtained here may also help to understand biological osmotic processes, especially the effects of atomic structures and chemical functionalization.
In the past few years, continuing efforts have been made in designing osmotic membranes using carbon nanostructures, as well as elucidating the underlying mechanisms. However, due to technical difficulties in quantifying the single-channel performance of individual carbon nanotube or porous graphene for FO and RO applications, these studies are mainly focused on the performance at the membrane level, which is made of carbon nanostructures assemblies such as their composites and porous functional graphene multilayers [31][32][33] . Only till very recently, single-channel water and ion transport have been measured in nanoscale channels [34][35][36][37][38] . Their findings suggest highly enhanced flow and ionic selectivity that validate our theoretical understandings. These progresses made substantial steps in establishing high-performance osmosis-related applications in the near future, given the developed capability in nano-engineering these nanostructures by their geometry and chemistry.
Methods
Atomic structures. We constructed squared 2D arrays of porous graphene and CNT membranes by using periodic boundary conditions (PBCs) with lateral dimensions of 2.982 and 2.947 nm, corresponding to a pore density of ρ 2D = 0.114 nm −2 . Pores in graphene can be created by chemical functionalization such as oxidization or irradiation, and the pore density could reach above 0.01 nm −2 in experiments 11,12 . This choice of geometrical parameters ensures the interference between neighboring pores in the array is avoided so the osmotic dynamics can be discussed from a single-pore perspective.
Compared to the squared CNT array considered here, the density of CNTs in a membrane in a close-pack triangular lattice is defined by its diameter d CNT measured in nm, i.e. ρ 2D = √3× (d+ 0.34) 2 /4 nm −2 . We use the interlayer distance in graphite (0.34 nm) as the interwall distance here. In this we, we consider armchair single-walled carbon nanotubes (SWNTs) only. For a typical CNT with d CNT = 1 nm, we have ρ 2D = 0.777 nm −2 , about 7 times higher than the value explored here, indicating the CNT channels operate individually. To model the membranes of aligned CNTs between two liquid reservoirs, the ends of CNTs are covalently linked to a perpendicular graphene sheet through implanted topological defects as illustrated in Fig. 1. The length of CNT channel is set as 1.6 nm due to the fact that there is negligible variation of water flux by increasing this length, at least for the small-diameter CNTs explored in this work 39 .
The PBC is applied along the direction in perpendicular to the membrane (along the pore), which is sandwiched by two liquid compartments filled with water solution and solvent, respectively. Two additional plates are placed to seal these two compartments, which can move freely and are adjusted to fit the pressure difference generated during the osmosis 10 .
Molecular dynamics (MD) simulations.
We perform MD simulations in this work using the large-scale atomic/molecular massively parallel simulator (LAMMPS) 40 . The all-atom optimized potential for liquid simulations (OPLS-AA) is used for carbon nanostructures and their functional groups, which can capture essential many-body terms in inter-atomic interactions, including bond stretching, bond angle bending, van der Waals and electrostatic interactions 41 . Following previous studies on similar systems, the extended simple point charge model (SPC/E) is used for water molecules due to its predictability of dynamical properties such as the viscosity 9,42-44 . The SHAKE algorithm is applied for the stretching bond terms between oxygen and hydrogen atoms to reduce high-frequency vibrations that require shorter time steps. The interaction between water and functional groups includes both van der Waals and electrostatic terms. The former one is described by the 12-6 Lennard-Jones potential 4ε[(σ/r) 12 − (σ/r) 6 The van der Waals forces are truncated at 1.2 nm and the long-range Coulomb interactions are computed by using the particle-particle particle-mesh (PPPM) algorithm 46 . The cations and anions are added in a way to maintain the charge neutrality. The time step of equation of motion integration is 2 fs. For temperature and pressure controls, we use the Nosé-Hoover thermostat and Berendsen barostat, respectively. | 5,929 | 2015-06-03T00:00:00.000 | [
"Chemistry",
"Engineering",
"Materials Science",
"Physics"
] |
Evaluating Models of Computation and Storage in Human Sentence Processing
We examine the ability of several models of computation and storage to explain reading time data. Specifically, we demonstrate on both the Dundee and the MIT reading time corpora, that fragment grammars, a model that optimizes the trade-off between computation and storage, is able to better explain people’s reaction times than two baseline models which exclusively favor either storage or computation. Additionally, we make a contribution by extending an existing incremental parser to handle more general grammars and scale well to larger rule and data sets. 1
Introduction
A basic question for theories of language representation, processing, and acquisition is how the linguistic system balances storage and reuse of lexical units with productive computation. At first glance, the question appears simple: words are stored; phrases and sentences are computed. However, a closer look quickly invalidates this picture. Some canonically computed structures, such as phrases, must be stored, as witnesses by verbal idioms like leave no stone unturned 2 (Nunberg et al., 1994). There is also compositionality at the sub-word level: affixes like ness in pine-scentedness, are almost always composed productively, whereas other affixes, e.g., th in warmth, are nearly always stored together with stems (O'Donnell, 2015). Facts such as these have led to a consensus in the field that storage and computation are properties that cut across different kinds of linguistic units and levels of linguistic structure (Di Sciullo and Williams, 1987)-giving rise to hetergeneous lexicon 3 theories, in the terminology of Jackendoff (2002b).
Naturally, the question of what is computed and what is stored has been the focus of intense empirical and theoretical research across the language sciences. On the empirical side, it has been the subject of many detailed linguistic analyses (e.g., Jackendoff (2002a)) and specific phenomena such as composition versus retrieval in word or idiom processing have been examined in many studies in experimental psycholinguistics (Hay, 2003;O'Donnell, 2015). On the theoretical side, there have been many proposals in linguistics regarding the structure and content of the heterogeneous lexicon (e.g., Fillmore et al. (1988), Jackendoff (2002b)). More recently, there have been a number of proposal from computational linguistics and natural language processing for how a learner might infer the correct pattern of computation and storage in their language (De Marcken, 1996;Bod et al., 2003;Cohn et al., 2010;Post and Gildea, 2013;O'Donnell, 2015).
However, there remains a gap between detailed, phenomenon-specific studies and broad architectural proposals and learning models. Recently, however, a number of methodologies have emerged which promise to bridge this gap. These methods make use of broad coverage probabilistic models which can encode representational and inferential assumptions, but which can also be applied to make detailed predictions on large psycholinguistic datasets encompassing a wide vari-ety of linguistic phenomena. In the realm of syntax, one recent approach has been to use probabilistic models of sentence structures, paired with incremental parsing algorithms, to produce precise quantitative predictions for variables such as reading times or eye fixation times (Demberg and Keller, 2008;Mitchell et al., 2010;Frank and Bod, 2011;Fossum and Levy, 2012;van Schijndel and Schuler, 2013). To date, no models of storage and computation in syntax have been applied to predict measures of human reading difficulty.
In this work, we employ several of the models of computation and storage studied by O'Donnell (2015), to examine human sentence processing. We demonstrate that the fragment grammars model (O'Donnell et al., 2009;O'Donnell et al., 2011)-a model that treats the question of what to store and what to compute productively as a probabilistic inference-better explains human reading difficulty than two "limiting-case" baselines, MAP adaptor grammars (maximal storage) and Dirichlet-multinomial PCFG (maximal computation), in two datasets: the Dundee eye-tracking corpus (Kennedy and Pynte, 2005) and the MIT reading time dataset ).
Goals and Scope of the Paper
Before moving on, we remark on the goals and scope of the current study. The emergence methods connecting wide-coverage probabilistic grammars and psycholinguistic data offer great potential to test theoretical models quantitatively, at scale, and on a variety of detailed phenomena. However, studies using these methods also involve many moving parts, often making their results difficult to interpret.
To connect probabilistic models of syntactic computation and storage to reading time or eye fixation data, practioners need to: 1. Preprocess train and test data sets by tokenizing words, limiting sentence lengths, and handling unknown words.
2. Decide on a suitable grammatical formalism: determine a hypothesis space of stored items and specify a probability model over that space.
3. Choose and implement a probabilistic model to extract grammars from the training set.
4. Pick a test set annotated with reading difficulty information, e.g., eye fixation or reading times.
5. Choose a specific incremental parsing algorithm to generate word-by-word parsing predictions.
6. Determine the theoretical quantity that will be used as a predictor, e.g., surprisal or entropy reduction.
7. Choose a suitable linking model to regress theoretical predictions against human data, controlling for participant-specific factors and nuisance variables.
Given this wide array of design decisions, it is often difficult to compare results across studies or to determine which theoretical assumptions are crucial to the performance of models. For the field to make progress, studies must be replicable and each of the above factors (and potentially others) must be varied systematically in order to isolate their specific consequences. We contribute towards this process in three ways.
First, we report results for three models which differ only in terms of how they address the problem of what to store and what to compute (see Section 3). Otherwise, modeling and analysis assumptions are exactly matched. Moreover, the models represent three "limiting cases" in the space of storage and computation -store all maximal structures, store only minimal structures, and treat the problem as a probabilistic inference. Although none of the models represents a state-ofthe-art model of syntactic structure, this study should provide important baselines against which to compare in future proposals.
Second, to make this study possible, we extend an existing incremental parser to address two technical challenges by: (a) handling more general input grammars and (b) scaling better to extremely large rule sets. This parser can be used with any model that can be projected to or approximated by a probabilistic context-free grammar. We make this parser available to the community for future research.
Third, and finally, unlike previous studies which only report results on a single dataset, we demonstrate consistent findings over two popular datasets, the Dundee eye-tracking corpus and the MIT reading times corpus. We make available our predicted values for all examined data points together with our analysis scripts. This should facilitate the replication of these specific results and direct numerical comparison with later proposals.
Approaches to Computation and Storage
In this paper we study the ability of three models to predict reading difficulty as measured by either eye-fixation or reading times -the full-parsing model, implemented by Dirichletmultinomial probabilistic context-free grammars (DMPCFG) (Kurihara and Sato, 2006;Johnson et al., 2007), the full-listing mode, implemented by maximum a posteriori adaptor grammars (MAG) (Johnson et al., 2006), and the inference-based model, implemented by fragment grammars (FG) (O'Donnell, 2015). All three models start with the same underlying base system-a context-free grammar (CFG) specifying the space of possible syntactic derivations-and the same training data-a corpus of syntactic trees. However, the models differ in what they store and what they compute. The full-parsing model can be understood as a fullycompositional baseline equivalent to a Bayesian version of the underlying CFG. The full-listing model, by contrast, stores all full derivations (i.e., all derivations down to terminal symbols) and subderivations in the input corpus. These stored (sub)trees can be thought of as extending the CFG base component with rules that directly rewrite nonterminal symbols to sequence of terminals in a single derivational step.
Finally, the inference-based model treats the problem of what tree fragments to store, and which parts of derivations to compute as an inference in a Bayesian framework, learning to store and and reuse those subtrees which best explain the data while taking into account two prior biases for simplicity. The first bias prefers to explain the data in terms of a smaller lexicon of stored tree fragments. The second bias prefers to account for each input sentence with smaller numbers of derivational steps (i.e., fragments). Note that these two biases compete and thus give rise to a tradeoff. Storing smaller, more abstract fragments allows the model to represent the input with a more compact lexicon, at the cost of using a greater number of rules, on average, in individual derivations. Storing larger, more concrete frag-ments allows the model to derive individual sentences using a smaller number of steps, at the cost of expanding the size of the stored lexicon. The inference-based model can be thought of as extending the base CFG with rules, inferred from the data, that expand larger portions of derivation-tree structure in single steps, but can also include nonterminals on their right-hand side (unlike the fulllisting model).
As we mentioned above, none of these models take into account various kinds of structure-such as headedness or other category-refinements-that are known to be necessary to achieve state-of-theart syntactic parsing results (Petrov et al., 2006;Petrov and Klein, 2007). However, the results reported below should be useful for situating and interpreting the performance of future models which do integrate such structure. In particular, these results will enable ablation studies which carefully vary different representational devices.
Human Reading Time Prediction
To understand the effect of different approaches to computation and storage in explaining human reaction times, we employ the surprisal theory proposed by Hale (2001) and Levy (2008). These studies introduced surprisal as a predictor of the difficulty in incremental comprehension of words in a sentence. Because all of the models described in the last section can be used to compute surprisal values, they can be used to provide predictions for processing complexity and hence, gain insights about the use of stored units in the human sentence processing. The surprisal values for these different models are dervied by means of a probabilistic, incremental Earley parser (Stolcke, 1995;Earley, 1968), which we describe below.
Surprisal Theory
The surprisal theory of incremental language processing characterizes the lexical predictability of a word w t in terms of a surprisal value, the negative log of the conditional probability of a word given its preceding context, − log P (w t |w 1 . . . w t−1 ).
Higher surprisal values mean smaller conditional probabilities, that is, words that are less predictable are more surprising to the language user and thus harder to process. Surprisal theory was first introduced in Hale (2001) and studied more extensively by Levy (2008). It has also been shown to have a strong correlation with reading time duration in both eye-tracking and self-paced reading studies (Boston et al., 2008;Demberg and Keller, 2008;Frank, 2009;Wu et al., 2010;Mitchell et al., 2010).
The Incremental Parser
The computation of surprisal values requires access to an incremental parser which can compute the prefix probabilities associated with a string s under some grammar-the total probability over all derivation using the grammar which generate strings prefixed by s (Stolcke, 1995). The prefix probability is an important concept in computational linguistics because it enables probabilistic predictions of possible next words (Jelinek and Lafferty, 1991) via the conditional probabilities P (w t |w 1 . . . w t−1 ) = P (w 1 ...wt) P (w 1 ...w t−1 ) . It also allows estimation of incremental costs in a stack decoder (Bahl et al., 1983). Luong et al. (2013) used prefix probabilities as scaling factors to avoid numerical underflow problems when parsing very long strings.
We extend the implementation by Levy (2008) of the probabilistic Earley parser described in Stolcke (1995) which computes exact prefix probabilities. Our extension allows the parser (a) to handle arbitrary CFG rewrite rules and (b) to scale well to large grammars. 4 The implementation of Levy (2008) only extracts grammars implicit in treebank inputs and restricts all pre-terminal rules to single-terminal rewrites. To approximate the incremental predictions of the models in this paper, we require the ability to process rules that include sequences of multiple terminal and non-terminal symbols on their right-hand side. Thus, we extend the implementation to allow efficient processing of such structures (property a).
With regards to property (b), we note that parsing against the full-listing model (MAG) is prohibitively slow because the approximating grammars for the model contain PCFG rules which exhaustively list the mappings from every nonterminal in the input corpus to its terminal substring, leading to thousands of rules. For example, for the Brown corpus section of the Penn Treebank (Mar-4 Other recent studies of human reading data have made use of the parser of Roark (2001). However, this parser incoporates many specific design decisions and optimizations-"baking in" aspects of both the incremental parsing algorithm and a model of syntactic structure. As such, since it does not accept arbitrary PCFGs, it is unsuitable for this present study. cus et al., 1993), we extracted 778K rules for the MAG model, while the number of rules in the DM-PCFG and the inference-based (FG) grammars are 75K and 146K respectively. Parsing the MAG is also memory intensive due to multi-terminal rules that rewrite to long sequences of terminals, because, for example, an S node must rewrite to an entire sentence. Such rules result in an exploding number of states during parsing as the Earley dot symbol moves from left to right.
To tackle this issue, we utilize a trie data structure to efficiently store multi-terminal rules and quickly identify (a) which rules rewrite to a particular string and (b) which rules have a particular prefix. 5 These extensions allow our implementation to incorporate multi-terminal rules in the prediction step of the Earley algorithm, and to efficiently incorporate which of the many rules can contribute to the prefix probability in the Earley scanning step.
We believe that our implementation should be useful to future studies of reading difficulty, allowing efficient computation of prefix probabilities for any model which can be projected to (or approximated by) a PCFG-even if that approximation is very large. publicly available at http://url.
Data
Our three models models are trained on the Wall Street Journal (WSJ) portion of the Penn Treebank (Marcus et al., 1994). In particular, because we have access to gold standard trees from this corpus, it is possible to compute the exact maximum a posteriori full-parsing (DMPCFG) and full-listing (MAG) models, and output PCFGs corresponding to these models. 6 We evaluate our models on two different corpora: (a) the Dundee corpus (Kennedy and Pynte, 2005) with eye-tracking data on naturally occurring English news text and (b) the MIT corpus ) with self-paced reading data on hand-constructed narrative text. The for-5 Specifically, terminal symbols are used as keys in our trie and at each trie node, e.g., corresponding to the key sequence a b c, we store two lists of nonterminals: (a) the complete list -where each non-terminal X corresponds to a multi-terminal rule X → a b c, and (b) the prefix listwhere each non-terminal X corresponds to a multi-terminal rule X → a b c . . . d. We also accumulated probabilities for each non-terminal in these two lists as we traverse the trie. 6 Note that for DMPCFG, this PCFG is exact, whereas for MAG, it represents a truncated approximation. mer has been a popular choice in many sentence processing studies (Demberg and Keller, 2008;Mitchell et al., 2010;Frank and Bod, 2011;Fossum and Levy, 2012;van Schijndel and Schuler, 2013). The latter corpus, with syntactically complex sentences constructed to appear relatively natural, is smaller in size and has been used in work such as Wu et al. (2010). We include both corpora to demonstrate the reliability of our results.
Detailed statistics of these corpora are given in Table 1. The last column indicates the number of data points (i.e., word-specific fixation or reading times) used in our analyses below. This dataset was constructed by excluding data points with zero reading times and removing rare words (with frequencies less than 5 in the WSJ training data). We also exclude long sentences (of greater than 40 words) for parsing efficiency reasons. Table 1: Summary statistics of reading time corpora -shown are the number of sentences, words, subjects, data points before (orig) and after filtering (filtered).
Metrics
Following (Frank and Bod, 2011;Fossum and Levy, 2012), we present two analyses of the surprisal predictions of our models: (a) a likelihood evaluation and (b) a psychological measure of the ability of each model to predict reading difficulty. For the former, we simply average the negative surprisal values, i.e., log p(w n |w 1 . . . w n−1 ), of all words in the test set, computing the average log likelihood of the data under each model. 7 This can be understood as simply a measure of goodness of fit of each model on each test data set.
For the latter, we perform a linear mixed-effects analysis (Baayen et al., 2008) to evaluate how well the model explains reading times in the test data. The lme4 package (Bates et al., 2011) is used to fit our linear mixed-effects models. Following (Fossum and Levy, 2012), eye fixation and reading times are log-transformed to produce more normally distributed data. 8 We include the follow-ing common predictors as fixed effects for each word/participant pair: (i) position of the word in the sentence, (ii) the number of characters in the word, (iii) whether the previous word was fixated, (iv) whether the next word was fixated, and (v) the log of the word unigram probability. 9 All fixed effects were centered to reduce collinearity. We include by-word and by-subject intercepts as random effects. The base model results reported below include only these fixed and random factors. To test the ability of our three theoretical models of computation and storage to explain the reading time data, we include surprisal predictions from each model as an additional fixed effect. To test the signficance of these results, we perform nested model comparisons with χ 2 tests.
Results
For the likelihood evaluation, the values in Table 2 demonstrate that the FG model provides the best fit to the data. The results also indicate a ranking over the three models, FG ≻ DMPCFG ≻ MAG.
Dundee MIT DMPCFG -6.82 -6.80 MAG -6.91 -6.95 FG -6.35 -6.35 For the psychological evaluation, we present results of our nested model comparisons under two settings: (a) additive in which we independently add each of the surprisal measures to the base model and (b) subtractive, in which we take the full model consisting of all the surprisal measures and independently remove one surprisal measure each time.
Results of the additive setting are shown in Table 3, demonstrating the same trend as observed in the likelihood evaluation. In particular, the FG model yields the best improvement in terms of model fit as captured by the χ 2 (1) statistics, indicating that it is more explanatory of reaction times when added to the base model as compared to the DMPCFG and the MAG predictions. The ranking is also consistent with the likelihood results: FG ≻ DMPCFG ≻ MAG. Table 3: Psychological accuracy, additive testsχ 2 (1) and p values achieved by performing nested model analysis between the models base+X and the base model.
For the subtractive setting, results in Table 4 highlight the fact that several models significantly (p < 0.01) explains variance in fixation times above and beyond the other surprisal-based predictors. The FG measure proves to be the most influential predictor (with χ 2 (1) = 62.5 for the Dundee corpus and 42.9 for the MIT corpus). Additionally, we observe that DMPCFG does not significantly explain more variance over the other predictors. This, we believe, is partly due to the presence of the FG model, which captures much of the same structure as the DMPCFG model. Table 4: Psychological accuracy, subtractive test -χ 2 (1) and p values achieved by performing nested model analysis between the models full-X and the full model.
Additionally, we examine the coefficients of the surprisal predictions of each model. We extracted coefficients for individual surprisal measures independently from each of the models base+X. As shown in the columns Indep in Table 5, all coefficients are positive, implying, sensibly, that the more surprising a word, the longer time it takes to process that word.
Moreover, when all surprisal measures appear together in the same full model (columns Joint), we observe a consistent trend that the coefficients for DMPCFG and FG are positive, whereas that of the MAG is negative.
Discussion
Our results above indicate that the inference-based model provides the best account of our test data, both in terms of the likelihood it assigns to the test corpora and in terms of its ability to explain human fixation times. With respect to the full-parsing model this result is unsurprising. It is widely known that the conditional independence assumptions of PCFGs make them poor models of syntactic strcutre, and thus-presumably-of human sentence processing. Other recent work has shown that reasonable (though not state-of-the-art) parsing results can be achieved using models which relax the conditional independence assumptions of PCFGs by employing inventories of stored treefragments (i.e., tree-substitution grammars) similar to the fragment grammars model (De Marcken, 1996;Bod et al., 2003;Cohn et al., 2010;Post and Gildea, 2013;O'Donnell, 2015). The comparison with the full-listing model is more interesting. Not only does the full-listing model produce the worst performance of the three models in both corpora and for both evaluations, it actually produces negative correlations with reading times. We believe this result is indicative of a simple fact: while it has become clear that there is lexical storage of many syntactic constructions, and-in fact-the degree of storage may be considerably more than previously believed (Tremblay and Baayen, 2010; Bannard and Matthews, 2008)-syntax is still a domain which is mostly compositional. The full-listing model overfits, leading to nonsensical reading time predictions. In fact, this is likely a logical necessity-the vast combinatorial power implicit in natural language syntax means that even for a system with tremendous memory capacity, only a small fraction of potential structures can be stored.
Conclusion
In this paper, we have studied the ability of several models of computation and storage to explain human sentence processing, demonstrating that a model which treates the problem as a case-by-case probabilistic inference provides the best fit to reading time datasets, when compared to two "limiting case" models which always compute or always store. However, as we emphasized in the introduction we see our contribution as primarily methodological. None of the models studied here represent state-of-the-art proposals for syntactic structure. Instead, we see these results together with the tools that we make available to the community, as providing a springboard for later research that will isolate exactly which factors, alone or in concert, best explain human sentence processing. | 5,336.8 | 2015-09-01T00:00:00.000 | [
"Computer Science"
] |
Search for charged Higgs bosons produced in vector boson fusion processes and decaying into a pair of W and Z bosons using proton-proton collisions at sqrt(s) = 13 TeV
A search for charged Higgs bosons produced via vector boson fusion and decaying into W and Z bosons using proton-proton collisions at sqrt(s) = 13 TeV is presented. The data sample corresponds to an integrated luminosity of 15.2 inverse femtobarns collected with the CMS detector in 2015 and 2016. The event selection requires three leptons (electrons or muons), two jets with large pseudorapidity separation and high dijet mass, and missing transverse momentum. The observation agrees with the standard model prediction. Limits on the vector boson fusion production cross section times branching fraction for new charged physical states are reported as a function of mass from 200 to 2000 GeV and interpreted in the context of Higgs triplet models.
Searches for charged Higgs bosons (H ± ) at the LHC currently focus on the production and the decay via couplings to fermions [24][25][26][27][28][29][30][31][32], well motivated by the minimal supersymmetric standard model [33].In this model, the H ± tb coupling is the dominant one irrespective of the mass of the charged Higgs boson (m(H ± )) and tan β, the ratio of the vacuum expectation values of the two Higgs doublets.Couplings to vector bosons are, however, largely suppressed in these models.
Higgs sectors extended by SU(2) triplets, however, give rise to charged Higgs bosons with couplings to W and Z bosons at the tree level.Higgs triplets appear in left-right symmetric [34][35][36], little Higgs [37][38][39], and supersymmetric models [40,41] and can generate neutrino masses via the seesaw mechanism [17-19, 42, 43].A particularly prominent model is the Georgi-Machacek (GM) model [44], where two SU(2) triplets (one real and one complex) are added to the SM Higgs sector and preserve custodial symmetry for large vacuum expectation values of the SU(2) triplets.In such models, the charged Higgs bosons are produced via vector boson fusion (VBF) and the couplings depend on m(H ± ) and the parameter sin θ H , or s H , where s 2 H denotes the fraction of the W boson mass squared generated by the vacuum expectation value of the triplets.A representative Feynman diagram for the production by and decay into a W and Z boson pair is shown in Fig. 1.In this Letter, we discuss the search for charged Higgs bosons that are produced via VBF and decay via couplings to W and Z bosons.The analysis is performed on a sample of protonproton collisions collected at √ s = 13 TeV center-of-mass energy by the CMS experiment at the LHC.The data sample corresponds to integrated luminosities of 2.3 and 12.9 fb −1 recorded during the years 2015 and 2016, respectively.The search is performed using W and Z bosons decaying into electrons and muons.The event selection requires two jets with large pseudorapidity separation and a high dijet mass to select a VBF topology.The data are compared to the predictions of the GM model for a charged Higgs boson mass range of 200 < m(H ± ) < 1000 GeV.In addition, an exclusion limit on the VBF production cross section times branching fraction (B) for 200 < m(H ± ) < 2000 GeV is derived.A similar search was performed by the ATLAS Collaboration in proton-proton collisions at √ s = 8 TeV in the semi-leptonic (WZ → qq ) final state [45].Other experimental constraints on the GM model can be obtained from studies of b-meson decays [46] and W ± W ± VBS processes [47,48].
The signal samples are produced with MADGRAPH5 aMC@NLO v2.2.2 [49].WZ production in association with two jets involving exclusively electroweak interactions at the tree level is generated at leading-order (LO) using MADGRAPH5 aMC@NLO and is referred to as an EW WZ background.Two-jet-associated WZ production with both the strong and electroweak interaction vertices at the tree level is simulated at next-to-leading order (NLO) using POWHEG 2.0 [50][51][52][53] and is denoted as a QCD WZ background.The Z+jets, Zγ, tZq, ttV, and VVV backgrounds, where V refers to a W or Z boson, are produced at NLO using MADGRAPH5<EMAIL_ADDRESS>tZq and ttV events are included in the background referred to as VVV.The gg → ZZ sample is generated at LO with MCFM [54] and normalized to NLO with a K-factor of 1.7 [55].The ZZ production via qq annihilation is simulated at NLO with POWHEG and normalized to the next-to-next-to-leading order (NNLO) cross-section prediction with a K-factor of 1.1 [56].The PYTHIA 8 [57] package is used for parton showering, hadronization, and the underlying event simulation with parameters affecting the underlying event simulation set to the CUETP8M1 tune [58,59].The NNPDF 3.0 [60] set is used as the default set of parton distribution functions (PDFs).For all processes, the detector response is simulated using a detailed description of the CMS detector, based on the GEANT4 package [61], and event reconstruction is performed with the same algorithms as used for the data.The simulated samples include additional interactions per bunch crossing (pileup) matching the observed multiplicity in the data of about 11 and 20 interactions per bunch crossing in 2015 and 2016, respectively.Details of the CMS detector, its performance, and the definition of the coordinate system can be found in Ref. [62].The detector features a superconducting solenoid with a diameter of 6 m, providing a magnetic field of 3.8 T, and surrounding a silicon pixel and strip tracking detector, a lead tungstate electromagnetic calorimeter, and a brass scintillator hadronic calorimeter.Gas ionization detectors embedded into the steel-flux return yokes, the muon system, are installed around the solenoid.The subdetectors are composed into a barrel and two end cap sections.The hadron forward calorimeter provides calorimetry to pseudorapidities from |η| > 3 to |η| < 5.A particle-flow technique [63,64] is employed to identify and reconstruct the individual particles emerging from each collision.
Electrons are reconstructed within |η| < 2.5.The reconstruction combines the information from clusters of energy deposits in the electromagnetic calorimeter and the trajectory in the tracker [65].The selection criteria depend on transverse momentum p T and |η|, and on a categorization based on observables sensitive to the amount of bremsstrahlung emitted.Muons are reconstructed within |η| < 2.4 [66].The reconstruction combines the information from both the tracker and the muon spectrometer.Leptons are required to be isolated from other charged and neutral particles in the event.The lepton relative isolation is defined as the ratio of the p T sum of charged hadrons and neutral particles within a cone of radius ∆R = √ (∆η) 2 + (∆φ) 2 < 0.4 (where φ is the azimuthal angle in radians) around the lepton and the lepton p T .The relative isolation, corrected for pileup contributions, is required to be less than 6.5% (15%) for electrons (muons).Overall efficiencies of the reconstruction, identification, and isolation requirements for the prompt leptons are measured in the data in several bins of p T and |η| using a "tag-andprobe" technique [67] applied to a sample of leptonically decaying Z boson events.Jets are reconstructed using the anti-k T clustering algorithm [68] with a distance parameter R = 0.4, as implemented in the FASTJET package [69,70], and jet energy corrections are applied [71,72].To suppress the top-quark background contribution in its decay to b quarks, the combined secondary vertex b-tagging algorithm [73,74] requirement is used, corresponding to an efficiency of about 45% with a light flavor quark misidentification probability of 0.1%.The missing transverse momentum vector p miss T is defined as the negative vectorial sum of the momenta of all reconstructed particles in an event projected onto the plane perpendicular to the beams, corrected for the pileup contribution [75].Its magnitude is referred to as p miss T .Events are selected by the trigger system requiring the presence of one or two high p T electrons or muons.The trigger efficiency is greater than 99% for events that pass all other selection criteria explained in the following.The selection of events aims to single out three-lepton events with the VBF topology.The event selection requires three lepton (electron or muon) candidates that meet the isolation and identification requirements.Two leptons are required to have p T > 20 GeV and the third lepton is required to have p T > 10 GeV.Events with an additional fourth lepton with p T > 10 GeV are rejected.Events are required to have at least two jets with p T > 30 GeV, and |η| < 4.7.The VBF topology is exploited by requiring that the two jets of highest p T have a large dijet mass, m jj > 500 GeV, and a large pseudorapidity separation, ∆η jj > 2.5.To reconstruct a Z boson candidate, a pair of same-flavor and opposite-charge leptons is required to have a dilepton invariant mass within 15 GeV of the nominal Z boson mass [76].When there are two or more candidate pairs, the one with the mass closest to the nominal Z boson mass is chosen.The remaining lepton is associated with the W boson decay, and it is required to have p T > 20 GeV.The p miss T in the event is required to be larger than 30 GeV to select W boson decays.To reject the top-quark background, the event must not have jets passing the b-tagging selection.After these requirements, the signal efficiency is about 10-15%, depending on m(H ± ).For extraction of the signal, the shape of the distribution of the transverse mass variable (m T ) obtained from the WZ system is used where p T (W) is reconstructed from the vectorial sum of p miss T and the lepton p T and E T (W) is calculated from the scalar sum of the lepton transverse energy and p miss T .Variables such as the invariant mass of the leptonically decaying WZ system using constraints on the neutrino momentum from the W boson mass [77] may be explored in future analyses.
A combination of methods using control samples in the data and detailed simulation studies is used to estimate background contributions.The following background categories are considered: WZ, ZZ → 4 , VVV, Zγ, and processes with nonprompt leptons.
The QCD and EW WZ background constitutes about 80% of the total expected SM background yield.The normalization of the QCD WZ background is obtained from a backgrounddominated sideband, outside of the search region and defined by the dijet variables, where the expected signal yield is negligible: 100 GeV < m jj < 500 GeV and |∆η jj | < 2.5.In this phase-space region, expected background contributions from EW WZ, ZZ → 4 , VVV, Zγ production, and nonprompt leptons are estimated to contribute about 40% to the yield and are subtracted from the overall 266 events observed in data.The simulated sample of QCD WZ processes is then normalized to match the observed number of events in this control region.The estimated normalization of events is consistent with the SM prediction obtained using the POWHEG NLO cross-section calculation.The EW WZ background contributes about 30% to the overall WZ background processes in the signal region.
The ZZ → 4 , VVV, and Zγ contributions are estimated from simulated samples, with corrections to the lepton reconstruction, trigger and selection efficiencies, and momentum scale and resolution, estimated from data control samples.The overall expected contribution from these processes to the total background yield is about 10%, and the uncertainties in the estimates are dominated by the statistical component introduced by the number of simulated events passing the event selection requirements.The ZZ → 4 background is largely reduced by the p miss T requirement and the veto on events containing an additional lepton.
The main contributions to nonprompt leptons are from Z+jets and top-quark (tt and tW) events, where at least one of the jets or a jet constituent is misidentified as an isolated lepton.The dominant background at the final-selection level is Z+jets.According to the simulation, fewer than 10% of the background events with at least one nonprompt lepton come from top-quark processes.Data control samples are used to estimate this background.Lepton candidates selected with loose identification requirements are defined in a sample of events dominated by dijet production.The efficiency for candidates to pass the full lepton selection criteria is measured and is parametrized as a function of p T and η.The calculated efficiencies are used as weights to extrapolate the yield of the sample of loose leptons to the sample of fully selected leptons.The background estimation method is validated on a nonprompt lepton W+jets and tt enriched sample, selected by inverting the Z boson mass or b-tagging criteria, where good agreement between the data and prediction is observed.
Uncertainties in the data-to-simulation scale factors applied to leptons in simulated samples result in an overall 4% normalization uncertainty for backgrounds estimated from the simulation.The experimental uncertainties in the lepton momentum scale and resolution, p miss T modeling, and jet energy scale are applied in simulated events by smearing and scaling the relevant observables and propagating the effects to the kinematic variables used in the analysis, in particular m T .Uncertainties in the lepton momentum scale and resolution are smaller than 1% per lepton depending on the p T and η of the lepton, and the effect on the yields at the analysis selection level is less than 1%.The uncertainties in the jet energy scale and resolution result in a 5% uncertainty in the signal yields.The uncertainty in the resolution of the p miss T measurement is 10%.Randomly smearing the measured p miss T by one standard deviation of the resolution gives rise to a 5% variation in the estimation of signal yields after the full selection.Uncertainties of 2.3% and 2.5% are assigned to the integrated luminosity measurements in the years 2015 and 2016, respectively [78,79].The effect of higher-order corrections to the signal cross section in the GM model is taken from Ref. [80].The theoretical uncertainty is dominated by missing higher-order EW corrections estimated to be 7%.Uncertainties in the signal acceptance due to PDF choice and renormalization and factorization scales are 2-3% and less than 1%, respectively, estimated using the LO signal samples.Added in quadrature, the contributions result in an 8% uncertainty in the normalization of the signal samples.
The uncertainty in the estimation of the expected number of QCD WZ events is 12%, which is estimated from the measured yields in the two-jet control region.An uncorrelated uncertainty of 30% is assigned on the normalization of WZ events produced via EW processes, estimated from the largest bin-by-bin differences after varying the renormalization and factorization scales.The total uncertainty in the prediction of the nonprompt background varies bin by bin in the m T distribution between 30% and 80%, dominated by the low number of nonprompt leptons passing the sideband selection.A summary of the relative systematic uncertainties in the estimated signal and background yields is shown in Table 1.
After applying the full selection, nine and 62 events are selected in the data collected in 2015 and 2016, respectively.The data yield together with the SM expectation for the different processes is given in Table 2.The distribution of the m T with bin boundaries given by m T = [0, 100, 200, 400, 600, 800, 1000, 1200, 1500, ∞) GeV (the last bin is an overflow bin) is shown in Fig. 2. No event with m T (WZ) > 800 GeV is observed in the data, and overall agreement between the data and SM background prediction is observed.
A combined fit of the predicted signal and background yields in bins of m T to the data is performed to derive expected and observed exclusion limits on σ VBF (H ± ) B(H ± → WZ) at 95% The model-independent exclusion limits are compared to the predicted cross sections at NNLO in the GM model [80] in the s H -m(H ± ) plane.For the probed parameter space and m T distribution used for signal extraction, the varying width as a function of s H is assumed to have negligible impact on the result.The value of the branching fraction B(H ± → WZ) is assumed to be one.In Fig. 3 (right), the excluded s H values as a function of m(H ± ) are shown.The blue shaded region shows the parameter space for which the H ± total width exceeds 10% of m(H ± ), where the model is not applicable due to perturbativity and vacuum stability requirements [80].
The observed limit excludes s H values greater than 0.45, 0.81, and 0.66 at m(H ± ) = 200, 400, and 1000 GeV, respectively.10.0 ± 1.6 59.9 ± 8.0 Signal (m(H ± ) = 700 GeV) 0.9 ± 0.1 4.7 ± 0.5 In summary, we present a search for charged Higgs bosons produced via vector boson fusion and decaying into W and Z bosons in proton-proton collisions at √ s = 13 TeV based on a sample corresponding to an integrated luminosity of 15.2 fb −1 .Events are required to have three leptons (electrons or muons), two jets with large pseudorapidity separation and high dijet mass, and missing transverse momentum.The number of events observed in the signal region agrees with the standard model prediction.The first limits on σ VBF (H ± ) B(H ± → WZ) at √ s = 13 TeV are obtained.The results are interpreted in the Georgi-Machacek model for which the most stringent limits to date are derived.
We congratulate our colleagues in the CERN accelerator departments for the excellent perfor- The blue shaded area covers the theoretically not allowed parameter space [80].mance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort.In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses.Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMWFW and FWF (Austria); [25] ATLAS Collaboration, "Search for charged Higgs bosons through the violation of lepton universality in t t events using pp collision data at √ s = 7 TeV with the ATLAS experiment", JHEP 03 (2013) 076, doi:10.1007/JHEP03(2013)076,arXiv:1212.3572.
[27] CMS Collaboration, "Search for a light charged Higgs
Figure 1 :
Figure 1: Example of a Feynman diagram showing the production of charged Higgs bosons via VBF.
Figure 2 :
Figure 2: Transverse mass distributions after full selection, for data collected in 2015 (left) and 2016 (right).The background yield predictions correspond to the background-only hypothesis fit result.The signal distribution is shown for m(H ± ) = 700 GeV and the cross-section prediction in the GM model at s H = 0.7.
Figure 3 :
Figure 3: Expected and observed exclusion limits at 95% confidence level as a function of m(H ± ) for σ VBF (H ± ) B(H ± → WZ) (left) and on the ratio of vacuum expectation values in the GM model (right) for 15.2 fb −1 of proton-proton collisions at 13 TeV collected in 2015 and 2016.The blue shaded area covers the theoretically not allowed parameter space [80].
Table 1 :
Relative systematic uncertainties in the estimated signal and background yields, in units of percent.
Table 2 :
Yields of selected events in 2015 and 2016 data, together with the expected yields from various background processes.The statistical and systematic uncertainties are shown.The signal yields are shown for values of s H = 0.7. | 4,509.4 | 2017-05-08T00:00:00.000 | [
"Physics"
] |
A Comprehensive Survey on the Metric Dimension Problem of Graphs and Its Types
: Consider a robot that is navigating a graph-based environment and trying to figure out where it is at the moment. It can send a signal to determine how far away it is from every set of fixed landmarks. We address the problem of finding exactly the minimum number of landmarks required and their perfect placement to make sure the robot can always locate itself. The graph's metric dimension is the quantity of landmarks, and the graph's metric basis is the set of nodes on which they are distributed. The metric dimension of a graph is the smallest set of nodes needed to uniquely identify every other node using the shortest path distances. Optimization, network theory, navigation, pattern recognition, image processing, locating the origin of a spread in a network, canonically labeling graphs, and embedding symbolic data in low-dimensional Euclidean spaces are a few examples of applications for metric dimension. Also, Due to its many and varied applications in fields like social sciences, communications networks, algorithmic designs, and others, the study of dominance is the kind of metric dimension that is developing at the fastest rate. This survey provides a self-contained introduction to the metric dimension and an overview of several metric dimension results and applications. We also present algorithms for computing the metric dimension of families of graphs.
Introduction
Let's assume that the connected, undirected, simple graph G=(V,E) has the vertex set V and the edge set E and d (u,v) be the shortest path between two vertices u,v ∈ V(G). An ordered vertex set B={x 1 ,x 2 ,...,x k }⊆ V(G) is a resolving set of G if the representation is unique for every v∈V(G). The metric dimension of G, abbreviated dim(G), is the cardinality of minimum resolving set of G [1].
In order to uniquely identify the location of an intruder in a network and a minimum number of sonar units must be deployed as part of the sonar system defending the coast line., Slater [2,3] developed the idea of a minimum resolving set as a locating set of G and uses the cardinality of B as a locating number. The concepts of the smallest resolving set as a metric foundation of G and the cardinality of B as the metric dimension of G were independently introduced by Harary and Melter in [4].
Metric Dimension
Computing the metric dimension of graphs using the metric dimension problem (MDP) is a difficult combinatorial optimization problem. The metric dimension of a connected graph G is the minimum number of vertices in a subset B of G such that all other vertices are uniquely determined by their distances to the vertices in B. In this case, B is called a metric basis for G. The basic distance of a metric twodimensional graph G is the distance between the elements of B. Giving a characterization for those graphs whose metric dimensions are two, they enumerated the number of n vertex metric two-dimensional graphs with the basic distance 1 [5].
Pan et al. [6] computed the metric dimension of the splitting graphs S(P n ) and S(C n ) of a path and cycle. They proved that the metric dimension of these graphs varies and depends on the number of vertices of the graph. Hussain et al. [7] introduced a line graph of honeycomb network and then they calculated the metric dimension on line graph of honeycomb network. Murdiansyah et al. [8] presented a PSO (Particle Swarm Optimization) algorithm for determining the metric dimension of graphs. They choosed PSO because of its simplicity, robustness, and adaptability for various optimization problems. Mulyono et al. [9] devoted to determine the metric dimension of friendship graph F n , lollipop graph L m,n and Petersen graph P n,m . Fernau et al. [10] presented a linear-time algorithm for computing the metric dimension for chain graphs, which are bipartite graphs whose vertices can be ordered by neighborhood inclusion. Garces et al. [11] computed the metric dimension of truncated wheels. Chuanjun et al. [12] showed that the metric dimension of the join of two path graphs is unbounded because of its dependence on the size of the paths. Mohamed et al. [13] studied the metric dimension of subdivisions of several graphs, including the Lilly graph, the Tadpole graph and the special trees star tree, bistar tree and coconut tree.
The metric dimensions of path powers three and four are unbounded, as demonstrated by Nawaz et al. [14]. They also showed multiple results about the edges of the power of path and power of total graph. Ahmad et al. [15] found the metric dimension of Kayak paddles graph and cycles with chord. Rehman et al. [16] computed the metric dimension of Arithmetic Graph A m , when m has exactly two distinct prime divisors. Imran et al. [17] studied the metric dimension of some classes of convex polytopes which are obtained by the combinations of two different graphs of convex polytopes. Mladenovic et al. [18] proposed a variable neighborhood search approach for solving the metric dimension and minimal doubly resolving set problems. Kratica et al. [19] computed the metric dimension of graphs by a genetic algorithm that used the binary encoding and the standard genetic operators adapted to the problem. Jäger et al. [20] found that the metric dimension of Z n × Z n × Z n , n ≥ 2 is ⌊ ⌋. Imran et al. [21] investigated the metric dimension of the barycentric subdivision of Möbius ladders, the generalized Petersen multigraphs P(2n, n) and proved that they have metric dimension 3 when n is even and 4 when n is odd. Nadeem et al. [22] discussed the metric dimension of toeplitz graphs with two and three generators. Korivand et al. [23] presented the metric dimension threshold of some families of graphs and a characterization of graphs of order for which the metric dimension threshold equals 2, n-2 and n-1. Munir et al. [24] discussed a new regular family of constant metric dimension. Nazeer et al. [25] computed the metric dimension of some new graphs and named them middle graphs, -total graphs, symmetrical planar pyramid graph, reflection symmetrical planar pyramid graph, middle tower path graph and reflection middle tower path graph.
Types of Metric Dimension
In this section, we discuss the types of metric dimension of some graphs.
Stephen et al. [26] determined the total metric dimension of paths, cycles, grids, and of the 3-cube and the Petersen graph. Kratica et al. [27] presented genetic algorithm for determining the strong metric dimension of graphs that used binary encoding and standard genetic operators adapted to the problem. Zafari et al. [28] determined the cardinality of minimal doubly resolving sets and strong metric dimension of jellyfish graph and cocktail party graph. Ameen et al. [29] discussed the localization problem in Kayak paddle graphs KP(l,m,n) for l,m ≥3 and n≥2 by computing edge version of metric and double metric dimensions. Zafari [30] determined the minimal resolving set, doubly resolving set, and strong metric dimension for a class of Cayley graphs. Chitra et al. [31] introduced the concept of non-isolated resolving set and non-isolated resolving number and presented several basic results. Okamoto et al. [32] presented the exact value of local metric dimension of some graphs. Gómez et al. [33] studied the problem of finding exact values for the local metric dimension of corona product of graphs. Wei et al. [34] studied the edge metric dimension problem for certain classes of planar graphs. Ramírez et al. [35] studied study the problem of finding exact values or bounds for the local metric dimension of strong product of graphs. Meera et al. [36] studied the radiatic dimension of some standard graphs and characterize graphs of diameter 2 that are radio graceful. Marsidi et al. [37] gave the local metric dimension of some operation graphs such as joint graph P n +C m , amalgamation of parachute, amalgamation of fan. Feng et al. [38] studied the (fractional) metric dimension for the hierarchical product of rooted graphs. Velázquez et al. [39] showed that the computation of the local metric dimension of a graph with cut vertices is reduced to the computation of the local metric dimension of the so-called primary subgraphs. The main results are applied to specific constructions including bouquets of graphs, rooted product graphs, corona product graphs, block graphs and chain of graphs. Budianto et al. [40] computed the local metric dimension of starbarbell graph, K m ⊙ P n graph and M¨obius ladder graph for even positive integers n ≥ 6. Moreno et al. [41] obtained tight bounds and closed formulae for the k-metric dimension of the lexicographic product of graphs in terms of the k-adjacency dimension of the factor graphs. Cynthia et al. [42] investigated the local metric basis and local metric dimension of Cyclic Split Graph. Laihonen [43] studied the problem of the ℓ-set-metric dimension in two infinite classes of graphs, namely, the two dimensional grid graphs and the ndimensional binary hypercubes.
Mohamed et al. [44] computed the exact value of the secure resolving set of some networks such as trapezoid network, Z-(P n ) network, open ladder network, tortoise network and also determined the domination number of the networks such as the twig network, double fan network, bistar network and linear kc 4 -snake network. Mohamed et al. [45] presented the first attempt to compute heuristically the minimum connected dominant resolving set of graphs by a binary version of the equilibrium optimization algorithm. Moreno et al. [46] studied the simultaneous metric dimension of families composed by lexicographic product graphs. Mohamed et al. [47] presented the first attempt to compute heuristically the minimum connected resolving set of graphs by a binary version of the Enhanced Harris Hawks Optimization. Cabaro et al. [48] investigated the 2-resolving dominating set in the join, corona and lexicographic product of two graphs and determined the bounds of the 2-resolving dominating number of these graphs. In [49] If a resolving set induces a star, it is said to be a star resolving set, and if it induces a route, it is said to be a path resolving set. The star resolving number and path resolving number are the minimal cardinality of these sets. They investigated these resolving parameters for the hypercube networks.
Applications of Metric Dimension
Robots that are in motion can send signals to a set of fixed landmarks to calculate their distance from them. Finding out how many landmarks and where to put them so that the robot can always identify its location is an issue that is essential to its ability to know where it is right now [50,51]. The number of landmarks is referred to as the graph's metric dimension, and the set of nodes on which they are distributed is known as the graph's metric basis.
The metric dimension problem has recently been widely applied to resolve several practical problems. It is used in chemistry to distinguish between different molecular compounds [52]. It is also used to create reliable sensor networks [53], where network invaders are verified using the networks' metric base, connected joins in graphs [54] and coin weighing problems [55]. It can be used to determine the source of information circulating on networks in addition to recognizing intruders. It is used, for instance, to find patient 0 or other items in complex networks.
Conclusion
In this paper, we have introduced an introduction to the metric dimension and an overview of several metric dimension results and applications and we have presented algorithms for computing the metric dimension of families of graphs. | 2,709 | 2023-07-13T00:00:00.000 | [
"Mathematics"
] |
Optical Multi-Tap RF Canceller for In-Band Full-Duplex Wireless Communication Systems
In-band full-duplex (IBFD) technology has become important for future wireless communications, due to its ability of increasing the radio-frequency (RF) spectrum efficiency. However, the benefits can only be realized if the self-interference (SI) is sufficiently suppressed. RF cancellation is important for IBFD systems due to its ability of SI mitigation. But it becomes more difficult for RF cancellation while the frequency and bandwidth increase. In real scenarios, the response of the multi-path SI channel is not frequency-flat, which also limits the cancellation performance. To solve these problems, we present a photonic-enabled multi-tap RF canceller in this paper. The proposed RF canceller has the ability of cancelling multi-path SI. The tap coefficients are precisely adjusted by optical spectrum processing. A prototype system with 8 taps is demonstrated in this paper. The measured results show 25 dB average cancellation depth over 1 GHz cancellation bandwidth under over-the-air conditions. To verify the signal of interest (SOI) recovery capability of the novel RF canceller, an IBFD wireless communication experiment based on 16-quadrature amplitude modulation (16-QAM) was demonstrated, the SOI was successfully recovered.
I. INTRODUCTION
I N-BAND full-duplex (IBFD) wireless communication systems doubles spectrum utilization by allowing the users to simultaneously occupy the same frequency band instead of using different time slots or different bands [1]. With the ability of transmitting and receiving on the same band and at the same time, IBFD technology facilitates several novel applications. IBFD systems have been studied for tactical communications and electronic warfare schemes due to its ability of providing physical-layer security and jamming enemy's receivers [2], [3]. IBFD technology also promotes cognitive radio technology, due to its capability of allowing users to simultaneously transmit and sense the spectrum [4]. However, the benefits mentioned above only become possible if the strong self-interference (SI) is sufficiently suppressed.
Partial transmitting signal leakages to the receiver may cause severe SI. The SI signal may reduce the dynamic range of the system and deteriorate receiver sensitivity. The SI cannot be mitigated by using notch filter or band-pass filter due to the band superposition of signal of interest (SOI) and SI.
To deal with this problem, the SI cancellation technology has been widely investigated. SI cancellation is typically conducted in three stages, including propagation domain suppression [5], [6], RF cancellation [7], [8] and digital cancellation [9], [10]. RF cancellation is of great important due to its ability of mitigating the SI before receiving and avoiding distortion. Traditional RF SI cancellation schemes based on electronic components have been widely investigated [11]. However, due to the electric bottleneck, the operating frequency and bandwidth of RF SI cancellation systems are limited. Compared to the traditional electronic RF cancellation schemes, the photonic-enabled RF cancellation technologies have the advantages of large bandwidth, high tuning precision and flat response, which can overcome the limitations of traditional electronic RF cancellers.
As summarized in [12], the incorporation of microwavephotonic technologies into RF SI cancellation systems effectively increase the operational bandwidth and cancellation depth. The photonic-enabled RF cancellation schemes can be timedomain focused or digitally assisted. To realize cancellation, the first type of cancellers precisely adjusts the frequency response of the canceller to make it opposite to the SI channel frequency response. Then, a small amount of original transmitting signal is coupled off before the antenna to serve as the reference signal. After processing in the optical domain, the reference signal is well-matched to SI signal and subtract it. Schemes have previously been proposed with direct laser modulation [13], [14], external optical intensity modulation [15], [16], [17], [18], [19], [20], [21], external polarization modulation [22], [23], and phase modulation [24], [25].
The majority of these schemes have only a few optical taps, which limits their performance under realistic over-the-air conditions. These schemes can only deal with the unrealistic situation that the response of SI channel is frequency-flat. Their ability of cancelling multi-path SI signal is also limited by the modest tap counts. The exception to that is the twenty-tap system in [25]. The cancellation depth of 20 dB over 1 GHz bandwidth and 25 dB over 500 MHz were achieved. However, due to the limited operating bandwidth and the imbalance between two outputs of the hybrid coupler, the cancellation performance is poor while cancelling high frequency and broadband SI signal. The tap delays are difficult to tune which also limits the cancellation performance. The digitally assisted schemes directly cancel the SI signal by utilizing an auxiliary transmit channel [27], [28], [29], [30]. These schemes can provide a significantly higher number of adaptive taps, which are realized in digital domain. Thanks to its high flexibility, the digital assisted canceller can effectively cancel multi-path SI signal. In [30], a digital-assisted multipath photonic SI cancellation and frequency down-conversion method was proposed, more than 26 dB cancellation depth of QPSK-modulated signal with the baud rate up to 1Gbaud has been achieved. However, the auxiliary transmit channel may worsen receiver's sensitivity because of the additive noise. Besides, it cannot eliminate the noise and the nonlinear components of the SI signal because they are not captured.
In [31], we have proposed a photonic-enabled SI canceller based on optical spectrum processor, and the prototype with one canceller tap was experimentally demonstrated. A novel multi-tap RF canceller is further proposed in this paper, and is able to be scaled to more than 8 taps demonstrated. To realize high cancellation depth, the frequency response of the canceller is precisely adjusted by tuning the tap coefficients to make it opposite to SI channel frequency response. With this purpose, the reference signal is modulated to multi-wavelength optical carriers, the phase and amplitude of each optical signal are finely tuned by an optical spectrum processor (OSP). After processing, the reference signal is well-matched to SI signal, and the SI is cancelled after the two photocurrents are combined at a photodetector (PD). Measured results show 25 dB cancellation depth over 1 GHz cancellation bandwidth under over-the-air conditions. Besides, IBFD wireless communication experiment based on 16-QAM has also been demonstrated, the signal of interest (SOI) was recovered.
A. Description of the Architecture
The architecture of the proposed multi-tap RF canceller is shown in Fig. 1. A small amount of transmission signal is coupled off before the transmitting antenna to serve as the reference signal. Because the SI channel responses are not frequency-flat under over-the-air conditions, the adjustment of reference signal should be different with frequencies over the whole frequency band, which can be realized by the proposed multi-tap architecture.
The tunable lasers (TLs) were utilized to emit optical carriers with different wavelengths. The reference signal is modulated to MZM1, and the received signal is modulated to MZM2, respectively.
We firstly analyze the upper branch. Multi-wavelength optical carriers are coupled into one path, which can be expressed as where p n and ω n are the optical intensity and angular frequency of the optical signals, N is the tap number. Assuming the transmission signal is T (t) = V 1 cos(ω r t), where V 1 , ω r are the amplitude and angular frequency of the transmitting signal. The reference signal can be seen as a copy of transmitting signal. Around the quadrature bias point, the optical fields at the output of MZM1 can be expressed as where m 1 = πV 1 /V π is the modulation indices, V π is the halfwave voltage of the MZM. Utilizing a small signal approximation, (2) can be rewritten as where J n is the nth-order Bessel function of the first kind. The reference signal is then amplified by an erbium-doped fiber amplifier (EDFA) and be adjusted by the OSP. OSP suppresses the upper sideband of each optical signal, as well as adjusts the amplitudes of the lower sidebands and the phases of the optical carriers. It is worth noting that, we can also adjust the phases of the lower sidebands and the amplitudes of the optical carriers, or introduce the amplitude and phase coefficients in one of them, for example, the carrier. These methods are the same to control the amplitudes and phases of the optical signals. After optical signal processing, the reference signal can be written as where α n and ϕ n are the amplitude and phase adjustment coefficients, respectively. Thanks to the sheer optical spectrum processing ability of liquid crystal on Silicon (LCoS) [32], the control of the amplitude and phase can be precise and flexible. The dispersion compensation fiber (DCF) is utilized to introduce the tap delay. After propagation through the DCF, the optical field can be written as where θ(ω) is an additional phase term added to the signal introduced by DCF, which can be expressed as where θ 0 is a constant of phase shift, θ 1 is the total group delay of DCF. θ 2 relates to the dispersion parameter D (in ps/nm/km) as where λ is the wavelength of the optical signal, L is the length of the DCF and c is the speed of the light. The higher order dispersion is negligible. After transmitting through the DCF, a photodetector (PD) converts the optical signals to the RF domain. The output reference signal can be written as where is the responsivity of the PD. The tap delay can be expressed as Therefore, the transfer function of the upper branch can be expressed as By taking an inverse Fourier transform of (10), we can write the time domain response function as Since the input reference signal shares the same source of transmitting signal, I ref (t) can be expressed as the convolution of h 1 (t) and T (t).
The upper branch of the canceller can be considered as a N-tap finite-impulse-response (FIR) filter with complex coefficients. The arbitrary frequency response of upper branch can be achieved by finely tuning the tap coefficients. Therefore, the proposed cancellation scheme has the capability to cancel the self-interference signal even if the SI channel response is not frequency-flat.
The signal received at the receiving antenna (RA) can be expressed as where h SI (t) is the impulse response of the self-interference channel, the operator '⊗' represents convolution, y SOI (t) is SOI. The received signal is modulated to a single-wavelength optical carrier with MZM2. The optical signal is then amplified by an EDFA, then it's up sideband is filtered out by OSP to avoid dispersion power fading. Unlike the optical signals in upper branch, the amplitude and phase of the optical signal in lower branch are not changed, as shown in Fig. 1. After transmitting through the DCF, the optical signal is converted to RF signal by the PD. According to the analysis above, the frequency response of the lower branch can be written as where p 0 is the optical intensity and ω 0 is the angular frequency of the optical signal emitted by TL0. By taking an inverse Fourier transform of (13), the time domain response function of the lower branch can be expressed as: After transmitting through the lower branch, the SI signal can be expressed as The addition of I ref (t) and y SI (t) is realized at the PD. Therefore, the conditions for cancellation can be found, which can be written as (16) can also be expressed in frequency domain: where H SI (ω r ) is the frequency response of the SI channel. Therefore, the target frequency response of the upper branch can be expressed as The tap coefficients should be precisely tuned to approach the target frequency response.
B. Tuning Algorithm
To approximate the target frequency response, a tuning algorithm is designed to find the optimal solution. The algorithm is necessary because of the large number of degrees of freedom which makes it difficult to find the optimal tap coefficients manually. Firstly, we model the canceller with a complex N-by-M matrix. The elements of the matrix indicate the frequency response of each tap, which are measured while others are disabled. The matrix can be expressed as where N is the total number of canceller taps, and M designates the number of samples for the cancellation bandwidth. The frequency response of the upper branch can be written as where − → w is the 1-by-N complex tap coefficient vector. Based on discrete mathematical model, the power of residual SI signal can be expressed as where − → G is a 1-by-M vector that represents the target frequency response. To minimize the power of the residual signal, we use CVX, which is a MATLAB-based modeling system for convex optimization, to find the optimal tap coefficients. The OSP is then programmed to realize cancellation.
C. Simulation Results
The system shown in Fig. 1 was simulated using a realworld SI channel, which was measured with a pair of K-band knife-edge antennas and a network analyzer. The simulation was focused on the SI between 18.0 and 19.0 GHz. In the simulation, we modeled the canceller as a FIR filter. The differential delay between taps was 0.5ns. With the tuning algorithm proposed in Section II-B, the simulation results are achieved. Fig. 2 shows the RF cancellation depth with a varying number of taps under ideal and nonideal situation. The nonideal factor that affects the cancellation performance is OSP's maximum attenuation. The adjustment of tap coefficients is limited due to the OSP's maximum attenuation, which results in a limitation of cancellation depth. The typical attenuation limitation for a commercial waveshaper is 35 dB. Therefore, the maximum attenuation was set to be 35 dB in the simulation. As can be seen, the cancellation performance is strongly depended on the number of taps. The cancellation depth can be improved by adding more taps, within limits. Fig. 3 shows the amplitude and phase responses of the canceller with 2 taps and 30 taps. It can be seen that the 30-tap canceller's magnitude response almost perfectly matches the SI channel magnitude response, and the phase response is nearly 180°offset. The 2-tap canceller's response cannot approach the SI channel response, which limits the cancellation performance. Fig. 4 illustrates the simulated residual signals of combing the SI signal and the canceller output for both situations shown in Fig. 3. As can be seen, the 30-tap canceller provides higher cancellation depth, the power of residual signal is much lower.
A. Over-the-Air Cancellation Performance
To evaluate the cancellation performance of the proposed scheme, an over-the-air cancellation experiment was conducted corresponding to Fig. 5. We used a Rohde & Schwarz's ZVA-67 vector network analyzer (VNA) to emit broadband transmitting signal and measure the residual SI. The K-band antennas mentioned above were employed for over-the-air IBFD demonstration. A multi-channel laser (Anristu, MT9812B) was used as the multi-wavelength optical source. 8 optical signals were emitted which covered 193. 8-195.2 THz with 200 GHz of spacing. The output power of each carrier was 6 dBm. TL0 was implemented by using a tunable semiconductor laser (TSL-550, Santec). The optical signals drove the MZMs (Fujitsu, FTM7938). The modulators have the half-voltage wave of 5 V and the 3-dB bandwidth of 37 GHz. The optical signals were then amplified by an EDFA. We used a waveshaper (Finisar, waveshaper 16000S) to process the optical signals. After processing in the optical domain, the signal went through the DCF with the dispersion of −320 ps/nm to introduce tap delay. Finally, the optical signals were converted back into RF domain via a PD (Finisar, MPRV1331A) with a bandwidth of 30 GHz and the SI was then cancelled.
The tap delay is 0.5ns in the experiment and simulation, and the maximum time delay difference of the 8-tap prototype system is 3.5ns. It is also possible to introduce time delay for paths with very long path difference. To achieve that, the frequency spacing of the optical carriers and the dispersion of the fiber should be very large according to (9). As discussed in [33], dispersion immunity is very important in application scenarios where fiber transmission is incorporated. To avoid dispersion power fading, the scheme removes the up sidebands of the optical signals by the OSP. Thus, this work is dispersion immunity even if the dispersion of the fiber is large.
The SI channel frequency response was firstly obtained by the VNA. The tuning algorithm described in the previous section was then utilized to configure the canceller's tap coefficients. The OSP was then programmed to mitigate SI. The simulation and experimental results of the 8-tap canceller are shown in Fig. 6(a) and (b), respectively. The SI was between 18.0 and 19.0 GHz. As can be seen, the canceller output is approximate to SI channel response. The simulated and experimental results showed 25.8 and 25.1 dB of average cancellation over the 1 GHz band in this instance. Furthermore, the cancellation performances over different frequency bands were provided. Fig. 7 Fig. 7, after cancellation, the magnitude of the residual signal is even over the whole frequency band. However, the magnitude of the interference is low in some bands, for example, 19 to 20 GHz and 24 to 25 GHz. Thus, the worst cancellation depth over the whole frequency band is low in some frequency bands. The experimental results show that, the canceller output is approximate to the SI channel response over the whole frequency band, even if the SI frequency band is not frequency-flat. The experimental results also indicate that the multi-tap scheme can mitigate multi-path SI signals.
In the experiment, the algorithm took about 0.85 s, and the CPU used for calculation is Intel(R) Core(TM) i5-10210U. The time for the commercial waveshaper to tune the tap coefficients is about 3 to 4 seconds. Therefore, if the SI channel response changes, the system has the ability of real-time reconstruction.
B. SOI Recovery
To evaluate the SOI recovery capability under over-the-air conditions, we built the experimental setup as shown in Fig. 8. We used a Tektronix's AWG70002A arbitrary waveform generator (AWG) to generate the baseband 16-QAM SOI and transmitting signal. We then used a microwave signal generator (MSG, Ceyear, 1465L-V) and mixers to up-convert the baseband signals. After finely adjusting the tap coefficients of the OSP, the SI was mitigated and the SOI was analyzed by using a digital signal oscilloscope (DSO). Fig. 9 shows the SOI recovery performance with and without cancellation when a 16-QAM SOI with 200 MHz bandwidth and a SI signal with 1 GHz bandwidth centered at 18.5 GHz were used. Fig. 9(a) shows the output spectrum of SI and SOI signal with and without cancellation. As can be seen, the SI (blue curve) was efficiently suppressed and the SOI (orange curve) was successfully recovered. The average cancellation depth is about 21 dB. The constellation diagram was not clear without cancellation, as shown in Fig. 9(b). After cancellation, the SOI was well recovered with an error vector magnitude (EVM) of 9.34%, as shown in Fig. 9(c). The proposed multi-tap RF canceller has the capability to provide effective SI cancellation and SOI recovery under overthe-air conditions.
IV. CONCLUSION
A novel multi-tap RF canceller based on optical signal processing is proposed in this paper. Thanks to the considerable tap count, the proposed scheme provides high cancellation depth under over-the-air conditions. A tuning algorithm has been proposed to find the optimal tap coefficients. An 8-tap prototype system was experimentally demonstrated. The tap number can be easily scaled by adding additional optical carriers. Measured results show 25 dB cancellation depth over 1 GHz cancellation bandwidth under over-the-air conditions. Furthermore, under the interference of SI signal with 1 GHz bandwidth, a 16-QAM SOI with 200 MHz bandwidth was well-recovered with an EVM of 9.34%. Due to its capability of providing high cancellation depth under over-the-air conditions, the proposed multi-tap RF canceller has the potential to enable IBFD wireless communication systems. | 4,579.4 | 2022-10-01T00:00:00.000 | [
"Engineering",
"Physics",
"Computer Science"
] |
Analysis of Secondary Flows in Centrifugal Impellers
Secondary flows are undesirable in centrifugal compressors as they are a direct cause for flow (head) losses, create nonuniform meridional flow profiles, potentially induce flow separation/stall, and contribute to impeller flow slip; that is, secondary flows negatively affect the compressor performance. A model based on the vorticity equation for a rotating system was developed to determine the streamwise vorticity from the normal and binormal vorticity components (which are known from the meridional flow profile). Using the streamwise vorticity results and the small shear-large disturbance flow method, the onset, direction, and magnitude of circulatory secondary flows in a shrouded centrifugal impeller can be predicted. This model is also used to estimate head losses due to secondary flows in a centrifugal flow impeller. The described method can be employed early in the design process to develop impeller flow shapes that intrinsically reduce secondary flows rather than using disruptive elements such as splitter vanes to accomplish this task.
INTRODUCTION
Strong circulatory secondary flows (vortex flows) are observed in mixed-flow impellers such as axial/centrifugal pumps, turbines, and compressors.These vortex flows are undesirable as they are responsible for head losses, flow nonuniformity, and slip.To reduce secondary flows and slip, turbomachinery designers often employ flow guiding/disruptive elements such as splitter vanes and other hardware modifications (which themselves negatively affect the efficiency of the machine) rather than focusing on the actual causes and intrinsic physical mechanism that generate vortex secondary flows.
Most modern commercially available three dimensional (3D) computational fluid dynamics codes can predict circulatory secondary flows in rotating machinery with a reasonable accuracy.However, the aim of this work is not to develop another "black-box" flow prediction tool (such as a 3D Navier-Stokes flow solver), but rather to derive a simplified model from the governing equations to study the underlying This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.physics of the secondary vortex flow phenomena.Results from this paper will provide the designer with a more fundamental understanding of how circulatory secondary flows behave and are affected by operational and geometric parameters of the turbomachine.
To limit the topic somewhat, this paper will focus only on prediction of vortex secondary flows in shrouded centrifugal compressors using the streamwise vorticity equation.(In unshrouded centrifugal compressors the viscous influence of the rotating wall/shroud and tip leakage effects complicate the secondary flows such that a simple model based on the vorticity equation is not directly applicable.)As the influence of the density gradient terms within the streamwise vorticity equation will be demonstrated to be negligible, results from this paper are certainly also applicable to centrifugal pumps.
Thus, a model to determine the rotational direction and magnitude of the passage circulatory secondary flows was derived based on the streamwise vorticity equation.The model applies known meridional velocities to the streamwise vorticity equations to determine normal, binormal, and streamwise vorticity, circulatory secondary velocities, and associated head losses.The influence of nondimensional operating parameters (Reynolds number, Rossby number) on vortex secondary flows is also analyzed.
BACKGROUND AND REVIEW OF RELEVANT LITERATURE
During the past 50 years a number of researchers have studied the flow fields in mixed-flow turbomachinery employing both analytical and experimental methods.For the sake of brevity only analysis relevant to the secondary flow field and jet/wake effects (as it relates directly to secondary flows) is presented herein.
Eckardt [1] used the laser-2-focus (L2F) method to measure velocities in radially bladed and backward swept impellers with diffusers.Suction side separation and wake flow was observed.More uniform flow was observed in the backswept impeller.
Fister et al. [2] used L2F to measure flow in simulated bends of multistage radial-flow impellers.Results were compared to predictions from a 3D, turbulent, viscous Navier-Stokes code.Reasonable agreement was found between experimental and computational results; however, the Navier-Stokes code failed to predict existing flow separation regions.
Krain [3] used L2F to study the effect of vaned and vaneless diffusers on impeller flow in a centrifugal compressor.Rapid boundary layer growth and wake flow was shown at the midpassage on the blade suction sides.Similarly, Hayami et al. [4] employed an L2F to measure velocities in the inducer of a centrifugal compressor.Also, static pressure measurements were taken at the shroud.Small separation regions were shown near the inducer inlet, while the flow along the blades was mostly stable, except near the shroud.
Hamkins and Flack [5], Flack et al. [6], and Miner et al. [7] used a two-directional Doppler laser velocimeter to measure the flow of a shrouded and unshrouded centrifugal impeller with logarithmic spiral volutes.Measurements were taken in the impeller and the volute.Nonuniform asymmetric flow was shown at impeller off-design conditions, but jet/wake flow was not observed.
Fagan and Fleeter [8] measured the flows in a centrifugal compressor impeller using a laser velocimeter and a shaft encoder.Significant flow changes as compressor stall approached were identified.Hathaway et al. [9] measured velocities in a large low-speed centrifugal fan using a laser velocimeter.Results were favorably compared to five-hole probe and other data.McFarland and Tiederman [10] used a two-directional laser velocimeter to measure flows in an axial turbine stator cascade.Unsteady flow due to the turbine upstream wakes were seen to affect the flow field throughout the stator.
Strong secondary flows were observed in the mixed-flow pump of a torque converter by Gruver et al. [11] and Brun et al. [12].Comparable secondary flows in other turbomachinery geometries were studied by a number of researchers.For example, Moore [13,14] used a hot wire probe to determine the secondary flow field in a rotating radial-flow passage and to compare the results to predictions from a potential flow code.Hawthorne [15], Kelleher et al. [16], and Sanz and Flack [17] studied secondary flows in stationary circular and rectangular bends.Ellis [18] experimentally and analytically studied the induced vorticity in a centrifugal compressor.Krain [19], Moore and Moore [20], Eckardt [1], Howard and Lennemann [21], and Brun et al. [12] experimentally determined the secondary flows in mixed-flow centrifugal impellers.Finally, Johnson and Moore [22] determined secondary flow mixing losses in a centrifugal impeller from pressure probes installed in the rotating impeller.
A number of analytical models have been derived for the development of streamwise vorticity and, thus, vortex secondary flows in turbomachines.Wu et al. [23], Smith [24], Hill [25], Horlock and Lakshminarayana [26], and Lakshminarayana and Horlock [27] derived equations for the development of streamwise vorticity in stationary and rotating systems.Analytical solutions of these equations were presented by Hawthorne [15] for stationary bends and rotating radial-flow passages.Later, Johnson [28] solved these equations to predict secondary flows in a rotating bend.
VORTEX FLOW THEORY
Secondary flows are always caused by an imbalance between a static pressure field and the kinetic energy in the flow.An example is the well-documented horseshoe vortex, where the incoming boundary layer flow meets a stagnation line which causes a motion of the fluid along the wall, and subsequently the formation of a vortex.The important observation herein is that the strength of the vortex is mostly determined by the starting conditions and the further development of the vortex is determined by the conservation of its angular momentum.In a rotating system the analogy is that the vortex flows are principally generated by the meridional flow field while the centrifugal and Coriolis forces only act to change the vortex vector direction (tilting of the vortex plane).
The meridional flow in centrifugal/mixed flow pumps and compressors is usually highly nonuniform, dominated by significant jet/wake flow with separation regions blocking up to half of the passage through-flow areas.At high Reynolds numbers, the peak meridional velocities are located at the blade hub-pressure sides due to potential flow effects; at low Reynolds numbers, the viscous jet/wake flow causes the flow to separate at the hub and, thus, the peak velocities are seen at the blade tip-pressure side.These through-flow profiles can be accurately predicted using simple jet/wake flow models (for low Reynolds number, low specific speed impellers), empirical models (based on the significant amount of experimental data available in the public domain), or even Euler flow solvers (for high Reynolds number impellers).Once the meridional flow profile is determined, the normal and binormal vorticity can be numerically evaluated and the results are directly applied to the rotating system vorticity equations to calculate the streamwise vorticity.Using simple potential flow solvers and the viscous dissipation function, the passage circulatory (vortex) secondary flow and associated head losses can be estimated, respectively.
SECONDARY FLOW MODEL
Streamwise vorticity and, hence, rotating secondary flows will develop whenever a moving fluid with a gradient of the reduced stagnation pressure (P rs = P + 1/2ρ(V 2 − ω 2 R 2 )) turns around a bend or is rotated about a fixed axis (Johnson [28]).A gradient in the reduced stagnation pressure, P rs , might result from a nonuniform velocity profile or a reduction of P rs due to boundary layer viscous dissipation.In centrifugal impellers the meridional flow field is highly nonuniform because of the jet/wake flow phenomena, the nonuniform flow field is both turned around a bend with a radius of curvature r, and is rotated around the shaft at an angular speed of ω.Hence, high values of streamwise vorticity and strong associated circulatory secondary flows are anticipated.
Equations for the generation of streamwise vorticity, and, thus, circulatory secondary flows, in an intrinsic rotating coordinate system were first derived by Hawthorne [15], Smith [29], Smith [24], and Ellis [18].These equations were then generalized to include viscous terms and compressibility effects by Howard [30] and Lakshminarayana and Horlock [27].The equations as derived by Lakshminarayana and Horlock were employed for the analysis herein.
Since a detailed derivation of these equations is available in the literature, only the main steps for the inviscid, incompressible streamwise vorticity generation equations are described here.The steady-state, incompressible Navier-Stokes equations for a rotating system are given in vector form by where V is the velocity vector, P is the total pressure, υ is the kinematic viscosity, and ω is the angular velocity of the system.One should note that the fourth term in (1) represents the Coriolis force and the fifth term represents the centrifugal force.Also, note that the equations are being derived with the assumption of incompressible flow; the subject analysis found that for the generation of streamwise vorticity in centrifugal compressors, the fluid compressibility effects were found to be negligible (see more detailed explanation below).
Introducing the vector identity, defining the vorticity vector, ξ, as and taking the curl of (1) with the knowledge that the curl of a gradient of a scalar always equals zero (∇ × ∇Φ = 0), one obtains Furthermore, introducing the vector identities, and knowing that for an incompressible flow from the continuity equation, one obtains which is the vorticity transport equation for an incompressible flow in a rotating system (Greenspan [31]).Unit vectors are now defined along the streamline, s (streamwise), in the inward radius of curvature direction, n (normal), and along the b (binormal) direction, so that s, n, and b form a right-handed set of unit vectors.In a centrifugal compressor these directions approximately correspond to s-through-flow direction, n-tip-to-hub side direction, and bsuction-to-pressure side direction (see Figure 1).
Taking the dot product of (7) (and neglecting the viscous term) with the streamwise unit normal vector, s, and using the dot product relations given by Bjørgum [32] for an intrinsic coordinate system, one obtains (Lakshminarayana and Horlock [27]) where r is the radius of curvature and s is along the streamwise direction.This expression can be simplified to obtain the fundamental generation of streamwise vorticity equation for a rotating system (Lakshminarayana and Horlock [27]), where ξ is the total vorticity vector, ξ n is the normal vorticity component, ξ s is the streamwise vorticity component, and r is the radius of curvature.The first term in ( 9) is a streamline curvature term and the second is a Coriolis force term.For an impeller with a fixed axis of rotation (such as a centrifugal compressor) this equation can be further reduced to where κ is the meridional flow angle relative to the axis of rotation and ξ b is the binormal component of vorticity.
The normal and binormal components of vorticity (ξ n , ξ b ) in ( 10) can be directly determined from where A is the through-flow area.For the purpose of this analysis the term ∂v/∂z in (11) and the term ∂u/∂z in (12) can be neglected as they are small compared to the meridional gradients (∂w/∂y and ∂w/∂x).Thus, Values for ξ n and ξ b can be calculated from ( 13) if the meridional flow profile is known by discretizing the equations and numerical integration.Namely, the normal and binormal components of the vorticity can be determined for a known meridional flow profile (from jet/wake models, 2D flow through-flow models, and/or experimental data).Equation (10) shows that there are primarily two force terms that contribute to the generation of streamwise vorticity in a centrifugal impeller.The first term shows that streamwise vorticity is generated whenever a flow that is nonuniform in the pressure-to-suction direction, and thus, has a normal vorticity component, ξ n , follows a curved bend with a radius of curvature, r.The second term shows streamwise vorticity generation whenever flow that is nonuniform in the hub-to-tip direction (ξ b ) is rotated around a centerline (shaft).The sine-term indicates that streamwise vorticity is only generated by the second term when a radial-flow component (κ = 0 • ) exists.Thus, in a compressor, a pressure-to-suction side nonuniform flow profile only contributes to the first term of (10) while a hub-to-tip side nonuniformity only contributes to the second term of (10).The meridional flow angle in (10) can be closely approximated by κ = πs/s total for a circular compressor torus.Consequently, (10) with the normal and binormal vorticities obtained from the simple 2D flow models, can be numerically integrated to calculate the streamwise vorticity in the compressor and, thus, can be used to approximately predict the compressor secondary flow circulation.
One should note that streamwise vorticity can also be generated by compressibility effects and viscosity; analytical terms for these effects can be found in Lakshminarayana and Horlock [27] but were found to be negligible in the analysis presented herein.Namely, compressibility and viscosity have a strong direct influence on the meridional flow field and, thus, on the normal and binormal vorticity components, but only an indirect effect on the streamwise vorticity.The secondary flow field is "shaped" by gradients in the reduced stagnation pressure (Johnson [28]) that are principally determined by the meridional flow field, centrifugal forces, and Coriolis forces.Once the meridional flow field is known, the secondary flow field can be determined neglecting compressibility and viscous effects.A vortex will behave mostly under the influence of its angular momentum vector.Clearly, the viscosity of the fluid leads to a small exchange of momentum between the vortex structure and the surrounding flow field, with the net effect that the radius of the vortex will increase and the core vortex strength will decrease as it travels downstream in the impeller.However, this influence is negligible when compared with the inertia of its angular momentum vector and the effects of centrifugal and Coriolis forces.
To qualitatively assess the secondary vortex velocity vector field from the streamwise vorticity, a modified approach to Hawthorne's [15] small shear/large disturbance method, as described by Lakshminarayana and Horlock [33], is used.In this method the relative displacement of the streamlines (and the center of circulation) is determined using the nondimensional meridional velocity profile (weighted mass flow).The small shear/large disturbance approximation is valid here because in the centrifugal compressor flow turning (bending) and not shear (as in an axial impeller) dominates the action on the working fluid (Howard [30]).
In the small shear/large disturbance method the 2D continuity equation (∂u/∂x + ∂v/∂y = 0) with the definition of a stream function, u = −∂ψ/∂y and v = ∂ψ/∂x, is used to obtain where w i, j is the local plane through-flow velocity, dA i, j is the incremental plane area, and w ave is the average plane through-flow velocity.Equation ( 14) must be solved for the streamfunction, ψ, with the boundary conditions of ψ = 0 on the walls.A solution for this can be obtained analytically in the form of a Fourier series or ( 14) can simply be solved by an iterative numerical approach.Since in a centrifugal compressor the passage planes are not necessarily a perfectly rectangular domain, the numerical solution is preferred for this case.A central difference discretization was applied to (14) to obtain This equation was solved for ψ (new) by successive iterations (updating ψ (old) in each step) marching over the entire mathematical domain (plane).The normalized through-flow velocities, w i, j /w average , are obtained from the predicted meridional flow profiles.Convergence (total residual of ψ of less than 0.01) is typically achieved after approximately 2000 iterations (passes) over the domain and a resolution of 100×100 grid points is usually adequate.Once a converged solution is obtained, the passage secondary vortex velocities can be determined from the numerical partial derivatives of the streamfunction (u = −∂ψ/∂y and v = ∂ψ/∂x).
HEAD LOSSES DUE TO SECONDARY FLOWS
The total flow head in a compressor or pump increases as tangential kinetic energy is transferred into the fluid by the rotating blades.However, due to fluid friction (viscosity) the work input to the machine does not equal the isentropic work out; that is, the efficiency is always less than 100%.Thus, the viscous head loss due to secondary flows is an important parameter to estimate the overall performance of a centrifugal compressor.
Using the streamwise vorticity secondary flow models as described above, an estimate of this loss can be determined from the laminar viscous dissipation of the internal flow.(Note that only head losses due to secondary flows are predicted; other significant head losses due to turbulence, laminar meridional dissipation, and unsteady viscous dissipation are not evaluated.Typically head losses due to secondary flows contribute less than 2% to the total head loss in a centrifugal compressor.) The laminar viscous dissipation function for incompressible flow (and neglecting all meridional flow terms), Φ ls , is By integrating the above laminar dissipation, Φ laminar secondary , across an entire compressor passage, the total head loss per passage due to secondary flows, ∆H passage , is determined.The total impeller head loss due to secondary flows, ∆H secondary , is then calculated by multiplying ∆H passage by the number of blade passages in the compressor, N. Thus Clearly, the secondary flow head loss is directly related to the streamwise vorticity function and thus also related to the nonuniformity of the meridional profile.
NONDIMENSIONAL FORCE PARAMETERS
The Rossby number, Ro = V/ωr, is a measure of inertial to Coriolis force and is commonly employed for turbomachinery flow analysis.However, as centrifugal forces have a stronger influence than inertial forces on the secondary flows in a rotating machine, a modified Rossby number can be introduced: Namely, Ro m is a measure of the relative influence of the centrifugal force (in the outward radial direction) versus the Coriolis force (in the counter-rotational tangential direction).
Brun [34] showed that the modified Rossby affects the pressure-to-suction side meridional (jet/wake) flow profile and the normal vorticity, ξ n .Consequently, the modified Rossby number should have a strong effect on the first term in the streamwise vorticity generation term in (10).On the other hand, the binormal vorticity-the second term in (10)-is not affected by the modified Rossby number directly.However, during actual compressor operation, the modified Rossby number typically changes with pump speed, ω, and thus indirectly relates the Rossby number to the second term of (10).
The Reynolds number, Re = Vr/ν, is an indicator of inertial versus viscous forces for a moving fluid.Since the Reynolds number primarily influences the hub-to-tip side meridional flow profile, the streamwise vorticity should mostly affect the second term (rotational Coriolis force term) of (10) while the influence on the first term should be weak.
Interestingly, streamwise vorticity theory thus predicts that vortex secondary flows are primarily related to the modified Rossby number (centrifugal/Coriolis force) via first term of (10) and the Reynolds number (inertial/viscous force) via the second term of (10).One should note that the terms of (10) act in the opposite direction: term one is positive and acts to generate vortex secondary flows circulating in the clockwise direction (seen radial-inward) while term two is negative and acts in the counterclockwise direction.That is, a centrifugal compressor can be designed in which the terms of (10) offset each other and circulatory secondary flow generation is minimized.
PREDICTED RESULTS AND COMPARISON WITH EXPERIMENTAL DATA
Using the above model, parametric studies were performed to evaluate the relative influence of the nondimensional operating parameters on the centrifugal compressor streamwise vorticity and subsequent passage vortex secondary flows.Of particular interest is the effect on the flow field of varying the nondimensional force parameters-the Reynolds number and the modified Rossby number-as they represent the changing operating conditions an impeller experiences.For these studies, normal and binormal vorticity results from the pressure-to-suction and hub-to-tip jet/wake flow studies as presented by Brun [34] were used in (10) to determine the streamwise vorticity component.The subject analysis is based on a 30 cm diameter mixed-flow centrifugal impeller geometry, rotating at 1000 rpm with an incompressible, medium viscosity fluid at low Reynolds number operating conditions.Figures 2 and 3 show predicted streamwise vorticity as a function of Reynolds and modified Rossby numbers.Limited experimental data for a mixed-flow shrouded impeller is shown as a comparison; results are within the uncertainty bands of the flow measurements.
The streamwise vorticity is seen to decrease with Re and Ro m .Consequently, circulatory secondary flow vectors are expected to increase their clockwise rotation as Re and Ro m are increased.Figure 4 shows the predicted secondary velocity field from (15) at 100% span.Clearly, a large circulatory secondary flow vortex, centered at the suction side of the blade, is seen.The secondary flow vortex assumes almost the entire passage width.These results compare favorable to experimental measurements of circulating secondary flows.
Secondary flow head loss trends as a function of modified Rossby number are shown in Figure 5.As a reference, the total head loss for this impeller is approximately 30-40 W. Secondary flow head loss increases with modified Rossby number, which is consistent with the observation that the clockwise circulatory secondary flows increase with modified Rossby number.
CONCLUSIONS AND SUMMARY
A model to determine the rotational direction and magnitude of the circulatory velocity in shrouded centrifugal impellers was derived based on the streamwise vorticity governing equation.The model applies known meridional velocities to the streamwise vorticity equations to determine vorticity, circulatory secondary velocities, and associated head losses.Streamwise vorticity, and thus circulatory secondary flow, is seen to be primarily generated by the centrifugal and Coriolis forces on the meridional flow field.Viscous and compressibility effects must be considered to determine the meridional flow field but can be neglected in the streamwise vorticity equations.
A parametric analysis of the generation of streamwise vorticity equation showed that (i) positive vorticity and, thus, counterclockwise secondary passage flow circulation is generated by the interaction of the pressure-to-suction side meridional flow gradient with the axial-to-radial turning of the flow in the blade passage, (ii) negative vorticity and, thus, clockwise secondary passage flow circulation is generated by the interaction of the hub-to-tip side meridional flow gradient with the rotation, ω, of the blade passage.
Hence, the nondimensional operational force parameters, modified Rossby number and Reynolds number, directly affected the velocity magnitudes of the vortex secondary flow: (i) increasing the Reynolds and/or modified Rossby number, Ro m , increases clockwise flow circulation, (ii) moderating the pressure-to-suction velocity gradient (e.g., by backsweeping the blades) increases the counterclockwise flow circulation or moderates the clockwise flow circulation.
Comparison with experimental data showed that analytical results from the above streamwise vorticity model are within the uncertainty band of flow measurements in a shrouded mixed-flow impeller; namely, the model can be employed to accurately predict secondary flow trends.The herein described method can be employed early in the design process to optimize impeller flow shapes that intrinsically reduce secondary flows rather than using flow disruptive elements such as splitter to accomplish this task.
Figure 2 :
Figure 2: Streamwise vorticity as a function of Reynolds number.
Figure 3 :
Figure 3: Streamwise vorticity as a function of modified Rossby number.
Figure 5 :
Figure 5: Pump head losses as a function of modified Rossby number. | 5,671.4 | 2005-01-01T00:00:00.000 | [
"Engineering",
"Physics"
] |
On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds
This paper studies the problem of recovering a signal from one-bit compressed sensing measurements under a manifold model; that is, assuming that the signal lies on or near a manifold of low intrinsic dimension. We provide a convex recovery method based on the Geometric Multi-Resolution Analysis and prove recovery guarantees with a near-optimal scaling in the intrinsic manifold dimension. Our method is the first tractable algorithm with such guarantees for this setting. The results are complemented by numerical experiments confirming the validity of our approach.
Introduction
Linear inverse problems are ubiquitous in many applications in science and engineering. Starting with the seminal works of Candès, Romberg and Tao [10] as well as Donoho [14], a new paradigm in their analysis became an active area of research in the last decades. Namely, rather than considering the linear model as entirely given by the application, one seeks to actively choose remaining degrees of freedom, often using a randomized strategy, to make the problem less ill-posed. This approach gave rise to a number of recovery guarantees for random linear measurement models under structural data assumptions. The first works considered the recovery of sparse signals; subsequent works analyzed more general union-of-subspaces models [17] and the recovery of low rank matrices [37], a model that can also be employed when studying phaseless reconstruction problems [11] or bilinear inverse problems [1].
Another line of works following this approach studies manifold models. That is, one assumes that the structural constraints are given by (unions of finitely many) manifolds. While this model is considerably richer than say sparsity, its rather general formulation makes a unified study, at least in some cases, somewhat more involved. The first work to study random linear projections of smooth manifold was [5], the authors show that Gaussian linear dimension reductions typically preserve the geometric structure. In [25], these results are refined and complemented by a recovery algorithm, which is based on the concept of the Geometric Multi-Resolution Analysis as introduced in [3] (cf. Section 2.1 below). These results were again substantially improved in [16]; these latest results no longer explicitly depend on the ambient dimension.
Arguably, working with manifold models is better adapted to real world data than sparsity and hence may allow to work with smaller embedding dimensions. For that, however, other practical issues need to be considered as well. In particular, to our knowledge there are almost no works to date that study the effects of quantization, i.e., representing the measurements using only a finite number of bits (the only remotely connected work that we are aware of is [32], but this paper does not consider dimension reduction and exclusively focuses on the special case of Grassmann manifolds).
For sparse signal models, in contrast, quantization of subsampled random measurements is an active area of research. On the one hand, a number of works considered the scenario of memoryless scalar quantization, that is, each of the measurement is quantized independently. In particular, the special case of representing each measurement only by a single bit, its sign, -often referred to as one-bit compressed sensing -has received considerable attention. In [27], it was shown that one-bit compressed sensing with Gaussian measurements approximately preserves the geometry, and a heuristic recovery scheme was presented. In [34], recovery guarantees for a linear method, again with Gaussian measurements, were derived. Subsequently, these results were generalized to subgaussian measurements [2], and partial random circulant measurements [13]. In [35], the authors provided a recovery procedure for noisy one-bit Gaussian measurements which provably works on more general signal sets (essentially arbitrary subsets of the euclidean ball). This procedure, however, becomes NP-hard as soon as the signal set is non-convex, a common property of manifolds.
Another line of works studied so-called feedback quantizers, that is, the bit sequence encoding the measurements is computed using a recursive procedure. These works adapt the Sigma-Delta modulation approach originally introduced in the context of bandlimited signals [21,33] and later generalized to frame expansions [6,7] to the sparse recovery framework. A first such approach was introduced and analyzed for Gaussian measurements in [22]; subsequent works generalize the results to subgaussian random measurements [28,19]. Recovery guarantees for a more stable reconstruction scheme based on convex optimization were proved for subgaussian measurements in [38] and extended to partial random circulant matrices in [20]. For more details on the mathematical analysis available for different scenarios, we refer the reader to the overview chapter [9]. In this paper we focus on the MSQ approach and leave the study of Sigma-Delta quantizers under manifold model assumptions for future work.
Contribution
We provide the first tractable one-bit compressed sensing algorithm for signals which are well approximated by manifold models. It is simple to implement and comes with error bounds that basically match the stateof-the-art recovery guarantees in [35]. In contrast to the minimization problem introduced in [35] which does not come with a minimization algorithm, our approach always admits a convex formulation and hence allows for tractable recovery. Our approach is based on the Geometric Multi-Resolution Analysis (GMRA) introduced in [3], and hence combines the approaches of [25] with the general results for one-bit quantized linear measurements provided in [35,36].
Outline
We begin by a detailed description of our problem in Section 2 and fix notation for the rest of the paper. The section also includes a complete axiomatic definition of GMRA. Section 3 states our main results. The proofs can be found in Section 4. In Section 5 we present some numerical experiments testing the recovery in practice and conclude with Section 6. Technical parts of the proofs as well as adaption of the results to GMRAs from random samples are deferred to the Appendix.
Problem Formulation, Notation, and Setup
The problem we address is the following. We consider a given union of low-dimensional manifolds (i.e., signal class) M of intrinsic dimension d that is a subset of the unit sphere S D−1 of a higher dimensional space R D , d D. Furthermore, we image that we do not know M perfectly, and so instead we only have approximate information about M represented in terms of a structured dictionary model D for the manifold. Our goal is now to recover an unknown signal x ∈ M from m one-bit measurements where A ∈ R m×D has Gaussian i.i.d. entries of variance 1/ √ m, using as few measurements, m, as possible. Each single measurement sign( a i , x ) can be interpreted as the random hyperplane {z ∈ R D : a i , z = 0} S D−1 (a) Tessellation of the sphere by random hyperplanes. Definition 2.1 (GMRA Approximation to M, [25]). Let J ∈ N and K 0 , K 1 , ..., K J ∈ N. Then a Geometric Multi Resolution Analysis (GMRA) Approximation of M is a collection {(C j , P j )}, j ∈ [J] := {0, ..., J}, of sets C j = {c j,k } Kj k=1 ⊂ R D of centers and of affine projectors which approximate M at scale j, such that the following assumptions (1)-(3) hold.
(1) Affine Projections: Every P j,k ∈ P j has both an associated center c j,k ∈ C j and an orthogonal matrix Φ j,k ∈ R d×D , such that i.e., P j,k is the projector onto some affine d-dimensional linear subspace P j,k containing c j,k .
(2) Dyadic Structure: The number of centers at each level is bounded by |C j | = K j ≤ C C 2 dj for an absolute constant C C ≥ 1. There exist C 1 > 0 and C 2 ∈ (0, 1], such that following conditions are satisfied: (3) Multiscale Approximation: The projectors in P j approximate M at scale j, i.e., when M is sufficiently smooth the affine spaces P j,k locally approximate M pointwise with error O 2 −2j . More precisely: (a) There exists j 0 ∈ [J − 1], such that c j,k ∈ tube C1·2 −j−2 (M), for all j > j 0 ≥ 1 and k ∈ [K j ].
(b) For each j ∈ [J] and z ∈ R D let c j,kj (z) be one of the centers closest to z, i.e., Then, for each z ∈ M there exists a constant C z > 0 such that for all j ∈ [J]. Moreover, for each z ∈ M there existsC z > 0 such that Remark 2.2. By property (1) GMRA approximation represents M as a combination of several anchor points (the centers c j,k ) and corresponding low dimensional affine spaces P j,k . The levels j control the accuracy of the approximation. The centers are organized in a tree-like structure as stated in property (2). Property (3) then characterizes approximation criteria to be fulfilled on different refinement levels. Note that centers do not have to lie on M (compare Figure 1b) but their distance to M is controlled by property (3a). Figure 2: The closest center c j,kj (x) is not identified by measurements. Dotted lines represent one-bit hyperplanes.
Additional Notation
Let us now fix some additional notation. Throughout the remainder of this paper we will work with several different metrics. Perhaps most importantly, we will quantify the distance between two points z, z ∈ R D with respect to their one-bit measurements by where d H counts the number of differing entries between the two sign patterns (i.e., d A (z, z ) is the normalized Hamming distance between the signs of Az and Az ). Furthermore, let P S denote orthogonal projection onto the unit sphere S D−1 , and more generally let P K denote orthogonal (i.e., nearest neighbor) projection onto the closure of an arbitrary set K ⊂ R D wherever it is defined. Then, for all z, z ∈ R D we will denote by d G (z, z ) = d G (P S (z), P S (z )) the geodesic distance between P S (z) and P S (z ) on S D−1 normalized to fulfill d G (z , −z ) = 1 for all z ∈ R D .
Herein the Euclidian ball with center z and radius r is denoted by B(z, r). In addition, the scale-j GMRA approximation to M, will refer to the portions of the affine subspaces introduced in Definition 2.1 for each fixed j which are potentially relevant as approximations to some portion of M ⊂ S D−1 . To prevent the M j above from being empty we will further assume in our results that we only use scales j > j 0 large enough to guarantee that tube C12 −j−2 (M) ⊂ B(0, 2). Hence we will have c j,k ∈ B(0, 2) for all k ∈ K j , and so C j ⊂ M j . This further guarantees that no sets P j,k ∩ B(0, 2) are empty, and that P j,k ∩ B(0, 2) ⊂ M j for all k ∈ K j .
Finally, we write a b if a ≥ Cb for some constant C > 0. The diameter of a set K ⊂ R D will be denoted by diam(K) := sup z,z ∈K z−z 2 , where · 2 is the Euclidian norm. We use dist(A, B) = inf a∈A,b∈B a−b 2 for the distance of two sets A, B ⊂ R D and by abuse of notation dist(0, A) = inf a∈A a 2 . The operator norm of a matrix A ∈ R n1×n2 is denoted by A = sup x∈R n 2 , x 2 ≤1 Ax 2 . We will write N (K, ε) to denote the Euclidian covering number of a set K ⊂ R D by Euclidean balls of radius ε (i.e., N (K, ε) is the minimum number of ε-balls that are required to cover K). And, the operators r (resp. r ) return the closest integer smaller (resp. larger) than r ∈ R.
The Proposed Computational Approach
Combining prior GMRA-based compressed sensing results [25] with the one-bit results of Plan and Vershynin in [35] suggests the following strategy for recovering an unknown x ∈ M from the measurements given in (1): First, choose a center c j,k whose one-bit measurements agree with as many one-bit measurements of x as possible. Due to the varying shape of the tessellation cells this is not an optimal choice in general (see Figure 2). Nevertheless, one can expect P j,k to be a good approximation to M near x. Thus, in the second step a modified version of Plan and Vershynin's noisy one-bit recovery method using P j,k should yield an approximation of P j,k (x) which is close to x. 1 See OMS-simple for pseudocode.
Algorithm OMS-simple: OnebitManifoldSensing -Simple Version I. Identify a center c j,k close to x via where d H is the Hamming distance, i.e., d H (z, z ) := |{l : z l = z l }|. If d H (sign(Ac j,k ), y) = 0, directly choose x * = c j,k and omit II.
II. If there is no center in the same cell as x (as in Figure 2), solve a noisy one-bit recovery problem as in [35], i.e., where R is a suitable parameter.
Remark 2.3. The minimization in (3) can be efficiently calculated by exploiting tree structures in C j . Numerical experiments (see Section 5) suggest this strategy to yield adequate approximation for the center c j,kj (x) in (2), while being considerably faster (we observed differences in runtime up to a factor of 10).
Though simple to understand, the constraints in (4) have two issues that we need to address: First, in some cases the minimization problem (4) empirically exhibits suboptimal recovery performance (see Section 5.1 for details). Second, the parameter R in (4) is unknown a priori (i.e., OMS-simple requires parameter tuning, making it less practical than one might like). Indeed, our analysis shows that making an optimal choice for R in OMS-simple requires a priori knowledge about P j,k (x) 2 which is only approximately known in advance.
To address this issue, we will modify the constraints in (4) and instead minimize over the convex hull of the nearest neighbor projection of P j,k ∩ B(0, 2) onto S D−1 , conv (P S (P j,k ∩ B(0, 2))) , to remove the R dependence. If 0 ∈ P j,k one has conv (P S (P j,k ∩ B(0, 2))) = P j,k ∩ B(0, 1). If 0 / ∈ P j,k the set conv (P S (P j,k ∩ B(0, 2))) is described by the following set of convex constraints which are straightforward to implement in practice. Denote by P c the projection onto the vector c = P j,k (0). Then, The first two conditions above restrict z to B(0, 1) and span(P j,k ), respectively. The third condition then removes all points that are too close to the origin (see Figure 3). A rigorous proof of equivalence can be found in Appendix A. Our analysis uses that the noisy one-bit recovery results of Plan and Vershynin apply to arbitrary subsets of the unit ball B(0, 1) ⊂ R D which will allow us to adapt our recovery approach. Replacing the constraints in (4) with those in (5) we obtain the following modified recovery approach, OMS. 0 0 P j,k (0) 1 2 (P j,k ∩ B(0, 2)) P j,k ∩ B(0, 2) P j,k (0) Figure 3: Two views of an admissible set conv(P S (P j,k ∩B(0, 2))) from (5) for a case with c 2 = P j,k (0) 2 < 1.
Algorithm OMS: OnebitManifoldSensing I. Identify a center c j,k close to x via where d H is the Hamming distance, i.e., d H (z, z ) := |{l : z l = z l }|. If d H (sign(Ac j,k ), y) = 0, directly choose x * = c j,k and omit II.
II. If there is no center lying in the same cell as x (see Figure 2), recover the projection of x onto P j,k , i.e., P j,k (x). To do so solve the convex optimization (−y l ) a l , z , subject to z ∈ conv (P S (P j,k ∩ B(0, 2))) .
As we shall see, theoretical error bounds for both OMS-simple and OMS can be obtained by nearly the same analysis despite their differences.
Main Results
In this section we present the main results of our work, namely that both OMS-simple and OMS approximate a signal on M to arbitrary precision with a near-optimal number of measurements. More precisely, we obtain the following theorem. There exist absolute constants E, E , c > 0 such that the following holds. Let ∈ (0, 1/16] and assume the GMRA's maximum refinement level J ≥ j := c log(1/ √ ε) for c > 0 as below. Further suppose that one has dist(0, M j ) ≥ 1/2, 0 < C 1 < 2 j , and sup x∈MCx < 2 j−2 . If then with probability at least 1 − 12 exp(−cC 2 1 ε 2 m) for all x ∈ M ⊂ S D−1 the approximations x * obtained by OMS satisfy Proof : See the proofs of Corollary 4.16 and Theorem 4.14 in Section 4.
Remark 3.2. The restrictions on C 1 andC x are easily satisfied, e.g., if the centers form a maximal 2 −j packing of M at each scale j or if the GMRA is constructed from manifold samples as discussed in [31] (cf. Appendix E). In both these cases C 1 andC x are in fact bounded by absolute constants. Numerical simulations (see Section 5) suggest that a slightly modified version of OMS performs better in some scenarios even though we cannot provide a rigorous theoretical justification for the modification's improved performance at present.
Note that Theorem 3.1 depends on the Gaussian width of M. For general sets this quantity provides a useful measure of the set's complexity. In the case of compact of Riemannian submanifolds of R D it might be more convenient to have a dependence on the geometric properties of M instead (e.g., its volume and reach). Indeed, one can show by means of [16] that w(M) can be upper bounded in terms of the manifold's intrinsic dimension d, its d-dimensional volume Vol(M), and the inverse of its reach. Intuitively, these dependencies are to be expected as a manifold with fixed intrinsic dimension d can become more complex as either its volume or curvature (which can be bounded by the inverse of its reach) grows. The following theorem , which is a combination of different results in [16], formalizes this intuition by bounding the Gaussian width of a manifold in terms of its geometric properties.
Then one can replace w(M) in above theorem by where C, c > 0 are absolute constants.
Proof : See Appendix B. Finally, we point out that Theorem 3.1 assumes access to a GMRA approximation to M ⊂ S D−1 which satisfies all of the axioms listed in Definition 2.1. Following the work of Maggioni, Minsker, and Strawn [31], however, one can also ask whether a similar result will still hold if the GMRA approximation one has access to has been learned by randomly sampling points from M without the assumptions of Definition 2.1 being guaranteed a priori. Indeed, such a setting is generally more realistic . In fact it turns out that a version of Theorem 3.1 still holds for such empirical GMRA approximations under suitable conditions; see Theorem E.7 . We refer the interested reader to Appendix D and Appendix E for additional details and discussion regarding the use of such empirically learned GMRA approximations.
Proofs
This section provides proofs of the main result in both settings described above and establishes several technical lemmas. First, properties of the Gaussian width and the geodesic distance are collected and shown. Then, the main results are proven for a given GMRA approximation fulfilling the axioms.
Toolbox
We start by connecting slightly different definitions of dimensionality measures similar to the Gaussian width and clarify how they relate to each other. This is necessary as the tools we make use of appear in their original versions referring to different definitions of Gaussian width.
(ii) the Gaussian mean width to be the Gaussian width of K − K and (iii) the Gaussian complexity: By combining Properties 5. and 6. of Proposition 2.1 in [35] on has In this sense, the Gaussian width extends the concept of dimension to general sets K. Furthermore, for a finite set K the Gaussian width is bounded by w This can be deduced directly from the definition (see, e.g., §2 of [35]). Now that we have introduced the notion of Gaussian width, we can use it to characterize the union of the given manifold and a single level of its GMRA approximation M ∪ M j (recall the definition of M j in Section 2).
Remark 4.4. Note that the first inequality holds for general sets, not only M and M j . Moreover, one only uses M j ⊂ B(0, 2) to prove the second inequality. It thus holds for M j replaced with arbitrary subsets of B(0, 2). We might use both variations referring to Lemma 4.3.
Proof : The first inequality follows by noting that To obtain the second inequality observe that where we used (10), the fact that M ⊂ S D−1 , and that M j ⊂ B(0, 2).
For the last inequality we bound w(M j ). First, note that (2). By Dudley's inequality (see, e.g., [15] ) we conclude via Jensen's inequality that where C is a constant depending on C Dudley and C C . Choosing C = 2C + 3 yields the claim as The following two lemmas concerning width bounds for fine scales will also be useful. Their proofs (see Appendix C), though more technical, use similar ideas to the proof of Lemma 4.3. The first lemma improves on Lemma 4.3 for large values of j by considering a more geometrically precise approximation to M, M rel j ⊂ M j .
It is not surprising that for general M ∈ S D−1 the width bound for w(M j ) (resp. w(M rel j )) depends on either j or log(D). When using the proximity of M rel j to M in Lemma 4.5 we only use the information that M rel j ⊂ tube C M 2 −2j and a large ambient dimension D will lead to a higher complexity of the tube. In the case of Lemma 4.3 we omit the proximity argument by using the maximal number of affine d-dimensional spaces in M j and hence do not depend on D but on the refinement level j.
The next lemma just below utilizes even more geometric structure by assuming that M is a Riemannian Manifold. It improves on both Lemma 4.3 and 4.5 for such M by yielding a width bound which is independent of both j and D for all j sufficiently large.
. Then, there exist absolute constants C, c > 0 such that Here the constants C z and C 1 are from properties (3b) and (3a), respectively.
Finally, the following lemma quantifies the equivalence between Euclidean and normalized geodesic distance on the sphere.
Proof : First observe that z, z = cos (z, z ) = cos(πd G (z, z )). This yields For the upper bound note the relation between the geodesic distanced G and the normalized geodesic distance d Gd We now have the preliminary results necessary in order to prove Theorem 3.1.
Proof of Theorem 3.1 with Axiomatic GMRA
Recall that our theoretical result concerns OMS-simple with recovery performed using (3) and (4). The proof is based on following idea. We first control the error c j,k − x 2 made by (3) in approximating a GMRA center closest to x. To do so we make use of Plan and Vershynin's result on δ-uniform tessellations in [36]. Recall the equivalence between one-bit measurements and random hyperplanes. . Let K ⊂ S D−1 and an arrangement of m hyperplanes in R D be given via a matrix A (i.e., the j-th row of A is the normal to the j-th hyperplane). Let d A (x, y) ∈ [0, 1] denote the fraction of hyperplanes separating x and y in K and let d G be the normalized geodesic distance on the sphere, i.e. opposite poles have distance one. Given δ > 0, the hyperplanes provide a δ-uniform tessellation of K if In words Theorem 4.9 states that if the number of one-bit measurements scale at least linearly in intrinsic dimension of a set K ⊂ S D−1 then with high probability the percentage of different measurements of two points x, y ∈ K is closely related to their distance on the sphere. Implicitly the diameter of all tessellation cells is bounded by δ.
The original version of Theorem 4.9 uses γ(K) instead of w(K). However, note that by (10) we get for K ⊆ S D−1 that γ(K) ≤ w(K − K) + 2/π ≤ 3w(K) as long as the w(K) ≥ 2/π which is reasonable to assume. Hence, ifC is changed by a factor of 9, Theorem 4.9 can be stated as above.
Using these results we will show in Lemma 4.13 that the center c j,k identified in step I. of the algorithm OMS-simple satisfies x − c j,k 2 ≤ 16 max{ x − c j,kj (x) 2 , C 1 2 −j−1 } in Lemma 4.13. Therefore, the GMRA property (3b) provides an upper bound on x − P j,k (x) 2 . What remains is to then bound the gap between P j,k (x) and the approximation x * . This happens in two steps. First, Plan and Vershynin's result on noisy one-bit sensing (see Theorem 4.11) is applied to a scaled version of (4) bounding the distance between P j,k (x) andx (the minimizer of the scaled version). This argument works by interpreting the true measurements y as a noisy version of the non-accessible one-bit measurements of P j,k (x). The rescaling becomes necessary as Theorem 4.11 is restricted to the unit ball in Euclidean norm. Lastly, a geometric argument is used to bound the distance between the minimum pointsx and x * in order to conclude the proof.
Then with probability at least 1−8 exp(−cδ 2 m), the following event occurs. Consider a signalx ∈ K satisfying x 2 = 1 and its (unknown) uncorrupted one-bit measurementsỹ = (ỹ 1 , . . . ,ỹ m ) given as Then the solutionx to the optimization problem Remark 4.12. Theorem 4.11 yields guaranteed recovery of unknown signals x ∈ K ⊂ B(0, 1) up to a certain error by the formulation we use in (4) from one-bit measurements if the number of measurements scales linearly with the intrinsic dimension of K. The recovery is robust to noise on the measurements. Note that the original version of Theorem 4.11 uses w(K − K) instead of w(K). As w(K − K) ≤ 2w(K) by (10) the result stated above also holds for a slightly modified constant C .
We begin by proving Lemma 4.13.
Lemma 4.13. If m ≥CC −6 1 2 6(j+1) max{w(M∪P S (C j )) 2 , 2/π} the center c j,k chosen in step I. of Algorithm OMS-simple fulfills Noting that Gaussian random vectors and Haar random vectors yield identically distributed hyperplanes, Theorem 4.9 now transfers this bound to the normalized geodesic distance, namely As by property (3a) the centers are close to the manifold, they are also close to the sphere and we have P S (c j,k ) − c j,k 2 < C 1 2 −j−2 , for all c j,k ∈ C j . Hence, we conclude We can now prove a detailed version of Theorem 3.1 for the given axiomatic GMRA and deduce Theorem 3.1 as a corollary.
Theorem 4.14 (Uniform Recovery -Axiomatic Case). Let M ⊂ S D−1 be given by its GMRA for some levels j 0 < j ≤ J, such that C 1 < 2 j0+1 where C 1 is the constant from GMRA properties (2b) and (3a). Fix j and assume that dist(0, where C is the constant from Theorem 4.11,C from Theorem 4.9, and C > 3 from Lemma 4.3. Then, with probability at least 1 − 12 exp(−c(C 1 2 −j−1 ) 2 m) the following holds for all x ∈ M with one-bit measurements y = sign(Ax) and GMRA constantsC x from property (3b) satisfyingC x < 2 j−1 : The approximations x * obtained by OMS fulfill Here C x := 2C x + C 1 .
Remark 4.15. For obtaining the lower bounds on m in (12) and (8) we made use of Lemma 4.3 leading to the influence of j which is suboptimal for fine scales (i.e., j large). To improve on this for large j one can exploit the alternative versions of the lemma, namely, Lemma 4.5 and Lemma 4.6. Then, however, some minor modifications become necessary in the proof of Theorem 4.14 as the lemmas only apply to M rel j : In (I), e.g., one has to guarantee that C j ⊂ M rel j , i.e., that each center c j,k is a best approximation for some part of the manifold. This is a reasonable assumption especially if the centers are constructed as means of small manifold patches which is a common approach in empirical applications (cf. Appendix D). Also, when working with M rel j it is essential in (II) to have a near-best approximation subspace of x, i.e., the k obtained in (I) has to fulfill k ≈ k j (x) as M rel j does not include many near-optimal centers for each point on M. Here, one can exploit the minimal distance of centers c j,k to each other as described in GMRA property (2b) and choose δ slightly smaller (in combination with a correspondingly strengthened upper bound in Lemma 4.13) to obtain the necessary guarantees for (I). As we are principally concerned with the case where j = O(log(D)) in this paper, however, we will leave such variants to future work.
Proof of Theorem 4.14 : Recall that k is the index chosen by OMS in (6). The proof consists of three steps. First, we apply Lemma 4.13 in (I). By the GMRA axioms this supplies an estimate for x − P j,k (x) 2 with high probability. In (II) we use Theorem 4.11 to bound the distance between P j,k (x)/ P j,k (x) 2 and the minimizer x * given by (−y l ) a l , z , subject to z ∈ K := conv(P S (P j,k ∩ B(0, 2))) with high probability. By a union bound over all events Part (III) then concludes with an estimate of the distance x − x * 2 combining (I) and (II).
Hence, we can apply Theorem 4.11 to obtain with probability at least 1 − 8 exp(−cδ 2 m) that the estimate (19) now follows.
(III) To conclude the proof we apply a union bound and obtain with probability at least 1 − 12 exp(−cδ 2 m) that GMRA property (3b) combined with (19) now yields the final desired error bound.
We are now prepared to explore the numerical performance of the proposed methods.
Numerical Simulation
In this section we present various numerical experiments to benchmark OMS. The GMRAs we work with are constructed using the GMRA code provided by Maggioni 2 . We compared the performance of OMS for two exemplary choices of M, namely, a simple 2-dim sphere embedded in R 20 (20000 data points sampled from the 2-dimensional sphere M embedded in S 20−1 ) and the MNIST data set [29] of handwritten digits "1" (3000 data points in R 784 ). In each of the experiments 5.1-5.4 we first computed a GMRA up to refinement level j max = 10 and then recovered 100 randomly chosen x ∈ M from their one-bit measurements by applying OMS. Depicted is the averaged relative error between x and its approximation x * , i.e., x − x * 2 / x 2 which is equal to the absolute error x − x * 2 for M ⊂ S D−1 . Note the different approximation error ranges of the sphere and the MNIST experiments when comparing both settings.
OMS-simple vs. OMS
The first test compares recovery performance of the two algorithms presented above, namely OMS-simple for R ∈ {0.5, 1, 1.5} and OMS. The results are depicted in Figure 4. Note that only R = 1.5 and, in the case of the 2-sphere, R = 1 are depicted as in the respective other cases for each number of measurements most of the trials did not yield a feasible solution in (4) so the average was not well-defined. One can observe that for both data sets OMS outperforms OMS-simple which is not surprising as OMS does not rely on a suitable parameter choice. This observation is also the reason for us to restrict the theoretical analysis to OMS. The more detailed approximation of the toy example (2-dimensional sphere) is due to its simpler structure and lower dimensional setting and can also be observed in 5.2-5.4.
Number of Measurements
Average Error
Modifying OMS
In a second experiment we compared OMS to a slightly different version in which (7) is replaced by [(−y l ) a l , z ] + , subject to z ∈ conv (P S (P j,k ∩ B(0, 2))) 2 The code is available at http://www.math.jhu.edu/~mauro/#tab_code.
where [t] + = max{0, t} denotes the positive part of t ∈ R. This is motivated by following observation: As stated in Theorem 4.11, Plan and Vershynin showed that can recover unknown signals from noisy one-bit measurements if K ⊂ B(0, 1) is a subset of the D-dimensional Euclidean ball. The minimization in (21) can be re-stated equivalently as arg min z∈K l : y l =sign( a l ,z ) where P Ha l denotes the orthogonal projection onto the D − 1 dimensional subspace H a l perpendicular to a l . To see this note that a l , z / a l 2 = sign( a l , z ) z − P Ha l 2 . Hence, (21) punishes incorrect measurements of a feasible point z ∈ K by its distance to the 'measurements border' H a l while rewarding correct ones. The second part which rewards might cause problems as it pushes minimizers away from the hyperplanes H a l of correct measurements. If the true x, however, lies close to one of them, this may be suboptimal. Hence, we dropped the rewarding term in (22) leading to which is still convex but performs better numerically in some cases. As depicted in Figure 5, the version with [·] + clearly outperforms the one without if M is the 2-dimensional sphere. In contrast, if M is more complex (MNIST data), the [·] + formulation clearly fails. We have no satisfactory explanation for this difference in behavior so far.
Number of Measurements
Average Error
Are Two Steps Necessary?
One might wonder if the two steps in OMS-simple and OMS are necessary at all. Wouldn't it be sufficient to use the center c j,k determined in step I. as an approximation for x? If the GMRA is fine enough, this indeed is the case. If one only has access to a rather rough GMRA, the simulations in Figure 6 show that the second step makes a notable difference in approximation quality. This behavior suits Lemma 4.13. The lemma guarantees a good approximation of x by c j,k as long as x is well approximated by an optimal center. In the MNIST case one can observe that the second step only improves performance if the number of one-bit measurements is sufficiently high. For a small set of measurements the centers might yield better approximation as they lie close to M by GMRA property (3a). On the other hand, only parts of the affine spaces are practical for approximation and a certain number of measurements is necessary to restrict II. to the relevant parts.
Number of Measurements
Average Error Figure 6: Comparison of the following: Approximation by step I. of OMS when using tree structure (dashed, blue) and when comparing all centers (solid, red); approximation by step I.+II. of OMS when using tree structure (dashed with points, yellow) and when comparing all centers (solid with points, purple).
Tree vs. No Tree
In the fourth test we checked if approximation still works when not all possible centers are compared in step I. of OMS but their tree structure is used. This means to find an optimal center one compares on the first refinement level all centers, and then continues in each subsequent level solely with the children of the k best centers (in the presented experiments we chose k = 10). Of course, the chosen center will not be optimal as not all centers are compared (see Figure 6). In the simple 2-dimensional sphere setting, step II., however, can compensate the worse approximation quality of I. with tree search. Figure 6 hardly shows a difference in final approximation quality in both cases. In the MNIST setting one can observe a considerable difference even when performing two steps.
A Change of Refinement Level
The last experiment (see Figure 7) examines the influence of the refinement level j on the approximation error. For small j (corresponding to a rough GMRA) a high number of measurements can hardly improve the approximation quality while for large j (corresponding to a fine GMRA) the approximation error decreases with increasing measurement rates. This behavior is as expected. A rough GMRA cannot profit much from many measurements as the GMRA approximation itself yields a lower bound on obtainable approximation error. For fine GMRAs the behavior along the measurement axis is similar to above experiments. Note that further increase of j for the same range of measurements did not improve accuracy.
Discussion
In this paper we proposed OMS, a tractable algorithm to approximate data lying on low-dimensional manifolds from compressive one-bit measurements, thereby complementing the theoretical results of Plan and Vershynin on one-bit sensing for general sets in [35] in this important setting. We then proved (uniform) worstcase error bounds for approximations computed by OMS under slightly stronger assumptions than [35], and also performed numerical experiments on both toy-examples and real-world data. As a byproduct of our theoretical analysis (see, e.g., §4) we have further linked the theoretical understanding of one-bit measurements as tessellations of the sphere [36] to the GMRA techniques introduced in [3] by analyzing the interplay between a given manifold and its GMRA approximation's complexity measured in terms of the Gaussian mean width. Finally, to indicate applicability of our results we show that they hold even if there are just random samples from the manifold at hand as opposed to the entire manifold (see, e.g., Appendix D and E). Several interesting questions remain for future research however: First, the experiments in Section 5.4 suggest a possible benefit from using the tree structure within C j . Indeed approximation of OMS does still yield comparable results if I. is restricted to a tree based search which has the advantage of being computable much faster than the minimization over all possible centers. It would be desirable to obtain theoretical error bounds even in this case, as well as to consider the use of other related fast nearest neighbor methods from computer science [23].
Second, the attentive reader might have noticed in the empirical setting of Appendix D and E that (A2) in combination with Lemma E.6 seems to imply that II. of OMS may be unnecessary. As can be seen from Section 5.3 though, the second step of OMS yields a notable improvement even with an empirically constructed GMRA which hints that even with (A2) not strictly fulfilled the empirical GMRA techniques remain valid, and II. of OMS of value. Understanding this phenomenon might lead to more relaxed assumptions than (A1)-(A4).
Third, it could be rewarding to also consider versions of OMS for additional empirical GMRA variants including, e.g., those which rely on adaptive constructions [30], GMRA constructions in which subspaces that minimize different criteria are used to approximate the data in each partition element (see, e.g., [24]), and distributed GMRA constructions which are built up across networks using distributed clustering [4] and SVD [26] algorithms. Such variants could prove valuable with respect to reducing the overall computational storage and/or runtime requirements of OMS in different practical situations.
Finally, as already pointed out in Section 5.2 we do not yet understand how inserting the positive part [·] + in II. affects recovery. There seem to be cases in which a massive improvement can be observed and others in which the performance completely deteriorates. The explanation might be decoupled from this work and OMS.
A Characterization of Convex Hull
Lemma A.1. Let P j,k be the affine subspace chosen in step I. of OMS-simple and define c = P j,k (0). If 0 / ∈ P j,k , the following equivalence holds: Proof : First, assume z ∈ conv (P S (P j,k ∩ B(0, 2))). Obviously, z 2 ≤ 1. As projecting onto the sphere is a simple rescaling, conv (P S (P j,k ∩ B(0, 2))) ⊂ span(P j,k ) implying that Φ T j,k Φ j,k z + P c (z) = z. For showing the third constraint note that any z ∈ P j,k can be written as z = c + (z − c) where z − c is perpendicular to c. If in addition z 2 ≤ 2, we get As z is a convex combination of different P S (z ) the constraint also holds for z. Let z fulfill the three constraints. Then z = ( c 2 2 / z, c ) · z satisfies z ∈ P j,k because of the second constraint and z , c = c 2 2 . Furthermore, by the first and third constraint z 2 ≤ ( c 2 2 / z, c ) ≤ 2 and hence z ∈ P j,k ∩ B(0, c 2 2 / z, c ) ⊂ P j,k ∩ B(0, 2). As P j,k ∩ B(0, c 2 2 / z, c ) is the convex hull of P j,k ∩ ( c 2 2 / z, c ) · S D−1 , there are z 1 , ..., z n ∈ P j,k and λ 1 , ..., λ n ≥ 0 with z k 2 = c 2 2 / z, c and λ k = 1 such that ( c 2 2 / z, c ) · z = λ k z k . Hence, z = λ k ( z, c / c 2 2 ) · z k . As ( z, c / c 2 2 ) · z k ∈ P S (P j,k ∩ B(0, 2)) we get z ∈ conv (P S (P j,k ∩ B(0, 2))).
B Proof of Theorem 3.3
Denote by τ the reach of M and by ρ the diameter diam(M). First, note that for a set K ⊂ R D by Dudley's inequality [15] w(K) ≤ C diam(K)/2 0 log(N (K, ε)) dε where C is an absolute constant. Second, [16,Lemma 14] states that the covering number N (M, ε) of a d-dimensional Riemannian manifold M can be bounded by for all d ≥ 1 for an absolute constant β > 1, this expression may be simplified to We can combine these facts to obtain w(M) ≤ C , by using Cauchy-Schwarz inequality for the second inequality. We now bound the first integral by Given a subset S ⊂ R D we will let N (S, ε) denote the cardinality of a minimal ε-cover of S by Ddimensional Euclidean balls of radius ε > 0 each centered in S. Similarly, we will let P(S, ε) denote the maximal packing number of S (i.e., the maximum cardinality of a subset of S that contains points all of which are at least Euclidean distance ε > 0 from one another.) The following lemmas bound N (M rel j , ε) for various ranges of j and ε.
Proof : By properties (3a) and (2b) every center c j,k has an associated p j,k ∈ M such that both where L j is defined as in the proof of Lemma 4.3 (this proof also discusses its covering numbers). As a result we have that C.1 Proof of Lemma 4.5 We aim to bound w(M rel j ) in terms of w(M). By the two-sided Sudakov inequality [39] and Lemma C.1 we get that where the last inequality follows from tube C M 2 −2j (M) ⊆ B(0, 1 + C M ) and Lemma C.2. Appealing to the Sudakov inequality once more to bound the second term above we learn that To bound the first term above we note that using the covering number of B(0, 1 + C M ) can be bounded as follows As ε → ε log( 4C M +4 ε ) is non decreasing for ε ∈ (0, 2C M 2 −2j ), we obtain by assuming that where C is an absolute constant. Appealing to (11) now finishes the proof.
C.2 Proof of Lemma 4.6
Let 2C M 2 −2j ≤ε ≤ 1 4 C 1 2 −j . We aim to bound w(M rel j ) in terms of covering numbers for M. To do this we will use Dudley's inequality in combination with the knowledge that M rel j ⊂ B(0, 2) (by definition). By Dudley's inequality where C is an absolute constant. Appealing now to Lemmas C.3 and C.2 for the first and second terms above, respectively, we can see that where the last bound follows from Jensen's inequality.
We can now bound the second term as in the proof of Theorem 3.3 in Appendix B. Doing so we obtain where τ is the reach of M, and C , c are an absolute constants. Appealing to (11) together with Theorem 3.3 now finishes the proof.
D Data-Driven GMRA
The axiomatic definition of GMRA proves useful in deducing theoretical results but lacks connection to concrete applications where the structure of M is not known a priori. Hence, in the following we first describe a probabilistic definition of GMRA which can be well approximated by empirical data (see [3,12,31]) and is connected to the above axioms by applying results from [31]. In fact, we will see that under suitable assumptions the probabilistic GMRA fulfills the axiomatic requirements and its empirical approximation allows one to obtain a version of Theorem 3.1 even when only samples from M are known.
D.1 Probabilistic GMRA
A probabilistic GMRA of M with respect to a Borel probability measure Π, as introduced in [31], is a family of (piecewise linear) operators {P j : R D → R D } j≥0 of the form Here, 1 M denotes the indicator function of a set M and, for each refinement level j ≥ 0, the collection of pairs of measurable subsets and affine projections {(C j,k , P j,k )} Kj k=1 has the following structure. The subsets C j,k ⊂ R D for k = 1, . . . , K j form a partition of R D , i.e., they are pairwise disjoint and their union is R D . The affine projectors are defined by where the minimum is taken over all linear spaces V of dimension d. From now on we will assume uniqueness of these subspaces V j,k . To point out parallels to the axiomatic GMRA definition, think of Π being supported on the tube of a d-dimensional manifold. The axiomatic centers c j,k are then considered to be approximately equal to the conditional means c j,k of some cells C j,k partitioning the space, and the corresponding affine projection spaces P j,k are spanned by eigenvectors of the d leading eigenvalues of the conditional covariance matrix Defined in this way, the P j correspond to projectors onto the GMRA approximations M j introduced above if c j,k = c j,k . From [31] we adopt the following assumptions on the entities defined above, and hence, on the distribution Π. From now on we suppose that for all integers j min ≤ j ≤ j max (A1)-(A4) (see Table 1) hold true.
Remark D.1. Assumption (A1) ensures that each partition element contains a reasonable amount of Πmass. Assumption (A2) guarantees that all samples from Π j,k will lie close to its expection/center. As a result, each c j,k must be somewhat geometrically central within C j,k . Together, (A1) and (A2) have the combined effect of ensuring that the probability mass of Π is somewhat equally distributed onto the different sets C j,k , i.e., the number of points in each set C j,k is approximately the same, at each scale j. The third and fourth assumptions (A3) and (A4) essentially constrain the geometry of the support of Π to being effectively d-dimensional and somewhat regular (e.g., close to a smooth d-dimensional submanifold of R D ). We refer the reader to [31] for more detailed information regarding these assumptions.
An important class of probability measures Π fulfilling (A1)-(A4) is presented in [31]. For the sake of completeness we repeat it here and also discuss a method of constructing the partitions {C jk } Kj k=1 from such probabilities measures. From here on let M be a smooth d-dimensional submanifold of S D−1 ⊂ R D . Let U K denote the uniform distribution on a given set K. We have the following definition.
(A3) Denote the eigenvalues of the covariance matrix Σ j,k by λ j,k 1 ≥ · · · ≥ λ j,k D ≥ 0. Then there exists σ = σ(Π) ≥ 0, θ 3 = θ 3 (Π), θ 4 = θ 4 (Π) > 0, and some α > 0 such that for all k = 1, . . . , K j , (A4) There exists θ 5 = θ 5 (Π) such that Let us now discuss the construction of suitable partitions {C jk } by making use of cover trees. A cover tree T on a finite set of samples S ⊂ M is a hierarchy of levels with the starting level containing the root point and the last level containing every point in S. To every level a set of nodes is assigned which is associated with a subset of points in S. To be precise, given a set S of n distinct points in some metric space (X, d X ). A cover tree T on S is a sequence of subsets T i ⊂ S, i = 0, 1, . . . that satisfies the following, see [8]: (i) Nesting: T i ⊆ T i+1 , i.e., once a point appears in T i it is in every T j for j ≥ i.
(ii) Covering: For every x ∈ T i+1 there exists exactly one y ∈ T i such that d X (x, y) ≤ 2 −i . Here y is called the parent of x.
(iii) Separation: For all distinct points x, y ∈ T i , d X (x, y) > 2 −i .
The set T i denotes the set of points in S associated with nodes at level i. Note that there exists N ∈ N such that T i = S for all i ≥ N . Herein we will presume that S is large enough to contain an -cover of M for > 0 sufficiently small.
Moreover, the axioms characterizing cover trees are strongly connected to the dyadic structure of GMRA. For a given cover tree (for construction see [8]) on a set X n = {X 1 , . . . X n } of i.i.d. samples from the distribution Π with respect to the Euclidean distance let a j,k for k = 1, . . . , K j be the elements of the jth level of the cover tree, i.e. T j = {a j,k } Kj k=1 and define With this a partition of R D into Voronoi regions can be defined. Maggioni et. al. showed in [31,Theorem 7] that by this construction all assumptions (A1)-(A4) can be fulfilled. The question arises if the properties of the axiomatic definition of GMRA in Definition 2.1 are equally met. As only parts of the axioms are relevant for our analysis, we refrain from giving rigorous justification for all properties.
1. GMRA property (1) holds by construction if the matrices Φ j,k are defined, s.t. Φ T j,k Φ j,k = P V j,k along with any reasonable choice of centers c j,k .
2. The dyadic structure axioms (2a) -(2c) also hold as a trivial consequence of the cover tree properties (i) -(iii) above if the axiomatic centers c j,k are chosen to be the elements of the cover tree set T j (i.e., the a j,k elements). By the (ρ, σ)-model assumption samples drawn from Π will have a quite uniform distribution all over supp(Π). Hence, the probabilistic centers c j,k of each C j,k -set will also tend to be close to the axiomatic centers c j,k = a j,k proposed here for small σ (see, e.g., assumption (A2) above).
3. One can deduce GMRA property (3a) from the fact that our chosen centers a j,k belong to M if supp(Π) = M (or to a small tube around M if σ is small).
4. The first part of (3b) is implied by (A4) with the uniform constant θ 5 for all x ∈ M if a j,k is sufficiently close to c j,k . To show the second part of (3b) note that where in the second last step we used our cover tree properties (recall that c j,k = a j,k ). Again, the constants C, C > 0 do not depend on the chosen x ∈ M as long as S is well chosen (e.g., contains a sufficiently fine cover of M).
Considering the GMRA axioms above we can now see that only the first part of (3b) may not hold in a satisfactory manner if we choose to set Φ T j,k Φ j,k = P V j,k and c j,k = a j,k . And, even when it doesn't hold with C z being independent of j it will still at least still hold with a worse j dependence due to assumption (A2).
D.2 Empirical GMRA
The axiomatic properties only hold above, of course, if the GMRA is constructed with knowledge of the true P V j,k -subspaces. In reality, however, this won't be the case and we are rather given some training data consisting of n samples from near/on M, X n = {X 1 , ..., X n }, which we assume to be i.i.d. with distribution Π. These samples are used to approximate the real GMRA subspaces based on Π such that the operators P j can be replaced by their estimators where {C j,k } Kj k=1 is a suitable partition of R d obtained from the data, and X j,k = C j,k ∩ X n . In other words, working with above model we have one perfect GMRA that cannot be computed (unless Π is known) but fulfills all important axiomatic properties, and an estimated GMRA that is at hand but that is only an approximation to the perfect one. Thankfully, the main results of [31] stated in Appendix E give error bounds on the difference between perfect and estimated GMRA with c j,k = c j,k ≈ c j,k ≈ a j,k that only depend on the number of samples from Π one can acquire. Following their notational convention we will denote the empirical GMRA approximation at level j, i.e., the set P j projects onto, by M j = { P j (z) : z ∈ B(0, 2)}∩B(0, 2) and the affine subspaces by P j,k = { P j,k (z) : z ∈ R D }. We again restrict the approximation to B(0, 2). The single affine spaces will be non-empty as all c j,k lie by definition close to B(0, 1) if supp(Π) is close to M, which we assume.
In the empirical setting OMS has to be slightly modified to conform to our empirical GMRA notation. Hence, (6) and (7) become Theorem E.1 states that under assumptions (A1)-(A4) the empirical GMRA approximates M as well as the perfect probabilistic one as long as the number of samples n is sufficiently large. For the proof of our main theorem we only need the following two bounds which can be deduced from (20) and (21) in [31] by setting t = 2 jd . As both appear in the proof of Theorem E.1, we state them as a corollary. The interested reader may note that n j,k appearing in the original statements can be lower bounded by θ 1 n2 −jd .
Corollary E.2. Under the assumptions of Theorem E.1 the following holds for any C 1 > 0 as long as j, α are sufficiently large and σ is sufficiently small: if n ≥ n min = 2 jd + log(max{d, 8}) min 144 Remark E.3. By Corollary E.2 with probability of at least 1 − O(2 jd exp(−2 jd )) the empirical centers c j,k of one level j have a worst case distance to the perfect centers c j,k of at most O(2 −j−2 ) if n O(2 3jd ). As a result, the empirical centers c j,k will also be at most O(2 −j−2 ) distance from their associated cover tree centers a j,k if n O(2 3jd ) by assumption (A2). The same holds true for the projectors P V j,k and P V j,k in operator norm.
The proof of Theorem 3.1 in this setting follows the same steps as in the axiomatic one. First, we give an empirical version of Lemma 4.13. Then we link x and x * as described in Section 4.2 while controlling the difference between empirical and axiomatic but unknown GMRA by Corollary E.2. The following extension of Lemma 4.3 will be regularly used. Note that we are now setting our empirical GMRA centers c j,k to be the associated mean estimates c j,k as a means of approximating the axiomatic GMRA structure we would have if we had instead chosen our centers to be the true expectations c j,k (recall Appendix D). We also implicitly assume below that there exists a constant C 1 > 0 for which the associated axiomatic GMRA properties in Section 2 hold when the centers c j,k are chosen as these true expectations c j,k and the Φ T j,k Φ j,k as P V j,k . Lemma E.6. Fix j sufficiently large. Under the assumptions of Theorem E.1 and n ≥ n min if m ≥ CC −6 1 2 6(j+1) w(M ∪ P S ( C j )) 2 the index k of the center c j,k chosen in step I of the algorithm fulfills x − c j,k 2 ≤ 16 max{ x − c j,kj (x) 2 , C 1 2 −j−1 }.
Proof : The proof will be similar to the one of Lemma 4.13. By definition we have d H (sign(A c j,k ), y) ≤ d H (sign(A c j,kj (x) ), y).
As, for all z, z ∈ S D−1 , d H (sign(Az), sign(Az )) = m · d A (z, z ), this is equivalent to d A (P S ( c j,k ), x) ≤ d A (P S ( c j,kj (x) ), x).
A union bound over both probabilities yields the result.
Having Lemma E.6 at hand we can now show a detailed version of Theorem 3.1 in this case. For convenience please first read the proof of Theorem 4.14. As above choosing ε = 2 √ j 2 −j yields Theorem 3.1 for OMSsimple with a slightly modified probability of success and slightly different dependencies on C 1 andC x in (9).
Theorem E.7. Let M ⊂ S D−1 be given by its empirical GMRA for some levels j 0 ≤ j ≤ J from samples X 1 , ..., X n for n ≥ n min (defined in Corollary E.2), such that 0 < C 1 < 2 j0+1 where C 1 is the constant from GMRA properties (2b) and (3a) for a GMRA structure constructed with centers c j,k and with the Φ T j,k Φ j,k as P V j,k . Fix j and assume that dist(0, M j ) ≥ 1/2. Further let m ≥ 64 max{C ,C}C −6 1 2 6(j+1) (w(M) + C dj) 2 .
(III) We conclude as in Theorem 4.14. | 14,315 | 2018-07-17T00:00:00.000 | [
"Computer Science",
"Mathematics"
] |
GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SPHERICALLY SYMMETRIC SOLUTIONS FOR THE MULTI-DIMENSIONAL INFRARELATIVISTIC MODEL
. In this paper, we establish the global existence, uniqueness and asymptotic behavior of spherically symmetric solutions for the multi-dimensional infrarelativistic model in H i × H i × H i × H i +1 ( i = 1 , 2 , 4).
1.
Introduction. As we know, the importance of thermal radiation in physical problems increases as the temperature is raised. Usually, the role of the radiation is one of transporting energy by radiative process at the moderate temperature, while the energy and momentum densities of the radiation field may become comparable to or even dominate the corresponding fluid quantities at the higher temperature. So the radiation field significantly affects the dynamics of the field. The theory of radiation hydrodynamics finds a wide range of applications, such as stellar atmospheres and envelopes, supernova explosions, stellar winds, physics of laser fusion, reentry of vehicles and many others. Therefore, the study of mathematical theory of radiation hydrodynamics is of great importance from both the mathematical theory and that of applications.
In this paper, we consider the motion of the compressible multi-dimensional viscous gas with radiation, which is a system of the Navier-Stokes equations coupled with a transport equation. We know that the energy in the radiation field to be carried by point, massless particles called photons, which are travelling at the speed c of light, characterized by their frequency ν, and their energy of each photon E = hν (where h is the Planck's constant), the momentum − → p = hν c − → Ω , where − → Ω is a unit vector and denotes the direction of travel of the photon (it requires two angular variables to specify − → Ω ). In a radiative transfer, it is conventional to introduce the specific radiative intensity I ≡ I(x, t, ν, − → Ω ) driven by the so-called radiative transfer integro-differential equation introduced and discussed by Chandrasekhar [3]. Meanwhile, we can derive global quantities by integrating with respect to the angular and frequency variables: the specific radiative energy density E R (x, t) per unit volume is then E R (x, t) = 1 c I(x, t, ν, − → Ω )d − → Ω dν, and the specific radiative Under the consideration of the three basic interactions between photons and matter, namely, absorption, scattering and emission, we find the transfer in the conventional form (see, e.g., [17,18,19] where I(ν, − → Ω ) ≡ I(x, t, − → Ω , ν), S n−1 is the unit ball in R n , S e (ν) ≡ S e (x, t, ν, ρ, θ), σ a (ν) ≡ σ a (x, t, ν, ρ, θ) and σ s (ν) ≡ σ s (x, t, ν, ρ, θ), respectively, denote the rate of energy emission due to spontaneous processes, the absorption coefficient and the scattering coefficient that also depend on the mass density ρ and the temperature θ of the matter. The scattering interaction serves to change the photon's characteristics ν and − → Ω to a new set of characteristics ν and − → Ω . The sign ν → ν stands for from ν to ν and − → Ω · − → Ω denotes the transfer from direction − → Ω to direction − → Ω as an argument of σ s (ν). Therefore, we can describe the scattering event by a probabilistic statement concerning this change as follows When the matter is in local thermodynamical equilibrium and radiation is present with coupling terms between matter and radiation, the coupled system can be read as (see, e.g., [18,19]) where ρ = ρ(x, t), U = U(x, t), θ = θ(x, t), e = e(x, t), Q = Q(x, t) stand for the density, the velocity, the absolute temperature, the internal energy and the heat flux, respectively, − → Π = −P (ρ, θ) − → I + − → π represents the material stress tensor for a Newtonian fluid with the viscous contribution − → π = 2µ − → D + λdiv U − → I with µ > 0 and nλ + 2µ ≥ 0, and the strain tensor the radiative energy source and the Planck's function B(ν, θ) describes the frequency-temperature black body distribution. The thermo-radiative flux Q satisfies the Fourier's law where κ(ρ, θ) is the heat conductivity coefficient. Now we would like to mention some results on this system. First, in the inviscid case, Lowrie, Morel and Hittinger [16], Buet and Després [2] have investigated the asymptotic regimes, and Dubroca and Feugeas [4], Lin [14] and Lin, Coulombel and Guodon [15] have considered the numerical aspects. Second, Zhang and Jiang [29] has given a proof of local-in-time existence and blow-up of solutions. Then Golse and Perthame [8] have investigated a simplified version of the system. Third, for the Cauchy problem in multi-dimension case, Li and Zhu [13] have investigated the blowup of smooth solutions under some sufficient conditions. For the one-dimensional initial-boundary value problem, Ducomet and Nečasová [5] have considered global existence and uniqueness of weak solutions in H 1 ×H 1 ×H 1 ×H 1 and Qin, Feng and Zhang [21] also proved the global existence and large-time behavior of solutions in H i ×H i 0 ×H i ×H i+1 (i = 1, 2) for the infrarelativistic model. Furthermore, Ducomet and Nečasová [6] obtained the asymptotic behavior of global strong solutions. In the pure scattering case, Ducomet and Nečasová [7] first investigated the asymptotic behavior of a motion of a viscous heat-conducting one-dimensional gas with radiation, and then Qin, Feng and Zhang [22] also proved the large-time behavior of solutions in H i × H i 0 × H i × H i−1 (i = 2, 3). Recently, Azevedo, Sauter and Thompson [1] also studied an approximation model of compressible radiative flow and established global classical solutions for this model in a slab under semi-reflexive boundary conditions using energy-entropy estimates and a homotopic version of the Leray-Schauder fixed point theorem together with classical Friedman-Schauder estimates for linear second order parabolic equations in boundary Hölder spaces. Qin and Zhang [24] obtained global existence and asymptotic behavior of cylindrically symmetric solutions for the 3D infrarelativistic model with radiation.
In this paper, we shall consider the radial solution on this model and establish the global existence, uniqueness and asymptotic behavior of spherically symmetric solutions for the compressible viscous gas with radiation. For spherically symmetric Navier-Stokes equations, we would like to refer to [9,10,11,12,28] and the references therein.
It is worth pointing out some difficulties encountered in this paper. The first difficulty encountered here is to establish the uniform point-wise upper bound of the specific volume v(x, t). To overcome it, we construct a key estimate (48) on the temperature θ 1+s (x, t) by Sobolev's and Hölder's inequalities. Then we can apply Gronwall's inequality to obtain the uniform-in-time upper bound of v(x, t). The second difficulty is to establish the H 1 estimate of the velocity u(x, t). To do this, motivated by [6], we introduce the auxiliary function F (ξ) (see Lemma 3.6) and adopt the similar technique to construct the corresponding estimate. The third difficulty is to deal with the radiation intensity I(x, t). From equation (24 4 ), we can obtain the expression (93) of the radiation density I by solving the ordinary differential equation. By virtue of (93), we mainly make full use of Lemmas 3.1-3.8 to establish some important estimates for I(x, t), such as Lemmas 3.9-3.10, 4.3 and 5.5. The last difficulty is to construct the estimates of the radiative energy source (S E ) R in equation (24 3 ). To overcome it, we mainly apply the relation between (S E ) R and I. By using the estimates on I, we can obtain the estimates on (S E ) R . In addition, in order to derive our desired results, we mainly use the embedding theorem and interpolation technique, and some idea from Qin [20], Qin and Huang [23] and Umehara and Tani [26,27]. Especially, compared with the 1D case, we have some essential new difficulties and techniques used in the proof. Firstly, the proof of (34) in Lemma 3.1 is obtained by the relation (38) and the integration by parts. Secondly, estimates on radiation term play a key role in our proofs. We construct these estimates by some new techniques, such as the Gronwall inequality in Lemma 3.9. Finally, high-order estimates can be established by some complicate calculations, such as (179), (219) and Lemma 5.5.
The notation in this paper will be as follows. Signs L p , 1 ≤ p ≤ +∞, and denote the usual Lebesgue spaces and Sobolev spaces on (0, L); · B denotes the norm in the space B, · := · L 2 .f (t) = L −1 L 0 f (x, t)dx. Letter C will denote the general constant but may be different, and letters C i (i = 1, 2, 4) will denote the universal constants depending on the norms of initial datum (v 0 , u 0 , θ 0 , I 0 ) in H i (see below the definitions of H i ) but being independent of t, respectively.
We organize our present paper as follows. In Section 2, we will induct the spherically symmetric infrarelativistic model and state our main results. Subsequently, we will complete the proofs of the global existence and asymptotic behavior to the generalized solutions in H i (i = 1, 2, 4) in Sections 3, 4 and 5, respectively.
Introduce the radiative energy the radiative flux and note pressure and energy of the matter have the thermodynamical relation Especially, if we assume that the fluid motion is small enough with respect to the velocity of light c so that we can drop all the 1 c factors in the previous formulation, then the system (17) can be rewritten as We assume that e, P, σ a , σ s , κ and B are C i+1 (i = 1, 2, 4) functions on 0 < v < +∞ and 0 ≤ θ < +∞ and for any v ≥ 0, we also suppose that the following growth conditions for any v ≥ v and θ ≥ 0: where constants s, q, α satisfy s ∈ [0, 1], q ≥ 1 + s, 0 ≤ α ≤ 2s + 1, the numbers c j (j = 1, · · · , 13) are positive constants and the nonnegative functions f, g, h, k, l, M are such that, for some γ > 0,
Remark 1. The Planck function in thermal equilibrium
characterizes the radiation, usually called blackbody radiation, emitted by a perfect radiator or black body, where h and k are the Planck and Boltzmann constants (see [17]). Obviously, this function satisfies our assumptions (A 8 ), (A 10 ) and (A 12 ).
We are now in a position to state our main theorems.
Theorem 2.3. Assume that the initial data (v 0 , u 0 , θ 0 , I 0 ) ∈ H 4 and the compatibility conditions hold. Then there exists a unique global solution (v(t), u(t), θ(t), where v, θ > 0 and r are also the same as those of Theorem 2.1. Moreover, we have, as t → +∞, In order to derive our results of time asymptotic behavior of the global solutions, we may use the following basic inequality (Lemma 2.4) in analysis by Shen and Zheng [25]. Lemma 2.4. Let T be given with 0 < T ≤ +∞. Suppose that y(t), h(t) are nonnegative continuous functions defined on [0, T ] and satisfy the following conditions: where A i (i = 1, 2, 3, 4) are given non-negative constants. Then for any r > 0 with 0 < r < T , the following estimates holds: where Proof. We can easily get (32) by integrating (24) 1 over Q t := (0, L) × (0, t) and noting the boundary conditions. Equation (24) 3 can be written as (36) We can deduce (33) from the maximal value principle and the positivity of θ 0 .
Multiplying (24) 2 by u, adding the resultant to (24) 3 , and then integrating it over Q t and using the boundary conditions, we deduce L 0 (e + 1 2 From the definitions of F R and (S E ) R , we can infer from (24) which, together with (19), leads to Thus, the contribution of the radiation term reads Combining (39) with (23) and assumptions ( Similarly to the proof of Lemma 2.1 in [21], estimate (35) can be shown, thus we omit it. The proof is now complete.
Remark 2. By Jensen's inequality, the mean value theorem and (35), we can know that there exists a point a(t) ∈ [0, L] and two positive constants α 1 , α 2 such that where α 1 , α 2 are two roots of the equation y − log y − 1 = C 1 . Let then, noting that r t = u, we can deduce from (24) 1 , by the mean value theorem, that there exists a point Proof. See, e.g., Lemma 4.1.8 in [20].
Proof. The main idea of the proof is similar to that of Lemma 5.2.4 in [23]. But the different key point here is that B(x, t) in the expression of v(x, t) depends not only on t but also on x. Thus we need a detailed analysis. It follows from Lemma 3.1 that which, together with the expression of D(x, t) in Lemma 3.2 and by Hölder's inequality, leads to (45) Noting that the assumptions (A 4 ), we deduce from Lemma 3.1 and Remark 2 that, for any 0 ≤ τ ≤ t, Now, by Hölder's inequality, we have for any x ∈ [0, L], v(x, τ ) and a(t) is defined in Remark 2. Then we have Thus it follows from Lemma 3.2, assumption (A 4 ), (46) and (48) that Applying Gronwall's inequality and Lemma 3.1, we can derive On the other hand, we also infer from (45) Thus we obtain the estimate (43). The proof is complete.
Proof. Estimate (51) has been obtained in Lemma 2.3 of [21]. The proofs of estimates (52)-(53) are similar to those of Lemma 2.4 in [21]. Thus we omit the details.
Lemma 3.5. Under the assumptions in Theorem 2.1, the following estimate holds for any t > 0, Proof. Multiplying (24) 4 by I and then integrating the resultant over [0, L] × S n−1 and using the boundary conditions, we obtain Noting the boundary condition (19), we know Integrating (55) with respect to ν over [0, +∞) and using Young's inequality, (56) and the assumption ( Similarly, we also infer from (55) by Young's inequality and the assumptions ( Therefore, we complete the proof of (54).
Obviously, we can obtain the following result from Lemmas 3.1 and 3.5.
Corollary 1. Under the assumptions in Theorem 2.1, the following estimate also holds for any t > 0, Lemma 3.6. Under the assumptions in Theorem 2.1, the following estimates hold for any t > 0, Proof. Here we adopt the technique from Lemma 7 in [6]. Noting the formula (40) in Remark 2, we can define the auxiliary function for any ξ > 0, Thus it follows from the assumption ( Noting that and using the assumptions (A 1 ) and (A 5 ) − (A 6 ), Lemma 3.3 and the Sobolev embedding theorem, we have for any ε > 0, Using the Cauchy-Schwarz inequality and the Sobolev embedding inequality, Lemma 3.1 and Lemma 3.5, and noting that the assumption α ≤ 1 + 2s, we can obtain
Now repeating the derivation of (47)-(48) and applying (57), we can conclude for Thus we readily obtain the next corollary.
Corollary 3. Under the assumptions in Theorem 2.1, the following estimate holds for any ( Proof. It follows from Corollary 2 and (53) and (57) that Lemma 3.7. Under the assumptions in Theorem 2.1, the following estimate holds for any t > 0, Proof. Multiplying (24) 2 by u t over Q t and using Young's inequality, we have for any ε > 0, which, by taking ε > 0 small enough, along with Lemmas 3.4 and 3.6, leads to (63).
Lemma 3.8. Under the assumptions in Theorem 2.1, the following estimates hold that for any t > 0, Proof. Let Then it is easy to verify that But we easily know from the assumptions ( We rewrite (24) 3 as Multiplying (67) by K t and integrating the resultant over Q t , we easily obtain Now we use Lemmas 3.1-3.7 to estimate each term in (68). Obviously, and applying Cauchy's inequality, we can deduce and applying Corollaries 2-3 and Lemma 3.6, we deduce for q 1 = max{ q 2 −2s−1, 0}, which, along with (71) and (72), gives It follows from Lemma 3.6 and Corollaries 2-3 that Now let us consider the various contributions in the second integral of (68). By Lemmas 3.1-3.7 and Corollaries 1 and 3, we have Noting the following facts and from equation (24) 3 , we can deduce Thus, by the Sobolev inequality, Lemmas 3.4 and 3.7, we can conclude By Lemma 3.4 and Corollary 3, using Cauchy's inequality, we have The last contribution in (68) can be estimated as follows, It follows from Corollaries 1-3 that Using the assumption (A 9 ), Cauchy's inequality and Corollary 1, we have Using the same technique, we also get Inserting the estimates (83)-(85) into (82), we get Inserting all previous estimates (69)-(71), (74)-(78), (80)-(81) and (86) into (68), we obtain with λ = max{q + s + 2, q + 2α − s, 3 2 (q − s) + α − s, 2q − s + 2, 3q−s+2 2 }. By Lemmas 3.1, 3.4, 3.6 and the Hölder inequality, there exists a point b(t) ∈ [0, L] such that for any t > 0, Thus we get sup 0≤τ ≤t Using assumptions on q, s and α, we easily know that λ < 2(q + s + 2). Thus, by Young's inequality and (87), it follows that Therefore, we complete the proof.
Lemma 3.9. The following estimates hold that for any t > 0, Proof. We consider the following integro-differential equation Using Young's inequality and Lemmas 3.5 and 3.8, we have for all ω ∈ (0, 1),
Lemma 3. 10. Under the assumptions in Theorem 2.1, the following estimates hold that for any t > 0,
YUMING QIN AND JIANLIN ZHANG
Proof. By Lemma 3.9, we have By virtue of the direct computation, we also have Using Lemma 3.9, we see that Similarly, Inserting (109)-(110) into (108), we obtain the desired estimate.
The next two lemmas are aimed at showing the asymptotic behavior of solutions to the problem (24) with the initial boundary conditions (18)- (20) in H 1 .
Lemma 3.12. Under the assumptions in Theorem 2.1, we have as t → +∞, Proof. Similarly to the proof of Lemma 3.4 in [21], we can also obtain (124). Here we omit it.
Till now we have completed the proof of Theorem 2.1.
Global existence and asymptotic behavior in
Proof. Estimate (125) has been obtained in Lemma 1.3.1 of [23]. Differentiating (24) 3 with respect to t and multiplying the result by θ t over [0, L], we have that for any ε > 0, d dt Integrating (127) with respect to t and using Lemmas 3.1-3.8 and Young's inequality, we derive for any ε > 0, It follows from Lemmas 3.7-3.9 that Inserting (129) into (128) and then taking ε > 0 small enough, we obtain Using the Gagliardo-Nirenberg interpolation inequality and Young's inequality, we derive from (24) 3 that Combining (130) and (131), we get (126).
Lemma 4.2.
Under the assumptions of Theorem 2.2, the following estimates hold that for any t > 0, Proof. Similarly to the proof of Lemma 1.3.2 in [23], we easily obtain (132). It follows from (24) 2 that Similarly, we can infer from (24) 3 that By the definition of (S E ) R and Lemma 3.9, it follows from that which, together with (134)-(135), implies (133).
Lemma 4.3.
Under the assumptions of Theorem 2.2, the following estimate holds for any t > 0, Proof. It follows from (24 4 ) and the definitions of I and I that Employing the Gagliardo-Nirenberg interpolation inequality and using Lemmas 3.9 and 4.2, we conclude and Similarly, we also infer that which, along with (138)-(140), leads to (137).
The next lemma concerns the asymptotic behavior of the global solution in H 2 .
Till now we have completed the proof of Theorem 2.2.
5.
Global existence and asymptotic behavior in H 4 . In this section, we shall prove Theorem 2.3, that is, the global existence and asymptotic behavior of solutions in H 4 to the problem (24) with the initial boundary conditions (18)- (20) under some relative assumptions.
Differentiating (24) 2 with respect to t twice, multiplying the resultant by u tt in L 2 (0, L), performing an integration by parts, and using Theorem 2.2 and the embedding theorem and the Young inequality, we can deduce Thus, by Theorem 2.2, which, along with (163) and (165) and Lemma 3.9, gives estimate (155).
In the same manner, differentiating (24) 3 with respect to t twice, multiplying the resultant by θ tt and performing an integration by parts over L 2 (0, L), and using the embedding theorem and the Young inequality, we have By virtue of Theorems 2.1-2.2 and Lemmas 4.1-4.3, and using the embedding theorem, we deduce that for any ε ∈ (0, 1), It follows from (174) by the Hölder inequality that Now we can estimate A 8 as By the induction of (129), we can easily obtain Using Hölder's inequality and the interpolation theorem, we can deduce from The- Differentiating (93) with respect to t twice and after the lengthy calculation, we can deduce Applying Gronwall's inequality to (180), we can obtain Inserting (178)-(179) and (181) into (177), we have Thus we infer from (168)-(176) and (182) that for any ε ∈ (0, 1) small enough, Therefore taking supremum in t on the left-hand side of (183), picking ε ∈ (0, 1) small enough, and using (165), we can derive estimate (156). The proof is thus complete.
Differentiating (24) 2 with respect to x three times, using Lemmas 5.1-5.2 and Theorem 2.2 and applying Poincaré's inequality, we deduce Thus, Using the same technique, we can deduce from (24) 3 that Hence, we complete the proofs of (193) and (194).
By Lemmas 5.1-155, we have proved the global existence of solutions in H 4 to the problem (24) in H 4 with arbitrary initial datum (u 0 , v 0 , θ 0 ) ∈ H 4 and the uniqueness of solution follows from that of solution in H 1 or in H 2 . Next, we shall show the asymptotic behavior of solutions.
Proof. Differentiating (24) 1 with respect to x three times and then multiplying the resultant by v xxx over L 2 (0, L), we have Applying Holder's inequality and the interpolation inequality, we can estimate each term in (246) as follows, Inserting (247)-(250) into (246), we have Analogously, we also deduce from equation (24) Naturally, we can also get the following estimates | 5,485.2 | 2019-04-01T00:00:00.000 | [
"Mathematics"
] |
An Assessment of the Nexus Between Government Expenditure and Inflation in Nigeria
Abstract Research Background: The on-going debate concerning the exact relationship that exists between inflation and government expenditure especially in the long and short run prompted this research. Purpose: The study assesses the relationship between government expenditure and inflation in Nigeria. Apart from government expenditure and inflation rate, other variables such as exchange rate and money supply are included to ensure a robust model. Research Methodology: Secondary data from 1980 to 2017 were collected and analysed using the Johansen Cointegration analysis and vector error correction model. Results: The results showed that apart from the bi-directional relationship that exists between the variables, there exists a strong relationship between government expenditure and inflation rate and that a significant impact is sustained from the short run through the long run. The exchange rate and money supply also exhibit a strong association with government expenditure. Novelty: The study has underscored the importance of the inflation rate in Nigeria as it affects government spending by focusing more on inflation rather than the movement that was the focus of most of the previous studies. It has also shown the causality flow from both inflation and government expenditure, which hitherto remains contentious.
Introduction
In both developed and developing countries, there is concern for raising the standard of living over time, but this need is more pronounced in developing countries given the extent and depth of poverty in these countries. The implication of this is that government at all levels needs to provide incentives for investment via government spending. In Nigeria, government spending rose by about 39.5% in 2009, this value was almost doubled between 2013 and 2014 at the peak of the increase in oil price (CBN, 2015). The implication of increase in government spending is directly felt on the money supply (Abu, Abdullahi, 2010).
At the twilight of bank recapitalization in Nigeria between 2006 and 2008, there was an increase in money supply when the government increased spending to increase the deposit base of some commercial banks and consequently increase money supply (NDIC, 2011).
Theoretically, the expected overall effect is the general upward price movement of goods and services in the economy (often caused by an increase in the supply of money), usually as measured by the consumers' price index and the producer price index. Overtime, as the cost of goods and services increases, the value of the currency falls because a person cannot purchase as much with that amount as he or she previously could do. This shows that there is a likelihood of inflation when money supply rises.
Considering the trend of inflation in Nigeria, it appears that there were periods when the Naira was very strong in 1970 and yet there was a high inflation rate then due to an increase in money supply as a result of the rise in oil price. However, the situation appears to be different now because since the inception of the fourth republic till 2010, the situation of inflation in Nigeria has assumed epidemic proportions due to excessive government spending (Olayemi, 2010). This scenario has thrown up a debate as to the correct relationship that exists between inflation and government spending.
These debates rest mainly on economic theories and some empirical findings. The first line of thought is the aggregate demand and supply theories as propounded by the Keynesian school. From the theory, when aggregate demand rises as a result of an increase in consumption and investment in the private and public sector occasioned by a rise in government expenditure, there will be upward pressure on the general price level. On the other way round, inflation can affect government expenditure and even cause it to be negative and then it is viewed from the supply side where a government issues bonds. This will put pressure on interest rate and hence cause investment and output to fall. At this point any expansionary government spending will not have the desired effect and it may even have a negative multiplier effect as a result of the rise in the general price level especially if the crowing out effect is large (Romer, 1996). These two views have been supported by the following empirical studies (Odusola, Akinlo, 2001;Oniore, Obumneke, Torbira, 2015;Tai, 2014).
Based on the discussions above, it appears that there are two schools of thought. Some believe that increase in government spending may lead to a rise in inflation but other authors believe that the situation can only exist in the short run because the influence of government expenditure on boosting output will in the long run lead to a fall in inflation (Wooldridge, 2013;Williams, Adedeji, 2004). However, the debate on inflation growth and government expenditure nexus is still on going. The argument had centered on whether or not increasing public spending has the potential to induce inflation (Ezirim et al, 2006). Consequently, there is still an unresolved issue theoretically as well as empirically as to the effect of government spending on inflation.
Again, the direction of causality between the two has also generated a lot of debates. While V. Piana (2001) agreed that government spending has a bidirectional relationship with inflation, J.O. Oniore, E. Obumneke and M.T. Torbira (2015) are of the contrary opinion that it is just a unidirectional causality that flows from government expenditure to inflation.
Considering the explained lack of consensus regarding the relationship between inflation and government spending, this study will be contributing to the existing literature by investigating this using Nigerian historical data from 1980 to 2017. The remaining part of the paper is divided into methodology, results and discussion, and finally conclusions.
Literature review
Although there are many empirical literatures on inflation and government expenditure relationships the few that are on Nigeria are discussed as follows.
D.O. Olayungbo (2013) examined an asymmetry causal relationship between government
spending and inflation in Nigeria from the period of 1970 to 2010. The asymmetry causality test shows that a uni-directional causality exists from negative government expenditure changes (low or contractionary government spending) to positive inflation changes (high inflation) in the Vector Autoregression (VAR) model. The finding implies that inflationary pressure in Nigeria is state dependent, that is high inflation is caused by low or contractionary government spending. It is evident from the reviewed literatures that there are lack of consensus on what exactly is the relationship between inflation and government expenditure in Nigeria. This study apart from contributing to the growing literatures on this will also focus more on inflation rather than the movement that was the focus of most of the papers reviewed above.
Model specification
Leveraging on the aggregate demand and supply theory of Keynes, which has been tested and applied in different studies such as A.C. Pigou (1989), this study will include money supply and exchange rate as additional control variables. Therefore, m odel specification in the study consists of a system of o n e equation, which includes three explanatory variables. The model is specified thus: where: GEXP t -government spending at period t (proxies as total expenditure as a percentage of GDP), EXR t -exchange rate at period t (proxies as real exchange rate), MS 2t -broad money supply at period t (proxies as broad money supply as a percentage of GDP), -stochastic variable (error term), -constant term, θ, β and γ -parameters to be estimated.
Method of analysis
Quantitative method is applied to analyse the data. The time series analysis is embraced and it involves the following procedures: unit root or stationarity tests, co-integration tests, and Granger Causality tests. The details of these are presented as follows:
Unit root test
This procedure is part of the pre-estimation test necessary for most time series estimations.
Since many macroeconomic data are largely non stationary therefore, there is the need to make them stationary so as to make them suitable for estimation and to guide against spurious regression. In this study the Augmented Dickey-Fuller (ADF) Techniques are used to test and verify the unit root property of the series and stationarity of the model (Dickey and Fuller, 1997).
Co-integration test
It is possible for a non-stationary variable to have a long run stationary relationship hence the application of cointegration (Gujarati, 2004, p. 167;Yang, 2000, p. 78). The cointegration test is important to examine the existence of co-movement among or between two variables, in this case inflation and government expenditure. The study uses the Johansen co-integration test to for long run relationship since it is the one of the prominent tests which can estimate more than tone co-integration relationship if the data set contains two or more time series as well as gives the maximum rank of co-integration (Johansen, Juselius, 1994).
Causality test
In order to determine which variable in the model causes the other, the Granger causality test is used. The F-statistics are used to reject or accept the null hypothesis of no causation between the variables. The granger specification is described in equations 2 and 3.
The reverse is stated thus: where: GEXP is government expenditure, INF is inflation rate, m's are lag periods, β 1j and β 2j are parameters to be estimated and µ t denotes the stochastic error term.
Error correction model (ECM)
The Engle -Granger representation theorem proves that, if a co-integrating relationship exists among a set of I(1) series, then a dynamic error-correction (EC) representation of the data also exists. The methodology used to find this representation follows the "general-tospecific" paradigm (Hendry, 1987). Initially, the first difference of each variable in the model for this study, a constant term, and a one-lagged EC term (EC t-1 ) generated from the static regression procedure were used. Then the dimensions of the parameter space were reduced to a final parsimonious specification by sequentially imposing statistically insignificant restrictions or eliminating insignificant coefficients (Williams, Adedeji, 2004 Where GEXP is government expenditure, INF is inflation rate, EXR is exchange rate, MS 2 is broad money supply, ECM is error correction term (i.e. measure of the speed of adjustment), Δ is the first-difference operator, p's are lag periods, β 0 is constant, β 1 -β 5 are parameters to be estimated and µ t denotes the stochastic error term.
Sources of data and measurement
The data used for this study are basically time series data covering 1980-2017, that is thirty-eight (38) years. The data were sourced from the Central Bank of Nigeria (CBN) Statistical Bulletins. In terms of measurement, government total expenditure as percentage of GDP is used to proxy government spending, inflation rate is used; real exchange rate is used for the exchange rate while broad money supply (MS 2 ) as a percentage of gross domestic product (GDP) is used as a proxy for money supply.
Results and discussions
This section involves the results and interpretation of the unit root test, co-integration test, Granger causality test and vector error correction model.
Unit root test
In order to estimate the vector error correction model, the variables must be free from unit root problems, meaning that they have to be stationary at the same order of integration.
The software for the ADF test automatically selects the optimal lag length of 2. Therefore, the result of the Augmented Dickey-Fuller Unit Root Test is presented as follows: Step model estimation approach that the variables do not have unit a root problem at the integration of order one, I(1). On the basis of this, a null hypothesis of being non-stationary is rejected and it is safe to conclude that the variables are stationary.
Co-integration test
The Johansen Co-integration test was carried out to determine the long run relationship among the variables in the model. The trace statistics and the maximum Eigen value are compared with the Mackinnon critical value at 5% of significance in order to determine the number of co integrating vector equations in the model using one lag interval with intercept and trend. The result of the Johansen co-integration Test is presented below in Table 2. From Table 2, the trace statistics exceeds the critical value at the 5% level of significance for hypotheses rank 0, meaning that the hypothesis that there is no co-integration equation or error term in the model is rejected. This is ascertained, as a critical value is less than the trace statistics at none rank of co-integration. These results showed that only one co-integrating equation exists among the variables. Therefore it is shown that there is an existence of a longrun dynamic relationship among the variables and an Error Correction Model is thus justified.
Co-integration equation
After the establishment of a long run relationship via the co-integration test, there is the need to estimate the long run equation that shows the relationship among the variables. The long run relationship is presented below in Table 3.
The relationship between government expenditure and inflation in the long run is described in Table 3. In addition, the results include the relationship in the long run between government expenditure and other variables such as exchange rate and money supply. The results give the coefficient of inflation in the long run to 0.038685. This value is significant at 5% meaning that inflation as a variable has a significant impact on government expenditure in the long run. Since the coefficient is positive, it indicates that a rise in the inflation rate will cause government expenditure to rise in the long run. The exchange rate also has the same relationship with government expenditure showing a coefficient of -0.070847. However, there is a significant inverse relationship between the two. It simply means that as the exchange rate is rising, government expenditure will be falling significantly. Money supply is also relatively significant in the model but at 10%. The implication is that money supply has a direct and significant relationship with government expenditure.
The Granger Causality test
The test is carried out using the Pairwise Granger Causality method and the maximal lag difference chosen is 1 in order to make the test effective. Again, the causality test as illustrated in equations 2 and 3 only involves the two core variables in the study namely; inflation rate and government expenditure. It is shown from the results in Table 4 that the statements that inflation (INF) does not granger cause government spending (GEXP) and GEXP does not granger cause INF are both rejected at 5%; the F statistics of both have probabilities that are less than 0.05. Therefore, we can conclude that there exists a bidirectional causality between inflation and government expenditure.
Estimation of the error correction model
According to the Granger Representation theorem, when variables are co-integrated, there must also be an error correction model that describes the short-run dynamics or adjustments of the co-integrated variables towards their long-run equilibrium values. ECM consists of one-period lagged co-integrating equation and the lagged first differences of the endogenous variables. Using the Vector Auto-regression (VAR) method with a lag interval of 1 to 2 and intercept (no trend) in co-integration (CE), the ECM is estimated as can be seen below with government spending (GEXP) as a dependent variable and the rest of the variables are said to offer an explanation to government expenditure behaviour in Nigeria. The result of the error correction model is shown above in Table 4. The speed of adjustment coefficient of the ECM is -1.7128 and it is significant at 1%. This implies that at every interval that is whenever there is disequilibrium, the recovery of the government spending back to equilibrium is 71.28%.
The implication of this is that there is a short run dynamics running from the inflation rate, exchange rate and broad money supply to government spending in Nigeria.
Short-run causality relationship
The result from this study as is shown above in Table 5 shows that government spending is statistically significant for the lagged periods in the short-run dynamic associations. The estimation reveals that the lag values of government spending are significant. Again, inflation exhibits a significant short run relationship with government expenditure. This result further affirms the strong association between government expenditure and inflation in Nigeria. Exchange rate and money supply in the same vein show a strong short run association with government expenditure.
The implication of this result is that the impact of inflation of government expenditure on the inflation rate is sustained from the short run period through the long run period.
Model overall significance
This is deduced from the F-statistics probability. Table 5 shows that the F-statistics probability is 0.00, which indicates that all the explanatory variables, will significantly influence government spending. Therefore, inflation rate, exchange rate and money supply are important determinants of government expenditure in Nigeria.
Model goodness of fit
This is estimated by using the R 2 , which shows a value of 0.7064 in Table 5. This value indicates that 70.64% systemic variations in government expenditure is explained by the inflation rate, exchange rate and broad money supply. This also indicates that the remaining 29.36% not captured by the explanatory variables in the model is due to changes in other variables or error terms.
Autocorrelation test
Two methods are used for the autocorrelation test in the study. Firstly, the correlogram approach via ACF and PACF are applied and the Breusch-Godfrey Serial Correlation LM Test.
Their results are shown in the following tables.
From both tests shown in Table 6, it is obvious that the estimated model does not have an autocorrelation problem. All the probabilities of both the ACF and PACF are not significant.
In addition, the Breusch-Godfrey Serial Correlation test also has the probability of the F statistics to be greater than 0.05 thus, showing that the null hypothesis of no autocorrelation is accepted at a 5% significant level.
Conclusions
The results from the analysis further underscore the importance of the inflation rate in relationship shows that rising inflation causes a government to spend more. The implication of this conclusion is that an increase in inflation rate has the tendency of increasing the prices of goods and service on which government expenditure is expended. Hence, there is the need for a government to jack up its expenses in order to meet the initial quantity of commodity budgeted.
A.M.O. Anyafo (1996) opined that the incessant upward review of the budget allocated for various infrastructures in Nigeria is as a result of the persistent rise in the general price level.
It can also be concluded from the study that apart from the inflation rate, exchange rate also exerts a significant impact on government expenditure. Findings from the study reveal that currency depreciation that is a fall in the value of the naira will have the tendency of increasing government expenditure. The mechanism through which this happens is very obvious as explained by Y.K. Adamson (2000). According to him, more naira will have to be sacrificed for the same commodity denominated in foreign currency e.g. US dollars whenever the naira depreciates. The implication is that the government will have to increase its spending to cover up for the increase in the naira. Nigeria remains the largest importer in the whole of Sub Sahara Africa; therefore, any devaluation is bound to have a significant impact on government expenditure.
Money supply is also an important factor that affects government expenditure. An upward movement in money supply in Nigeria influences government expenditure positively. The study found a strong positive relationship between money supply and government expenditure.
The largest spender in Nigeria is the government. This is because the economy is not driven by the private sector but largely, by the government.
This study has further shown the causality flow from both inflation and government expenditure. The implication is that government expenditure exerts a great influence on inflation pressure in Nigeria and vice versa. It is recommended that government policy on its expenditure should target output increase so that it can cushion the effect of the resulting inflation trend. | 4,627 | 2019-12-01T00:00:00.000 | [
"Economics"
] |
CO2 gas sensing properties of Na3BiO4-Bi2O3 mixed oxide nanostructures
In this paper, we report Na3BiO4-Bi2O3 mixed oxide nanoplates for carbon dioxide gas sensing applications. These nanoplates have been synthesized using electrochemical deposition with potentiostatic mode on ITO substrate and characterized using scanning electron microscopy (SEM) and X-ray diffraction (XRD) to analyze their surface morphology and structure. SEM study shows the presence of horizontally aligned nanoplates stacked on top of one another (thickness ≈ 40 to 75 nm). XRD pattern shows the presence of monoclinic Na3BiO4 and Bi2O3. The gas percentage response is evaluated by measuring the change in electrical resistance of the nanoplates in the presence of carbon dioxide for different pressures at 50 °C, 75 °C, and 100 °C. Percentage response of more than 100% is seen at 30 psi gas pressure which increases to ≈ 277% at 90 psi at 100◦C.
Introduction
Modern industrialized society possesses a great threat to our safety and well-being, mainly due to the release of greenhouse gases like carbon dioxide. These gases are responsible for the unstable environmental phenomena like droughts and famines Dimitriou et al. (2021); Shahbazi et al. (2021).
A lot of environmental friendly compounds are being explored for their possible application in solid-state gas sensors. Metal oxide semiconductors and carbon nanotubebased composites are few examples of materials that show good potential for sensing Barsan et al. (2007); Rai et al. (2014); Philip et al. (2003); Rai et al. (2015). Low cost, high sensitivity, and quick response time makes the sensors based on metal oxide semiconductors very attractive. They mainly work by adsorption and desorption of gas on the surface causing a change in their electrical resistance Fine et al. (2010); Seiyama et al. (1962).
Metal oxide sensors based on Bi 2 O 3 , SnO 2 , ZnO, La 2 O 3 , and Ag-doped CuO have been explored in the past. They tend to give acceptable results at low gas concentrations, but their resistance change at higher concentrations of CO 2 is negligible Shinde et al. (2020). However, nanoplates of Bi 2 O 3 showed significant sensing performance even at high concentrations of CO 2 Shinde et al. (2020). This suggests that nanostructures show better sensing characteristics as compared to traditional bulk materials. This may be because a large surface area is highly desirable for a good sensor. Nanostructures provide an ideal way of achieving this, and their morphology has a direct impact on the gas sensing behavior of the material Gurlo (2011).
A number of mixed metal oxide nanostructures have also been explored so far for CO 2 sensing. CuO-Cu x Fe 3x O nanocomposite has shown a high response of 50% for CO 2 concentration of 5000 ppm Chapelle et al. (2010). BaTiO 3 -CuO sputtered thin film has also been used for CO 2 sensing. Resistance change on CO 2 exposure were mainly found to depend on the work function changes in the p-n hetero junctions Herrán et al. (2008); Chavali and Nikolova (2019). Bismuth oxide and its derivatives are also known to show good sensitivity towards CO 2 and other gases Bhande et al. (2011);Gou et al. (2009);Cabot et al. (2004). These compounds are environmental friendly and economical as well.
In this paper, horizontally aligned nanoplates of Na 3 BiO 4 -Bi 2 O 3 mixed oxide have been synthesized using potentiostatic electrodeposition, and their CO 2 sensing properties have been studied at different pressures.
Synthesis
Potentiostatic electrodeposition with standard three electrode system was used for synthesis with indium tin oxide (ITO)-coated glass plate as working electrode Jiang et al. (2017); Rivera et al. (2017). Platinum wire was used as the auxiliary electrode, and Ag/AgCl (saturated KCl) was used as the reference electrode. Electrolyte was prepared by dissolving bismuth nitrate pentahydrate (Bi(NO 3 ) 3 .5H 2 O), sodium nitrate (NaNO 3 ), and 69% nitric acid (HNO 3 ) in distilled water to obtain molarities of 0.013 M, 0.013 M, and 1 M respectively. For horizontally aligned nanoplates, deposition was done at a reduction potential of −0.07 V, 100 rpm stirring speed, and 10-min deposition time. These parameters have been optimized to obtain the desired morphologies Morales et al. (2005).
Sensor setup
A chemiresistor-type sensor has been prepared for studying the gas sensing behavior of these nanoplates ( Figure 1). The nanoplates are deposited on to the ITO substrate using potentiostatic electrodeposition. After drying at room temperature, two leads of copper wire were attached using silver paste. This sensor was then installed inside a homemade stainless steel gas sensing chamber ( Figure 2). Keithley SourceMeter (2601B) was connected to the sample for resistance measurement at a constant current of 10 mA. Keithley power supply (2600B-250-4 360W) and a Keithley digital multimeter (2700) were used to power the heater and measure the temperature inside the chamber. Inlet and outlet valves were installed to inject and release the gas from the chamber. Chamber pressure was measured with the help of pressure meter fitted at the top of the chamber. CO 2 gas was introduced from a pressurized cylinder (100 % CO 2 ). Figure 3 shows cyclic voltammetry studies on ITO electrode in an electrolyte containing 0.013 M Bi 3+ ions, 0.013 M Na + ions, and 1 M H + ions. Peaks corresponding to reduction of cations are seen at cathodic potentials. Similar results have been reported earlier on fluorine-doped tin oxide gas substrate Sadale and Patil (2004). A shift in reduction peak potential is seen in successive cycles. This effect is mainly due to change in the concentrations of reactants and products near the electrode in each cycle Fried (2012).
Morphological studies
SEM image shows the presence of horizontally aligned nanoplates with thickness ranging from 40 to 75 nm (Figure 4). Edge length varies from 4 to 12 µm. These nanoplates appear to be stacked on top of one another with smooth surfaces.
Gas sensing
The percentage response of the Na 3 BiO 4 -Bi 2 O 3 mixed oxide nanoplates towards CO 2 was determined by measuring the change in resistance of the sample on exposure to carbon dioxide using the formula: Response (%) = ((R o -R g )/R g )*100 Rella et al. (1997). R o is the resistance of sample in presence of air, while R g is the resistance in presence of CO 2 gas. These measurements were initially carried out at 90 psi CO 2 pressure for 50°C, 75°C, and 100°C (Figure 6). At first, CO 2 gas was flushed trough the chamber to remove the air present in the chamber. The output valve was then closed, and the required CO 2 pressure was built up (indicated by CO 2 ON). In the third step (indicated by CO 2 OFF), inlet valve was closed, and the outlet valve was opened to release the CO 2 pressure. Percentage response of 0%, 15.5%, and 276.8 % was seen at 50°C, 75°C, and 100°C, respectively.
Effect of variation in CO 2 pressure was further evaluated at different pressures and at a fixed temperature of 100°C. Figure 7a, b, and c show the percentage response curve for 90 psi, 60 psi, and 30 psi CO 2 pressures respectively at 100°C. Comparison of response time at different pressures is shown in Figure 8. Details of percentage response, response time, and recovery time are shown in Table 1.
The highest percentage response value of 276.8 % is obtained at 90 psi, which decreases to 254.5 % and 116.5 % at 60 psi and 30 psi, respectively, for Na 3 BiO 4 -Bi 2 O 3 mixed oxide nanoplates. Response time increases (250 ms at 90 psi, 500 ms at 60 psi, and 650 ms at 30 psi), while recovery time decreases (78 s at 90 psi, 53.5 s at 60 psi, and 24.5 s at 30 psi) as the pressure is decreased from 90 to 30 psi This may be due to deeper adsorption of gas molecules at higher pressures. Bi 2 O 3 nanoplates prepared by the similar route do not show significant percentage response (3.5 % at 100°C and 90 psi gas pressure), while ITO substrate shows no sensitivity at all. To further analyze the relationship between CO 2 pressure and percentage response, a linear fit is plotted (Figure 9). A sensitivity of 3.2 %/psi is seen (R 2 = 0.94).
Repeatability studies are shown in Figure 10 for 90 psi pressure. Each successive cycle shows similar characteristics with almost equal values for percentage response, response time, and recovery time.
Gas sensing mechanism
The gas sensing mechanism can be explained by taking into account the interaction of CO 2 with the surface nanoplates ( Figure 11). An almost instantaneous decrease in resistance is seen on exposure to CO 2 gas.
When the heated metal oxide nanoplates are exposed to air, oxygen gets adsorbed on the surface. At temperatures < 150°C, oxygen is predominantly adsorbed as O 2− Ranwa et al. (2014). The detailed mechanism can be explained with the help of following equations: In this process, oxygen takes up electrons from the conduction band. This leads to the formation of an electron depletion layer for an n-type material or a hole accumulation layer for a p-type material. When an oxidizing gas like CO 2 gas is introduced into an n-type metal oxide semiconductor surface, the gas molecules get adsorbed onto the surface of the material by taking up free electrons. The mechanism of CO 2 adsorption can be understood with the help of the following equations (Bhande et al. (2011)): CO 2 breaks up into CO and O on surface interaction. The oxygen atoms released takes up electrons from the surface forming O 2− . This causes a further expansion of electron depletion layer which in turn causes a decrease in conductivity. However, when a p-type material is involved, CO 2 causes an expansion of hole accumulation layer thereby causing an increase in conductivity or decrease in resistance Hung et al. (2017).
In the present work, a significant decrease in resistance is observed for Na 3 BiO 4 -Bi 2 O 3 mixed oxide nanoplates on introduction of CO 2 gas ( Figure 11). This suggests that this material is behaving as a strong p-type semiconductor ( Figure 12). Nanoplates offer a very large surface area leading to good adsorption. Results suggest that this adsorption is reversible, and the original conductivity of the material is restored after the gas is removed.
Conclusion
Na 3 BiO 4 -Bi 2 O 3 mixed oxide nanostructures have been synthesized using potentiostatic electrodeposition. XRD analysis shows peaks corresponding to monoclinic Na 3 BiO 4 and Bi 2 O 3 with weight percentage of 20 % and 80%, respectively. SEM studies reveal the presence of horizontally aligned nanoplates with thickness ranging from 40 to 75 nm. The percentage response shows a linear dependence on pressure in the range of 0 to 90 psi and 100°C (R 2 = 0.94). A sensitivity of 3.2 %/psi is observed. These mixed oxide nanoplates shows a very quick response to CO 2 gas, which is a highly sought-after characteristic for a gas sensor. Repeatability and stability makes this material an ideal candidate for sensor development. | 2,609.6 | 2022-02-16T00:00:00.000 | [
"Materials Science",
"Engineering"
] |
Restriction beyond the restriction point: mitogen requirement for G2 passage
Cell proliferation is dependent on mitogenic signalling. When absent, normal cells cannot pass the G1 restriction point, resulting in cell cycle arrest. Passage through the G1 restriction point involves inactivation of the retinoblastoma protein family. Consequently, loss of the retinoblastoma protein family leads to loss of the G1 restriction point. Recent work in our lab has revealed that cells possess yet another mechanism that restricts proliferation in the absence of mitogens: arrest in the G2 phase of the cell cycle. Here, we discuss the similarities and differences between these restriction points and the roles of cyclin-dependent kinase inhibitors (CKIs) herein.
Introduction
During each division cycle, cells need to duplicate their genome and distribute the two copies equally over the two daughter cells. The processes of DNA-duplication (Sphase) and cell division (mitosis) are separated by two gap phases, G 1 and G 2 , respectively. During these phases, several mechanisms operate to prevent cells from continuing the cell cycle under inappropriate conditions such as the absence of growth factors or the presence of DNA damage. The gap phases provide a window of time during which cells assess whether the environment still favours proliferation (during G 1 ) or whether S-phase was performed correctly (during G 2 ). If this is not the case, normal cells can interrupt the cell cycle in the gap phases through growth inhibitory mechanisms that activate the retinoblastoma proteins or the p53 transcription factor. In cancer cells, these growth inhibitory pathways are often disrupted, leading to unscheduled proliferation [1].
The G 1 restriction point
One critical environmental factor for cell proliferation is the presence of growth factors and normal cells respond to their absence with cell cycle arrest in G 1 . However, during the G 1 phase, growth factors are only required until 2-3 hours prior to initiation of S-phase [2]. This moment in G 1 was first described in 1974 by Arthur Pardee and termed the restriction point R. Pardee found that cells that have passed the G 1 restriction point can progress through S-phase and complete mitosis independently of mitogens [3]. Since entry into S-phase after growth factor induction was found to rely on protein synthesis, it was suggested that cells need to accumulate a protein in order to pass the restriction point [4]. This hypothetical protein was referred to as the R-protein, and is apparently induced by mitogens. Importantly, Pardee found that the restriction point was defective in cancer cell lines, providing physiological relevance for the restriction point. In addition, cancer cells were much more resistant to inhibition of protein synthesis, suggesting that the R-protein was either stabilized in these cells or not required [5]. The transformed cell lines that were used in this study carried simian virus 40 (SV40) [2]. The finding that the oncogenic products of DNA tumor viruses, such as SV40 large T antigen, adenovirus E1A and HPV E7, disrupt G 1 /S control through their inhibitory interaction with the retinoblastoma gene product [6,7], provided a crucial link to the machinery underlying the restriction point.
The retinoblastoma gene encodes a 105 kD nuclear phosphoprotein (pRB) that in its unphosphorylated state can bind to and repress E2F transcription factors whose activity is essential for G 1 /S transition [8][9][10][11][12]. Since pRB is dephosphorylated late in mitosis by PP1 phosphatase [13], it needs to be phosphorylated during G 1 to allow entry into S-phase and this requires mitogenic signalling. Mitogenic signalling results in increased transcription and stabilization of CYCLIN D [14], which stimulates its catalytic partners CDK4 and CDK6 to phosphorylate pRB early in G 1 , causing partial inactivation of pRB and release of E2F [15]. E2F transcription factor activity results in increased transcription of several genes involved in cell cycle progression among which CYCLIN E. CYCLIN E/CDK2 activity phosphorylates pRB to a higher extent, triggering full release of E2F and onset of Sphase. Conversely, in the absence of mitogens, decreased transcription of CYCLIN D1 and decreased stability of CYCLIN D1 protein favor the pRB unphosphorylated state, which inhibits E2F activity and causes cell cycle arrest in G 1 . Additionally, mitogen deprivation causes accumulation of the cyclin dependent kinase inhibitor (CKI) p27 KIP1 through activation of the FOXO transcription factor [16,17]. p27 KIP1 is a potent inhibitor of CYCLIN E/CDK2 kinase activity [18], and will therefore prevent inactivation of pRB.
Somewhat unexpectedly, Rb-deficient mouse embryonic fibroblasts (MEFs) still arrested in G 1 when mitogen starved, although a small fraction of the cells could enter S-phase [19,20]. This has been explained by the activity of two other retinoblastoma protein family members, p130 and p107, which have redundant functions in regulating E2F transcription factors [21]. Together, these proteins make up the so-called family of pocket proteins, which refers to their highly conserved 'pocket-region' that is essential for interacting with E2Fs [10,22,23]. Indeed, MEFs that have lost all three pocket proteins are no longer capable of arresting in G 1 when mitogen starved [24,25].
The retinoblastoma proteins can thus be seen as molecular switches that operate at the restriction point: when switched -off-by mitogens, they allow passage through the restriction point and initiation of S-phase, while the -onstate results in cell cycle arrest. The downstream target of the switches are the E2F transcription factors, whose activity results S-phase entry [12]. The switches are operated by cyclin-associated kinase activities in G 1 that can be modulated by the stability of the cyclin subunit, as is the case for CYCLIN D, or by inhibition of the kinase activity, as is the case for CYCLIN E/CDK2. CYCLIN D has been suggested as an appropriate candidate for the R-protein [26], since it is dependent on mitogens for its synthesis, is destabilized in the absence of mitogens and operates the 'molecular switch'. However, ablation of all three CYCLIN D family members (Cyclin D1, D2 and D3) did not block re-stimulation of serum-arrested cells (i.e., 60-80% of the cells were able to re-enter the cell cycle when stimulated with 10% serum) [27]. In contrast, MEFs in which both CYC-LIN E family members (CYCLIN E1 and E2) were ablated, failed to re-enter the cell cycle after mitogen deprivation due to failure in loading MCM proteins to the DNA, which is essential for S-phase initiation [28,29]. Since CYCLIN E accumulates during G 1 and its ablation results in failure of cell cycle re-entry, CYCLIN E may be a good candidate for the R-protein [30].
Mitogen dependence of Rb/p107/p130-deficient MEFs
Pardee originally suggested that once cells have passed the restriction point, the cell cycle can proceed independently of mitogens until mitosis [2]. Accordingly, ablation of the retinoblastoma gene family, resulting in complete loss of the G 1 restriction point [24,25], should allow mitogenindependent proliferation. However, this was shown not to be the case: pocket-protein deficient cells are prevented from entering mitosis in the absence of mitogens by two mechanisms: (1) the majority of cells undergoes apoptosis [24,25,31]; (2) surviving cells arrest in the G 2 phase of the cell cycle within 3-5 days [31]. Apparently, mitogenic signaling is not only required for passing the G 1 restriction point, but also for passage through G 2 . While activation of the G 1 restriction point in normal cells involves inhibition of D-and E-type cyclins, mitogen-starvation-induced G 2 arrest is effected by accumulation of p27 KIP1 and p21 CIP1 that act as inhibitors of CYCLIN B1-and CYCLIN A-associated kinase activities [31].
CKI mediated inhibition of CDK1, the catalytic partner of CYCLIN B1, has been described in other systems as well. In addition to its CDK2-inhibiting activity [32], p21 CIP1 was shown to induce a G 2 arrest upon DNA damage [33] or upon over-expression [34] by inhibiting CDK1 kinase activity through direct interaction. In contrast to an earlier report [18], recent work from several laboratories has revealed that also p27 KIP1 can inhibit CDK1 kinase activity through direct interaction. E.g., p27 KIP1 is highly expressed in thymocytes and splenocytes and binds to and inhibits CYCLIN B1-CDK1 kinase activity in these cells [35]. In mice, ablation of SKP2, an F-Box protein that targets p27 KIP1 to an SCF ubiquitin-ligase complex, resulted in elevated p27 KIP1 levels associated to CDK1. Most defects in these animals are the result of decreased CDK1 and CDK2 kinase activities and can be rescued by concomitant ablation of p27 KIP1 , which restores physiological cyclindependent kinase activities [36].
G 2 arrest: a second restriction point?
The mitogen-starvation-induced G 2 arrest shows several similarities to the G 1 restriction point. E.g., both depend on inhibition of cyclin-associated kinase activities and in both, accumulation of p27 KIP1 plays an important (although not exclusive) role [31]. Importantly, both are reversible: mitogen stimulation of G 2 -arrested pocket-protein-deficient cells results in reactivation of the cell cycle and synchronous entry into mitosis after approximately 15 hours. Is there also a true restriction point in G 2 in the sense that a time point can be identified after which cells do no longer require serum to enter mitosis? To address this issue, we serum-starved pocket-protein deficient MEFs for 7 days, and then re-fed the cells with serum-containing medium at time point 0. At several time points hereafter, we replaced the serum-containing medium for serum-free medium. To quantify G 2 exit, we trapped the cells in mitosis using the microtubule-stabilizing drug Taxol. 21 hours after serum-stimulation, we harvested the cells and determined the mitotic fraction by FACS-staining for the mitotic marker MPM2 as described previously [31]. Figure 1A shows that the fraction of cells entering mitosis gradually increased upon longer duration of serum exposure. However, at 6 hours of serum exposure, the maximum amount of mitotic cells was reached. This indicates that mitogen-starved G 2 arrested cells only required a window of 3-6 hours of serum in order to re-enter the cell cycle, identifying a G 2 restriction point at approximately 10 hours before mitotic entry.
Next, we wondered whether cell cycle re-entry of serumstarved G 2 -arrested cells relies on protein translation, as was previously shown for recovery from G 1 arrest. We therefore compared serum stimulation of G 2 -arrested cells in the presence and absence of the translation inhibitor cycloheximide. Figure 1B shows that inhibition of protein synthesis precluded cell cycle re-entry of serum-stimulated cells. This suggests that passage through the G 2 restriction, like passage through the G 1 restriction point, depends on synthesis of one or multiple proteins.
An important question now is: why was the G 2 restriction point not identified in the original experiments of Pardee? A first explanation is that activation of pocket proteins in serum-starved normal cells (i.e., wild type MEFs) imposes an arrest in G 1 that largely prevents subsequent cell cycle events. However, if cells possess two restriction points, and mitogen deprivation results in inhibition of all cyclinassociated kinase activities, why then do normal cells mainly arrest in G 1 and is G 2 arrest only seen in pocketprotein compromised MEFs? One reason could be that the levels of suppression of CYCLIN/CDK activity required for G 1 or G 2 arrest are different. In wild type cells, minor inhibition of D-and E-type cyclins may already impose a G 1 arrest through accumulation of hypophosphorylated pocket proteins. In contrast, G 2 arrest imposed by inhibition of CYCLIN A-and B kinase activities requires high levels of p21 CIP1 and p27 KIP1 , which need several days to accumulate. Apparently, when these levels are reached in pocket-protein-deficient cells, the remaining CDK2 kinase activity is still sufficient to drive cells through S-phase, while the remaining CDK1 activity is too low to allow entry into mitosis, resulting in G 2 arrest.
Secondly, G 2 arrest in serum-starved, pocket-protein defective cells relies on functional p53 [31]. The cancer cell Evidence for a G 2 restriction point Figure 1 Evidence for a G 2 restriction point. A. Cell cycle reentry from G 2 requires 6 hours of mitogen-stimulation. Serum-starved cells were stimulated by the addition of serum-containing medium. Subsequently, at the indicated times medium was replaced with serum-free medium containing Taxol for the last 9 hours. At 21 hours cells were harvested and fixed in 70% ethanol and mitotic entry was determined by MPM2 FACS staining. Error bars indicate the standard deviation for two experiments. B. Cell cycle reentry from G 2 requires protein synthesis. Serum-starved cells were serum-stimulated in the absence or presence of 50 µg/ ml cycloheximide (CHX). Cells were fixed at 21 hours and mitotic entry was determined by MPM2 FACS staining. The level of MPM2 positivity in serum-stimulated cells at 21 hours is set at 100%.
line that was used for the original experiments contained SV40 Large T antigen, which inactivates the pocket proteins, but also p53 [37]. Therefore, both the G 1 and the G 2 restriction points were inactivated in these cells.
Conclusion
The G 1 restriction point defines a window of mitogen requirement in G 1 . However, in the absence of pocket protein activity, another growth-restricting mechanism in G 2 becomes manifest that prevents unconstrained proliferation under mitogen-starved conditions. This G 2 arrest has the following features: 1. It allows cell cycle progression only in the presence of mitogens.
2. It is reversible: mitogen-starved, G 2 -arrested cells reenter the cell cycle synchronously upon mitogen stimulation.
3. A specific moment in G 2 exists, approximately 10 hours before mitotic entry, after which cells can progress into mitosis independently of mitogens.
4. Recovery from G 2 arrest relies on accumulation of one or multiple proteins.
5. The G 2 arrest is effectuated by inhibition of CYCLIN-CDK activity through association with CKIs.
These properties of serum-starvation induced G 2 arrest identify a true restriction point in G 2 . However, the G 1 and G 2 restriction points are not completely identical at the molecular level. For one: whereas the G 1 restriction point critically depends on the activity of the pocket proteins, the G 2 restriction point only becomes manifest when pocket protein activity is diminished or absent. Furthermore, the G 1 restriction point involves degradation of CYCLIN D in addition to CKI-mediated inhibition of CYCLIN E, whereas the G 2 restriction point appears to rely solely on CKI-mediated inhibition of CYCLIN A-and CYCLIN B-associated kinase activities.
Taken together, we postulate that cells possess two restriction points defining the requirement for mitogenic signaling in G 1 and in G 2 to stimulate CYCLIN D/E and CYCLIN A/B kinase activities, respectively ( Fig. 2A). In both, accumulation of p27 KIP1 plays an important role. When growth factors are removed from normal cells, rapid disappearance of CYCLIN D1 and inhibition of CYCLIN E by accumulation of p27 KIP1 results in hypophosphorylated pRB, low E2F activity and G 1 arrest (Fig. 2B). In cells that have lost the pocket proteins and hence the G 1 restriction point, the G 2 restriction point comes into play. Accumulation of p21 CIP1 and p27 KIP1 apparently leaves sufficient CDK2 activity to allow cells to cross the G 1 /S border and complete S phase (likely because of elevated E2F activity in the absence of pocket proteins). However, inhibition of CYCLIN A-and B kinase activity now arrests cells in G 2 (Fig. 2C).
We envisage that the G 2 restriction point serves as a backup mechanism to prevent unconstrained proliferation of cells that have lost proper G 1 /S control. Indeed, a substantial amount of circumstantial evidence suggests a role for the G 2 restriction point in the suppression of cancer [38]. E.g., it is possible that tumor cells in a primary tumor retain a normal G 2 arrest that does not perturb proliferation at the site of origin but only becomes activated under special conditions such as dissemination to distant sites. Indeed, occult, non-proliferating tumor cells that were found in the bone marrow and bloodstream of cancer patients without overt metastases, may present an example of this scenario [39]. Elucidation of the mechanism of cell cycle arrest is of paramount importance to control the behavior of such cells.
MEFs: mouse embryonic fibroblasts
Extending the restriction point | 3,742.2 | 2006-05-18T00:00:00.000 | [
"Biology"
] |
Seasonal Variations of Polarization Diversity Gain in a Vegetated Area considering High Elevation Angles and a Nomadic User
Seasonal variations of the polarization diversity gain are addressed for a nomadic user in a vegetated area taking high elevation angles andnongeostationary satellites into consideration.Corresponding experimental datawere obtained at a frequency of 2.0 GHz at Stromovka Park in Prague, the Czech Republic, within the full in-leaf and out-of-leaf periods of 2013 and 2014, respectively. By detecting copolarized and cross-polarized components of the transmitted leftand right-handed circularly polarized signals, the corresponding diversity gain was obtained for multiple-input single-output (MISO), single-input multiple-output (SIMO), and combined MISO/SIMO cases. It was found that tree defoliation results in a significant decrease of the polarization diversity gain achieved for low time percentages in particular scenarios.
Introduction
One of the standard satellite-to-earth scenarios of the future is a nomadic user in an outdoor vegetated area relying on satellite services in a variety of locations over an extended period of time.Such a user can be characterized as being static for the time spent within a particular location.As satellites on nongeostationary Earth orbits, such as medium or low Earth orbits, provide the required high-data rates with small time delays, the position of a particular satellite, with respect to the user, may change dramatically within the period of time the user remains in a fixed position, in contrast to low elevation links such as in [1].
Mobile [2,3] or static [4][5][6] users have been the focus of most studies in vegetated areas.On the one hand, in order to characterize a propagation channel for a static user, a representative scenario is selected and a vast range of elevation and azimuth angles is considered to account for different satellite positions.On the other hand, the land mobile propagation channel may be characterized by static elevation and azimuth angles while focusing on rapidly changing user surroundings.
Characterizing the propagation channel for a nomadic user is more complex.Apart from specifying a scenario of interest, one must take into account the wide range of elevation and azimuth angles achieved between the user and a nongeostationary Earth orbit satellite for arbitrarily fixed positions of the user terminal within the scenario.Consequently, there are an unlimited number of users, surroundings, and satellite orientations, each of which impacts upon the corresponding propagation channel [7].Thus, from a measurement campaign point of view, it is feasible to address typical representative scenarios only.
It should be noted that, apart from the empirical approach presented in this paper, attenuation and scattering by vegetation can also be treated in an analytical way as, for example, in the case of the multiple scattering theory [8] where lossy dielectric cylinders and thin disks are utilized to model a tree canopy within which their distribution is considered to be uniform [9,10] or more specific [11].
Considering a vegetated area at different seasons, which have a significant impact from the propagation point of view [4,12], full in-leaf and out-of-leaf conditions can be achieved.
As polarization diversity at the satellite's transmitter and multiple antennas at the user terminal are expected to ensure a certain quality of service [13], it is of great interest to investigate the corresponding diversity gain with respect to its seasonal variations.As tree defoliation has mainly been addressed from the vegetation attenuation point of view for the case of a single-input single-output propagation channel [4,12], its influence on the polarization diversity gain has not been thoroughly documented in the literature.
Thus, experimental data regarding the influence of tree defoliation on the polarization diversity gain are not publicly available, apart from [3] where the nomadic satellite channel is considered, albeit only for the case of a geostationary satellite and full in-leaf vegetation.This is why we have performed a series of measurements at 2.0 GHz in a vegetated area in Prague, the Czech Republic.During these trials, a remotecontrolled airship was utilized as a pseudosatellite following predefined fly paths.Transmit (Tx) antennas were instantly pointed towards a receiver (Rx) kept in a fixed position.These trials were performed at four selected representative scenarios and, to achieve both summer and winter seasons' measurements, they were carried out in July, 2013, and March, 2014, respectively.As both the left-handed (LHCP) and right-handed (RHCP) circularly polarized continuous wave signals were transmitted at the same time and a dualpolarized receive antenna was utilized, seasonal variations of the diversity gain for the case of multiple-input single-output (MISO), single-input multiple-output (SIMO), and combined MISO/SIMO (represented here by two inputs and two outputs) propagation channels were addressed.Contrasted to [4,5] or [6], in addition to the Tx antenna positioner, such measurements were made possible by utilizing a sensitive, custom-made Rx with four channels sampled in parallel at a rate of 10 kHz.
Section 2 describes the measurement setup and selected scenarios while Section 3 introduces the data processing method.Section 4 presents the obtained results and their analysis.Section 5 discusses the influence of the Rx antenna radiation patterns on the experimental data and Section 6 concludes this paper.
Measurement Setup and Selected Scenarios
The measurement setup includes an LHCP and an RHCP transmit planar wideband spiral antenna attached at the bottom of the airship to a 3D positioner enabling instant pointing towards the location of the Rx based on the airship GPS coordinates.Two unmodulated continuous wave signals separated by a 200 kHz frequency offset were transmitted with a stable, constant output power of 27 dBm and were received by a dual-circularly-polarized (LHCP and RHCP) antenna.This antenna consisted of a dual-linearly-polarized patch antenna and an H-hybrid coupler which shifted the received orthogonal linearly polarized components by 90 ∘ in phase in order to create RHCP and LHCP signals; see Figure 1 for more details.The Rx antenna was placed on a tripod at a height of 1.5 meters above ground level and oriented so that its main lobe pointed towards the zenith.Received Lin.pol.Lin.pol.
H-hybrid
Rx antenna signal levels were recorded by a computer connected to a sensitive, four-channel radio receiver with a sampling rate of 10 kHz so that four samples were obtained concurrently every 0.1 ms.This custom-made receiver had a low noise floor of −126 dBm for a 12.5 kHz measurement bandwidth and its first two channels were tuned to 2.00106 GHz and the other two to 2.00086 GHz.Both copolarized and cross-polarized components of the transmitted signals were detected enabling MISO/SIMO channel investigations.Under line-of-sight propagation conditions, the dynamic range of the system is about 45 dB for the lowest elevation angle achieved, namely, 30 degrees, and about 70 dB considering the overhead position of the Tx.This considers the free space loss when the altitude of the airship is approximately 200 meters above ground level.Thus, with respect to the roughly 10 dB vegetation attenuation at 2 GHz for the whole range of elevation angles, as reported in [4], it was possible to detect signal envelope fades of at least 35 dB.
At Stromovka Park, the following scenarios for a nomadic user in a vegetated area were selected as shown in Figures 2 and 3. Within scenarios A and B, the Rx location was next to and inside an alley of deciduous trees.Scenario C represented a heavily shadowed case with the Rx in the middle of a dense group of coniferous trees, while at scenario D, the Rx was surrounded by a group of tall deciduous trees.In this way, a representative set of scenarios was addressed enabling a generalization of the obtained results.
The airship followed a predefined, straight flyover above these scenarios in a south-north direction with a near-constant speed of about 8 m/s, as indicated in Figure 2, allowing a wide range of elevation angles starting from 30 degrees to be achieved.Moreover, the flyovers were almost perfectly aligned with the orientation of the alley for scenarios A and B. During gusty conditions, the transmit antenna positioner did not keep the direction towards the Rx perfectly and, thus, the data obtained within airship pitch and roll periods of more than 15 degrees were excluded from data processing.Further, similar to [4], the influence of free space loss for various distances between the Tx and the Rx was removed by recalculating received signal levels to a uniform distance of 20 km.It should be noted that measurement time stamps were International Journal of Antennas and Propagation used to synchronize the experimental data with the flight data provided by the airship's sensors.
Data Processing
As the experimental data contain copolarized and crosspolarized components of the transmitted signals TxRx in dBm, they were processed according to ( 5)-( 10) by using the maximum ratio combining (MRC) approach [2,14] to calculate the corresponding diversity gain for the MISO, SIMO, and combined MISO/SIMO cases.
First, the amplitude of the received power TxRx in linear units had to be obtained for each of the four received channels (1) based on the levels TxRx which were recorded in dB: Here, the first and second indices Tx and Rx stand for the polarization of the transmitted and received signals, represented in the following text by indices R and L denoting RHCP and LHCP, respectively.Then, the maximum ratio combining algorithm was applied and an equivalent envelope power eq was calculated.
As [14] states that the signal-to-noise ratio (SNR) is simply the sum of the SNRs of the individual signal branches for the MRC algorithm, the SIMO case considering a RHCP transmitted signal can be written as eq,SIMO = RR + RL , where an uncorrelated noise of power is assumed to be received by both signal branches.To obtain the polarization diversity gain in dB, the equivalent envelope power is expressed in logarithmic scale and the copolarized signal power RR is subtracted: As there were two separate transmitters with an equal output power for the MISO and MISO/SIMO cases during the experimental trials, the combined powers must be divided by 2 so that the total output power is the same as that for the SIMO case.As a result, ( 5)-( 7) and ( 8)- (10) were applied for the RHCP and LHCP cases, respectively: SIMO,LHCP = 10 ⋅ log 10 ( LL + LR ) − LL ,
Results and Analysis
Prior to providing an overall analysis for the whole range of elevation angles, it was necessary to address the seasonal variations of the polarization diversity gain within a range of elevation angles where the large-scale variations of the received signal envelope may be neglected.For such purposes, ten-degree intervals in elevation were selected as the propagation conditions, together with copolarized and crosspolarized radiation patterns of the Rx antenna, do not change considerably within this range and, moreover, a sufficient amount of data samples are available to ensure their thorough statistical interpretation.The polarization diversity gain achieved at scenario B during the summer and winter seasons is presented in Figures 4-6 for the intervals at elevations of 30 ∘ -40 ∘ , 50 ∘ -60 ∘ , and 70 ∘ -80 ∘ .This scenario represents heavy tree shadowing propagation conditions and since it is leafless during the winter season, corresponding seasonal variations of the polarization diversity gain should be the most significant from all of Considering, for example, the elevation interval of 50 ∘ to 60 ∘ (Figure 5), a more detailed analysis can be presented based on the raw time series of the copolarized and crosspolarized received signal levels and their CCDFs; see Figures 7 and 8, respectively.A median 6 dB decrease of the copolarized received signal level for the summer season is obvious in Figure 8 due to the additional attenuation caused by the presence of leaves.This decrease can also be observed in the raw time series data shown in Figure 7. On the other hand, apart from significant small-scale variations of the cross-polarized components clearly seen in Figure 7, their median decrease is only 3 dB for the summer season as seen in Figure 8.This indicates that, in accordance with [12], the presence of branches is more significant than the presence of leaves when the scattering phenomenon is considered.Similar behavior was observed for all ten-degree elevation intervals from 30 to 80 degrees at all the investigated scenarios, making it possible to proceed with the analysis and provide results for the whole range of elevation angles, as shown in Figures 9-12.
To compare the polarization diversity gain achieved at the selected scenarios during the summer and winter seasons, corresponding CCDFs are shown in Figures 9-12.Here, the range of elevation angles between 30 degrees and 80 degrees was considered as it contained the majority of the experimental data.Producing a CCDF of the diversity gain for such a wide range of elevation angles takes into account the fast movement of the satellites on nongeostationary Earth orbits during the time period the user is in a fixed position.As the results obtained for the LHCP and RHCP cases were similar, only the RHCP case is shown in Figures 9-12.
International Journal of Antennas and Propagation
It is clear that when considering time probabilities below 50%, the highest and lowest diversity gains were achieved at scenario C, the most vegetated, and at scenario A, with the Rx located next to an alley, respectively.As expected, the more vegetated the scenario, the more significant the benefits of the diversity approach.This can be explained by [12] where the mean scattering amplitude per unit volume of the tree canopy depends linearly on the density of branches or leaves.Thus, for more vegetated scenarios with rich scattering, more scattered power should be received resulting in an increase of the diversity gain.
Apart from such a brief analysis, the polarization diversity gain differences for the summer and winter seasons are addressed below.Figure 9 shows that even though the trees in the alley are leafless during the winter season a negligible decrease of only about 0.5 dB of the diversity gain for time percentages below 10% can be observed when the Rx was located next to the alley.The effect of the leafless season is clearly limited by the existence of almost clear line-ofsight propagation conditions on one side of the Rx.On the other hand, more than a 2 dB decrease of the diversity gain for the winter season is observed in Figure 5 for scenario B when considering time percentages below 10%, which demonstrates the significant effect of defoliated trees.As scenario C comprises only evergreen coniferous trees, one would expect the diversity gain to be the same during both the summer and winter seasons.However, following the airship flyover denoted in Figure 2, the Rx was located deeper in the vegetated area during the winter season measurements due to maintenance works in the park area.This resulted in about a 1 dB higher diversity gain illustrating the advantage of diversity systems for more shadowed scenarios.
Results similar to those obtained at scenario B were identified for scenario D which also consists of deciduous trees.However, these trees do not form an alley and, based on Figure 3, the effect of defoliation was expected to be more pronounced here.This is shown well in Figure 7 where, for time percentages of 10%, the diversity gain decreases from approximately 4.6 dB in the summer season to about 2.2 dB in the winter season considering the MISO/SIMO case.
Influence of Rx Antenna Radiation Pattern
Considering the results presented in Figures 4-6 and 9-12, it is important to address their dependence on the fact that, although the copolarized radiation patterns of the Rx antenna are similar, the cross-polarized radiation patterns differ by up to 5 dB for elevation angles below 50 degrees according to the simulations performed in CST Microwave Studio using the time domain solver.This is illustrated in Figure 13 which presents the dependence of the Rx antenna gain on elevation angle when considering a phi-cut of 90 ∘ and theta angles from −60 ∘ to 0 ∘ which translate into elevation angles from 30 ∘ to 90 ∘ .This feature of a dual-polarized antenna, together with the inability to compensate for the radiation pattern in an environment where the scattered waves are impinging on the Rx from a wide range of elevation and azimuth angles, results in the need to address the error introduced by such radiation patterns asymmetries.Following (3) for the SIMO case, it is straightforward to calculate the difference in the diversity gain Δ in dB when the level of the received cross-polarized component is changed by a dimensionless parameter .This parameter represents a deviation from an ideal radiation pattern, that is, the one which would be the same for both the cross-polarized RHCP and LHCP cases, and we can write Using to represent the ratio between the cross-polarized and copolarized received signal levels RR and RR , (12) reduces to where considering that RL and RR are the received signal levels in dBm.Further, as defines the difference from the ideal crosspolarized radiation pattern in dB, we can write Based on the Microwave CST simulations of the Rx antenna, a typical value of a 10 dB difference between RL and RR and the maximum value of of about 5 dB may be International Journal of Antennas and Propagation considered.Then, one obtains Δ of 0.78 dB and −0.28 dB for cases where = 5 dB and = −5 dB, respectively, which plays a negligible role in the presented results, especially when considering the low time percentages below 10%.
It should be noted that the expressions for the MISO case reduce after basic logarithm calculations to the form of (13), where represents the ratio between LR and RR .For the combined MISO/SIMO case, (13) can be used if RR = LL and LR = RL are considered.
Conclusion
We have presented a thorough analysis of polarization diversity gain measurements at 2.0 GHz for a nomadic user in a vegetated area considering high elevation angles and both the summer and winter seasons.The case of orthogonal circular polarizations was considered.It was shown that, depending on the scenario, tree defoliation has a significant impact on the achieved diversity gain regardless of the MISO, SIMO, or combined MISO/SIMO configuration.At first, this was demonstrated on experimental data selected within tendegree intervals in elevation and, after that, for the whole range of elevation angles from 30 degrees to 80 degrees.In addition, the influence of asymmetrical cross-polarized radiation patterns of the Rx antenna on the diversity gain calculations was addressed.Based on a typical discrimination of the copolarized and cross-polarized radiation patterns of the Rx antenna, only a negligible impact on the presented results was found.
Considering time percentages below 10%, we have shown that tree defoliation resulted in a negligible decrease of 0.5 dB of the diversity gain when the Rx was located next to the alley, but a decrease of more than 2 dB was observed for the case of the Rx located inside the alley.Similar results were obtained when the Rx was in the middle of a group of deciduous trees.Here, the diversity gain decreased from about 4.6 dB in the summer season to about 2.2 dB in the winter season for the combined MISO/SIMO case.Considering the scenario consisting of evergreen coniferous trees, the Rx was located deeper in the vegetated area during the winter season measurements, which resulted in an increase of about 1 dB of the diversity gain.
As a rule of thumb, we have demonstrated that the polarization diversity gain achieved in the full in-leaf season decreases in the leafless season to half of its value when considering time percentages below 50% for the SIMO and combined MISO/SIMO case for the case of the maximum ratio combining algorithm.This rule can be utilized to estimate polarization diversity gain seasonal variations and can thus decrease the complexity of corresponding measurement campaigns which would have to be carried out during both the full in-leaf and out-of-leaf conditions.
Figure 1 :
Figure 1: The measurement system in detail.One RHCP and one LHCP continuous wave signals at frequencies 1 and 2 , respectively, are transmitted and their orthogonal components with a linear polarization are received by a dual-linearly-polarized patch antenna.An H-hybrid coupler then creates RHCP and LHCP signals at its output ports so that the copolarized (co-pol.) and cross-polarized (x-pol.)components of the transmitted signals can be detected by the four-channel receiver (CH1-CH4).
Figure 2 :
Figure 2: Scenarios A, B, C, and D together with the fly path of the airship denoted by the straight line.The symbols represent the actual positions of the receiver.Image taken from Google Earth.
Figure 3 :
Figure 3: From top to bottom: scenarios A, B, C, and D in detail during the summer (on the left) and winter (on the right) seasons together with the Rx position denoted by a circle.
Figure 8 :Figure 9 :
Figure 8: CDF of received signal levels for scenario B recalculated to a uniform distance of 20 km, elevation 50 ∘ -60 ∘ .The first and second indices in the legend represent the polarization of the transmitted and received signals with R and L representing RHCP and LHCP, respectively.
Figure 10 :Figure 11 :
Figure 10: CCDF of the diversity gain for scenario B.
Figure 12 :
Figure 12: CCDF of the diversity gain for scenario D.
Figure 13 :
Figure 13: Dependence of the Rx antenna gain on elevation angle considering the copolarized (LL, RR) and cross-polarized (RL, LR) radiation patterns. | 4,926.6 | 2015-02-22T00:00:00.000 | [
"Engineering",
"Environmental Science",
"Physics"
] |
Characterization of Initial Parameter Information for Lifetime Prediction of Electronic Devices
Newly manufactured electronic devices are subject to different levels of potential defects existing among the initial parameter information of the devices. In this study, a characterization of electromagnetic relays that were operated at their optimal performance with appropriate and steady parameter values was performed to estimate the levels of their potential defects and to develop a lifetime prediction model. First, the initial parameter information value and stability were quantified to measure the performance of the electronics. In particular, the values of the initial parameter information were estimated using the probability-weighted average method, whereas the stability of the parameter information was determined by using the difference between the extrema and end points of the fitting curves for the initial parameter information. Second, a lifetime prediction model for small-sized samples was proposed on the basis of both measures. Finally, a model for the relationship of the initial contact resistance and stability over the lifetime of the sampled electromagnetic relays was proposed and verified. A comparison of the actual and predicted lifetimes of the relays revealed a 15.4% relative error, indicating that the lifetime of electronic devices can be predicted based on their initial parameter information.
Introduction
The lifetime of an electronic device is generally estimated by conducting a whole lifetime test on a batch of device samples to calculate the statistical reliability of these samples. However, the service life of the device cannot be estimated with this method. Lifetime prediction can contribute toward improving the operational reliability and system reliability of electronics. Several studies have been conducted to investigate two forms of product lifetime prediction [1][2][3][4]: model-based prediction and data-based prediction.
Lifetime prediction models can be divided into classical and online prediction models. A classical prediction model is an offline prediction model based on the generalization of the results of multiple tests [5][6][7]. For example, Fontana established a mathematical model to determine the relationship between the lifetime and operating parameters (load current, ambient temperature and operating frequency) of a relay by using these parameters as predictor variables and assuming the lifetime of the relay to follow the Weibull Distribution [8]. The Center for Advanced Life Cycle Engineering at the University of Maryland proposed life consumption monitoring (LCM) and, based on its analyses of the failure mechanisms [9] and modes [10] of electronics, established a model to analyze the fretting wear of the devices under various stress conditions of temperature, humidity, vibration, voltage, and current [11], and integrated data obtained from these different stress conditions with a model to identify the health states of the devices that predicted their residual lifetime [12,13]. Online prediction models use mathematical theories to monitor the degradation of predictor variables in realtime and perform modeling [14][15][16]. Lu et al. applied LCM to measure the damage to electronics operating under various stress conditions and propose an optimized autoregressive model for lifetime prediction that accounted for the degradation of the devices and the effects of abrupt stress changes on prediction; however, the authors yielded inaccurate results at the early stage of prediction [17]. Based on the measurability of the super-path time and pick-up time of relays, Zhai et al. developed a time-series mathematical model that used both variables to predict the lifetime of electronics [18]. This model-based prediction method examines the physical characteristics of electrical systems to illustrate the nature of the systems and enable the real-time prediction of their lifetime. However, it fails to establish accurate mathematical models for complex dynamical systems and, when applied for engineering purposes, can only handle systems with accurate mathematical models.
Contrary to the aforementioned, data-based prediction methods have higher adaptability and operability and are extensively applied in studies on product lifetime prediction across the world [19][20][21]. However, because of their limited capability, existing data-based prediction methods predict electronics lifetimes largely based on the static contact resistance [22,23]. For example, Yao et al. examined the time-varying pattern of contact resistance to classify the closing of contact points into steady, erratic, and upward states and determine the stability of these points [24]. The authors used contact resistance as a predictive parameter to develop an integrated prediction model for these different closed states of contact points, which successfully predicted the steady and upward changes in contact resistance on a short-term basis. Caesarendra et al. collected the real-trending data of low-methane compressors and used a statespace model and particle filtering to predict the operational degradation of the compressors, thereby validating a prognosis algorithm of particle filtering that they proposed for application in real dynamic systems [25]. Jin et al. utilized historical degradation data to perform degradation modeling [26]. They applied a particle filter-based state and static parameter joint estimation method to obtain an iteratively updating posterior degradation model [27] and predict the degradation state of individual batteries [28] in spacecrafts. Lin and Zhang established the relationships of furfural concentration and carbon and carbon dioxide volumes in an oilimmersed power transformer with the reliability, aging degree, and remaining lifetime range of its solid insulating materials to develop a back-propagation (BP) neural network that predicted the residual lifetime of the device [29]. The aforementioned studies, which examined the performance parameters of electronics over their lifetimes, used estimation methods to establish models explaining the relationship between the lifetime and the degradation of the parameters [30][31][32]. However, some of these parameters, when in application, may yield highly uncertain and incomplete data, which can add considerable difficulty to lifetime prediction.
The service life of electronic devices that are difficult to monitor constantly in real-time can be estimated only on the basis of their early performance parameter values, rather than data on their lifetime or performance degradation. These parameter values are referred to as initial parameter information, which is obtained before an electronic device is used or after it has begun its first-time operation for a set time. However, the potential defects of the device may exist in the initial parameter information and affect its lifetime to some extent. Initial parameter information that contains such defects can be identified and the values and stability of the parameters be quantitatively analyzed to model the relationship of parameter value and stability with lifetime, thereby providing a new approach to predict the lifetime of the device.
Characterization of initial parameter information
The operation of an electronic device is affected by multiple factors. Its parameters therefore exhibit some degree of uncertainty and dispersion and cannot accurately indicate its performance. Thus, this study defined the performance parameters of an electronic device that were obtained in its first-time operation for a set time as the initial parameter information of its performance.
Some electronics perform at their best with appropriate parameter values and low parameter stability. Thus, the performance of an electronic device, which reflects the levels of its potential defects, can be determined by the initial parameter information values and stability of its samples. An electronic device with samples for which initial parameter information values are closer to their optimal levels and have lower stability has lower levels of potential defects and a longer lifetime. Fig 1 depicts the relationship between initial parameter information value and stability.
In Fig 1, the dotted line 0 is the optimal level of a performance parameter; the solid lines 1 and 2 indicate almost the same parameter values but different levels of parameter stability, and line 1 is more stable than line 2. The solid lines 1 and 3 indicate almost the same levels of parameter stability but different parameter values, line 3 indicates exceeding the optimal level of a performance parameter, while the line 1 indicates not reach the optimal level of a performance parameter. Although they all deviate from the best running state, but the impact of actual operation are not same. The solid lines 2 and 3 indicate different parameter values and different levels of parameter stability. The performance of an electronic device depends on the distances of its performance parameters from their optimal levels and on the stability of these parameters.
Values of the initial parameter information
The initial parameter information constitutes a time series of performance parameters obtained from a newly manufactured electronic device that was operated for a set time. The performance parameters of the device were characterized by set degrees of randomness and uncertainty because of multiple factors affecting its operation.
To reduce the effects of randomness and uncertainty on parameter values, the weighted arithmetic mean was used to calculate the means of the initial parameter information of the samples, and the mean values were defined as the indicators of the parameters. The weight of each sample was defined by the relative probability density (PD) of its parameters, which was derived by estimating the probability density functions (PDFs) for these parameters. A high PD value indicates the high occurrence of an individual point and a high weight value.
2.1.1 Estimation of probability density function. PD values derived using the rule-ofthumb estimation of density vary according to the partitioning of intervals by the method. Thus, kernel density estimation (KDE) was alternatively applied to estimate the PDFs for the initial parameter information [21].
x im } is the set of the initial parameter information of the i-th sample, and m is the number of the initial parameter information of the i-th sample was supposed. Thus, the PDF for the initial parameter information of the i-th sample was defined as f i (x), and the KDE valuef i ðxÞ for f i (x) at the random point x aŝ Where h is the window width or bandwidth and K is a kernel function. And K was chosen as the Gaussian kernel function, and s was the sample standard deviation with the optimal window width of h = 1.06sn −0.2 . Fig 2 presents a PDF curve for the initial parameter information (contact resistance) of a sample relay, with the number of operations denoted by the x-axis and contact resistance by the y-axis. In this figure, "•" represents the level of contact resistance for the first 200 operations of the relay, and the PDF curve for the contact resistance was plotted through KDE.
Weighted average probability of the initial parameter information.
The weights and means of the initial parameter information for the i-th sample were derived using its PDF, as expressed by (2): Where i = 1,2,Á Á Á,n, w i (j) is the weight of the j-th initial parameter information x ij of the i-th sample, and x i is the mean of the initial parameter information of the i-th sample.
Stability of the initial parameter information
To measure the stability of the initial parameter information, a least-squares polynomial fit [22] was performed with the raw data points of the parameters, and yielded a smooth fitting curve. This fitting curve, which showed the overall changes in the parameters, had multiple parameter values in the neighborhood of the extrema. Accordingly, the differences of the extrema and these adjacent parameters between them reflected the levels of the stability of the parameters.
Deriving the extrema and end points.
That t i = {t i1 ,t i2 ,Á Á Á,t im } was the set of measurement time periods for the set of the initial parameter information of the i-th sample x i = {x i1 ,x i2 ,Á Á Á,x im } was supposed. Thus, the set of discrete data points for these parameters was expressed by {(t ij ,x ij ), j = 1,2,Á Á Á,m}.
When the sum of the square error between the polynomial function valuexðt ij Þ at the point t ij (j = 1,2,Á Á Á,m) and the original value x ij was at its minimum, a k-polynomial function was used to fit the discrete data point set for the initial parameter information of the i-th sample and a k-polynomial function is derived, as expressed by (3): Thus, the curve expressed by this polynomial function denoted the fitting results of the initial parameter information of the samples. Furthermore, the curve-fitting function was estimated to enable its derivative to satisfy (4): The solutions of (4) were the x-axes of the extrema. The number of the solutions was (k−1). The solutions were arranged in value from the smallest to the largest: t i1 . Their corresponding extrema on the fitting curve were arranged asx i ðt à i1 Þ;x i ðt à i2 Þ; Á Á Á ;x i ðt à iðkÀ 1Þ Þ. The function valuesx i ðaÞ andx i ðbÞ of the fitting functionx i ðtÞ respectively denotes the values of the interval endpoints a and b for the number of operations.
Representation of parameter stability. That
Þ;x i ðbÞg is the set of all extrema and end points for the initial parameter information of the fitting curve for the i-th sample, and the number of elements for the set y i is k + 1. Thus, y i (j) was defined as the j-th element of the set y i . Hence, the difference between elements adjacent to the set y i was estimated using (5): Where max(y i ) is the maximum of all the elements of the set y i and min(y i ) is the minimum of all the elements of the set y i . Hence, the maximum difference between all the extrema and end points on the y-axis of the fitting curve was estimated using (6): In In sum, the stability of the initial parameter information was related to not only Δy i (j), j = 1,2,Á Á Á,k but to Δy max . Thus, the weighted-average adjacent difference and maximum difference between end points and extrema were defined as the levels of parameter stability; larger differences were related to higher weight values of these differences. The weight w i (j) of the j-th difference for the i-th sample and the weight w i (k + 1) of Δy max were estimated using (7): The stability of the initial parameter information for the i-th sample was estimated using (8)
Selection of the best wavelet packet basis
Based on their equations, the initial parameter information value was defined as the level of parameter value and the parameter stability was defined as the level of parameter variation. However, the orders of magnitude of parameter value and stability might differ from each other. To facilitate a comprehensive analysis of both indicators and neutralize the influence of the difference between their orders of magnitude, both indicators were normalized and their relationship with lifetime was subsequently modeled.
Normalization
When the performance of an electronic device is measured, parameters that perform better with higher values are defined as benefit parameters; parameters that perform better with lower values are defined as cost parameters; and parameters that perform well with moderate values are defined as moderate parameters. Respectively, I1, I2, and I3 denote the sets of benefit, cost, and moderate parameters. The equation X = {x 1 ,x 2 ,Á Á Á,x n } was defined as the sample set; n was defined as the number of samples; X ¼ fx 1 ; x 2 ; Á Á Á ; x n g was defined as the set of parameter values in n samples; and y ¼ fỹ 1 ;ỹ 2 ; Á Á Á ;ỹ n g was defined as the set of parameter stability levels in n samples. Hence, the normalized parameter value x g (i) of the i-th sample was estimated using (9): 8 > < > : Where i = 1,2,Á Á Á,n and x c1 , x c2 , x c3 represent the optimal values for I 1 , I 2 and I 3 , respectively; and x max and x min are the maximum and minimum of the set x The normalized parameter values yg(i) of the i-th sample were estimated using (10): Where i = 1,2,Á Á Á,n;ỹ max is the maximum of the setỹ; and y c is the reference value of parameter stability when the device operated at its highest performance.
When an electronic device operates at its highest performance, the performance parameters x c1 , x c2 , and x c3 and the reference value y c should be specified on the basis of its design parameters. Furthermore, after parameter value and stability were normalized using (9) and (10) respectively to [0, 1], the closer the values of both indicators were to 1, the more poorly the device performed, whereas the closer these values were to 0, the more efficiently the device performed.
Data modeling
The equation x g = {x g (1),x g (2),Á Á Á,x g (n)} was defined as the sample set, x g = {x(1),x(2),Á Á Á,x(n)} as the set of normalized parameter values in n samples, y g = {y g (1),y g (2),Á Á Á,y g (n)} as the set of normalized parameter stability levels in n samples, and T g = {T 1 ,T 2 ,Á Á Á,T n } as the set of the actual lifetime periods of n samples.
When n is large, artificial intelligence algorithms such as BP neural networks can be used to model the relationship of x g and y g with lifetime T. Details about modeling algorithms are referred to in [33]. When n is small, a criterion should be developed and the relationship between the criterion and lifetime should be established, instead of using artificial intelligence algorithms. And Fig 5 illustrates the possible distributions of two criteria for the initial parameter information, with x g being the horizontal axis and y g the vertical axis.
In Fig 5, a 1, a 2 and a 3 denote the distributions of normalized parameter means and volatilities of three different samples. The distributions of a 1 and a 2 on the x-axis are identical, as well as those of a 1 and a 3 on the y-axis. This indicates that a 1 performed more efficiently than a 2 and a 3 did but that the performance of a 2 and a 3 could not be determined. Thus, the criteria of samples were obtained by estimating the weighted distance between the data points and origin in the samples, as expressed by (11): Where α and β are weighting factors, and α + β = 1. The values of α and β depended on the ration of x b (i)/y b (i), which was determined by the relative contribution of initial parameter value and stability to the performance of electronic devices. If the initial parameter information value contributed more than initial parameter information stability did to device performance, then α > β. If initial parameter information stability contributed more than initial parameter information value did to device performance, then α < β. If both equally contributed to device performance, then α = β = 0.5.
Based on the definition of criterion, the function model of criterion and device lifetime is established, as expressed by (12): Where T is device lifetime and d is the criterion of a device.
Case analysis
Contact resistance is one of the main performance indicators for electromagnetic relays, and when it is low and stable, the electronic devices perform optimally. Accordingly, this study defined the contact resistance for the first 1000 operations of electromagnetic relays as the initial contact resistance of the relays. A whole lifetime test was performed on eight samples relays to obtain their individual lifetimes. The contact resistance after each closing of the contact point was measured.
The initial contact resistances and parameter stability of the samples were quantified to model the relationship between these values and the lifetime of the samples: 1. The PDFs for the initial contact resistance of all the samples were derived using KDE, and (2) was applied to derive the means of the initial contact resistance of the samples.
2. Curve fitting was performed on the initial contact resistance of the samples to derive the extrema and end points, and (5), (6), and (7) were used to derive parameter stability.
3. The contact resistance of the samples was a cost parameter; thus, x c2 = 0 and y c = 0, and (9) and (10) were used to derive the normalized parameter values and stability.
4. Because of the limited sample size, a modeling algorithm was employed to establish lifetime prediction models for the samples. Furthermore, with α = 0.7 and β = 0.3, criteria for the samples were obtained using (11). Table 1 tabulates the actual lifetime and initial contact resistance of each sample.
5. The relational function for the criterion d and lifetime T (unit: 10,000 times) for each relay that were obtained using polynomial fitting was expressed by (13): T ¼ À 609:4d 3 þ 1242:7d 2 À 816:9d þ 174:8 ð13Þ The aforementioned estimation method was subsequently applied to estimate the initial contact resistance of an additional sample, and its parameter mean and stability before and after normalization can be seen from Table 2. A whole lifetime test was conducted on the sample to estimate its actual lifetime, and (13) was used to derive its predicted lifetime. Comparison of predicted life and actual life can be seen from Table 3.
Conclusion
Initial parameter information indicates potential defects in electronics; higher levels of such defects suggest shorter lifetimes. This study proposed models for the relationships between the initial parameter information and lifetimes of several samples of an electronic device when the levels of benefit, cost, and moderate parameters were appropriate and stable. Parameter value and stability were quantified for small-sample modeling to model the relationship between the initial contact resistance and lifetime of several sample relays. The relative error between prediction lifetime obtained by prediction model and actual lifetime obtained by whole lifetime test is 15.4%. And the findings of this study indicate two conclusions: 1. The means of the initial parameter information derived using the probability-weighted average method denote the values of the parameters, and the difference between the extrema and end points on the fitting curve of the parameters represents the stability of the parameters. These quantitative analyses inform the lifetime prediction of electronics based on their initial parameter information.
2. When the sample size is limited, the relationship between criteria and lifetime that is established using the weighted distance method can be modeled to perform lifetime predictions. The lower the criteria are, the longer the predicted lifetime is. | 5,203.8 | 2016-12-01T00:00:00.000 | [
"Engineering",
"Physics"
] |
An End-to-End Steel Surface Defect Detection Approach via Fusing Multiple Hierarchical Features
A complete defect detection task aims to achieve the specific class and precise location of each defect in an image, which makes it still challenging for applying this task in practice. The defect detection is a composite task of classification and location, leading to related methods is often hard to take into account the accuracy of both. The implementation of defect detection depends on a special detection data set that contains expensive manual annotations. In this paper, we proposed a novel defect detection system based on deep learning and focused on a practical industrial application: steel plate defect inspection. In order to achieve strong classification ability, this system employs a baseline convolution neural network (CNN) to generate feature maps at each stage, and then the proposed multilevel feature fusion network (MFN) combines multiple hierarchical features into one feature, which can include more location details of defects. Based on these multilevel features, a region proposal network (RPN) is adopted to generate regions of interest (ROIs). For each ROI, a detector, consisting of a classifier and a bounding box regressor, produces the final detection results. Finally, we set up a defect detection data set NEU-DET for training and evaluating our method. On the NEU-DET, our method achieves 74.8/82.3 mAP with baseline networks ResNet34/50 by using 300 proposals. In addition, by using only 50 proposals, our method can detect at 20 ft/s on a single GPU and reach 92% of the above performance, hence the potential for real-time detection.
. Defect classification and defect detection task. (a) Defect classification task aims to "What," only outputting a defect class score. (b) Defect detection task aims to "What" and "Where," outputting a bounding box with a defect class score. in industry, which is unreliable and time-consuming. In order to replace the manual work, it is desirable to allow a machine to automatically inspect surface defects from steel plates with the use of computer vision technologies.
The founder of computer vision, British neurophysiologist Marr, considers that a vision task can be defined as "What is Where" that is the process of discovering what presents in an image and where is it [1]. Therefore, the object classification and detection are the most fundamental problems in the field of computer vision research [2]. Similarly, the automated defect inspection (ADI) can also be divided into two types: defect classification and defect detection. Given a defect image, the defect classification task is to solve if this image contains some class of defect [ Fig. 1(a)], and the defect detection task is to solve where a defect exists in this image, represented by a bounding box with a class score [ Fig. 1(b)]. Therefore, a complete defect detection task consists of two parts: defect classification, determining specific categories of defects, and defect localization, obtaining detailed regions of defects. For defect inspection on steel plates, the detection task has superior advantages to complicated defects, e.g., multiple defects [ Fig. 2(a)], multiclass defects [ Fig. 2(b)], and overlapping defects [ Fig. 2(c)]. The classification task can only find 0018-9456 © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See https://www.ieee.org/publications/rights/index.html for more information. The block is regarded as a detection region, which is a coarse box without refining. (b) Detectors based on DL mainly use regression methods to refine a predicting box. Through a large amount of iterative learning, the predicting box is gradually close to the groundtruth box. Finally, the refined box is regarded as the bounding box of the defect, which can represent the precise location information of the defect.
the defect with the highest category confidence in an image and not know the number of defects shown in Fig. 2(a), classes of defects shown in Fig. 2(b), and emerge of an overlapping defect shown in Fig. 2(c). However, for the follow-up quality assessment system, the quantity, category, and complexity of defects would be served as the chief indicators to evaluate the quality of a steel plate. It is apparent that defect detection can achieve a more comprehensive information reflection of a steel plate surface. The previous ADI methods have two common problems: the one is the unclear usage of hand-craft features [3]- [5]. The determination of features is too subjective, and thereby human experience usually plays a decisive role in it. The other problem is imprecise defect localization [ Fig. 3(a)]. Most methods only perform defect classification [6]- [8] or an incomplete defect detection. For example, some methods perform binary classification to find the regions of defects [9], [10] or only provide a coarse region of a defect [11], [12]. The recent developed deep learning (DL) technology can overcome the drawbacks of traditional ADI methods and have achieved significant results on many vision tasks. The DL can extract discriminative representations through a deep network [e.g., a convolution neural network (CNN)]. These representations can reach a high level of abstract and therefore have strong representation ability. The hand-craft features, by contrast, are merely the combination of low-level features [16]. Moreover, DL can train on location-annotated samples to obtain precise location information.
At present, some studies have already applied DL for ADI. However, most methods can only perform defect classification due to the lack of special data sets [18]- [21]. The defect classification seems to be oversimplify and unable to provide location information. Other methods use a combination of DL and traditional image processing to perform defect detection or segmentation [17]. These methods always use a DL classifier in parallel with a detector or a segmenter that based on traditional image processing. This way can eliminate the need for special training data sets but damage the end-to-end characteristic of DL system and lose the intelligence and generalization to some extent. Unlike the above-mentioned methods, we attempt to establish an endto-end defect detection system for ADI, which can provide a bounding box with a class score for precisely classifying and locating a defect [ Fig. 3(b)]. A DL-based segmenter like Mask R-CNN [13] seems to be better for showing the shape of a defect. However, this kind of segmenter will consume huge amounts of computation source, which cannot meet the real-time demand of industrial inspection. Furthermore, it is highly impracticable for the industry to build a large instancelevel defect segmentation data set, and thereby this kind of segmenter is almost impossible to apply. Therefore, it is the best tradeoff to perform defect detection for ADI at present. This paper mainly addresses three challenges. First, the detection system needs strong classification ability. The common classification problems such as interclass similarity, intraclass difference, and background interference are also present in ADI [9], [11]. Therefore, we equip a deep network ResNet into the system as the backbone [23]. As current research in transfer learning [15], the key to drive large networks is pretraining on ImageNet [22]. The detection system can gain strong classification power by training ResNet on enough data.
Second, the challenge of performing defect localization using CNN features in DL-based methods remains. As we known, the convolutional layers of CNN can be regarded as filters, which results in some location details will be gradually lost when an image flows in the CNN. Usually, DL-based methods perform localization based on the last convolutional feature map [14], [28], [34]. Our method is to fuse multiple feature maps. Because the feature maps exhibit diverse characteristics at each stage of CNNs: the shallow features have rich information but not discriminative enough, and the deep features are semantic robustly but lose too many details. In other fields [34], the Hypernet also uses more features but they are mainly selected from the latter part of the network. The proposed multilevel-feature fusion network (MFN) combines the multiple features covering all stages. We address the detection from the industrial perspective. Since gray images have less information than color images, the MFN must include lower level features that are discarded by HyperNet. Furthermore, the MFN uniforms the size of multiple features before fusion, which can not only save more details of images but also use less parameters of models.
Third, in defect detection, data annotation is expensive, because one has to draw a defect's bounding box and assign a class label to it. Recent progress in this field can be attributed to two factors: 1) ImageNet pretrained models and 2) large baseline CNNs, which made great progress in DL-based defect classification [18]- [20]. However, the limited data and expensive annotation still limit the development of defect detection. In this paper, we open a defect detection data set NEU-DET for fine-tuning models. When the DL models have finished training on a special data set, they can be used to perform the defect detection task.
This paper establishes an end-to-end ADI system, called defect detection network (DDN), in an attempt to overcome the above-mentioned challenges. The DDN 1) adopts a strong ResNet in defect classification; 2) proposes the MFN to assemble more location details; and 3) sets up a defect detection data set for fine-tuning and reports improvements on it. In more detail, first, we pretrain the ResNet on the ImageNet and fine-tune all the models on the NEU-DET. The MFN can fuse the selected features into a multilevel feature, which has characteristics covering all the stages of the ResNet. Next, a region proposal network (RPN) is adopted in proposals generation based on the multilevel features and then the DDN can output the class scores and the coordinates of bounding box. Finally, we evaluate the proposed method on NEU-DET and the results can demonstrate a clear superior to other ADI methods.
To summarize, the main contributions of this paper are as follows.
1) The introduction of the end-to-end defect detection pipeline DDN that integrates the ResNet and the RPN for precise defect classification and localization. 2) The proposed MFN for fusing multilevel features. Compared with other fusing methods, MFN can combine the lower level and higher level features, which makes multilevel features to have more comprehensive characteristics. 3) A defect detection data set NEU-DET for fine-tuning networks and a demonstration that the proposed DDN has a very competitive performance on this data set.
A. Defect Inspection
Generally, a defect classification method includes two parts: a feature extractor and a classifier. The classic feature extractor is to obtain hand-craft features such as HOG and LBP, and they are always followed by a classifier, e.g., SVM. Therefore, the combination of different feature extractors and classifiers produces a variety of defect classification methods. For instance, Song and Yan [3] improve the LBP to against noise and adopt NNC and SVM to classify defects. Ghorai et al. [9] is based on a small set of wavelet features and use SVM to perform defect classification. Different from above-mentioned two methods, Chu et al. [8] employ a general feature extractor and enhance SVM. From the perspective of computer vision, the defect classification task is essentially defect image classification, which is struggled in complicated defect images. To solve it, the simple and direct way is to perform defect localization before defect classification making the inspection task classify on regions of defects instead of a whole defect image, which is the defect detection task. For example, the defect detectors in [11] and [12] first perform a 0-1 classification to judge features whether belong to a defect class or a nondefect class, and then finds defect regions based on the boundary of defect-class features, finally perform different classification methods to determine the specific class of a defect. In addition, there is another simplified detector for the requirement of quick detection, which only focuses on regions of defects but regardless of the defects are in different categories [10].
However, the DL-based methods differ radically from the above methods. Hand-craft feature extractor locally analyses a single image and extract features. However, CNN is to construct the representation of all the input data through a large amount of learning. CNN has fine generalization and transferability so that there are some defect inspection methods based on CNN. For example, Chen and Ho [21] demonstrate that an object detector like Overfeat [24] can be transferred to be a defect detector by some means. Similar to [18] and [19], they demonstrate that using a sequential CNN to extract features can improve classification accuracy on defect inspection. Similarly, based on a sequential CNN, Ren et al. [17] perform an extra defect segmentation task on classification results to define the boundary of a defect. Moreover, Natarajan et al. [20] employ a deeper neural network VGG19 for defect classification. With the depth of CNN, the defect classification accuracy has been further improved.
B. Baseline Networks
There are three popular CNN architectures at present, which are used as baseline networks for pretraining. The early successful networks are based on the sequential pipeline architecture [25], which establish the basic structure of CNN and prove the importance of depth of networks. Subsequently, the inception networks employed modular units, which increase both the depth and width of a network without the increment of computational cost [26]. The third type is ResNet using residual blocks to make networks deeper without overfitting [23]. ResNet is widely applied in various vision tasks, achieving competitive results with a few parameters.
Choosing a proper baseline network is the key to gain good results for DL methods. A large network has strong represent-ability for input data hence the extracted features at high-abstract level, but there is a great demand for training data.
C. CNN Detectors
The CNN detectors aim to classify and locate each target with a bounding box. They are mainly divided into two methods: one is the region-based method and another is the direct regression method. The most famous region-based detectors are the "R-CNN family" [27], [28], [14]. In this framework, thousands of class-independent region proposals are employed for detection. Region-based methods are superior in precision but require slightly more computation. The representative direct regression methods are YOLO [29] and SSD [30]. They directly divide an image into small grids and then for each grid predict bounding boxes, which then regressed to the groundtruth boxes. The direct regression method is fast to detect but struggles in small instances.
III. DEFECT DETECTION NETWORK
In this section, the DDN is described in detail (see Fig. 4). A single-scale image of an arbitrary size is processed by a CNN, and the convolutional feature maps at each stage of the ConvNet are produced (ConvNet represents the convolutional part of a CNN). We extract multiple feature maps and then aggregate them in the same dimension by using a lightweight MFN. In this way, MFN features have the characteristics from several hierarchical levels of ConvNet. Next, RPN [14] is employed to generate region proposals Fig. 4. DDN. In a single pass, we extract features from each stage of the Baseline ConvNet, which then fused into a multilevel feature by MFN. RPN is adopted to generate ROIs based on the multilevel feature. For each ROI, the corresponding multilevel feature is transformed into a fixed-length feature through the ROI pooling and the GAP layers. Two fc layers process each fixed-length feature and feed into output layers producing two results: a one-of-(C + 1) defect class prediction (cls) and a refined bounding box coordinate (loc).
[regions of interest (ROIs)] over the MFN feature. Finally, the MFN feature corresponding to each ROI is transformed into a fixed-length feature through the ROI pooling [28] and the global average pooling (GAP) layers. The feature is fed into two fully connected (fc) layers. One is a one-of-(C + 1) defect classification layer ("cls") and the other is a bounding-box regression layer ("loc").
The rest of this section introduces the details of DDN and motivates why we need to design MFN into the network for the defect detection task.
A. Baseline ConvNet Architecture
As we know that pretraining on the ImageNet data set is important to achieve competitive performance, and then this pretrained model can be fine-tuned on a relatively small defect data set. In this paper, we select the recent successful baseline network ResNet as the backbone. ResNet presents several attractive advantages as follows.
1) ResNet can achieve the state-of-the-art precision with extremely few parameters, in comparison with the CNN of sequential pipeline architecture of the same magnitude (ResNet50 vs. VGG16, 0.85 M vs. 138 M parameters). It implies that ResNet has lower computational cost and less probability of overfitting. 2) ResNet uses GAP to process the final convolutional feature map instead of the dual stacked fc layers, which can be in a manner of preserving more comprehensive location information of defects in the image. 3) ResNet has a modularized ConvNet, which is easy to integrate. In this paper, we select ResNet34 and ResNet50 as baseline networks. The detailed structures of both networks are shown in Table I, and residual blocks are denoted as {R2, R3, R4, R5}.
B. Produce Multilevel Features
Previous excellent approaches only utilize high-level features to extract region proposals (like the faster R-CNN extract proposals upon the last convolutional feature maps). In order to obtain quality region proposals, single-level features should be extended to multilevel features. Obviously, the simplest way is to assemble feature maps from multiple layers [31]. Therefore, now comes the question, which layers should be combined? There are two essential conditions: nonadjacent, because adjacent layers have highly local correlation [32], and coverage, including features from low level to high level. For a ResNet, the most intuitive way is to combine the last layers in each residual block.
To fuse features at different levels, the proposed network MFN is appended on the pretrained model. MFN has four branches, denoted as {B2, B3, B4, B5}, and each branch is a small network. B2, B3, B4, and B5 are sequentially connected to the last layer of R2, R3, R4, and R5. When an image flows through the baseline ConvNet, the Ri features are produced in order. The Ri feature means the feature map output from the last layer of the residual block Ri , i = 2, . . . , 5. Similarly, the Bi feature is the feature map produced from the last layer of the MFN batch Bi , i = 2, . . . , 5. Then, each of Ri features is led to the corresponding branch in MFN producing Bi features. Finally, multilevel features are obtained via concatenating the B2, B3, B4, and B5 features, which come from different stages of a CNN.
As a final note, MFN is efficient in computation and strong in generalization. MFN can reduce required parameters via modifying the number of filters of 1 × 1 conv. This operation may hurt accuracy but prevent overfitting in the case of insufficient training data.
C. Extract Region Proposals
The RPN is employed to extract region proposals by sliding on the multilevel feature maps. RPN takes an image of arbitrary size as input and outputs anchor boxes (candidate boxes), each with a score representing whether it is a defect or not. The originality of RPN is the "anchor" scheme that makes anchor boxes in multiple scales and aspect ratios. Then, anchor boxes are hierarchically mapped to the input image so that region proposals of multiple scales and aspect ratios produced. As a result of the resolution size of MFN feature, the RPN can be considered as sliding on the R4 feature. Follow [14], we set three aspect ratios {1:1, 1:2, 2:1}. Considering multiple sizes of defects, we set four scales {64 2 , 128 2 , 256 2 , 512 2 }. Therefore, RPN produces 12 anchor boxes at each sliding location.
The region proposal extractor always ends with an ROI pooling layer. This layer performs a max-pooling operation over a feature map inside each ROI to convert it into a small feature vector (512-d for ResNet34 and 2048-d for ResNet50) with a fixed size of W × H (in this paper, 7 × 7). At last, based on these small cubes, calculate the offset of each region proposal with an adjacent groundtruth box and the probability whether there exist defects.
For a single image, RPN may extract thousands of region proposals. To deal with the redundant information, the greedy nonmaximum suppression (NMS) is often applied for eliminating high-overlap region proposals. We set the intersection over union (IOU) threshold for NMS at 0.7, which can discard a majority of region proposals. After NMS, the top-K ranked region proposals are selected from the rest. In the following, we fine-tune DDN using top-300 region proposals owing to the extracted quality region proposals, but reduce this number to accelerate the detection speed without harming accuracy at test-time.
IV. TRAINING
A. Multitask Loss Function
The defect detection task can be divided into two subtasks, hence DDN has two output layers. The cls layer outputs a discrete probability distribution, k = (k 1 , . . . , k C ), for each ROI over C + 1 categories (C defect categories plus one background category). As usual, k is computed by a softmax function. The cls loss L cls is a log loss over two classes (defect or not defect). L cls = − log(k, k * ) where k * is the groundtruth class. The loc layer outputs bounding box regression offsets, t = (t x , t y , t w , t h ), for each of the C defect categories. As in [28], the loc loss L loc is a smooth L1 loss function.
where t * is the groundtruth box associated with a positive sample. For bounding box regression, we adopt the parameterizations of t and t * given in [27] where the subscripts x, y, w, and h denote each box's center coordinates and its width and height. The variables x, x a , and x * separately represent the predicted box, anchor box, and groundtruth box (the same rules for y, w, and h).
With these definitions, we minimize a multitask loss function, which is defined as where λ is the weight parameter balancing both cls and loc terms. During training, we set λ = 2 indicating that DDN is devoted to achieving better defect locations. p * is the activation parameter of the loc term. The localization loss is involved in the subsequent calculation only for positive samples ( p * = 1) and is disabled otherwise ( p * = 0). We follow the "IOU" strategy in [14] to determine the positive and negative samples from anchors.
B. Joint Training
For pretrained network, MFN and RPN are new layers. Hence, we need to make these three networks share the common convolutional features through training. The pretrained model is essentially a classification network, and multilevel features generated from MFN can be directly fed into the cls layer. Therefore, the pretrained network and MFN can be merged into one network, and then performed an end-to-end training. Without RPN, the rest of DDN is a detector network. To share features with RPN, the four-step alternating training strategy in [14] is adopted, alternating between training RPN and training detector network. Combining these two strategies, we develop a practicable five-step joint training algorithm, which is shown in Algorithm 1.
After step 2 and step 3, RPN and the detector network are initialized with the ImageNet pretrained model in succession. However, these two networks have not shared the convolutional features at this point. They get it until the fine-tuning processes of step 3 and step 4 are finished. Specifically, we freeze the shared convolutional layers and only fine-tune the unshared layers. Finally, we combine two networks as a united network.
C. Implementation
For DDN, we adopt image-centric training strategy. Images are resized such that their short side is 600 pixels. We use stochastic gradient descen to train with a weight decay of 0.0001 and a momentum of 0.9. We take a single image per minibatch iteration. The minibatch size is 64 for detector network training (include MFN training) and 128 for RPN training. We fine-tune the model using a learning rate of 0.001 for 200k minibatch iterations and 0.0001 for another 100k minibatch iterations. We use "Xavier" initialization for all new layers [33]. To avoid overfitting, we also use several data augmentation methods such as rotation, reflection, and shift, but remove the dropout module.
V. EXPERIMENTS
The performance of DDN is evaluated on our defect data sets: NEU-CLS and NEU-DET. We demonstrate that DDN achieves a reasonable design and promising results.
A. NEU-DET Data Set
NEU surface defect 1 is a defect classification data set that we opened seven years ago [3]. There are six types of defects from hot-rolled steel plates, including crazing, inclusion, patches, pitted surface, rolled-in scales, and scratches. Each class has 300 images, but it does not mean that an image consists of a single defect. Examples of defect images are shown in Fig. 5.
To perform defect detection tasks, we provide annotations saved as XML files. With them, the classification data set is upgraded to a detection data set. The annotation marks the class and bounding box of each defect appearing in an image. Each bounding box is regarded as a groundtruth box, which is represented by its top left and bottom right coordinates. There are nearly 5000 groundtruth boxes in total. For simplicity, we call the original data set NEU-CLS, and the complemented data set NEU-DET. Examples of annotations are also shown in Fig. 5.
B. Defect Classification on NEU-CLS
As mentioned above, MFN can be merged into baseline CNNs for defect classification tasks. Therefore, we first report results on defect classification to demonstrate that our approach can achieve the competitive accuracy over other related methods, and merging MFN does not significantly affect the classification ability. Fig. 6 shows the defect classification results compared with other methods. According to Fig. 6, we can get the following conclusions.
1) The networks with MFN can perform well on defect classification so the multilevel features still have strongly semantical capability. 2) For ResNet34, MFN slightly harms the classification results. However, this influence is vanished for the deeper network ResNet50. It indicates that features extracted from deeper network are more distinctive hence the entire network becomes more robust. 3) With MFN, the ResNet34 obtains 99% of the accuracy of the ResNet50, which indicates that, in practice, a very deep network is not really required for defect classification task. As we know, stronger performance on defect classification should be positively correlated with stronger performance on defect detection. A good classification result is the prerequisite for subsequent defect detection experiments.
C. Defect Detection on NEU-DET
We carry out defect detection experiments on NEU-DET data set. Conventionally, we divide the NEU-DET into training set and test set, and fix the training/testing split. The training set containing 1260 images used for fine-tuning the network introduced in Section IV-B, and the test set containing 540 images. We compare DDN with faster R-CNN and Hyper-Net [34] on the test set and both methods use the same baseline network (VGG16 [40]) mentioned in their papers. In addition, DDN and faster R-CNN are also experimented on ResNet34/50 due to the similar proposals generator. Unlike defect classification, only accuracy is not an appropriate performance measure in case of defect detection. Therefore, we evaluate the results of detection experiments by average precision (AP), which is a good tradeoff between the two significant detection indexes: Precision and Recall. These indexes are defined as follows: where TP, FP, and FN represent the number of true positives, false positives, and false negatives, respectively. The mean AP (mAP) is also calculated to evaluate the overall performance, which is the mean value of the AP of all the classes. Table II HyperNet is also a detector based on the multiple features, but our method can extract higher quality region proposals, which will be discussed in Section VI in detail. The examples of detection results on NEU-DET are shown in Fig. 7.
Through the previous defect classification experiments, it is proven that MFN effects slightly on classification accuracy. Therefore, the improvement of mAP is benefited from the quality region proposals extracted from multilevel features. That means that MFN contributes to improve the localization accuracy. We specifically evaluate the performance of MFN in Section V-D.
D. Analysis on MFN
To verify MFN is able to improve the localization accuracy, we compare with several region proposal extractors, sliding window, Edge Boxes [35], and Selective Search [36]. In addition to these methods, RPN + MFN is also compared with the naive RPN (extract proposals based on single-level features). If the quality of proposals gets improved, the detector can use fewer proposals and stricter IOU thresholds without harming recall. Therefore, we evaluate recall on NEU-DET test set with different numbers of proposals and IOU thresholds. The number of proposals is the top-K ranked region proposals selected by these methods. IOU denotes a ratio between intersection and union of the predicted boxes and the groundtruth boxes. Fig. 8 shows the defect recall with various IOU thresholds at three different numbers of region proposals. The larger the IOU threshold, the more quality the selecting proposals. Unsurprisingly, the performance of the methods based on convolutional features is strongly higher than the methods without CNN [37]. When IOU > 0.7, the recall of naive RPN drops sharply compared with RPN + MFN. The naive RPN only extracts proposals from high-level features and some location information is filtered by the preceding Examples of detection results on NEU-DET. For each defect, the yellow box is the bounding box indicating its location and the green label is the class score. The subset to which the image belongs (a) crazing, (b) inclusion, (c) patches, (d) pitted surface, (e) rolled-in scale, and (f) scratches.
layers making the decline of proposals in quality. With the increasing number of proposals, the naive RPN drops more sharply when IOU > 0.7. This is because RPN extract too many low-quality proposals and it is more obvious with the increase of proposals. The naive RPN works badly with the strict IOU threshold (e.g., IOU > 0.7). MFN can help RPN to obtain location information from low-level and mid-level features, which makes RPN is under a higher tolerance for strict IOU threshold. Increasing the number of proposals can get a promising recall, but this will greatly increase the runtime of the detection [38], and what is worse, low-quality proposals would be involved in the process of detection, leading to failure of defect detection in some cases. Therefore, a good detector should select as few proposals as possible and meanwhile a relatively strict IOU threshold. Fig. 9 shows the defect recalls with various numbers of proposals at three different IOU thresholds. The naive RPN achieves a desirable recall with top-300 proposals, but RPN + MFN only needs top-100 proposals to get a similar performance.
As shown in Fig. 10, for RPN + MFN with ResNet34, we achieve 92% of the performance of selecting 300 proposals by selecting only 50 proposals, which reduces the run time by half. We consider selecting top-50 proposals as a good tradeoff in practical defect detection task.
VI. DISCUSSION
In this section, to demonstrate our design is logical and advanced, we discuss several implicit factors that can influence on defect detection.
A. Combine Which Layers for MFN?
MFN combines features from various levels into a multilevel feature, which is effective for improving detection. In Section III-B, it is briefly discussed that what kind of layers should be combined. In DDN, we select four layers that are the last layers of R1, R2, R3, and R4. Therefore, whether other combination manners of these four layers may result in better performance. Therefore, we train DDN + ResNet34 in five different combination manners on NEU-DET data set. As shown in Table III, combining all the four layers outperform the other manners. It indicates that the multilevel feature is effective for improving the accuracy of detection. Furthermore, low-level feature (e.g., R1 feature) should be paid more attention than high-level feature (e.g., R5 feature) for defect detection because R2 feature has richer location information than R5 feature.
B. Is the Simple Design More Effective for MFN?
The major role of MFN is to uniform the features from different levels in resolution and dimensionality. To keep the dimension consistent, a straightforward approach is using 1×1 conv to reduce/increase the dimensionality. There are two placement patterns for 1 × 1 conv: front-mounted and backmounted. The front-mounted pattern means that 1 × 1 conv is placed before concatenating multilevel feature. What we use in this paper is the front-mounted pattern, that is, a 1 × 1 conv is placed at the end of each branch of MFN, and the back-mounted pattern means that a 1 × 1 conv is placed after concatenating multilevel feature. This pattern seems simple but in fact needs more parameters. Similar to [34], we use multiple 5 × 5 convs to uniform the resolution and dimensionality simultaneously. However, the 5 × 5 conv is an expensive operation, which has the same effect as the double stacked 3 × 3 conv but requiring additional parameters. Table IV shows the comparable results among three patterns in detail. The front-mounted style uses three times fewer parameters than the back-mounted, and five times fewer than hyperstyle. Therefore, MFN in the front-mounted style has less possibility to be overfitting. Moreover, in case of the same resolution size, MFN features can preserve more complete information due to its larger dimensionality than Hyper feature's (512 vs. 126).
C. Do We Need More Defect Data?
As we known, an object detector can improve performance with more training data [39]. Therefore, whether this rule is also effective for industrial defect data? In order to make clear this problem, we train the DDN on not only the complete NEU-DET data set but also each subset separately. As shown in Fig. 11, for AP of each defect class, the performance of separate training is worse than the complete training in general. Specifically, the crazing, rolled-in scale, and scratches dropped sharply, whereas the inclusion, patches, and pitted surface present moderate decline. This may be due to the former requiring more data for learning than the latter. Although the total amount of training data is the same, results emerge dramatical difference. We consider that more training data can improve the represent ability of CNN for special instances. That is to say, if DDN can be trained on more detection data, the AP may also be improved. Finally, it is need to emphasize that other types of training data may be useless (e.g., common object) because the DDN is fine-tuned on the ImageNet pretrained model.
D. Failure Case Analysis
Though our method achieves promising results in general, in some cases, there is a poor performance for defect classes such as "crazing," "inclusion," "patches," and "rolled-in scale." Combining with the success cases shown in Fig. 7, we visu- alize some failure cases, as shown in Fig. 12, for analysis and attempt to explore the reasons for the unsatisfactory detection. We can observe that the DDN is robust to the continuous linear "crazing" defects but fails to find the discontinuous one in the lower right of Fig. 12(a). It means that the overdistinctive defect is hard to be correctly recognized, which, due to the defect data provided, is not comprehensive. It is also difficult to define the confusing defects, as shown in Fig. 12(b), and even the human eye cannot accurately distinguish them from the background. Two kinds of defects, the "inclusion" and "patches" as shown in Fig. 12(c), are overlapped and the "inclusion" gets a lower score. It is no doubt that the DDN has the ability to handle the overlapped defects and the success case is shown in Fig. 7(f). We guess the reason is that the "inclusion" and the "patches" in the figure are similar, and they influence each other when they are very close. For the "rolled-in scale," the bounding box may ignore some edge defects shown in Fig. 12(d) due to such defects that are too scattered to define their scope. A more ideal defect detector is yet wanted because there is still room for improvement.
VII. CONCLUSION
In this paper, the DDN, a defect inspection system for steel plates is proposed. This system is a DL network that can obtain the specific category and detailed location of a defect by fusing the multilevel features. For defect detection tasks, our system can provide detailed and valuable indicators for quality assessment system, such as the quantity, category, complexity, and area of a defect. Furthermore, we set up a precious defect detection data set-NEU-DET. Experiments show that DDN can achieve 99.67% accuracy for defect classification task and 82.3 mAP for defect detection task. In addition, the system can run at a detection speed of 20 ft/s while keeping the mAP at 70.
In the feature, we will focus on two directions as follows: the one is data augmentation technology due to the expensive manual annotations in detection data sets. The other is to perform the defect segmentation task with DL technologies, which can obtain a more precise defect boundary. | 8,654.8 | 2020-04-01T00:00:00.000 | [
"Computer Science"
] |
Stereoselective Synthesis and Application of Gibberellic Acid-Derived Aminodiols
A series of gibberellic acid-based aminodiols was designed and synthesized from commercially available gibberellic acid. Exposure of gibberellic acid to hydrochloric acid under reflux conditions resulted in aromatization followed by rearrangement to form allo-gibberic acid. The key intermediate, ethyl allo-gibberate, was prepared according to literature methods. Epoxidation of key intermediate and subsequent ring-opening of the corresponding epoxide with different nucleophiles resulted in N-substituted aminodiols. The regioselective ring closure of N-benzyl-substituted aminodiol with formaldehyde was also investigated. All aminodiol derivatives were well characterized using modern spectroscopic techniques and evaluated for their antiproliferative activity against a panel of human cancer cell lines. In addition, structure–activity relationships were examined by assessing substituent effects on the aminodiol systems. The results indicated that aminodiols containing aromatic rings on their nitrogen substituents displayed significant cytotoxic effects. Among these agents, N-naphthylmethyl-substituted aminodiols were found to be the most potent candidates in this series. One of these molecules exhibited a modest cancer selectivity determined by non-cancerous fibroblast cells. A docking study was also made to exploit the observed results.
Introduction
Cancer, characterized by uncontrolled growth and spread of abnormal cells, is the most feared disease second only to heart disease as a leading cause of death all over the world [1]. Therefore, the development of anticancer agents is the major focus for scientists across the world. Over the past few decades, extensive research has led to the development of a plethora of chemotherapeutic agents [2,3]. However, the limitations of current anticancer drugs, increased incidence, and rapid development of drug resistance have highlighted the need for the discovery of new anticancer agents [4], preferably with novel mechanisms of action. Natural products represent an attractive source of biologically active agents, since they may have different mechanisms compared to those of conventional drugs and could be of clinical importance in health care improvement [5]. These efforts have led to the discovery of various important clinical drugs, such as anticancer agents (e.g., taxol and doxorubicin), immunosuppressants (e.g., cyclosporine and doxorubicin), antimalarial agents (e.g., quinine and artemisinin), and lipid-level regulating drugs (e.g., lovastatin and relatives) [6]. Even today, natural products still serve as a fundamental source of diverse biological functions, facilitating the development of chemical biology and drug discovery [7,8].
Gibberellins, a large class of tetracyclic diterpenoid carboxylic acids, regulate several physiological processes throughout the whole plant life cycle [9]. Gibberellic acid (GA3), one of these gibberellins, is industrially produced by liquid cultivation of the ascomycetous fungus Gibberella fujikuroi [10]. GA3 is considered an essential hormone for plant growth [11,12], affecting seed germination, stem elongation, leaf area expansion, and maturation of plant sexual organs, as well as reducing the time to flowering [13][14][15]. Therefore, the plant hormone GA3 is widely used to increase the number and weight of fruits, induce organ differentiation, promote shoot elongation, and break seed dormancy in agricultural industries [16,17]. Gibberellic acid formed complex with Terbium could reduce impairment functions in liver and kidney tissues through scavenging against free radicals and antioxidant properties [18]. However, Gibberellic acid has lost the ability to scavenge reactive oxygen that lead to damage in rat tissue's antioxidative system reasoning in cell death [19][20][21]. The carcinogenic effect and tumor formation of gibberellic acid have been documented after treatment of mice for 22 months [22,23]. Furthermore, GA3 could prevent testicular cell function in rats through loss of germ cells, derangement of the germinal cells, and reduction in the size of the seminiferous tubules and dystrophy of Leydig cells [24,25].
Besides itself pharmacological interest of Gibberellic acid, a series of Gibberellin derivatives bearing two α,β-unsaturated ketone units showed strong anticancer activities toward a number of human cancer cell lines including HT29, A549, HepG2, and MKN28 [26]. Furthermore, allo-gibberic acid derived with saturated linear amide or with meta-substituted benzyl ester functionalities could inhibit FGFR 1 activation and KDR activation [27]. In addition, GA3-based amides also reduced cellular uptake of free cholesterol in prostate cancer cells, suggesting a novel role of gibberellic acid derivatives in deregulating cholesterol metabolism [28]. Moreover, recent studies have also shown that some aminoalcohols derived from gibberellic acid exhibit considerable potential against a diverse panel of multidrug-resistant Gram-negative pathogens [29]. Stimulation by this result and continuation of our interest in structural modification of natural products for the development of anticancer agents have led us to the field of diterpene-based aminoalcohols and aminodiols [30,31]. Herein, we report the synthesis of new gibberellic acid-based 3-amino-1,2-diol derivatives and their in vitro antiproliferative evaluation against different human cancer cell lines. A docking-model study was also carried out for the most potent analog.
Preparation of Epoxyalcohol 3 Based on Allo-Gibberic Acid
The key intermediate, allo-gibberic acid 1, was prepared from commercially available gibberellic acid according to literature methods [27,32]. The esterification of 1 was successfully performed by using ethyl iodide in the presence of a stoichiometric amount of tetrabutylammonium fluoride (Bu 4 NF) as the base resulting in ethyl ester 2. The utility of TBAF, a cheap, non-toxic, air-stable eco-safe organocatalyst [33], plays two important roles in this esterification. First, the F − anion derived from TBAF serves as an effective base for deprotonation of the carboxylic acid; second, the resulting Bu 4 N + carboxylates are partially soluble in organic media and therefore the reaction of carboxylates with alkyl halides via the S N 2 mechanism would be accelerated [34]. Furthermore, since the cesium ion is well known for its key properties, such as solubility in different organic solvents, high reactivity and large ionic radius [35], O-alkylation of 2 mediated by cesium carbonate (Cs 2 CO 3 ) was efficiently carried out under mild conditions to give the corresponding ester 2 on a gram scale [36]. The esterification process applying C 2 H 5 I as reactant and Cs 2 CO 3 was completed at ambient temperatures and delivered the desired ester smoothly and exclusively in high yield [37]. Epoxidation of the terminal alkene group in 2 with m-CPBA furnished cis-13,16-epoxy alcohol 3 in a stereospecific reaction [30]. The highly stereoselective formation of 3 was explained by hydrogen bonding between the electrophilic peracid oxygen and the olefin in the transition state [38] (Scheme 1).
Synthesis of Allo-Gibberic Acid-Based Aminodiol Derivatives
Since our earlier results demonstrated that substituents at the nitrogen of aminodiols exerted a definite influence on the efficiency of their antiproliferative activity [30], aminodiol library 4-23 was prepared by aminolysis of 3 with different primary and secondary amines in the presence of LiClO4 as catalyst (Scheme 2, Table 1
Synthesis of Allo-Gibberic Acid-Based Aminodiol Derivatives
Since our earlier results demonstrated that substituents at the nitrogen of aminodiols exerted a definite influence on the efficiency of their antiproliferative activity [30], aminodiol library 4-23 was prepared by aminolysis of 3 with different primary and secondary amines in the presence of LiClO 4 as catalyst (Scheme 2, Table 1) [30]. LiClO4 shows enhanced reactivity for the ring-opening of epoxides through the coordination of Li + with the epoxide oxygen, rendering the epoxide more susceptible to nucleophilic attack by amines and, therefore, dramatically reducing reaction times and improving yields [39]. Although ClO4 − can be served as oxidative reagent, there is no oxidation under these condition (NMR determination) [39].
Synthesis of Azole Derivatives Based on Allo-Gibberic Acid
As azoles are known to be endowed with a variety of biological activities [41], we have tried to perform the azole-mediated ring-opening of 3 with a variety of azoles (Table 2). Likewise amines, the oxirane ring could only be opened in the presence of K2CO3 owing to the lower reactivity of N-containing heterocycles. A possible reaction pathway through K2CO3-promoted azole nucleophilicity and subsequent nucleophilic addition to epoxide 3 afforded derivatives 26-30 [42]. The reactions were completely clean, furnishing azole-based aminodiol adducts with moderate to satisfactory yields (45-75%) (Scheme 4, Table 2). Nowadays, CuAAC reaction (copper-catalyzed azide-alkyne cycloaddition) has become the main approach to access 1,2,3-triazoles with high regioselectivity [43]. In order to expand the family of allo-gibberic acid-based azole scaffolds, oxirane 3 was subjected to ring-opening reaction using propargyl amine in acetonitrile under reflux conditions and subsequent 1,3-dipolar cycloaddition reaction [30]. This method is typically called Huisgen cycloaddition [44]. In our case, the reaction of terminal acetylene bearing N-propargyl-substituted aminodiol with benzyl azide under Sharpless click chemistry condi-
Synthesis of Azole Derivatives Based on Allo-Gibberic Acid
As azoles are known to be endowed with a variety of biological activities [41], we have tried to perform the azole-mediated ring-opening of 3 with a variety of azoles (Table 2). Likewise amines, the oxirane ring could only be opened in the presence of K 2 CO 3 owing to the lower reactivity of N-containing heterocycles. A possible reaction pathway through K 2 CO 3 -promoted azole nucleophilicity and subsequent nucleophilic addition to epoxide 3 afforded derivatives 26-30 [42]. The reactions were completely clean, furnishing azolebased aminodiol adducts with moderate to satisfactory yields (45-75%) (Scheme 4, Table 2). tions (CuSO4·5H2O and sodium ascorbate in t-BuOH/H2O (2:1)) afforded 1,4-disubstituted-1,2,3-triazole 31 in a regioselective manner in satisfactory yield [30]. On the other hand, various triazole derivatives of allo-gibberic acid were synthesized through azidegenerated epoxide 3 and NaN3 followed by Cu(I)-catalyzed alkyne−azide [3 + 2]
Isomerization of the Ester Group
Our previous work demonstrated that the configuration of the ester group has a significant effect on biological activity [45]. Therefore, to explore the role of the configuration of the carboxyl group, isomerization of ester 2 at the carboxyl function was carried out under alkaline conditions, resulting in ester 33 with (S)-configuration in excellent yield similar to literature results [46,47]. The missing NOE effect between the H-6 on the 5membered ring and the proton at 8 position proves that the isomerization took place only at the carboxylic group ( Figure 1). This rapid and quantitative isomerization allowed the gram-scale synthesis of ester 33. Subsequently, ester 33 underwent similar reactions including epoxidation, then amine-mediated ring-opening of the corresponding epoxide to afford aminodiols 35-38 in moderate yields (Scheme 5, Table 3). Nowadays, CuAAC reaction (copper-catalyzed azide-alkyne cycloaddition) has become the main approach to access 1,2,3-triazoles with high regioselectivity [43]. In order to expand the family of allo-gibberic acid-based azole scaffolds, oxirane 3 was subjected to ring-opening reaction using propargyl amine in acetonitrile under reflux conditions and subsequent 1,3-dipolar cycloaddition reaction [30]. This method is typically called Huisgen cycloaddition [44]. In our case, the reaction of terminal acetylene bearing Npropargyl-substituted aminodiol with benzyl azide under Sharpless click chemistry conditions (CuSO 4 ·5H 2 O and sodium ascorbate in t-BuOH/H 2 O (2:1)) afforded 1,4-disubstituted-1,2,3-triazole 31 in a regioselective manner in satisfactory yield [30]. On the other hand, various triazole derivatives of allo-gibberic acid were synthesized through azide-generated epoxide 3 and NaN 3 followed by Cu(I)-catalyzed alkyne−azide [3 + 2] cycloaddition of the corresponding azide with phenylacetylene to produce target compound 32 in good yield (Scheme 4) [30].
Isomerization of the Ester Group
Our previous work demonstrated that the configuration of the ester group has a significant effect on biological activity [45]. Therefore, to explore the role of the configuration of the carboxyl group, isomerization of ester 2 at the carboxyl function was carried out under alkaline conditions, resulting in ester 33 with (S)-configuration in excellent yield similar to literature results [46,47]. The missing NOE effect between the H-6 on the 5-membered ring and the proton at 8 position proves that the isomerization took place only at the carboxylic group ( Figure 1). This rapid and quantitative isomerization allowed the gram-scale synthesis of ester 33. Subsequently, ester 33 underwent similar reactions including epoxidation, then amine-mediated ring-opening of the corresponding epoxide to afford aminodiols 35-38 in moderate yields (Scheme 5, Table 3
Determination of Relative Configuration of Allo-Gibberic Acid Derivatives
The relative stereochemistry of aminodiols 35-38 was proven through NOESY examinations. Significant NOE signals were found between the H-8 and H-15 together with H- under alkaline conditions, resulting in ester 33 with (S)-configuration in excellent yield similar to literature results [46,47]. The missing NOE effect between the H-6 on the 5membered ring and the proton at 8 position proves that the isomerization took place only at the carboxylic group ( Figure 1). This rapid and quantitative isomerization allowed the gram-scale synthesis of ester 33. Subsequently, ester 33 underwent similar reactions including epoxidation, then amine-mediated ring-opening of the corresponding epoxide to afford aminodiols 35-38 in moderate yields (Scheme 5, Table 3).
Determination of Relative Configuration of Allo-Gibberic Acid Derivatives
The relative stereochemistry of aminodiols 35-38 was proven through NOESY examinations. Significant NOE signals were found between the H-8 and H-15 together with H-15 and H-17, OH-16 and OH-13, as well as between OH-16 and H-14 protons ( Figure 1).
The relative configuration of compounds 4-30 was determined through NOESY experiments. Clear NOE signals were observed between OH-13 and OH-16, as well as between H-14 and OH-16 together with H-15 and H-17. Thus, the structure of aminodiols derived from allo-gibberic acid was determined as outlined in Figure 2.
Determination of Relative Configuration of Allo-Gibberic Acid Derivatives
The relative stereochemistry of aminodiols 35-38 was proven through NOESY examinations. Significant NOE signals were found between the H-8 and H-15 together with H-15 and H-17, OH-16 and OH-13, as well as between OH-16 and H-14 protons ( Figure 1).
The relative configuration of compounds 4-30 was determined through NOESY experiments. Clear NOE signals were observed between OH-13 and OH-16, as well as between H-14 and OH-16 together with H-15 and H-17. Thus, the structure of aminodiols derived from allo-gibberic acid was determined as outlined in Figure 2.
Since neither aminolysis of parent oxirane 3 in alkaline condition nor the hydrogenolysis of N-benzyl analog 4 affected the absolute configuration, the relative configuration of the chiral centers of 4-25 and 26-30 is known to be the same as that of epoxide 3.
In Vitro Antiproliferative Studies of Gibberellic Acid-Based Aminodiols
The in vitro antiproliferative activities of the synthesized aminodiols 4-38 against a panel of different human cancer cell lines of gynecological origin, including cervical (SiHA and HeLa), breast (MCF7 and MDA-MB-231), and ovary (A2780) cancers were assayed by the MTT method [48]. Moreover, the most active molecules (13-15) were additionally tested using non-cancerous fibroblast cells to obtain data concerning their cancer selectivity. Cisplatin, a clinically applied anticancer agent, was used as a reference compound and Since neither aminolysis of parent oxirane 3 in alkaline condition nor the hydrogenolysis of N-benzyl analog 4 affected the absolute configuration, the relative configuration of the chiral centers of 4-25 and 26-30 is known to be the same as that of epoxide 3.
In Vitro Antiproliferative Studies of Gibberellic Acid-Based Aminodiols
The in vitro antiproliferative activities of the synthesized aminodiols 4-38 against a panel of different human cancer cell lines of gynecological origin, including cervical (SiHA and HeLa), breast (MCF7 and MDA-MB-231), and ovary (A2780) cancers were assayed by the MTT method [48]. Moreover, the most active molecules (13)(14)(15) were additionally tested using non-cancerous fibroblast cells to obtain data concerning their cancer selectivity. Cisplatin, a clinically applied anticancer agent, was used as a reference compound and the results are summarized in Figure 3 and Table S1 in Supporting Information. The obtained results indicated that N-benzyl-substituted aminodiols exhibit considerable cancer cell growth-inhibiting capacities. Among them, N-naphthylethyl-substituted aminodiol derivatives showed the most pronounced antiproliferative activities comparable to those of reference agent cisplatin. One of these agents, (13) exhibited a modest cancer selectivity with a higher calculated IC 50 value on NIH/3T3 fibroblast cells (10.88 µM) than on the malignant cell lines (4.38-7.49 µM). Compounds 12 and 14 inhibited the growth of cancer cells and fibroblasts in the same concentration range. On the other hand, none of the prepared azole derivatives exerted relevant activity.
In Vitro Antioxidant Activity Studies of Gibberellic Acid-Based Aminodiols
Since oxidative stress and free radicals are generally regarded as crucial factors of carcinogenesis, antioxidants and free-radical scavengers can be considered to be useful agents for preventive or therapeutic intervention [49]. Moreover, a substantial part of natural products and their derivatives exert antioxidant or scavenging activity, this can be a relevant component of the bioactivity of the presented diterpene analogs. As a consequence, in vitro antioxidant activities of selected N-aliphaticand N-aryl-substituted aminodiols were determined by 1,1-diphenyl-2-picrylhydrazyl (DPPH) assay. In order to obtain results concerning the relationship between the potential antioxidant properties and the antiproliferative actions of the tested molecules, three potent (12,13,14) and three substantially less active analogs (16,25,30) were tested. None of the six molecules elicited considerable activity in the applied concentration range (3-100 µM). In the same range, the reference agent Trolox exerted a pronounced scavenging activity with a calculated IC 50 value of 20.2 µM (see relevant data in Figure S1, Supporting Information).
Molecular Docking
Protein kinases are enzymes that function as components of signal transduction pathways, playing a central role in diverse biological processes, such as control of cell growth, metabolism, differentiation, and apoptosis [50]. Therefore, they have become an important target of many types of cancer cells and numerous new inhibitors targeting these enzymes have been developed as anticancer drugs [51]. The recent report highlighted the significant inhibitory activity of GA 3 derivatives against RPTK (Receptor protein-Tyrosine Kinase) enzymes [27]. Besides that, many ent-kaurene type tetracyclic diterpenes, such as amethystoidin A [52], oridonin, and ponicidin [53], might possibly inhibit PSTK (Receptor serine/threonine kinases) activation. In order to identify whether the antiproliferative activity of prepared allo-gibberic acid derivatives was related to the activation and expression of RPTK or RSTK receptor, a docking study was employed to predict the possible target of the bioactive compounds (12, 13, and 14). To reach this goal, a variety of protein kinases, such as serine/threonine kinase (Pim-1, AKT and RAFI) and tyrosine kinases (MAP and ALK), were used as templates for the docking study (Table S2 in the supplementary file). The obtained results indicated that these compounds could have a high affinity toward Anaplastic lymphoma kinase (ALK) by forming strong bonds with the hinge region and the ATP binding site. The CDocker energy of the tested compounds varied between −43.4401 and −46.6684. Figure 4 shows the complexes of compounds 12, 13, and 14 with the ALK ATP binding site (PDB code: 3AOX, resolution: 1.75 Å) [54]. The docking results of the three studied compounds show the importance of the aminodiol function in forming hydrogen bonding and ionic interactions with the key amino acids. The results of in-silico ADMET study showed that all tested compounds might have good absorption properties with moderate ability to penetrate the BBB.
the results are summarized in Figure 3 and Table S1 in Supporting Information. The obtained results indicated that N-benzyl-substituted aminodiols exhibit considerable cancer cell growth-inhibiting capacities. Among them, N-naphthylethyl-substituted aminodiol derivatives showed the most pronounced antiproliferative activities comparable to those of reference agent cisplatin. One of these agents, (13) exhibited a modest cancer selectivity with a higher calculated IC50 value on NIH/3T3 fibroblast cells (10.88 μM) than on the malignant cell lines (4.38-7.49 μM). Compounds 12 and 14 inhibited the growth of cancer cells and fibroblasts in the same concentration range. On the other hand, none of the prepared azole derivatives exerted relevant activity.
In Vitro Antioxidant Activity Studies of Gibberellic Acid-Based Aminodiols
Since oxidative stress and free radicals are generally regarded as crucial factors of carcinogenesis, antioxidants and free-radical scavengers can be considered to be useful Figure 4 shows the complexes of compounds 12, 13, and 14 with the ALK ATP binding site (PDB code: 3AOX, resolution: 1.75 Å) [54]. The docking results of the three studied compounds show the importance of the aminodiol function in forming hydrogen bonding and ionic interactions with the key amino acids. The results of in-silico ADMET study showed that all tested compounds might have good absorption properties with moderate ability to penetrate the BBB.
Discussion
Based on results acquired by the antiproliferative assay, the structure-activity relationship (SAR) was built up as follows.
The N-benzyl-substituted aminodiol showed moderate antiproliferative activity (approximately 30% at 10 µM). Either debenzylation or ring closure drastically reduced the potency. Moreover, the introduction of an alkyl group to the (α) position of the benzyl group showed almost no significant change in the activity regardless of the stereochemistry or length of the introduced alkyl group. Similarly, replacement of the benzyl substituent by N,N-dibenzyl or aliphatic groups eliminated the activity of the resultant compounds, suggesting the importance of the secondary amine moiety as a hydrogen bond donator (HBD).
Substituted N-benzyl derivatives with electron-withdrawing substituents (for example, fluorine) exerted a moderate increase in activity, while the electron-donating (methoxy) showed a similar effect against the tested cancer cell lines. The combination of (R)-(α)methyl group and fluorine as aromatic substituent at the para position failed to show any remarkable antiproliferative activity.
The 1-or 2-Naphthyl-substituted aminodiols showed enhanced activity against all studied cell lines. The introduction of either (R) or (S) methyl group at the (α) position exerted a very potent improvement on activity against all tested cancer cell lines with an IC 50 value as low as 4-7 µM, demonstrating the crucial role of the methyl group at (α) position for the design and synthesis of novel antiproliferative agents.
Considering the effect of the stereochemistry of the carboxyl group on antiproliferative activity, aminodiols with R configuration were found to be more effective compared to their corresponding isomers.
General Methods
Commercially available compounds were used as obtained from suppliers (Molar Chemicals Ltd., Halásztelek, Hungary; Merck Ltd., Budapest, Hungary, and VWR International Ltd., Debrecen, Hungary), while solvents were dried according to standard procedures. Optical rotations were measured in MeOH at 20 • C, with a Perkin-Elmer 341 polarimeter (PerkinElmer Inc., Shelton, CT, USA). Chromatographic separations and monitoring of reactions were carried out on Merck Kieselgel 60 (Merck Ltd., Budapest, Hungary). HR-MS flow injection analysis was performed with a Thermo Scientific Q Exactive Plus hybrid quadrupole-Orbitrap (Thermo Fisher Scientific, Waltham, MA, USA) mass spectrometer coupled to a Waters Acquity I-Class UPLC™ (Waters, Manchester, UK). Melting points were determined on a Kofler apparatus (Nagema, Dresden, Germany) and are uncorrected. 1 H-and 13 C JMOD NMR spectra were recorded on Brucker Avance DRX 500 spectrometer (Bruker Biospin, Karlsruhe, Baden Württemberg, Germany) [500 MHz ( 1 H) and 125 MHz ( 13 C), δ = 0 (TMS)]. Chemical shifts are expressed in ppm (δ) relative to TMS as the internal reference. J values are given by Hz. For 13 C JMOD NMR spectra, quaternary carbon, carbonyl, and methylene signals have opposite phase to those of methine and methyl resonances. 1 H, 13 C JMOD, COSY, HSQC, HMBC, and NOESY NMR spectra of new compounds are available in the Supplementary Materials (Figures S2-S95).
Ethyl (2R,4b S,7 S,9a R,10 R)-7 -hydroxy- After stirring for 4 h at room temperature, the mixture was evaporated. The crude product was then diluted with water (40 mL) and extracted by DCM (3 × 50 mL). The organic phase was washed with brine, dried over sodium sulfate, and then evaporated under reduced pressure. The crude product was purified by column chromatography on silica gel (n-hexane: EtOAc = 2:1) to afford ester 2 as white crystals (92%).
General Procedure for Epoxidation
To the solution of 2 or 33 (2 g, 6.4 mmoL) in dry CH 2 Cl 2 (100 mL), m-CPBA (3.95 g, 16 mmol, 2.5 equ., 70% purity) was added. After stirring for 2 h in dark at room temperature (indicated by TLC), the mixture was washed with a saturated solution of NaHCO 3 (3 × 100 mL). The organic phase was then dried over Na 2 SO 4 , filtered, and evaporated. The crude product was purified by column chromatography (CHCl 3 : MeOH = 19:1) and subsequently recrystallized in an n-hexane: Et 2 O mixture. added in 2 different concentrations (10 µM and 30 µM) and incubated for another 72 h under cell-culturing conditions. Then, 20 µL of 5 mg/mL MTT solution was added to each well and incubated for a further 4 h. The medium was removed, and the precipitated formazan crystals were dissolved in DMSO during 60 min of shaking at 37 • C. As the final step, the absorbance was measured at 545 nm by using a microplate reader (SPECTROStar Nano, BMG Labtech, Offenburg, Germany). Untreated cells were included as controls. In case of the most effective compounds (i.e., compounds eliciting higher than 50 or 85% at 10 or 30 µM, respectively), the assays were repeated with a set of dilutions (0.1-30.0 µM) to determine the IC 50 values. These agents were additionally tested against NIH/3T3 fibroblasts to obtain results about their cancer selectivity. Two independent experiments were performed with five wells for each condition. Cisplatin (Ebewe GmbH, Unterach, Austria), a clinically used anticancer agent, was used as a positive control. Calculations were performed utilizing the GraphPad Prism 5.01 software (GraphPad Software Inc., San Diego, CA, USA).
Determination of Antioxidant Effects by Free Radical Scavenging (DPPH Assay)
The antioxidant effects of the aminodiol derivatives were tested on 1,1-diphenyl-2picrylhydrazyl (DPPH) radicals according to Brand-Williams (1995) [55] and Sánchez-Moreno (2002) [56], with some modifications. A serial dilution of the tested compounds was made in absolute methanol and DPPH solution was added to each concentration in order to have a 0.1 mM concentration DPPH in each well of a 96-well plate. After a 30 min incubation period at room temperature (25 • C) the absorbances were measured at 517 nm by a microplate reader (SPECTROStar Nano, BMG Labtech, Offenburg, Germany). Trolox (3,4-Dihydro-6-hydroxy-2,5,7,8-tetramethyl-2H-1-benzopyran-2-carboxylic acid) was used as a positive control. All measurements were performed in duplicate with 5 parallels.
Docking Study
Anaplastic lymphoma kinase (ALK) crystal structure was obtained from PDB (protein data bank). ChemBioDraw Ultra 11.0 was used to draw the tested structures for the docking study. Docking study and in-Silico ADMET prediction were performed by Accelrys discovery studio 2.5 software.
Preparation of the Crystal Structure of ALK
It is well known that the extracted crystal structure from PDB does not have hydrogen atoms, so hydrogen atoms must first be added by applying several force fields (CHARMm). Adding hydrogen atoms leads to steric hindrance and subsequently to a high-energy and unstable molecule, which should be minimized. Minimization of the complex energy was performed by using adopted basis minimization, aiming at finding the most stable structure with the least energy and reducing H-H interactions without affecting the basic protein skeleton atoms. Then, the active site was determined and 10 Å radius sphere surrounded [57].
Docking Study (CDocker)
By using the CDocker method, all possible conformations of the compound in the protein active site could be generated. Then, the results can be evaluated by both the CDocker energy and the number of interactions between the ligand and the active site. This method requires preparing the crystal structure (as mentioned before) and preparing the designed compound by using Accelrys Discovery Studio protocol and applying a force field.
Before starting this study, it is important to emphasize that the method used here is valid by comparing the conformation of the reference compound with its conformations generated by the applied docking method, where RMSD (Root Mean Square Deviation) should not exceed 2 Å (Plot of Polar Surface Area (PSA) vs. LogP is given in Supplementary Materials Figure S96).
In-Silico ADMET Analysis
ADMET properties of compounds 12, 13, and 14 were predicted by using ADMET descriptors in Accelrys Discovery studio 2.5. There are six mathematical models used to quantitatively predict properties of a set of compounds. These models contain: aqueous solubility (predict solubility in water at 25 • C, blood-brain barrier (BBB) penetration, cytochrome P450 (CYP450) 2D6 inhibition, human intestinal absorption (HIA), and plasma protein binding (PPB) [58]. An ADMET model was also generated to predict the human intestinal absorption (HIA) and blood-brain barrier (BBB) penetration of tested compounds. The model includes 95 and 99% confidence ellipses in the ADMET_PSA_2D and ADMET_ALogP98 plan. Table S2 containing in silico ADMET properties is given in Supplementary Materials Table S3.
Conclusions
In summary, starting from commercially available gibberellic acid, a new family of gibberellic acid-derived 3-amino-1,2-diols was designed and synthesized.
The resulting N-naphthylmethyl-substituted aminodiols exert marked antiproliferative action on a panel of human cancer cell lines. The in vitro pharmacological studies have clearly shown that the N-naphthylmethyl substituent on the aminodiol system seems to be essential for reliable antiproliferative activity.
Finally, molecular docking results exemplified that aminodiols 12, 13, and 14 could foster potent affinity by forming significant hydrogen and hydrophobic interactions with ALKwt (PDB ID code: 3AOX). Hence, N-naphthylmethyl-substituted aminodiols can be regarded as new potential drug candidates and further studies concerning molecular dynamics will be performed and reported in the future.
Literature revealed that allo-gibberic acid derivatives containing saturated linear amides or substituted benzyl esters showed strong anticancer activities in MTT assay toward a number of human cancer cell lines [27]. Therefore, in the next stage of our project, the modification of carbonyl group in N-naphthylmethyl-substituted aminodiols was performed to improve their antiproliferative activities on a panel of different cancer cell lines. For the optimized derivatives, additionally, docking studies and a molecular dynamics study will also be performed to gain insight into the dynamics of ligand interaction. | 6,743.8 | 2022-09-01T00:00:00.000 | [
"Chemistry"
] |
Universal detection of foot and mouth disease virus based on the conserved VP0 protein
: Foot and mouth disease virus (FMDV), a member of the Background picornaviridae that causes vesicular disease in ungulates, has seven serotypes and a large number of strains, making universal detection challenging. The mature virion is made up of 4 structural proteins, virus protein (VP) 1 – VP4, VP1-VP3 of which form the outer surface of the particle and VP4 largely contained within. Prior to mature virion formation VP2 and VP4 occur together as VP0, a structural component of the pre-capsid which, as a result of containing the internal VP4 sequence, is relatively conserved among all strains and serotypes. Detection of VP0 might therefore represent a universal virus marker. : FMDV virus protein 0 (VP0) was expressed in bacteria as a SUMO Methods fusion protein and the SUMO carrier removed by site specific proteolysis. Rabbit polyvalent sera were generated to the isolated VP0 protein and their reactivity characterised by a number of immunoassays and by epitope mapping on peptide arrays. : The specific VP0 serum recognised a variety of FMDV serotypes, as Results virus and as virus-like-particles, by a variety of assay formats. Epitope mapping showed the predominant epitopes to occur within the unstructured Loureiro and co-workers describe the expression of FMDV strain O1 Manisa Tur/69 protein VP0 ('uncleaved' VP4/VP2) as a His-tagged SUMO fusion protein in a bacterial expression system: Following purification using the His-tag , the SUMO fusion partner was removed by the SUMO-specific proteinase: the purified VP0 was then used to raise (rabbit) anti-VP0 antibodies. These polyclonal antibodies were then tested for cross-reactivity against proteins from other FMDV serotypes. I do not think the title (as it stands) is justified by the data presented in Figure 2, panels A and B (could data from naive Sf9 cells be included here?). 'Universal' is a reach. Naturally, not every FMDV serotype/strain needs to be tested, but more 'coverage' would give more confidence. On this point, could some indication as to the degree of conservation (across all FMDVs) of each amino acid shown in Figure 3 Panel B be given? These data are readily available..The structural analyses and discussion of the particle structure ('breathing') was very informative. This study aims to test the hypothesis that antisera raised against VP0 from one strain of FMDV (O1M) may serve as a detection reagent for all strains of the virus. The hypothesis is predicated on the assumption that the VP4 polypeptide segment within VP0 is relatively conserved between FMDV serotypes. The paper describes the generation of a bacterial expression vector for a his-SUMO-tagged VP0 protein, the use of this protein to generate antisera in rabbits, and characterisation of the antisera against a selected range of antigens. Loureiro et al. describe the reactivity of a rabbit serum preparation from animals injected by bacterially expressed and purified VP0 protein from foot-and-mouth disease virus (FMDV). The authors show cross reactivity with a number of FMDV serotypes but the serum is non neutralising. From epitope mapping and transmission electron microscopy analysis using gold labelled antibodies the authors suggest that the region of VP0 recognised by the serum is only exposed some of the time in virus like particles and that this may reflect 'breathing' of the particles as described for other picornaviruses but not FMDV. Overall the work is clearly presented and well written and the experiments are well performed. There are a number of areas however in which the text could be expanded to help the reader appreciate the significance of the results.
Abstract
: Foot and mouth disease virus (FMDV), a member of the Background picornaviridae that causes vesicular disease in ungulates, has seven serotypes and a large number of strains, making universal detection challenging. The mature virion is made up of 4 structural proteins, virus protein (VP) 1 -VP4, VP1-VP3 of which form the outer surface of the particle and VP4 largely contained within. Prior to mature virion formation VP2 and VP4 occur together as VP0, a structural component of the pre-capsid which, as a result of containing the internal VP4 sequence, is relatively conserved among all strains and serotypes. Detection of VP0 might therefore represent a universal virus marker.
: FMDV virus protein 0 (VP0) was expressed in bacteria as a SUMO Methods fusion protein and the SUMO carrier removed by site specific proteolysis. Rabbit polyvalent sera were generated to the isolated VP0 protein and their reactivity characterised by a number of immunoassays and by epitope mapping on peptide arrays.
: The specific VP0 serum recognised a variety of FMDV serotypes, as Results virus and as virus-like-particles, by a variety of assay formats. Epitope mapping showed the predominant epitopes to occur within the unstructured but highly conserved region of the sequence shared among many serotypes. When immunogold stained VLPs were assessed by TEM analysis they revealed exposure of epitopes on the surface of some particles, consistent with particle breathing hitherto reported for some other picornaviruses but not for FMDV.
: A polyvalent serum based on the VP0 protein of FMDV Conclusion represents a broadly reactive reagent capable of detection of many if not all FMDV isolates. The suggestion of particle breathing obtained with this serum suggests a reconsideration of the FMDV entry mechanism. report report report report
Introduction
Foot-and-mouth disease virus, FMDV, classified in the aphthovirus genus of the Picornaviridae family, causes vesicular disease in a number of cloven-footed species, typically cattle, sheep and pigs 1 . In developed economies outbreaks of the disease in farmed herds are associated with significant financial loss while in less developed economies a loss of milk yield and fecundity have a direct community impact. Where possible the disease is controlled by vaccination and slaughter 2 but the virus evolves constantly to evade host immunity leading to multiple strains 3 . The antibodies raised during natural infection, or following vaccination, are restricted to predominant immunogenic regions on the virion surface and frequently have a very narrow spectrum of reactivity 4,5 . Antibodies to virus non structural proteins are more cross reactive (e.g. 6,7) but are of limited value for vaccine research programs which are necessarily focused on only the structural proteins. Some broad-ranging detection agents such as recombinant integrin, a soluble form of the virus receptor, have been developed 8,9 but as alternate virus receptors have been described 10 these may not react with all isolates.
We have developed systems for the expression of recombinant empty FMDV capsids, principally for use as potential vaccines 11,12 . Since these capsids contain no genome, PCR-based methods of quantitation 13 are impossible and their characterisation relies extensively on antibody reactivity. However, strain divergence is such that antibodies suitable for the detection of a wide range of isolates can be difficult to source.
To generate an antibody reagent capable of detecting the majority of FMDV isolates we made use of the recent finding that fusion of the individual structural proteins of the virus, VP0, VP1 and VP3 to the small ubiquitin-related modifier (SUMO) protein as a carrier allows efficient expression and purification of each mature protein in E.coli 14,15 . Of these, VP1 and VP3 exhibit extensive serotype variation making them unsuitable as the basis of a universal serum reagent while much of VP0 is less variable. VP0 is an assembly intermediate protein that is incorporated into virus particles and then cleaved autocatalytically into VP4+VP2 coincident with the incorporation of the RNA genome 1 . Part of the VP2 sequence lies on the surface of the virus particle and is subject to antigenic variation, similar to that observed for VP1 and VP3, but sections of VP2, and all of VP4, lie on the inside of the particle, are not under immune selection, and are highly conserved across serotypes. Thus, VP0 is a suitable candidate for the generation of a serum with potentially broad cross-reactivity.
Results and discussion
To produce VP0 protein, the sequence encoding VP0 from FMDV strains O1 Manisa Tur/69 one of the seven serotypes of FMDV worldwide, was fused in frame to the SUMO sequence in a T7 promoter driven bacterial expression vector ( Figure 1A). Following transformation of an E.coli strain expressing the T7 polymerase, growth and induction, a SUMO-VP0 fusion protein with the predicted molecular mass of ~46kDa was identified in bacterial extracts ( Figure 1B). Purification to homogeneity was achieved by virtue of the poly histidine tag present at the N-terminus of the SUMO domain and incubation with the SUMO specific protease Ulp1 16 produced two fragments representing the 11.5 kDa SUMO and ~33.5 kDa VP0 domains ( Figure 1C). The free SUMO domain and any uncleaved SUMO-VP0 fusion protein were subsequently removed by adsorption to an IMAC resin and the resultant pure VP0 protein was used for immunisation.
A standard regimen of immunisation generated polyvalent sera in rabbits which were screened by western blot for reactivity with FMDV antigen expressed in insect cells 11,12 . In these tests, VP0 is produced in insect cells as part of the processing and assembly reaction of the P1 precursor protein (cf. Figure 1A) and the cleaved mature capsid proteins assemble into empty capsids, otherwise called virus like particles. As the genomic RNA is not present, VP0 does not generally undergo further cleavage to VP4 and VP2. Reactivity was apparent with a band of 37kDa consistent with the apparent molecular mass on SDS-PAGE of VP0 synthesised by a range of FMDV serotypes. Antibody reactivity in the serum generated reacted well with empty capsids representing serotypes A Iran 7/13, O1 Manisa, O Turkey 05/2009, Asia1 Shamir ( Figure 2A) and SAT2 Zim 7/83. To address if reactivity was also apparent on non-denatured antigen, the VP0 serum was also used as the primary antibody for flow cytometry of insect cells expressing each serotype following fixation and permeabilization. Reactivity was apparent with all samples ( Figure 2B) but the intensity of staining was somewhat lower than might be expected from the strength of reaction to denatured antigen. However, as relatively little of the VP0 sequence used to generate the sera is exposed on the surface of the virus particle, a lower reactivity to assembled capsids is plausible. Reactivity was also apparent with individual empty capsids when the serum was used for immunogold transmission electron microscopy ( Figure 2C). Interestingly only some particles bound gold suggesting a subset with exposed epitopes. Finally, the VP0 serum was used to probe western blots of sucrose gradient purified virus from infected cell supernatants. These samples contain largely VP2, not VP0, as authentic virus has undergone VP0 maturation but nevertheless residual VP0 was detected for many of the samples tested, as was the more major cleavage product VP2 ( Figure 2D). Despite reaction with whole virus the serum showed no neutralising activity (unpublished study, Eva Perez), consistent with the principle neutralising determinants of FMDV being present in the VP1 protein 1 . To identify the linear epitopes underpinning the breadth of the observed reactivity, epitope mapping was done using peptide microarrays of both O1 Manisa sequence used for VP0 expression and, to include a more phylogenetically distant serotype, the SAT2 Zim VP0 sequence. Multiple epitopes were apparent, but in the main they clustered in the amino-terminal VP4 region of the protein representing only ~10% of the polypeptide used as immunogen ( Figure 3A). Specifically, the major epitopes spanned residues 8-18 near the amino terminus of VP4 and residues 28-40 further downstream. The major epitope in VP2 comprised residues 5-14 at the amino terminus with more minor reactivity towards the carboxyl terminus ( Figure 3B). In the three-dimensional structure of FMDV O1 Manisa 17 the identified VP4 epitopes lie in a disordered region where no clear polypeptide chain mapping is possible ( Figure 4). The predominant VP2 epitope is visualised but is distended away from the main body of the protein while the minor VP2 epitopes at residues 145-152 and 200-207 lie within the main fold. The epitope mapping data would be consistent with poor antibody induction by the tightly folded β-sheet rich "jelly-roll" fold of the VP2 domain but ready antibody induction to the much less ordered and distended regions. A similar observation has been made for a related picorna-like virus, Israeli acute paralysis virus, following expression, immunisation and epitope mapping of the resulting serum 18 . The lack of epitopes in the classic fold of VP2 within the VP0 protein lends support to the suggestion that the unprocessed polyprotein in solution adopts a structure not dissimilar to that found in the native virus 19,20 .
Virus diversity in the natural environment, such as that shown by FMDV, provides the impetus for the development of novel control solutions, such as new candidate vaccines. But a corollary is often that the reagents available to characterise such novel products, for example those developed to newly emerged strains, are limited. Our data show that a focus on the most conserved polypeptide sequence of the virus particle, coupled with efficient, non-denaturing purification of the requisite protein can provide an immunogen able of generating a serum that is cross reactive for many strains. Epitope mapping confirmed the basis of such cross reactivity was short conserved sequences predominantly at the N-terminus of VP4. The serum performed well on denatured antigen whether it was VP0 (empty capsids) or VP2 (virus) but titres were reduced on assembled forms of the same proteins consistent with most epitopes being inside the particle. The low but very specific labelling of particles observed by TEM could therefore represent deformed particles which expose the inner surface or the transient exposure of internal epitopes on the intact particle surface, originally observed for rhinovirus and termed "breathing" 21 .
Interestingly, for picornavirus examples where the breathing intermediate has been captured structurally, it is residues 1-50 at the N terminus of VP4 that are exposed 22,23 , consistent with the predominant targets of the serum generated here.
Conclusions
The picornaviridae contain many examples where strain variation among family members is extensive. Our data suggest that the same principle of serum generation by highly purified VP0 could be used to generate a broadly reactive serum in these cases also.
Cloning and expression vector construction
The sequences encoding the VP0 section of the FMDV strains described were taken from the databases but synthesised de novo as dsDNA fragments (gBlocks -Integrated DNA Technologies, Leuven, Belgium). They were assembled into SUMO expression cassettes by ligation of a restriction fragment or by an infusion reaction such that fusion of the VP0 sequence was at the C-terminus of the SUMO domain. All vectors were sequence verified before use (Sanger sequencing service, Source Bioscience, Nottingham, UK). Expression generally used E.coli BL21 DE3 pLysS as described 24,25 . A number of FMDV
SDS-PAGE analysis
Samples of E.coli were resuspended directly in SDS loading buffer, boiled for 5 minutes, cooled, vortexed to shear bacterial DNA and spun briefly to remove insoluble murein (3 min, 13000 rpm bench microfuge). The equivalent of 50 microliters Western blot analysis Gels were transferred to Immobilon filters (Immobilon P Cat. No. IPVH00010 EMD Millipore) by semi-dry electro transfer using a HorizeBLOT 4M-R (Cat. No. WSE-4040 ATTO Corporation, Tokyo, Japan) operating at 12V for 60 minutes and the membrane blocked using 5% dried milk powder in PBS for 1 hour at room temperature or 4°C overnight. Following blocking, membranes were rinsed and washed twice in PBS + 0.5% Tween-20 (Sigma) (PBS-T). The primary rabbit antibody, produced as described herein, was diluted in PBS-T + 0.5% milk powder and incubated with the membrane for 1 hour at room temperature, followed by washing twice (15 minutes each) in PBS-T. A polyclonal anti-rabbit IgG conjugated to HRP (Cat. No. P0448, Agilent DAKO, Cheshire, UK) was diluted in PBS-T + 0.5% dried milk powder and incubated with the corresponding blot for 1 hour at room temperature. HRP detection used an ECL western blot detection reagent (EZ-Chemiluminescence Cat. No. K1-0170 GeneFlow Ltd, Lichfield, UK) and the filter was imaged while luminescent on a Syngene Chemi XL imager.
Immunogold labelling
Empty FMDV capsids, purified as described 11 were adsorbed to carbon coated formvar grids by floating the grid on a droplet of sample for 5 minutes at room temperature. The grid was washed briefly in water and floated sequentially on a 1:5 dilution of the VP0 serum followed by a 1:50 dilution of a polyclonal anti-rabbit antibody conjugated to 10nm gold (Cat. No. G7402 Sigma-Aldrich, Poole, UK), each for 10 minutes at room temperature. The grids were washed with distilled water and counter stained with 2% uranyl acetate before examination using a Joel TEM operating a 200kV. anti-rabbit IgG conjugated to FITC (Cat. No. F9887 Sigma-Aldrich, Poole, UK). Cells were analysed on a BD FACscan using CellQuest (Version 3.3 BD Bioscience) and the mean fluorescence intensity plotted.
Serum generation
Serum generation was outsourced to Covalab Cambridge, UK. VP0 sera were raised in 2 New Zealand female rabbits following a standard regimen of prime and two boosts with Freund's complete and Freund's incomplete adjuvant respectively (Standard Polyclonal Service Pack, 53 day protocol, Covalab Cambridge, UK). Each immunisation used 25 micrograms of purified VP0 protein and seroconversion was confirmed by western blot of a test bleed taken 2 weeks after the first boost. The VP0 serum has been registered with the Antibody Registry as Ian Jones; University of Reading, Cat# Anti-VP0 Man, RRID: AB_2732804.
Microarray epitope mapping
The serum was subject to epitope mapping at single amino acid resolution on commercial peptide arrays of the VP0 protein comprising 20mer peptides overlapping by 1 amino acid (PEPperMAP® Service, PEPperPRINT, Heidelberg, Germany).
Data availability
The VP0 serum described here has been registered with the Antibody Registry with the designation AB_2732804.
The data underlying this study is available from the Open Science Framework. Loureiro and co-workers describe the expression of FMDV strain O1 Manisa Tur/69 protein VP0 ('uncleaved' VP4/VP2) as a His-tagged SUMO fusion protein in a bacterial expression system: Following purification using the His-tag , the SUMO fusion partner was removed by the SUMO-specific proteinase: the purified VP0 was then used to raise (rabbit) anti-VP0 antibodies. These polyclonal antibodies were then tested for cross-reactivity against proteins from other FMDV serotypes. I do not think the title (as it stands) is justified by the data presented in Figure 2, panels A and B (could data from naive Sf9 cells be included here?). 'Universal' is a reach. Naturally, not every FMDV serotype/strain needs to be tested, but more 'coverage' would give more confidence. On this point, could some indication as to the degree of conservation (across all FMDVs) of each amino acid shown in Figure 3 Panel B be given? These data are readily available..The structural analyses and discussion of the particle structure ('breathing') was very informative.
If applicable, is the statistical analysis and its interpretation appropriate? Not applicable
Are all the source data underlying the results available to ensure full reproducibility? Partly
Are the conclusions drawn adequately supported by the results? Partly
No competing interests were disclosed. Competing Interests: This study aims to test the hypothesis that antisera raised against VP0 from one strain of FMDV (O1M) may serve as a detection reagent for all strains of the virus. The hypothesis is predicated on the assumption that the VP4 polypeptide segment within VP0 is relatively conserved between FMDV serotypes. The paper describes the generation of a bacterial expression vector for a his-SUMO-tagged VP0 protein, the use of this protein to generate antisera in rabbits, and characterisation of the antisera against a selected range of antigens.
I have read this submission. I believe that I have an appropriate level of expertise to confirm that
In its present state the work represents an interesting set of observations, but there are some shortcomings in the experimental design and the reporting of the results that should be addressed. These are as follows: 1. The claim of 'universal detection' made in the title of the article is not supported because not all seroytypes have been tested. No viruses of type C, SAT-1 or SAT-3 were included. Clearly an interesting range of serotypes has been used, giving some indication of the broad specificity of the antisera, but this is some way shy of 'universal'. Either the title should be modified or the missing serotypes included.
intermediates and some denatured material?
6. In the legend to Fig. 2C it is revealed that the type A strain used is A22, which is different to the A strains used in the experiments in panels A and B. it would be helpful to mention this in the body of the text where the result is described.
7. On page 4, it is stated that the authors have achieved "efficient, non-denaturing purification of the requisite protein" (i.e. VP0) -but no data is shown to support this. (See point 3 above).
8. On the same page a claim is made for "very specific labelling of particles observed by TEM" but there were no controls or comparators presented to support this. The claim should be removed or appropriate controls presented. 9. Fig. 2B -how many independent measurements were made to determine the mean fluorescence for each antigen type? This should be stated and an error estimate provided.
10. Fig. 2D -what is the source and specificity (i.e. which FMDV strain) of the anti-VP2 antibody used in the middle panel?
11. Fig. 3a. It would be useful to indicate the boundary between VP4 and VP2. The reader would also benefit from a VP4 sequence alignment of the FMDV strains included in this study -and/or a quantitative analysis of the sequence conservation in VP4.
If applicable, is the statistical analysis and its interpretation appropriate? Partly
Are all the source data underlying the results available to ensure full reproducibility? Yes
Are the conclusions drawn adequately supported by the results? Partly
No competing interests were disclosed.
Competing Interests:
Referee Expertise: Structural virology, picornaviruses I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. Loureiro et al. describe the reactivity of a rabbit serum preparation from animals injected by bacterially expressed and purified VP0 protein from foot-and-mouth disease virus (FMDV). The authors show cross reactivity with a number of FMDV serotypes but the serum is non neutralising. From epitope mapping and transmission electron microscopy analysis using gold labelled antibodies the authors suggest that the region of VP0 recognised by the serum is only exposed some of the time in virus like particles and that this may reflect 'breathing' of the particles as described for other picornaviruses but not FMDV.
Overall the work is clearly presented and well written and the experiments are well performed. There are a number of areas however in which the text could be expanded to help the reader appreciate the significance of the results.
Introduction, first paragraph, sentence 3: 'Where possible the disease is controlled by vaccination and slaughter but the virus evolves constantly to evade host immunity leading to multiple strains This sentence could be modified by splitting into two and removing the 'but'. Viral outbreaks can be controlled by vaccination and slaughter despite viral evolution, the sentence as currently written suggests this is not the case.
Results and Discussion, Figure 1: Is there a reason why the VP0 signal is so disperse in lane 6 compared to the that in lane 4, as both samples were run on SDS-PAGE gels before different subsequent treatments?
Results and Discussion, Figure 2: 2A, the additional bands in lanes 3 and 4 are overlooked in the text and should at least be noted. 2C, is the remaining signal (aside form the obvious capsids) in this microgram from denatured protein in the samples prep or a result of the adsorption procedure?
Results and Discussion: last paragraph, the results/discussion would benefit from a description of the current understanding of FMDV entry and how the presence of breathing would alter our understanding of this.
Title and abstract: The title states 'universal detection' but not all serotypes have been tested. For the same reason the 'if not all' should be removed from the first sentence on the Abstract Conclusion.
Is the work clearly and accurately presented and does it cite the current literature? Yes
Is the study design appropriate and is the work technically sound? 2 '. 3 1.
Are sufficient details of methods and analysis provided to allow replication by others? Yes
If applicable, is the statistical analysis and its interpretation appropriate? Not applicable Are all the source data underlying the results available to ensure full reproducibility? Yes Loureiro et al., have expressed the foot-and-mouth disease virus capsid component VP0 in a bacterial expression system and generated polyclonal antisera against it. Note VP0 is cleaved during particle assembly to the mature VP4 and VP2 products. The anti-VP0 antisera has then been characterized for its ability to detect FMDV in a variety of assays. Due to the relatively high conservation of the N-terminus of VP0, it is not surprising that the antiserum recognizes multiple serotypes of FMDV. Indeed, monoclonal antibodies that recognize all serotypes of FMDV have been described previously . These reagents have formed the basis for the pan-FMDV antigen detection systems used in lateral flow devices used in "penside" tests. The Pirbright Institute had a major role in the development of these tests and so it is very surprising that this information is not mentioned anywhere. Such monoclonal antibodies recognize epitopes within VP2 .
Major points
The text and Fig. 1 legend refer to the structural protein precursor P1, this is incorrect. For FMDV, the structural protein precursor is P1-2A (in the enteroviruses (like poliovirus) the precursor is P1) and it would be better if both Fig.1 and the text were modified to indicate this. It would also be useful if the His-tag within the SUMO fusion protein was also indicated.
In the Results and Discussion section, it is indicated that the VP0 was purified to homogeneity but this is not actually shown-why not? Fig 1C only shows the products prior to the removal of the His-tagged SUMO. Even here, the VP0 product appears to migrate as a rather heterogeneous 1.
2.
His-tagged SUMO. Even here, the VP0 product appears to migrate as a rather heterogeneous band-why is this?
The text indicates that VP0 cleavage to VP4 and VP2 does not generally occur in the absence of encapsidated RNA. However, as some of these authors have shown, this is not actually the case for FMDV empty capsid particles , at least when produced in mammalian cells (maybe this is different in the insect cell system which would be interesting).
The text indicates the anti-VP0 antibody reacts well with the empty capsids from 5 different serotypes of FMDV when analysed by Western blot (see Figure 2A). However, in my view, good reactivity is only seen with 2 of the strains (O Turkey (lane 3) and SAT 2 Zim (lane 4), I think the text needs modifying. In contrast, the reactivity of the serum with insect cells expressing the empty capsids of the different serotypes shows very weak reactivity with the O Turkey and SAT 2 Zim samples (lanes 3 and 4, Fig 2B). This does not match the text which needs to be modified. Is it significant that the strains poorly recognized in the flow cytometry assays are those best recognized in the Western blot? The authors should comment. In Fig 2C, gold labeling of A22 empty capsids is shown. The text indicates "only a subset of particles are labeled", this is undoubtedly the case. Unfortunately, there are no controls here, e.g. with a different antiserum, thus I am not sure how the authors can justify the statement that this is "very specific labeling of particles" ((P.4). Indeed, it also seems impossible to know whether the particles that are labeled are damaged particles or not (as mentioned on P.4) and I think the Discussion of virus "breathing" is excessive. The earlier work on rhinovirus "breathing" would suggest exposure of VP4 was relatively frequent but that does not appear to be the case here. Thus the sentence in the Conclusion of the Abstract (P.1) stating "The suggestion of particle breathing obtained with this serum suggests a reconsideration of the FMDV entry mechanism." seems far from justified; indeed this is not even mentioned in the main text and should be deleted from the Abstract. In Fig 2D, it is surprising that the anti-VP2 monoclonal antibody apparently fails to recognize the A22 VP2. Has this been observed previously? A positive control for the presence of FMDV capsid proteins in the samples would have been useful. It is also unfortunate that there are no negative control lanes (e.g. poliovirus empty capsids) within Fig 2D, why not? It would be interesting to know if the anti-VP0 antisera recognizes VP4 on Western blots. This should have been apparent in the right hand panel of Fig 2D since purified native virus particles were used but the VP4 may migrate faster than the 10kDa marker and thus maybe was not detected on this gel, a higher percentage gel would have been helpful. This should be determined. I am not convinced it is possible to draw any conclusions about the nature of the recombinant VP0 structure based on previous data for the whole P1-2A precursor, I think the text needs modifying.
Minor points
There are many minor errors and inconsistencies in the text that should have been corrected by careful reading before submission. In Fig 3 B, the sequence of VP0 is shown here with an N-terminal Met (M) residue. This is incorrect; the VP0 sequence is preceded by the Leader protease in the viral polyprotein and in the SUMO fusion, the VP0 sequence is preceded by the SUMO sequence so there is no need for an initiator methionine residue. I think it would be better to show a comparison of the VP0 sequences from O1 Manisa and the SAT 2 Zim as used for the peptide arrays to show the regions with high similarity in the VP0 of these viruses. | 7,000 | 2018-07-25T00:00:00.000 | [
"Biology",
"Medicine"
] |
One-Loop Charge-Breaking Minima in the Two-Higgs Doublet Model
We analyze the vacuum structure of the one-loop effective potential in the two Higgs doublet model. We find that electroweak-breaking vacuua can coexist with charge breaking ones, contradicting a theorem valid at tree-level. We perform a numerical analysis of the model and supply explicit parameter values for which charge-breaking vacuua can be the global minimum of the theory, and deeper than charge-preserving ones.
Introduction
The discovery by the LHC collaborations of the Higgs boson [1,2] provided the missing piece of the puzzle for the Standard Model (SM) of particle physics. Since then, measurements of the Higgs' properties [3] have shown that this scalar, with mass around 125 GeV, behaves largely as expected in the minimal SM: thus far, and within the measured precision, no significant deviations from SM-like behavior have been observed. But the SM leaves a great many questions unanswered, such as the origin of the matter-antimatter asymmetry, the nature of dark matter as a particle, the observed fermion mass hierarchy, and the strong CP problem. SM extensions are therefore of interest to attempt to provide answers to these, and other, unsolved problems. Models with extended scalar sectors, in particular, are quite popular and widely studied in the literature. One of the simplest beyond the SM theories is the two Higgs doublet model (2HDM), first proposed by Lee in 1973 [4] to provide an additional source of CP violation stemming from the scalar sector through spontaneous symmetry breaking.
In the 2HDM, the gauge and fermion content are the same as in the SM, but instead of a single SU(2) doublet with hypercharge Y = 1,we now have two, Φ 1 and Φ 2 . This leads to a rich phenomenology (see [5] for a review), boasting a richer scalar spectrum than the SM's, with two CP-even scalars, a pseudo-scalar and a charged scalar. The model can have tree-level flavor-changing neutral currents mediated by scalars, can provide a dark matter candidate and have spontaneous CP violation. The 2HDM easily reproduces all experimental results from the SM, and indeed it has a decoupling limit where the extra scalars are very massive and the model's predictions can be made to be virtually indistinguishable from those of the SM. The 2HDM also has a richer vacuum structure then the SM -whereas in the SM the only possible vacuum is the one which breaks electroweak symmetry, in the 2HDM spontaneous CP breaking is also possible, as well as minima where the electromagnetic symmetry U (1) em is broken. These latter minima are unwanted since they would imply a massive photon. The possibility of charge (and color) breaking already arises in SUSY models, and leads to bounds on some of the parameters of the model [6].
The possibility of reducing the 2HDM parameter space in a similar manner -imposing bounds on the model's parameters to avoid global charge-breaking (CB) minima -is very appealing. In many cases, sufficient conditions to avoid CB minima were considered [4,7,8], but at the time it wasn't known whether such conditions were too restrictive. However, in [9,10] a remarkable result was obtained: the structure of the tree-level 2HDM scalar potential is such that, if an electroweak breaking minimum exists, any CB extremum that might then occur is necessarily a saddle point lying above the minimum. Likewise, it was shown that if a CB minimum exists, any stationary point which would break the normal electroweak symmetries is a saddle point lying above it. Analogous results were also proved for the relationship between electroweak extrema and CP breaking ones. Thus a 2HDM electroweak breaking minimum, if it exists, is guaranteed, at tree level, to be stable against tunneling to deeper CB or CP breaking vacuua, since such deeper minima were shown to not exist. This result was further studied in refs. [11][12][13][14][15]. In particular, using a Minkowski formalism to rewrite the 2HDM scalar potential, Ivanov was able to show [13,14] the stability of the different vacuua through geometric arguments. Other results concerning neutral minima in the 2HDM were also obtained -it was shown [13,14,16] that neutral minima can coexist in the 2HDM scalar potential, provided they break the same symmetries. This had implications for the Inert model [17][18][19], a version of the 2HDM where a discrete Z 2 symmetry is preserved by both the Lagrangian and by the vacuum -the vacuum preserves Z 2 since only one of the doublets acquires a non-zero vacuum expectation value. Two possibilities for minima then arise, depending on which of the doublets has the non-zero VEV, the Inert Minimum (where fermions acquire mass after spontaneous symmetry breaking) and the Inert-Like Minimum (where the fermions remain massless). In [14,16] expressions relating the depth of the potential at each of these minima were found, and it was shown that, for specific regions of parameter space, they could coexist.
However, powerful though the demonstrations of [9,10] and [13,14] were, those works dealt with the tree-level potential. The expressions found there comparing the depth of the potential at different extrema depended heavily on tree-level formulae for the scalar masses; for the minimization conditions determining the vacuum expectation values (VEVs); and for the potential itself. A valid question is therefore whether these results are robust when one considers loop corrections to the potential -will the stability theorems deduced for the tree-level potential still hold at one-loop? The first hint that that may not be the case was obtained in [20], where a one-loop calculation was undertaken to analyze the coexistence of neutral minima in the Inert model. The effective potential formalism was employed and it was shown that, in certain cases, a tree-level local minimum could become a one-loop global one, and vice-versa. This (rare) possibility occurred only for regions of parameter space where the tree-level minima were close to degenerate, hence it did not correspond to a breakdown in perturbation theory, rather it implied loop corrections could change the nature of tree-level vacuua. Further, the one-loop calculation enlarged the region of parameter space for which different neutral minima could coexist.
The purpose of this paper is to investigate, using the one-loop effective potential, whether the conclusions concerning the (non-)coexistence of neutral and charge breaking vacuua in the 2HDM hold when radiative corrections are taken into account. We review the tree-level results for the classical 2HDM potential in section 2 then proceed to review the formalism of the one-loop effective potential in section 3, including a discussion of issues related with gauge fixing. The numerical methods we use to carry the minimization of the one-loop potential are detailed in section 4 where we also present results of numerical scans of the model's parameter space and give a few illuminating examples. We draw our conclusions in section 6.
2 The tree-level vacuum structure of the 2HDM The 2HDM contains two hypercharge 1 SU (2) scalar doublets, and the most general scalar potential one can write has a total of 14 real parameters. Since both doublets are identical, any linear combination of them which preserves the scalar kinetic terms should lead to the same physics. This basis invariance, which corresponds to a redefinition of the fields via a 2 × 2 unitary matrix U 1 , allows one to reduce the number of free parameters to 11 [21]. This most general 2HDM will include flavor changing neutral currents (FCNC), mediated by neutral scalars at tree-level, when one considers the full Lagrangian, including fermions. To prevent this, a discrete Z 2 symmetry is introduced [22,23] which is extended to the Yukawa sector in such a way that each class of same-charge fermions (up and down-type quarks and charged leptons) only couple to one of the doublets. This eliminates tree-level FCNC and, due to the several possibilities of extending Z 2 to the Yukawa sector leads to four types of 2HDMs (type I, type II, lepton specific and flipped [5]). So that the model can possess a decoupling limit [8], a softly Z 2 breaking quadratic term, m 2 12 , is usually introduced, so that the scalar potential is characterized by 8 real independent parameters.
Classical Potential
The 2HDM scalar potential we will be studying possesses a softly broken Z 2 symmetry and is therefore given, at tree-level, by where all the parameters are taken to be real 2 . The scalar doublets, Φ 1 and Φ 2 contain a combined eight real component fields which can be parameterized as follows: It is well know that the 2HDM classical potential exhibits three-different types of extrema (for instance, see section 5.8 of [5] for a demonstration): a U (1) EM and CP-conserving extremum, which we denote by Φ i EW with the vev α = 0 breaking electric charge conservation and consequently giving a mass to the photon and a CP-violating extremum: where δ = 0. In this work, we will be focusing on the EW and CB extrema.
Classical Extrema
To investigate the relative depths of the classical potential evaluated at the EW and CB extrema, it is useful to introduce the following gauge-invariant variables [7,9]: 2 By real we mean the CP symmetry that the unbroken Z2 potential had is left unbroken. Considering a complex coefficient m 2 12 would lead to a model with explicitly broken CP, known as the Complex 2HDM [24][25][26][27][28][29][30][31][32][33]. Further promoting the Z2 symmetry to a continuous U (1) but keeping the complex soft breaking term and allowing for the possibility of flavor violation in the quark sector yields models with interesting phenomenology [34,35], but not the subject of the current paper.
In terms of these variables, then, the classical potential of Eqn. (2.1) is written as with real parameters a i and b ij = b ji . In terms of the original parameters of Eqn. (2.1), the a i and b ij are given by with all the unspecified parameters equal to zero. Collecting the x i 's, a i 's and b ij 's in vectors X, A and symmetric matrix B, respectively, we can rewrite the classical potential as 14) The values of the vector X at the EW and CB extrema are given by We can then see that the non-trivial minimisation conditions of the classical potential at the EW extremum may be expressed in terms of X EW as We can therefore see that and we note that this expression implies the following relation: Combining this expression with ∇ X V = A + BX, we obtain Therefore, the classical potential evaluated at the EW extrema is equal to: In a similar manner, we find what the non-trivial minimisation conditions imply for X CB : From these equations it is clear that from which one obtains the value of the classical potential at the CB extrema, to wit Combining the above results, we obtain: Using this result, Eqn. (2.30), Eqn. (2.29) and the fact that B = B T , we find that We thus find that Now suppose that V EW is a local minimum of the theory. It is possible to show that the mass of the charged Higgs is given by: Using this, we finally obtain that The implications of this expression are clear: if the potential has coexisting EW and CB stationary points, and the EW solution is actually a minimum, then all of its squared scalar masses will necessarily be positive; therefore, since the quantity in square brackets is guaranteed to be positive, an EW minimum implies V CB − V EW > 0 and therefore the EW minimum is deeper than the CB stationary point. Further, it can be shown that under these conditions the CB extremum is a saddle point. Thus, in refs. [9][10][11][12][13][14][15] the following tree-level theorem was established: • If the 2HDM tree-level scalar potential has an electroweak minimum, any charge breaking extremum that eventually exists will necessarily lie above that minimum.
• Further, the charge breaking extremum will necessarily be a saddle point.
We will now investigate these properties of the 2HDM vacuum structure at the loop level.
One-Loop Corrections to the Scalar Potential
The classical scalar potential of a quantum field theory is not the true scalar potential. In an interacting quantum field theory, quantum effects will induce corrections to the scalar potential. The standard way of computing the corrections to the classical scalar potential is to use the path integral and background field method. For clarity, we will explain this formalism in a quantum field theory of a single interacting scalar field. We begin by writing down the so-called generating functional of the theory in terms of a path integral over field configurations: where Φ is the scalar field, j is an external source and S[φ] is the action of the theory. By taking n-functional derivatives of Z[j] with respect to j, one can generate the n-point Green's function consisting of the connected and disconnected Feynman diagrams with nexternal propagators. We redefine the field Φ to consist of a classical component φ cl and a fluctuation field φ: Φ = φ cl + φ(x). Here φ cl is chosen to satisfy the classical equations of motion in the presence of the external source j. We can expand the action of the theory around the classical field using: where the · · · represent higher-order functional derivatives of the action (which aren't of interest to use here.) Using the expansion of the action in Z[j], where again, the · · · represent higher-order terms. Since φ cl satisfies the classical equations of motion in the presence of the source j, the term linear in φ vanishes. The quadratic term can be integrated exactly, yielding: , which is the generating functional for the connected Green's functions. To order , this is: From now on, we will drop the log(N ) term, since it a constant and will not play any role. Lastly, we define the effective action Γ[φ] through the Legendre transform of W [j]: whereφ(x) = δW [j]/δj(x). To order , the fieldφ(x) is given by (using Eqn. (3.5)): Using this relationship, we can write φ cl =φ + φ 1 , where φ 1 is of order . We can now replace φ cl in favor ofφ. Given that δS/δφ φ=φ cl = −j, we can think of j as a functional of φ cl , replacing φ cl in favor ofφ. Writing Γ 1 [φ cl ] = i /2 log det δ 2 /δΦ(x)δΦ(y) φ=φ cl , we find, to order : where we dropped terms that go like O φ 2 1 since they are O 2 . If we takeφ to be spacetime independent, the classical action evaluated atφ is simply −(V T )V 0 (φ) where V T is the space-time volume and V 0 is the tree-level scalar potential. We thus define the effective potential as: It is straightforward to evaluate the log det δ 2 S/δΦδΦ term by using the identity log(det(A)) = tr(log(A)). For a real scalar field, one has δ 2 S/δΦδΦ = + m 2 (φ) (where m 2 (φ) is the field-dependent mass computed by diagonalizing ∂ 2 V 0 (φ)/∂φ 2 ) and hence: The integral can be computed by replacing log −p 2 + m 2 with − lim α→0 ∂ ∂α (−p 2 + m 2 ) −α and using standard one-loop integral tables. The result is divergent and requires the couplings of the theory to be renormalized. Once the infinities are canceled off (using MS), the result is: with µ being the renormalization scale. It is straight forward to add in additional scalar fields, gauge bosons, and fermions. The form of effective potential to O( ) is [36]: where i runs over all the particles of the theory, s i is the spin of the particle, n i is the number of degrees of freedom of the particle, µ is the renormalization scale and M 2 i (φ) is the field dependent squared mass. The value of c i is renormalization-scheme-dependent. For MS [36], c i = 5/6 for gauge fields and 3/2 for all other particles. In principle, one needs to take into account the order correction present inφ when computing V 0 (φ). The terms of order arising from V 0 (φ) play an important role in ensuring that the effective potential is gauge-independent order-by-order in . We will discuss this further in Sec. (3.4). In the remaining subsections, we provide results for the various contributions from the particles involved in the 2HDM and discuss the expansion of the effective potential.
Scalar Contributions
For the scalar fields, the one-loop correction to the scalar potential is (3.14) In the expression above, the values of the squared masses are the eigenvalues of the second derivative of the tree-level potential, M 2 ij (Φ): with {φ i , φ j } any of the real components defined in eq. (2.2). In a general gauge, there are additional gauge dependent pieces which contribute to the scalar squared mass matrix. These gauge contribution have the effect of giving the Goldstones masses which are ξ times the corresponding massive gauge bosons (see below for the gauge masses), where ξ is the gauge-fixing parameter. However, we will chose the Landau gauge ξ = 0, where the additional gauge-dependent pieces do not contribute to the scalar mass matrix. For a general field configuration, this 8 × 8 mass matrix is extremely complicated, preventing us from giving explicit expressions to its eigenvalues. It is, however, possible to compute the scalar masses and their derivatives (which we will need) for the cases where c 2 = c 3 = c 4 = i 1 = i 2 = 0. These expressions are lengthy and we will, therefore, omit the results, having in any way developed a numerical procedure to obtain their values for our calculation.
Gauge Contributions
The field-dependent squared masses of the W and Z bosons and the photon are generated from the kinetic terms of the two Higgs doublets: Plugging in the expectation values for the Higgs doublets, the result is: where g and g are the U (1) Y and SU (2) L gauge couplings and σ a = σ 1 , σ 2 , σ 3 are the Pauli-sigma matrices. In order to compute the squared masses of the gauge fields, it is useful to organize the gauge fields into the following vector: Computing the second derivative of L gauge,mass with respect to the components of G µ generates the following 4 × 4 mass squared matrix for the gauge bosons: where we have defined: t W ≡ tan(θ W ) = g /g and the parameters x, y, z and w as: It is possible to explicitly compute the eigenvalues of the gauge mass squared matrix. In terms of the above parameters, the squared masses of the W, Z and photon are 3 : In general, one also needs to consider the effects of ghosts. Ghost fields add additional contributions to the effective potential with squared mass equal to ξ i m 2 g,i , for each of the massive gauge bosons. However, we will work in the ξ = 0 Landau gauge where the ghosts and Golstone bosons are massless.
Top quark Contribution
For simplicity, the only fermion we consider is the top quark. The contributions to the effective potential from other fermions will be significantly smaller than the top quark contribution since the top mass is almost two orders of magnitude greater than the next heaviest fermion. To compute the field-dependent squared mass of the top quark, we consider the Yukawa interactions between the Higgs doublets and the top quark: where Φ = Φ 1 or Φ 2 and the · · · terms represents Yukawa interactions involving the remaining fermions, which we ignore. Following the usual convention, we take Φ = Φ 2 , for which the top quark mass is given by: The Yukawa coupling y t will depend on the values we choose for the r 2 , i 2 , c 3 and c 4 . We define the Yukawa coupling through the EW VEV, i.e. with r 2 = v 2 and i 2 = c 3 = c 4 = 0.
The resulting Yukawa coupling is given by: Given this Yukawa coupling, the field dependent top quark mass is: Given that we will not consider the (much smaller than the top's) contributions from other quarks or leptons, the results we present here will (within that approximation) therefore be valid for the several Yukawa-types of 2HDM (Type I, II, lepton-specific and flipped [5]).
-Expansion
As is well known, the effective potential is a gauge-dependent quantity. In principle, however, physical quantities calculated from the effective potential should not be gauge dependent. In practice, however, how such physical quantities are calculated determines whether or not the gauge dependence appears. The theoretical backbone for these issues are the so-called Nielsen identities [37], which can be cast as the fact that variations of the effective potential with respect to the gauge parameter ξ are proportional to variations with respect to the field itself, The equation above holds order by order in perturbation theory and, in particular, it implies that the value of V eff at critical points, i.e. where ∂V eff /∂φ = 0, is gauge independent.
The key issue with the "brute force" minimization of the effective potential to compute physical quantities lies with the fact that truncating the perturbative expansion means that incomplete higher-order terms are, implicitly, introducing a spurious gauge dependence. The proposal of Ref. [38], known as the expansion method, consists of casting the effective potential (and its derivatives) as a series in , after "reintroducing" the in the partition function. The minimization is then carried out by an "inversion of series" method [38]. Notice that while the -expansion method was originally developed for the finite-temperature effective potential, its applicability extends (in fact, in a much more straightforward way) to the zero-temperature effective potential we are concerned with here.
The -expansion method is manifestly gauge-independent, and unlike "brute force" minimization, it does not introduce an imaginary part in the broken phase. Also, it is valid at all types of extrema, including maxima and saddle points. In practice, the method's prescription is simply to find the extrema of the tree-level potential, with the perturbative series generating the corrections order by order.
As mentioned in Eqn. (3.13), the effective potential can be expanded in terms of . To be consistent, we must also include the order contributions present in the vacuum configuration: The effects of including the O( ) contribution to the vacuum configuration is to introduce additional terms arising from the tree-level potential that contribute to the effective potential at order . The full scalar potential evaluated at φ vac , expanded to order O( 2 ) is: The extrema conditions for the full effective potential are then given by: From this expression, we can immediately interpret the meaning of φ vac is a vacuum configuration that extremizes the classical scalar potential. Eqn. (3.33) also shows us how to find the extrema of the full effective scalar potential to order . One simply needs to determine all the extrema of the tree-level potential. Then, setting the term of order in Eqn. (3.33) to zero, we can determine the one-loop correction to the classical vacuum configuration, φ (1) vec . Once the classical extrema have been determined, the minimum of the effective scalar potential will be the configuration which gives the smallest value of vac extremizes the classical scalar potential. Ref. [39] and [40] revealed IR divergences in the Landau gauge arising from massless Goldstone bosons, and argued that a resummation is necessary. However, e.g. Ref. [41] argued that the -expansion obviates the need for a resummation because the IR divergences cancel order by order in perturbation theory. Notice that this procedure was extended in Ref. [42] to the small mass limit. In the case of small, non-Goldstone masses, a resummation is necessary. If negative masses are found corresponding to a one-loop minimum, which would always be the case in our theory (because remember, a tree-level EW minimum implies that any coexisting tree-level CB extremum is a saddle point), one would additionally need to perform a resummation of the two-point correlation functions to obtain a more accurate result for the scalar masses. In the -expansion method, attempting to find a counterexample to the tree-level theorem, e.g. simultaneous minima at one-loop, would always result in at least one set of negative squared masses (since either the EW or CB vacuum would be a saddle point at tree-level) and thus one would be left with imaginary one-loop potentials. Therefore, using the -expansion method to find counterexamples to the tree-level theorem would always require a resummation to provide a sensible result. We, therefore, will instead perform a numerical minimization of the effective potential and require that the tree-level potential is convex at one-loop minima, the one-loop effective potential thus becoming free of any imaginary pieces. Any gauge dependence of the results will be residual, stemming from the truncated perturbative expansion and arising, at least at the two-loop level, at order O 2 .
Numerical Methods
In this section, we describe the procedure we employ in finding counterexamples to the tree-level theorem on EW vacuum stability against charge breaking at one-loop order. A counterexample to the tree-level theorem is obtained if we can find a set of parameters for which there exist simultaneous EW and CB minima -this, at tree-level, is impossible. Further, we will show that one-loop EW minima may have deeper CB minima and thus their stability is not guaranteed. In brief, the algorithm we use to find counterexamples is as follows: 1. Generate EW and CB VEVs for Φ 1 and Φ 2 by sampling from a uniform distribution.
2. Generate initial random guesses for all eight of the 2HDM parameters: m 2 11 , m 2 22 , m 2 12 , λ 1 , λ 2 , λ 3 , λ 4 and λ 5 by sampling from uniform distributions. These will be used later as initial "seeds" for a numerical minimization of the potential.
3. Extremize the effective potential at both the EW and CB by solving the following five non-linear root equations: We solve these equations by holding the EW and CB VEVs fixed and varying five of the 2HDM parameters. We randomly chose which of the five 2HDM parameters we use to solve these equations each time.
4. Choose a set of 50 random vacuua and perform minimizations at each to find remaining extrema.
5. Categorize all of the extrema (as minimums, maximums or saddle points) by computing the eigenvalues of the effective potential Hessian.
Below, we describe the algorithm is more detail. Note that all the code was written in Julia and is available on GitHub.
Randomly choosing VEVs: Our starting point is to choose EW and CB vacuua at which we will attempt to extremize the effective potential. We characterize the mass scale of our problem in terms of the renormalization scale µ which we set to be the SM Higgs VEV: µ = 246 GeV. Since the effective potential contains logarithms of the form log M 2 /µ 2 , we choose all of our dimensionful parameters to be of the order of the renormalization scale. We do this to avoid unwanted large logarithms which can ultimately spoil our perturbative expansion. As we did in Sec.
(2), we define the EW and CB vacuua as: In terms of the individual components of the fields Φ 1 and Φ 2 (see Eqn. (2.2)), this means that the following real components will have non-zero VEVs, with all other component fields of Eqn. (2.2)) have expectation values equal to zero. As stated above, we choose the scale of the VEVs to be on the order of the renormalization scale. That is, we set: We set v 2 1 + v 2 2 = µ 2 = (246 GeV) 2 to of course in order obtain a SM-like EW vacuum, with gauge boson and quark masses in accordance wit experiment, but with an arbitrary value of tan β = v 2 /v 1 . However, when we search for other minima by numerically minimizing the effective potential w.r.t. the fields r 2 , r 2 and c 1 (see below), we may find deeper EW minima which no longer satisfy this condition v 2 1 + v 2 2 = (246 GeV) 2 (this is a well known property of the 2HDM, already occurring at tree level). However, this condition allows us to find situations where at least there is a SM-like vacuum.
Initializing the 2HDM Parameters: In the 2HDM we consider, there are a total of 3 dimensionful mass parameters and 5 dimensionless quartic couplings (see Eqn. (2.1)): As with the vacuua, we choose the dimensionful mass parameters to be of the same order as the renormalization scale. That is, we choose: As we stated above, we make this choice to avoid generating large scalar masses which in turn could lead to large logarithms. In choosing the values of the dimensionless couplings, we keep in mind that sufficiently large couplings will result in a breakdown of perturbation theory. In practice, the breakdown occurs when dimensionless expansion parameters exceed 4π (since the perturbative expansion is in powers of (expansion parameter)/4π.) To satisfy perturbative unitarity, we keep all of the quartic couplings to be below 10. In addition to perturbative unitarity, we also wish to have a stable potential for the scalars. The tree-level conditions for stability of the scalar potential are: With these conditions and perturbative unitarity in mind, we choose the quartic couplings such that: − λ 1 λ 2 ≤λ 3 ≤ 10 + λ 1 λ 2 (4.13) −1 ≤λ 4 , λ 5 ≤ 1. (4.14) Even with these choices, it is possible to violate the stability conditions. Thus, we generate parameters according to the above prescriptions and then check if the three-level potential is bounded. If it is, we continue, otherwise, we continue to generate parameters until the potential is stabilized.
Extremize the Effective Potential: Our goal is ultimately to have minima at the EW and CB vacuua we have chosen. As a first step, we simultaneously extremize (not knowing ahead of time whether or not we are at a minimum, maximum or saddle point) the effective potential at the EW and CB vacuua. To do this, we must simultaneously solve the following five root equations: The derivatives of the effective potential are given by: Here M 2 s,i (Φ) are the eigenvalues of the scalar squared-mass matrix, M 2 g,i (Φ) are the eigenvalues of the gauge squared-mass matrix and M 2 top (Φ) is the squared top mass. Note that the factor of 3 on the log of the gauge contribution comes from the polarization of the massive gauge fields (the fact that the W boson is charged is also taken into account on the sum over the four eigenvalues of the gauge boson mass matrix of Eqn (3.18)) and the factor of 12 for the top contribution accounts for the 3 colors, 2 spins, and charge of that particle.
To solve the five root equations, we must have five independent parameters which can vary. Since we wish to fix the EW and CB vacuua, we must resort to varying five of the 2HDM parameters. To ensure that we can sample the entire parameter space, we randomly choose any five 2HDM parameters (i.e., any given five of the quadratic or quartic parameters) to vary each time we solve the extremal equations. We employ the NLsolve.jl Julia library [43] using the Trust Region method. Since we allow five of the 2HDM parameters to vary, we could potentially find solutions which make the scalar potential unstable or spoil the perturbative expansion. We thus reject solutions which for which the stability conditions are violated or solutions which have 2HDM parameter which are too large (m 2 ij > (10µ) 2 or |λ i | > 10.) As explained in Sec. (3), there are no analytical expressions for the squared scalar masses for an arbitrary vacuum configuration. They must, therefore, be computed numerically by calculating the eigenvalues of the scalar squared mass matrix. This makes computing the derivatives of the eigenvalues of the scalar mass matrix extremely difficult. To obtain those (first and second-order) derivatives, then, we employ an algorithm using forward-mode automatic differentiation through the use of dual-numbers, which we explain in App. (A). We use the FowardDiff.jl package [44], which implements a dual-number type in Julia. This allows us to simply pass dual-number types into the effective potential, and we obtain automatic derivatives without ever needing to use Eqn. (4.16) 4 .
Finding Additional Minima: As explained above, we solve the minimization conditions of the one-loop effective potential so as two obtain two different extrema. But beyond those two vacuua -one EW breaking, the other CB -the 2HDM potential may yet have other extrema. For instance, if at tree-level the CB minimum is unique (see [9,10]) other neutral minima may exist ( [13,14,16,45]). To search for any remaining minima of the effective potential, we randomly generate 50 vacuum configurations and perform a numerical minimization starting from these vacuua, verifying whether the potential may assume deeper values than the starting points. The minimization is performed using the Broyden-Fletcher-Goldfarb-Shanno algorithm provided from the Optim.jl library [46]. After performing this procedure, we sometimes find a minimum which is not one of the initial solutions found by solving the extremal equations of Eqn. (4.15). For these deeper neutral minima, it is likely that we will now have v 2 1 + v 2 2 = 246 2 GeV 2 , the so-called "panic vacuua" of refs. [47,48].
Characterizing Extrema: After we have found extrema of the effective potential, we need to determine if they are minima, maxima or saddle points. In general, an extremum of a scalar function can be characterized by computing the eigenvalues of the Hessian matrix. The Hessian matrix is the matrix consisting of all second derivatives of the function, which in our case is an 8 × 8 matrix with components: ∂ 2 V eff /∂φ i ∂φ j . The components of the Hessian matrix of the effective potential are given by: If the Hessian matrix is positive semi-definite (i.e. all the eigenvalues are greater than or equal to zero), then the extremum is a minimum (note that the zero eigenvalues signal a flat direction, which we will explain momentarily.) Similarly, if the eigenvalues of the Hessian are negative semi-definite or neither positive nor negative semi-definite, then the extremum is a maximum or saddle point, respectively. When the two Higgs doublets attain their non-trivial VEVs, the SU(3) c × SU(2) L × U(1) Y gauge group is broken. In the case of the EW VEVs, the gauge group is broken down to SU(3) c × U(1) EM and in the case of CB VEVs, the gauge group is broken down to SU(3) c . In either case, we expect there to be Goldstone bosons corresponding to each broken generator of the gauge-group. The Goldstone bosons will manifest themselves as zero eigenvalues 5 of the Hessian matrix, i.e. flat directions of the effective potential. In Tab. (1), we list the various extrema type corresponding to the eigenvalues of the effective potential Hessian. As with computing first derivatives of the effective potential, to compute the second derivatives, we use automatic differentiation. This again allows us to simply pass dual-numbers into the effective potential (in this case we pass nested dual numbers, i.e. dual numbers consisting of dual-numbers, see App. (A)) and we obtain the second derivatives without ever having to use Eqn. (4.17).
Notice that the second derivatives of the one-loop effective potential provide the one-loop ∂ 2 V eff /∂φ i ∂φ j Eigenvalues Extrema Type 3 zero, 5 positive EW minimum 3 zero, 5 negative EW maximum 3 zero, 5 positive and negative EW saddle 4 zero, 4 positive CB minimum 4 zero, 4 negative CB maximum 4 zero, 4 positive and negative CB saddle Table 1: Characterization of the extrema of the 2HDM effective potential. squared scalar masses computed at zero external momentum. For massive scalars they are therefore an approximation to the exact result, but for the massless Goldstones -which must be computed at precisely zero external momentum -they yield the exact result. Obtaining the correct number of massless Goldstones for either the EW or CB extrema is a powerful check of our calculations.
Results
In this section, we describe the results of running the algorithm described in the previous section to find counter-examples to the tree-level theorem described in Sec. (2). To wit, our purpose is to investigate whether at the one-loop level an EW minimum is guaranteed to be stable against charge breakingi.e., whether still at one-loop there is no deeper CB extremum. Further, we will verify whether at one-loop the existence of an EW minimum also implies that any CB extremum must need be a saddle point. All computations were run on a 2015 Mac Book Pro using 8 threads. We developed all of the code for this algorithm using the Julia language, using various well-developed Julia packages. For example, we use the ForwardDiff.jl [44] package for automatic differentiation, NLsolve.jl [43] for solving the root equations of Eqn. (3.33) and Optim.jl [46] for performing minimizations. All the code developed for this project can be viewed/downloaded on GitHub. For more details, the interested reader may e-mail the authors.
To consider a set of vacuua (EW and CB) and 2HDM parameters to yield a counterexample to the tree-level theorem, we set various requirements. First, to be a counterexample to the tree-level theorem, we must have a minimum of the effective potential at an EW and CB vacuum. We consider a vacuum to be an extremum of the effective potential if the infinity-norm of the gradient is less than 10 −5 (although in many cases we obtain much higher accuracy.) We categorize the extremal type (minimum, maximum or saddle) of a vacuum using the conditions in Tab. (1). In particular, we consider an EW vacuum a minimum if the Hessian of the effective potential evaluated at the vacuum contains three zero masses (Goldstone bosons corresponding to the breaking of SU(2) L ×U(1) Y → U(1) EM ) and five positive masses. In the case of a CB vacuum, we require four zero masses (the additional zero mass due to the explicit breaking of U(1) EM ) and four positive masses. In addition, we require that the tree-level potential is bounded from below (following the conditions of Eqns. (4.9-4.10).) We also require that the values of the 2HDM be constrained to be of natural order: |m 2 ij | < (10µ) 2 , |λ i | < 10 where µ is the renormalization scale. We make these requirements to preserve our perturbative expansion and avoid generating large masses which could result in large logarithms.
After running our algorithms for roughly 24 hours, we found ∼ 3000 sets of parameters which yield simultaneous one-loop EW and CB minimathis is the first demonstration that the tree-level vacuum stability theorem is no longer valid at one-loop. Out of these 3000 sets, for ∼ 1000 of then, the global minimum of the one-loop effective potential was the CB vacuum; the remaining ∼ 2000 had the EW vacuum as the global minimum. To get a sense of how common the sets of parameters yielding counter-examples were, we also recorded those sets of parameters for which there was only an EW minimum (no CB) and for which there was only a CB minimum (no EW). The former yielded ∼ 54000 sets of parameters, while the latter ∼ 17000. Thus, we can see that parameters which yield both a CB and an EW minimum are roughly 5% of those which yield a single minimum -thus even at one-loop, we can expect that the exclusion of regions of parameter space due to CB vacuum instability will be rare. Furthermore, only 4 out of the 1000 points which yielded a deeper CB minimum have positive tree-level masses and 10 for the case where the EW was deeper (the remaining contained at least one negative tree-level mass from either the CB or EW vacuum.) We should stress, however, that our purpose is not to perform a thorough scan of the 2HDM parameter space to find charge breaking bounds of the model, but rather to prove that the tree-level vacuum stability theorem no longer holds. As mentioned in Sec. (3.4), for parameters with negative tree-level masses which result in one-loop minima, one likely needs to perform a resummation to obtain a sensible result (i.e. one that doesn't exhibit an apparent instability -imaginary part of the effective potential), which we have not done. But having performed the scan over the model's parameters such that the tree-level masses at the one-loop minima were always positive, the issue of a complex one-loop effective potential is no longer an issue that should worry us. Table 2: Parameter values. Quadratic parameters in GeV 2 , VEVs in GeV and potential values in GeV 4 . All values have been rounded for readability.
We provide two sets of parameters yielding counterexamples to the tree-level theorem in Tab. (2): one for the case where the CB vacuum is deeper than the EW one (left column) and one where the EW minimum is deeper than the CB one (right column.) 6 We reiterate that both of these points are convex at tree-level, meaning all of the squared scalar masses at tree-level are positive at the one-loop extrema, yielding no complex contributions to the effective potential. To better visualize the behaviour of the potential at both extrema for both sets of parameters, consider Fig. (1). Of course, it is impossible to visualize the full, 8-dimensional potential at these points, but to give some sense of what it looks like in the vicinity of the one-loop vacuua, we resort to one-and two-dimensional "slices". Thus, in Fig. (1), we display the one-loop and tree-level potential evaluated at each vacuum and along a line linearly interpolating the EW and CB vacuua for the parameters/vacuua given in Tab. (1). This means we are evaluating the potential along values of the fields given by, for each component of the doublets, φ(t) = (1 − t) φ EW + t φ CB . Thus, at t = 0, the potential is being evaluated at the EW vacuum and at t = 1 at the CB vacuum. Fig. (1) show that the potential always has minima at the EW and CB extrema, both at tree and one-loop level. This is, however, deceiving -at tree-level, the vacuum stability theorem states that if there is an EW minimum, any CB extrema will be a saddle point. However, the tree-level potential is not in fact at minima for both the EW and CB one- Figure 1: One dimensional slices of the effective scalar potential. The horizontal-axis represents vacuum configurations interpolating between the CB and EW vacuua. i.e. we interpolate between φ(t) = (1 − t)φ EW + tφ CB . Hence, at t = 0, φ(t = 0) = φ EW and at . The values of the VEVs and parameters are given in Tab. (2).
loop-vacuua. For both points given, the parameters give no solutions for the tree-level minimization conditions, and the one-loop EW vacuum is near the global tree-level vacuum but the one-loop CB is simply at some convex point at tree-level (but not an extremum). It would be easy to see that along some other direction(s) in field space the seeming tree-level extrema would not be minima at all. What is however clear from Fig. (1) is, as soon as we realize that at one-loop both the EW and CB extra are minima, the tree-level vacuum stability theorem is once again violated at the one-loop levelit is possible, at one-loop, to obtain a potential with an electroweak breaking minimum, which also possesses a deeper charge breaking minimum. Thus the absolute stability of 2HDM EW minima found at treelevel is broken by radiative corrections -the quantum mechanical effects on the effective potential can change the vacuum properties of the model. To further illustrate the behaviour of the 2HDM potential close to these extrema consider Figs. (2) and (3). There we display a two-dimensional slice of the effective and tree-level potentials. In these figures, the horizontal axis is identical to that of the onedimensional plots of Fig. (1) -that is, a line interpolating between both one-loop minima. The vertical axis in Figs. (2) and (3) represents variation along a direction s in r 1 − r 2 − c 1 space which is orthogonal to the line interpolating the EW and CB vacuua. These figures give us a slightly more convincing visualization of the minimization at the EW and CB vacuua, and show the distortion induced upon the tree-level potential by the loop corrections. Having said that, they are nonetheless incomplete images of the full 8-dimensional picture and can not illustrate, for instance, the conversion between tree-level saddle points and one-loop extrema that the violation of the tree-level vacuum theorem implies.
We have fixed the renormalization scale µ to 246 GeV, and the procedure we fol- Figure 2: A two-dimensional slice of the effective potential (left) and the corresponding tree-level potential (right) for the case where V eff (φ CB ) < V eff (φ EW ). The horizontal axis is identical to that of Fig. (1). The vertical axis is an line in r 1 − r 2 − c 1 space orthogonal to the t-axis, i.e. orthogonal to a line connecting φ EW and φ CB . The scale of s vertical axis is identical to the scale of the horizontal axis, i.e. distance in field space from (t = 0, s = 0) and (t = 1, s = 0) is identical to the distance in field space between (t = 0, s = 0) and (t = 0, s = 1) (both these distances are the distances between φ EW and φ CB .) lowed should, obviously, not depend on that choice. To verify that the results we obtained are indeed not dependent on a particular choice of µ, we took the parameters given in Tab. (2) and evolved them according to their RG equations (see the appendix of Ref. [49] for explicit expressions for the RG equations for the THDM parameters.) We use the DifferentialEquations.jl [50] package to perform the RG evolution of the parameters from µ = 246 GeV to µ = 400 GeV. At all renormalization scales between 246 − 400 GeV, we re-minimize the effective potential starting from both the EW and CB vacuua, determining the new VEVs at each minimum for the new values of the parameters of the potential at the new scales. We then compute the value of the one-loop effective potential at each minimum, which we show as a function of the renormalization scale in Fig. (4), for both sets of parameters given in Tab. (2). As we can see, the separation of the EW and CB vacuua is preserved as a function of the renormalization scale. Also, we can see that the difference of the values of the potentials is nearly a constant, which is a consequence of the fact that the effective potential at the minimum is RG independent. The values of the effective potential These plots demonstrate that our results are independent of the particular choice of renormalization scale that we chose.
only change due to us not including the RG evolution of the field-independent piece of the effective potential (which is the same for both the curves). To better understand this point consider the discussion in [51,52]: the one-loop effective potential depends on a set of parameters λ i , fields φ j and renormalization scale µ, and it may be written generically as where the field-independent term Ω is the same for any extremum of the potential. The crucial insight to understand the behavior shown in Fig. (4) is that, unlike what one usually thinks, the sum V 0 + V 1 of the tree-level and one-loop contributions to the potential, is not RG independent. Rather, the independence of the renormalization scale on the full effective potential, dV /dµ = 0, is accomplished at the one-loop level by "compensating" the µ dependence on V 0 + V 1 with that of the Ω term [53]. But since Ω does not depend on the value of the fields it will not change between the EW and CB minima, and as such it is trivial to obtain d(V 0 + V 1 ) EW /dµ = d(V 0 + V 1 ) CB /dµ -meaning, one expects that by varying the value of the renormalization scale, the value of the potential at the EW minimum evolves "parallel" to that of the CB minimum, and that is exactly the behavior one witnesses in Fig. (4). Thus the conclusion is that indeed our one-loop result is not an artifact of a specious choice of renormalization scale, but rather it is independent of the value of µ. However, we emphasize that these parameter sets exemplify the best case scenario obtained in our numerical calculations, boasting nearly perfect RG evolution. Not all parameter sets we found behave as well. In particular, we find some parameter sets for which the RG curves cross. Crossing of the RG curves signals that 2-loop corrections to the effective potential and RG equations are likely important for those particular sets of parameters. Before concluding, it is worth mentioning the consequences of these results. At treelevel, it was clear that, since it is impossible to have simultaneous EW and CB minima, an EW vacuum would be stable against the possibility of charge breaking, i.e. no tunneling could occur that would spoil the residual U(1) EM gauge symmetry and disastrously give the photon a mass. This is no longer the case when one considers the quantum corrections to the classical potential. That is, simultaneous EW and CB minima can exist at oneloop. This implies that, if we lived in a EW vacuum of the one-loop effective potential in a scenario where there is an additional, deeper CB vacuum, it would be possible to tunnel to the CB vacuum. The decay rate of the EW vacuum would be highly suppressed since the simultaneous minima are only realized at one-loop. In particular, we would then expect the decay rate to be a two-loop effect and of the order O 2 .
Conclusions
In this work, we have analyzed the vacuum structure of the one-loop effective potential of the 2HDM. At tree-level, the 2HDM scalar potential is found to have a remarkable stabilityany minimum which breaks the ordinary electroweak symmetries and thus preserves charge conservation (and furthermore, also preserves CP) is guaranteed to be stable against the possibility of charge breaking vacuua -meaning, any CB extremum that eventually might coexist with that minimum is guaranteed to lie above it, and furthermore to be a saddle point. This theorem was found in 2004 via analytical calculations with the 2HDM potential, along with a series of other remarkable results concerning the model's vacuum structure [9,10,13,14].
The first hint that these vacuum stability theorems might not hold at one-loop was obtained analyzing the coexistence of neutral minima in a version of the 2HDM, the Inert Model. Comparing tree-level minima with one-loop ones, using the formalism of the effective potential, it was possible to show that the loop corrections might indeed change the nature of the vacuum -for certain choices of parameters, a minimum which at tree-level was global would become a local one at one-loop [20]. It then became clear that an analysis of the one-loop potential was required to ascertain whether the stability of EW minima against deeper CB vacuua remained a valid conclusion. This work shows that the theorem does not hold at one loop.
We have indeed obtained, through extensive numerical scans of the parameters of the model, many cases where an EW minimum of the one-loop effective potential can coexist with a CB minimum -this is a first violation of the tree-level theorem, which stated that an EW minimum implied necessarily CB saddle points. We have also determined that one-loop EW minima can coexist with deeper CB minima -and hence the tree-level stability against CB of the 2HDM no longer holds at one-loop. The conclusion one must draw from these results is that quantum corrections to the potential may change the vacuum structure of said potential. Conclusions drawn at tree level for which kind of minimum is the global one, and whether it is stable, may well not survive a higher-order calculation. And this, in fact, perhaps should not surprise us -after all, this is indeed what one already obtained in the case of the Coleman-Weinberg potential [54].
Our calculations were performed using tried-and-true computational algorithms and numerical minimization routines which are widely available, and we offer two examples of parameter sets to be checked by interested readers. Issues of gauge dependence of the effective potential should not affect the validity of the conclusions drawn here since we are fundamentally comparing the value of the effective potential in different minima. Though we only included the contribution of the top quark, clearly the results would not qualitatively mutate with the inclusion of further fermions. And the calculations underwent a rigorous check via the computation, at each EW and CB extremum, of the respective one-loop Hessian matrices. That check had a twofold purpose: to verify the nature of any given extremum, so that we could be certain when claiming to have found minima and to verify whether the correct number of Goldstone bosons was found -three for any EW vacuum, four for a CB one. Further, a verification of the independence of our results from the value of the renormalization scale µ we chose was undertaken -an RG evolution of the parameters of the potential in an interval of values of µ was performed, followed by a re-minimization of the potential to obtain the values of the VEVs at each new scale. The comparison of the values of the potential showed that the relative depth of the minima remained unchanged with the renormalization scale, and thus our conclusions are RG stable.
Should this mean that we are witnessing a breakdown in perturbation theory, wherein higher-order corrections invalidate our calculations? Hardly -the RG evolution performed showed us that perturbation theory is working as one would expect. The results of [20] should further illuminate our conclusions -what was found there was that loop corrections could change tree-level expectations for the nature of the vacuua by "swapping" global and local minima, but that this could only occur if both minima were nearly degenerate. Thus, one concludes, at least for the results of [20], the loop corrections are small and acceptable perturbations that "flip" the system between two states of nearly degenerate energies. Likewise, the interpretation of the results we present in the current work points to perturbation theory still holding: a vast numerical scan of the model's parameters only yields counterexamples to the tree-level theorem for a small subset of the parameter space. Also, the tree-level result was strongly dependent on the specific form of the potential; of its derivatives; of the scalar squared masses. At one-loop something remarkable occursthe vacuum is determined, not only by the scalar sector but by all sectors of the theory, gauge and Yukawa included. It is therefore unsurprising that different statements can be made.
To conclude, the 2HDM electroweak vacuua is not guaranteed to be stable against charge breaking vacuua -there may well be, for certain regions of parameter space, deeper CB minima below an EW one, and it may well happen that the tunneling time to the deeper minimum is smaller than the age of the universe. Though we expect this situation to be rare, this work raises the necessity to perform a wide reassessment of bounds imposed upon the parameters of the 2HDM, by fully analyzing the one-loop vacuum structure of the model. The task is not an easy one, for the one-loop effective potential is very complex and unwieldy, especially at CB vacuua. Finally, two comments-first, we have used the results from [9,10] concerning the simplest form one could take for CB vacuua; but those results stem from an analysis of the tree-level potential, so they too might change when considering a one-loop calculation. Second, in [9,10] the tree-level theorems deduced concerned the stability of EW vacuua against, not only CB, but also minima with spontaneous CP violation. As for the case of CB, the conclusion therein obtained was that any EW minimum cannot have a deeper CP breaking extremum, and any such extremum is found to lie above the EW minimum and be a saddle point. Given that we have shown that at one-loop an EW could coexist with a deeper CB minimum, there are strong reasons to believe that the same will apply to coexistence with CP minima. differences in which the derivative is approximated using (with forward finite differences): This method suffers from many issues. First off, to get a good approximation of the derivative, one would like to make as small as possible. However, due to the finite precision of machine numbers, as becomes sufficiently small, round-off errors will seep into the calculation and the error in the approximation will increase [55]. Thus, there is a given value of for which finite-differences yields the smallest error and one can do no better. Another method for evaluating derivatives is to use the complex-step method [56], in which the derivative is approximated using: This method doesn't suffer from the round-off errors that arise from finite differencing. can be taken arbitrarily small. However, the complex step method requires one to only use real numbers (if one mixes complex derivatives with the complex step method, the results will be non-sense.) A slightly more complicated, but robust method of numerically computing derivatives in forward-mode automatic differentiation [55]. The core idea of forward-mode automatic differentiation is the concept of dual-numbers. A dual-number is defined similarly to infinitesimals: where has the property that 2 = 0. The algebra of dual numbers is defined as follows: If we set d = x + (i.e. set b = 1), then we find f (x + ) = f (x) + f (x). We thus obtain f (x) and f (x) by evaluating f at the dual number x + . Using dual-numbers provides us with a method of computing exact derivatives (up to machine precision.) Dual-numbers can also be used to compute higher-order derivatives by nesting dual-numbers: i.e. have dualnumbers of dual-numbers. For example, if d = a + 1 b with a = a 1 + a 2 2 and b = b 1 + b 2 2 , with 2 1 = 2 2 = 0 and 1 2 = 0, then we find the following: = f (a 1 ) + 2 a 2 f (a 1 ) + 1 (b 1 + 2 b 2 ) · (f (a 1 + 2 f (a 1 ))) (A.8) = f (a 1 ) + b 1 1 f (a 1 ) + a 2 2 f (a 1 ) + b 2 1 2 f (a 1 ) + a 2 b 1 1 2 f (a 1 ) (A.9) If we set a = x + 2 and b = 1 + 0 2 , then we obtain: f ((x + 2 ) + 1 (1 + 0 2 )) = f (x) + 1 f (x) + 2 f (x) + 1 2 f (x) (A.10) Hence, the 1 component of the number gives the first derivative of f and the 1 2 -component gives the second derivative of f . If we continue nesting dual-numbers, we can compute arbitrary derivatives of f (x). Given the power of template meta-programming and multiple-dispatch built into Julia, it is an easy task to implement dual-numbers numerically. Below we provide code snippets of how this is done (note that this is not what we use, instead we use ForwardDiff.jl a well-developed Julia package.) The basic idea of implementing dual-numbers is to define a new type, which we call Dual. We then overload all necessary operations that we need, i.e., addition, subtraction, multiplication, division and any other functions we wish to use with dual-numbers. Our type Dual contains two attributes: val (the real component of the dual-number) and eps (the infinitesimal part): where the second component of the dual number is: ∂ ∂x (xy) = y = 2. Another example would be to take the sine of a dual number: julia> sin(d1) Dual{Float64}(0.8415, 0.5403) which we notice has sin(1) in the first component and cos(0) in the second component. Once basic operations like the above have been defined, one can then chain together very complicated functions and easily obtain their derivatives. Additionally, we can easily take second derivatives as well by nesting the dual numbers. If we define a cos overload, we can then take the second derivative of the sine function: Base.cos(z::Dual{T}) where T<:Real = Dual{T}(cos(z.val), -sin(z.eps)) julia> d3 = Dual{Dual{Float64}} (Dual{Float64}(1., 0.), Dual{Float64}(0., 1.)) julia> sin(d3) Dual{Dual{Float64}}(Dual{Float64}(0.8415, 1.0), Dual{Float64}(1.0, -0.8415)) Here, the second component of the first dual is d/dx sin(x) = cos(1), the first component of the second dual is the same and the second component of the second dual is the second derivative of sin at x = 1. | 14,392 | 2019-10-18T00:00:00.000 | [
"Physics"
] |
Numerical results for the lightest bound states in $\mathcal{N}=1$ supersymmetric SU(3) Yang-Mills theory
The physical particles in supersymmetric Yang-Mills theory (SYM) are bound states of gluons and gluinos. We have determined the masses of the lightest bound states in SU(3) $\mathcal{N}=1$ SYM. Our simulations cover a range of different lattice spacings, which for the first time allows an extrapolation to the continuum limit. Our results show the formation of a supermultiplet of bound states, which provides a clear evidence for unbroken supersymmetry.
Supersymmetry (SUSY) plays a fundamental role in the physics of elementary particles beyond the standard model. The understanding of the nonperturbative phenomena of SUSY theories is important since they might explain the supersymmetry breaking at low energies. Besides the relevance for extensions of the standard model, supersymmetric gauge theories also provide insights into nonperturbative phenomena that also occur in QCD, such as confinement of color charges, at least in certain regimes since supersymmetry constrains the nonperturbative contributions. Nonperturbative numerical methods such as lattice simulations are essential to complement and extend the obtained analytical understanding from SUSY models to theories with less or no supersymmetry.
Supersymmetric extensions of the standard model must include the superpartners of the gluons, the so-called gluinos, which are Majorana fermions transforming under the adjoint (octet) representation of SU (3). The gluino would interact strongly, and the minimal theory describing the interactions between gluons and gluinos is N ¼ 1 supersymmetric SU(3) Yang-Mills theory, abbreviated SU(3) SYM theory. The strong interactions between gluons and gluinos are expected to give rise to bound states organised in supermultiplets degenerate in their masses, if supersymmetry is unbroken. The structure of the supermultiplets has been theoretically investigated in Refs. [1][2][3]. The boson-fermion degeneracy is expected to appear at the nonperturbative level and, as a consequence, the singlet mesons and glueballs of QCD-like theories have an exotic fermion superpartner, the gluino-glue, which is a bound state of a single valence gluino with gluons. These predictions are based on formal considerations since a detailed analysis with nonperturbative methods for the theory at low energies has been missing. Unbroken supersymmetry is usually expected due to a nonvanishing Witten index of the theory. However, in presence of relevant nonholomorphic contributions the general picture might be questionable [4] and an investigation without any previous assumption would be desirable. SU(3) SYM theory is of a complexity comparable to QCD, and Monte Carlo lattice simulations are an ideal ab initio approach to investigate this theory. In particular, a study of the mass gap of the particle spectrum requires numerical simulations. As supersymmetry is explicitly broken by any lattice discretization [5][6][7][8], it is a challenging task to show that the bound states masses are consistent with the formation of supermultiplets in the continuum limit. It would open up the possibility of much further reaching numerical investigations of SYM theory and correspond to the first step towards a numerical investigation of supersymmetic QCD and gauge theories with extended supersymmetry, since SYM theory is one sector of these theories. Such a result would also provide evidence for the correctness of the conjectured bound state spectrum and for the absence of an unexpected breaking of supersymmetry by the nonperturbative dynamics. In this Letter, we focus on the spectrum of bound states of the N ¼ 1 supersymmetric Yang-Mills theory with gauge group SU(3). In previous projects we have investigated SYM theory with gauge group SU(2) [9][10][11], which can be considered to be a test case for the more realistic SU(3) SYM theory that contains the gluons of QCD. The gauge group SU(3) brings new physical aspects; for instance, it has complex representations in contrast to SU (2), and other types of bound states are possible. The breaking pattern of the global chiral symmetry group is also quite different from the case of SU (2). In particular, in the region of spontaneously broken symmetry, it is expected that CP-violating phases exist, which are related to each other by discrete Z 3 transformations.
We have presented our first data at a single lattice spacing in Ref. [12] together with some estimates of systematic uncertainties. The present Letter is the first final analysis for the lowest chiral supermultiplets of SU(3) SYM theory with a complete chiral and continuum extrapolation.
In the continuum the (on shell) Lagrangian of SU(3) supersymmetric Yang-Mills theory, containing the gluon fields A μ and the gluino field λ, is where F μν is the non-Abelian field strength and D μ denotes the gauge covariant derivative in the adjoint representation of SU(3). The gluino mass term with the bare mass parameter m 0 breaks supersymmetry softly. The gauge coupling g is represented in terms of β ¼ ð6=g 2 Þ, and the mass in terms of the hopping parameter κ ¼ ½1=2ðm 0 þ 4Þ. The technical details of our approach for the numerical simulations of SU(3) SYM theory have been described in our previous publication [12]. We employ the lattice discretization of SYM proposed by Curci and Veneziano [13]. In our approach the bare mass parameter is tuned to the chiral limit determined by the point where the adjoint pion m a-π mass vanishes. The basic Wilson action for the gluino is in our case improved by the clover term to reduce the leading order lattice artifacts, see Ref. [12] for further details. We have used the one-loop value for the coefficient c sw [14], leading to a one-loop OðaÞ improved lattice action at finite lattice spacings a. As indicated by our first results [12], the perturbative c sw is already sufficient to provide a drastic reduction of lattice artifacts even at quite coarse lattice spacings.
Alternative approaches have been investigated for the simulation of SYM theory [15][16][17][18], but so far they did not succeed in the continuum extrapolation of the bound state spectrum.
The complexity and the cost of the numerical lattice simulations for this theory is at least as challenging as in corresponding investigations of QCD. Additionally, there are more specific challenges for the technical realization of numerical simulations of SYM theory, such as the unavoidable explicit breaking of supersymmetry on the lattice. Therefore, the most important task of our project is to demonstrate that the infrared physics emerging from the numerical simulations is consistent with restoration of supersymmetry in the continuum limit.
A further specific challenge is related to the integration of Majorana fermions, which leads to an additional sign factor in the simulation [12]. This Pfaffian sign has to be considered in a reweighting of the observables.
The scale, i. e., the determination of the lattice spacings in physical units in terms of a common observable, is measured from gluonic observables. We are using chirally extrapolated values of the scale w 0 from the gradient flow [19][20][21]. The chiral values w 0;χ are obtained at each β by a fit of the data to a second order polynomial in the square of the adjoint pion mass in lattice units ðam a-π Þ 2 .
An improvement with respect to our work on SU(2) SYM theory, where we extrapolated the observables first to the chiral limit and in a second step to the continuum limit, is that we now use a combined fit towards the chiral and continuum limit. The chiral continuum values O χ;cont of the observable O in units of w 0;χ are determined by where x ¼ ðw 0;χ m a-π Þ 2 and y ¼ ða=w 0;χ β 2 Þ (linear extrapolation). Due to the one-loop clover improvement of the action, we expect leading lattice artifacts to be of Oða=β 2 Þ for on shell observables, which leads to the dependence on the gauge coupling in y. The Oða=β 2 Þ contribution could, however, be very small since considerable improvements have been observed already with the tuning to the one-loop level. In order to compare both cases, we perform additional fits with the leading lattice artifact term Oða 2 Þ, i.e., y ¼ ða 2 =w 2 0;χ Þ in Eq. (2) (quadratic extrapolation). The main indication for restoration of supersymmetry in lattice simulations presented in this Letter is the formation of mass degenerate supermultiplets. An alternative indication is given by the supersymmetric Ward identities. The violation of the supersymmetric Ward identities in the chiral limit is an indication of lattice artifacts, since chiral symmetry and supersymmetry should be restored at the same point in the continuum theory, if there is no unexpected supersymmetry breaking. The Ward identities also provide a cross check for the tuning of the bare gluino mass parameter. We have found that the Ward identities are consistent with a restoration of supersymmetry, and the leading lattice artifacts are Oða 2 Þ as found in Ref. [23]. This analysis will soon appear in a separate publication.
We have performed simulations at a large range of values of the inverse gauge coupling β ranging from β ¼ 5.2 up to β ¼ 5.8 to search for an optimal window for the continuum PHYSICAL REVIEW LETTERS 122, 221601 (2019) limit extrapolation. In our previous work [12] we have presented the first results for the particle spectrum of SU(3) SYM theory obtained at a single lattice spacing. We have now investigated the systematic uncertainties regarding the finite size effects, the sampling of topological sectors, and the fluctuations of the Pfaffian sign, and found a parameter range where these effects are under control. Only a subset of the considered β range turned out to be reliable for the determination of the bound states. The coarsest lattice spacings (smallest β values) are too far away from the continuum limit, which makes the extrapolation unreliable. The finest lattice spacings (largest β values) suffer from large finite volume effects and a freezing of the topological fluctuations. According to these criteria, our final selection of β values is 5.4, 5.45, 5.5, and 5.6.
In the current Letter, we present the final results for the lightest particles of SU(3) SYM theory. We are now able to combine several different lattice spacings in an extrapolation to the continuum limit. In comparison to Ref. [12], we have also improved our determination of the bound states, leading to a clearer signal for the particle masses. These methods have been introduced and tested with the data of SU(2) SYM theory in Ref. [11].
The considered states and corresponding interpolating operators are the scalar meson a-f 0 (Õ a-f 0 ¼λλ), the pseudoscalar meson a-η 0 (Õ a-η 0 ¼λγ 5 λ), the scalar (0 þþ ) glueball, and the fermionic gluino-glue state gg (Õ gg ¼ P μν σ μν Tr½F μν λ), see Ref. [12]. The scalar glueball and the a-f 0 meson are combined in a common variational basis for the scalar channel. The lightest states are expected to form a chiral supermultiplet, which consists of a scalar, a pseudoscalar, and a fermionic spin 1=2 particle. From our previous investigations we expect a reasonable overlap of both the a-f 0 and the scalar glueball with the lightest scalar state, whereas the lightest pseudoscalar state seems to have FIG. 1. The chiral extrapolations of the particle masses at the different lattice spacings using the fit function (2) (y ¼ ða 2 =w 2 0;χ Þ). The gluino-glue (gg), the pseudoscalar a-η 0 meson, and the scalar channel (0 þþ ), which includes a mixing of the glueball and the a-f 0 meson, are extrapolated to the point where the adjoint pion mass vanishes. a dominant overlap with the a-η 0 rather than with the 0 −þ glueball. Therefore we consider the meson-glueball mixing only in the scalar channel, and neglect, at the moment, the 0 −þ glueball. Note that the measurement of the particle masses in SYM theory is quite challenging, involving only flavor singlet and glueball states.
The chiral extrapolations to the point of vanishing adjoint pion mass m a-π are shown in Fig. 1. Away from the chiral point, the particles have different masses and the chiral multiplet splits. This splitting is sizable at least for the coarsest lattice spacings. At these coarsest lattices, the gluino glue becomes the heaviest particle, whereas the scalar particle becomes the lightest state. There is an indication of a remaining mass splitting in the chiral limit at the three coarsest lattice spacings.
At our two finest lattice spacings (β ¼ 5.5 and β ¼ 5.6), there is no considerable splitting between the states of the multiplet in the chiral limit. The scalar, pseudoscalar, and fermion masses are degenerate within errors at β ¼ 5.6 [24]. The 0 þþ state has the largest error of around 20%, and it can not be expected to be more precise than the current glueball measurements in QCD.
A particular problem with our first data at the finest lattice spacing (β ¼ 5.6) has been the long autocorrelation due to topological freezing. As we have already shown in our previous publication [12], larger volumes allow for more topological fluctuations, but the autocorrelation time of quantities like w 0 is still considerably large.
The three different lattice spacings allow for the first time a complete extrapolation of the lightest states of SU(3) SYM theory to the continuum. Compared to our previous work with an unimproved Wilson fermion action for the investigations of SU(2) SYM theory, the differences of the masses in units of w 0;χ between the different lattice spacings are smaller and the continuum extrapolation is rather flat thanks to the clover improved fermion action. Due to the weak dependence on the lattice spacing, the linear and quadratic extrapolations are consistent with each other, see Fig. 2. The final results using the two different fit procedures are summarized in the following table [25]: For comparison, we have also added the data from our previous investigations of SU (2) SYM theory to the table.
We have finalized our first continuum extrapolation of the lightest bound states in supersymmetric SU(3) Yang-Mills theory. We have found a formation of a chiral supermultiplet in the continuum limit. In combination with the results from an analysis of the supersymmetric Ward identities, this is a good indication for the absence of supersymmetry breaking by the nonperturbative dynamics of the theory. It also shows that the unavoidable breaking of supersymmetry by the lattice discretization is under control in this nontrivial theory.
This important observation opens the way towards several further investigations of SU(3) SYM theory, in particular concerning the phase transitions and chiral dynamics of the theory. In addition, it is the first step towards investigations of supersymmetric QCD and other supersymmetric gauge theories that can not be accomplished without control of the supersymmetry breaking in the pure gauge sector.
Our investigation is based on the approach proposed in Ref. [13], which means that chiral symmetry is broken in a Wilson discretization. Our data indicate that the symmetries are restored by a tuning of the gluino mass parameter and the approach can be considerably improved by the clover fermion action.
Our results can be compared to the our previous analysis of SU (2) SYM theory, presented in Refs. [10,11]. We find that in units of w 0 the masses of the multiplets are compatible with each other. This indicates only a weak dependence of the multiplet mass on N c .
One interesting additional aspect for further investigations is the continuum limit of the splitting of the multiplet as a function of the soft supersymmetry breaking. Our current data in Fig. 1 show that the slope of the bound state masses as a function of the gluino mass has a significant dependence on the lattice spacing. Therefore the continuum extrapolations away from the chiral limit are more challenging and we plan further investigations in this direction. | 3,655.4 | 2019-02-28T00:00:00.000 | [
"Physics"
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Provider and female client economic costs of integrated sexual and reproductive health and HIV services in Zimbabwe
A retrospective facility-based costing study was undertaken to estimate the comparative cost per visit of five integrated sexual and reproductive health and HIV (human immuno-deficiency virus) services (provider perspective) within five clinic sites. These five clinics were part of four service delivery models: Non-governmental-organisation (NGO) directly managed model (Chitungwiza and New Africa House sites), NGO partner managed site (Mutare site), private-public-partnership (PPP) model (Chitungwiza Profam Clinic), and NGO directly managed outreach (operating from New Africa House site. In addition client cost exit interviews (client perspective) were conducted among 856 female clients exiting integrated services at three of the sites. Our costing approach involved first a facility bottom-up costing exercise (February to April 2015), conducted to quantify and value each resource input required to provide individual SRH and HIV services. Secondly overhead financial expenditures were allocated top-down from central office to sites and then respective integrated service based on pre-defined allocation factors derived from both the site facility observations and programme data for the prior 12 months. Costs were assessed in 2015 United States dollars (USD). Costs were assessed for HIV testing and counselling, screening and treatment of sexually transmitted infections, tuberculosis screening with smear microscopy, family planning, and cervical cancer screening and treatment employing visual inspection with acetic acid and cervicography and cryotherapy. Variability in costs per visit was evident across the models being highest for cervical cancer screening and cryotherapy (range: US$6.98—US$49.66). HIV testing and counselling showed least variability (range; US$10.96—US$16.28). In general the PPP model offered integrated services at the lowest unit costs whereas the partner managed site was highest. Significant client costs remain despite availability of integrated sexual and reproductive health and HIV services free of charge in our Zimbabwe study setting. Situating services closer to communities, incentives, transport reimbursements, reducing waiting times and co-location of sexual and reproductive health and HIV services may help minimise impact of client costs.
Introduction
In Zimbabwe, the public health system is the largest provider of health-care services complemented by Church run Mission hospitals.However, despite growing demand, service provision has negatively been impacted by suppressed health-care budgets due to economic challenges over the last 2 decades.Non-governmental organizations (NGOs) have increasingly come in to support public health provision.Under the Zimbabwe Integrated Support Programme, Population Services International (PSI) worked with the Ministry of Health and Child Care to delay first birth among women, space their children at least 24 months apart and limit childbearing once their desired family size was achieved.
The initiative aimed to scale up access to a full range of modern SRH services including long-term reversible and permanent contraceptive methods and cervical cancer screening and cryotherapy.In addition to counseling to support informed choice, these services were delivered through innovative service delivery models which were already offering HIV testing services and limited short term contraceptive methods such as injectables, oral contraceptives, emergency contraceptives, male, and female condoms.
In Zimbabwe, the same unsafe sexual behaviours which predispose women and young girls to risk of HIV (human immuno-deficiency virus) infection also put them at increased risk of unplanned pregnancies, cervical cancer, unsafe abortions and sexually transmitted infections (STIs) such as syphilis, gonorrhea, and chlamydia [1].Cervical cancer, strongly associated with HIV infection, is also the most prevalent cancer among Zimbabwean women with high mortality due to late screening [2][3][4].A comprehensive package of high quality, effective, and integrated sexual and reproductive health (SRH) and HIV services is clearly required [5][6][7][8][9][10].Integration involves offering clients both types of services during the same visit by one provider in the same room ("one-stop-shop/ kiosk" model) or during the same visit under the same roof or within the same clinic visit ("supermarket" model), with intra-referrals from one service to another [11][12][13][14].
Integrated SRH and HIV services may offer several benefits.Integration potentially enhances women and young girl's access and utilisation of ordinarily separate SRH service components such as family planning (FP), STI screening and management, and cervical cancer screening and treatment in addition to HIV prevention, treatment, and care as well as tuberculosis (TB) screening and treatment services compared to stand-alone models [15][16][17].Globally, integration of SRH and HIV/AIDS policies, programs, and services will help promote the achievement of international development goals and targets, such as the United Nations Sustainable Development Goal 3, which aims to ensure healthy lives and promote well-being of all [11].
A study in Uganda found integrated services promoted continuity of care, improved clientprovider relationships, increased risk perception and HIV-SRH service demand and utilization among young people [8].Moreover, HIV is transmitted predominantly sexually and vertically during childbirth and breastfeeding which are all reproductive health channels [18].In Botswana, training and technical support provided to nine pilot sites between 2012 and 2013 as part of a countrywide scale up of SRH and HIV linkages with antiretroviral roll-out resulted in an 89% increase in female family planning clients accessing both HIV and family planning services.It also led to a 79% increase in the number of female clients at HIV service delivery points accessing both HIV and family planning services [9].
Integration of SRH and HIV services may be cost-effective as it reduces need for frequent health facility visits while potentially improving coverage of services [16,[19][20][21][22].In addition to provider costs, client costs discourage health seeking behavior particularly among low-income earners and can impede continuity of treatment and care even where services are provided at no user fee.World Health Organization (WHO) and World Bank also estimate 100 million people in poorest countries are pushed into extreme poverty annually due to user fees or outof-pocket expenses (OOPEs) when attending public health services [23][24][25].
Despite the evidence strongly suggesting integrated SRH and HIV services as an important entry point for expanded HIV testing and modern contraceptive use, the huge gaps between promising national integration policies and actual programme implementation, siloed funding by external partners, and service delivery approaches that are not client friendly are a major factor behind missed opportunities [26].Also, integration can be associated with increased staff workload leading to long waiting times.It is therefore critical not only to assess how well integrated SRH and HIV services work, but also to evaluate the economic costs as there is a potential risk of introducing large, and potentially costly, yet ineffectual integration programmes at huge risk for health systems [27].
For Zimbabwe, which is rolling out integrated SRH and HIV services, it is necessary to understand both the provider costs and economic burdens borne by clients and households which could pose an impediment to provision (supply side) and access (demand side) to these services and to help optimize usage [21].We undertook a cost analysis to evaluate the economic costs of integrated SRH and HIV services from both the provider and client perspectives in Zimbabwe.
Cost study setting
We conducted a study to estimate the economic costs of four models of providing one-stop shop integrated SRH and HIV services to women in Zimbabwe as part of the Programme of Research on the Integration of HIV and Sexual and Reproductive Health (SRH) Service.Table 1 provides a detailed description of the service delivery models and the four sites purposively sampled for the costing study based on their advancement along the integration cascade.Cost data were collected at integrated non-governmental organisation (NGO) run clinic sites located in Harare, Zimbabwe's capital city, Bulawayo, the second largest city and Mutare on the eastern border with Mozambique.The other NGO site was in Chitungwiza, a satellite town 30 km south of Harare.
Ethical approval for the Programme of Research on the Integration of HIV and Sexual and Reproductive Health Services was provided by the Medical Research Council of Zimbabwe (MRCZ) and the University College London (UCL) Ethics Committee.Only verbal consent was administered following exemption from written informed consent by the institutional review board of the MRCZ as that would typically take at least 15 minutes for a 5-minute anonymous questionnaire.
We assessed the relative cost per visit of five integrated SRH and HIV services.Costs were assessed for HIV testing and counselling (HTC), STI screening and treatment, tuberculosis screening (TB) with smear microscopy, family planning (FP), and cervical cancer screening and treatment employing visual inspection with acetic acid and cervicography (VIAC) and cryotherapy.The Chitungwiza, New Africa House, and Bulawayo sites are directly run integrated SRH and HIV fixed NGO sites.The Mutare site is an NGO partner managed (Mutare City Council) fixed site.The Private Public Partnership (PPP) Profam clinic site was in a public health facility, Chitungwiza Hospital.For the integrated mobile outreach model, we assessed costs based on activities of outreach teams from New Africa House NGO site in Harare.
Costing overview
This economic cost analysis adopted both the provider and client perspective, including both costs of delivering integrated SRH and HIV services and costs borne by clients (transport, absenteeism from work, and caregiver costs) accessing services [28].Our costing approach followed international costing guidelines [28,30].The costing involved first a facility bottomup costing exercise (February to April 2015) conducted to quantify and value each resource input consumed for provision of individual SRH and HIV services (S1 File).Secondly overhead financial expenditures were allocated top-down from central office to sites and then respective integrated service based on pre-defined allocation factors derived from both the site facility observations and programme data for the 12 month period January to December 2014 [28][29][30][31][32].
Provider cost data collection
At each facility SRH and HIV service utilization data were collected for the retrospective 12-month period (January to December 2014) from program records, monthly reports, registers maintained in each unit or service department.This service utilisation data was important as it is directly related to the quantities of specific inputs that feed into individual integrated SRH and HIV services (S1 Table ).We worked with the provider monitoring and evaluation (M&E) teams to ensure that site records matched central databases on which cleaned and verified data was stored and to ensure data were de-duplicated.
We conducted time and motion analysis to understand how health provider staff shared their time across departments and the specific duration of tasks in integrated service provision to individual clients.Time and motion analysis is the gold standard for measuring staff allocation of time through direct observation [31][32][33].Health provider staff were randomly selected from a departmental staff roster or list of those providing integrated services (we aimed for all or every second participant if more than six) and asked to provide written informed consent to be observed during their work.Trained economics data collectors (two) conducted observations of health providers while they were providing integrated services, recording how much time it took to conduct specific activities.Observations were conducted from outside of consultation rooms to ensure client confidentiality was maintained.We then used the mean time estimates from this process not only to directly estimate provider time costs per individual service but also as an allocation factor for overhead personnel (supervision and other support personnel time) costs.
Client costing overview
We collected costs borne by women at the static NGO sites in Harare, Chitungwiza, and Bulawayo (S2 File).Client costs data collection among women attending the mobile outreach clinic model was precluded by study budget constraints.Female clients (n = 856) who had received one or more of the integrated services (SRH and HIV) were subsequently asked to participate in a 5-minute exit interview conducted by trained research assistants using a structured questionnaire.Costs accessed included direct service plus non-service costs and opportunity costs of time incurred by women seeking integrated SRH and HIV services [33].Direct non-service costs included lost income/productivity/wages from absenteeism whilst seeking health services, transport costs incurred travelling to and from health facilities, caregivers' time and transportation costs, food, and other incidentals.
Clients were asked to indicate occupation, related earnings in US$, transport cost to and from the clinic facility, time taken to get to the clinic (we assumed it would take equal time to get back home), time spent at the clinic, any additional money spent on food and other expenses, or any service (user fees) payments made.Clients were also asked to provide details of any accompanying caregivers on the day, their occupation, earnings per month in US$ and any costs incurred by caregivers while accompanying the women to the clinic facility.Other data collected was on patient characteristics, service(s) sought and recommended by staff and any family planning methods offered and taken up.Costs associated with seeking integrated services were recorded and uploaded in real time using tablets.
Cost data analysis
Provider costs.Provider costs were captured and analysed in a Microsoft Excel spreadsheet that we specifically designed to record and estimate the economic costs of providing integrated services.Each resource input identified from the bottom-up costing exercise and required to provide individual integrated SRH, and HIV services was valued using prices from the NGO's finance department and the NATPHARM reference pricing list [34].Overhead financial expenditures were allocated step wise from central office to sites and integrated SRH and HIV services [35,36].Shared overhead costs such as management, vehicles and space were allocated to clinic services based on recorded usage.Site security, reception, and caretaker services as well as utilities were allocated based on space utilised by respective integrated SRH and HIV services.S1, S6 and S7 Tables provide details on integrated SRH and HIV service utilisation, workforce composition per site and department and space measurements which we used to allocate shared costs.Capital and recurrent costs for each integrated SRH and HIV service were estimated separately and then added up to derive a full total service cost.Unit costs per client visit were estimated by dividing the full total service cost by the number of clients seen per service [33,37].All costs were analysed in 2015 United States dollars.United States dollars were the principal currency in use in Zimbabwe at the time following the demise of the local currency earlier in 2009 due to hyper-inflation [38].
Client costs.Time taken off by individuals from their daily work to seek health services potentially represents a loss not only to themselves directly in the form of lost income, but also to the economy overall.In this analysis we assessed the opportunity costs incurred by women (productivity losses) and their caregivers seeking integrated SRH and HIV services.The human capital approach, the traditional method for estimating productivity losses, assumes that individuals have the potential to produce a stream of outputs (productivity) over their working life and measures lost productivity as the amount of time by which working life is reduced due to illness [39].This work time lost is then valued at the market wage which reflects the value of that work to society.We multiplied the average time spent seeking integrated services (including travel to facility, time spent at facility and anticipated time travelling back home) by clients self-reported earnings per hour.Although traditionally, analysis of lost productivity has focused on paid work, there is increasing recognition that people's unpaid productivity, through roles such as caring for children or relatives, household tasks, and volunteering, also makes important contributions to society [40,41].In our analysis therefore to account for any lost productivity for clients and caregivers who report no earnings due to being unemployed, students or other we impute the median of the stipulated monthly minimum wages across 28 Zimbabwean industrial sectors ($120/month) as a proxy for (S8 Table ) lost income [42,43].In univariate and multivariate sensitivity and scenario analysis we alternatively impute the median monthly earnings of the clients and accompanying caregivers who reported being employed ($200 instead of $120/month) to those reporting no earnings.
Integrated service utilisation
S1 Table presents overall utilisation data by site for all integrated SRH and HIV services during the corresponding 12 months.Utilisation data is based on the pre-existing NGO provider M&E records.For the outreach service 77,278 clients accessed services composed of 69,942 (91%) for HIV testing and 7,063 (9%) for FP.Of the total 49,607 clients accessing services at the New Africa House (NAH) site 41,177 (83%) accessed HIV testing, 3,354 (7%) FP, 2,958 (6%) cervical cancer screening and cryotherapy, 1,561 (3%) TB screening.17,934 clients visited the Mutare site with 12,005 (67%) coming for HIV testing, 3,881 (22%) for FP and 1,922 (11%) for FP.The PPP site at Chitungwiza hospital had a total of 6, 037 visits broken down into 5,042 (84%) for FP, 412 (7%) HIV testing, 327 (5%) STI screening and treatment and 256 (4%) for cervical cancer screening and cryotherapy.
Client characteristics
In total 856 female clients were recruited for exit interviews during the period February to April 2015.We aimed to recruit every third participating woman who had just completed receiving (exiting) any (or all) of the integrated services.However, due to time and study budget constraints our approach also allowed a more purposive sampling strategy when the client flow was slower.S2 Table presents main reason for visit for the sample drawn from New Africa House (n = 456), Chitungwiza (n = 200), and Bambanani (n = 200).Most clients attended integrated clinic facilities to access FP services (48%), followed by cervical cancer screening and treatment (22%), and HIV testing (16%).At Chitungwiza New Start Centre (NSC) however, clients mainly attended for cervical cancer screening (42%).42%, 27% and 19% of clients reported seeking 1, 2 or 3 other services in addition to their main reason for visiting on the day.The other 12% of clients reported seeking 4, 5 or 6 other services in addition to their main reason for visiting.
S4 Table summarizes time spent by clients accessing the integrated SRH and HIV services and shows clients took an almost similar amount of time seeking integrated SRH, and HIV services across the three clinic facilities (Mean = 5 hours).Time (both waiting and receiving services) at the facility (Mean = 3 hours) contributed more to income/productivity losses (63%) in comparison to travel time to (18%), and from clinics (18%), respectively.
Unit costs per service visit by integration model
S5 Table presents the total program and unit cost per visit for each of the 5 integrated SRH and HIV model sites.Total programme costs per model site were $466,000 for Chitungwiza NGO site, $288,000 for Mutare NGO site, $723,000 for the larger Harare NGO site, and $1,168,000 for NGO outreach respectively.The total program cost for the Chitungwiza Profam clinic located in a government facility was $101,000.
Mean costs per service.The mean cost per visit for the 5 integrated SRH and HIV services ranged from a low of $6.06 (TB screening and treatment visit) to a high of US$194 (cervical cancer screening and cryotherapy) at the partner managed model site.Results show some variability in costs per visit across the model sites with highest variability observed for cervical cancer screening and cryotherapy which ranged between US$23 at the NGO managed site and US $194 for the NGO partner managed site.HTC showed least variability in costs ranging between US$11 for the NGO mobile outreach and US$19 at the PPP model site (Fig 1).
The model with the lowest unit costs per visit overall was the NGO outreach model site (US $15) and the highest in the PPP model ($17).The model site that offered integrated services at the lowest unit costs was PPP (US$19 for HTC, US$9 for STI screening, $16 for FP and US$26 for cervical cancer screening and cryotherapy) although costs for this site exclude TB screening costs.The model site with the highest costs was partner managed site (US$14 for HTC, US $137 for STI screening, $10 for TB screening, US$22 for FP and US$26 for cervical cancer screening and cryotherapy).Unit costs were mainly recurrent costs driven (Fig 2 ) particularly by personnel 54% (42% -62%), supplies 30% (23% -36%) and management and administration costs 10% (5% -22%).In sensitivity and scenario analysis we varied the key cost contributors, personnel, supplies and management and administration up and down (+/-20%) to assess impact of future salary adjustments, inflation and clinic level client throughput.Results remained robust ranging from 53% to 54% for personnel, 30% to 31% for supplies and unchanging at 10% for management and administration.
Client costs
All clients in this study sample incurred zero OOPE's for services as these were fully borne by the provider.However, clients incurred other direct non-service costs of transport (mean = $1.67) to and from the facility, food, and other related expenses (mean = $1.16), and lost income (productivity losses) due to time spent seeking services (mean = $7.27).For a breakdown of the component costs see Table 2.
The main client cost driver was lost income (productivity losses) from absenteeism measured in time spent travelling (to and from facility) and at the clinic facility waiting and seeking integrated SRH and HIV services (S4 Table ).The longer the distance (measured through time spent travelling to and from facilities), the higher the cost of time expended by clients accessing integrated SRH, and HIV services.Its proportional contribution to client cost per visit was 72% compared to 17% for transport, and 11% for other incidental expenses.Overall, mean total client cost per visit was $10.10, a figure which accounted for 45% of the daily family income ($22.56).When alternatively imputing the median monthly earnings of only the clients and accompanying caregivers who reported being employed ($200 instead of the base case $120/month) to those reporting no earnings client costs increased from $10.10 to $11.62 (56% of the daily family income).
In univariate and multivariate sensitivity and scenario analysis (Fig 3 above) client costs were highly sensitive to variations in time travelling to the facility, receiving services and onwards to next destination.
Discussion
This to our knowledge is the first study to evaluate both provider and client costs of integrated SRH and HIV services across various service delivery models in Zimbabwe.It potentially contributes to a better understanding of the funding needs required to ensure well-funded, managed and delivered health services as called for in "The Framework on Integrated People-
Average time spent travelling to facility (in mins)
Average time spent at facility (in mins)
Average time spent travelling home (in mins)
Total time spent accessing integrated services (Hours) 4 Client cost/daily family income (%) 39% 53% 41% 45% Client cost/daily client income (%) 94% 114% 86% 99% https://doi.org/10.1371/journal.pone.0291082.t002 Centred Health Services" which aims to support countries progress towards universal health coverage by shifting away from health systems designed around diseases and health institutions towards health systems designed for people [44].It provides comprehensive evidence on service utilisation, costs of five of the integrated SRH and HIV services, a complete breakdown of the various cost components contributing to total costs of the five services as well as the main cost contributors to client costs.Services with higher utilisation rates were found at sites that had been offering those services for longer (before launch of integrated services) pointing to service maturity.Personnel, supplies and management and administration costs were the main cost drivers highlighting the relative influence of fixed inputs when uptake of services across sites is lower or higher.Variation in unit costs of integrated SRH and HIV services (partly explained by variation in the proportion of visits) and percentage distribution of cost components across the four models suggests room to improve efficiencies.Elsewhere demand generation initiatives have been shown to increase demand for other integrated HIV programs such as VMMC leading to lower costs per client [45,46].Results of this study highlight the need for more demand generation for integrated SRH and HIV services to fully utilise fixed capital inputs such as human resources and thus achieve lower unit costs.
The study shows that provision of integrated SRH and HIV services in Zimbabwe is generally not only inexpensive, and feasible but it is also cheapest within a PPP Profam model integrated into public sector facilities.In Kenya and Swaziland variability in unit costs and cost components suggested potentially reduced costs through better use of both human and capital resources [45,46].Staff salaries made up a significant proportion of total costs across all services followed by other costs such as diagnostics and supplies.Furthermore there was wide variation in unit cost per visit for all services across facilities.The least variation was found in family planning services and the widest in HIV care [45,46].
We also examined the direct and indirect economic costs incurred by clients accessing integrated SRH and HIV services.For this study, although clients incurred zero direct payments for integrated SRH, and HIV services (fully absorbed by the provider as is often the case in NGO and public sector service for no fee facilities); clients did incur other non-service costs, including transport, food, and productivity losses.Non-service costs constituted 86% of the daily family income and were more than double the daily client income clearly presenting a significant barrier to integrated service access.Furthermore, attendees from poorer households (as measured through earnings) parted with a higher proportion of their daily income inorder to access same services compared to those with higher daily incomes buttressing findings from elsewhere that show client costs discourage access to public health services.Client costs of accessing integrated SRH and HIV services virtually wiped out the daily client income and were 45% of the daily family income.Poorer households therefore lost a higher proportion of their daily income accessing integrated SRH and HIV services in comparison to those with relatively higher daily income.
Our findings suggest that the main client cost driver was lost income (productivity losses) resulting from absenteeism measured in time at clinic facility seeking services, and distance (measured through time spent travelling to and from facilities).The higher the amount of time spent at facilities by clients and the further away from the facility a client's home was situated, the higher the productivity losses.In Malawi living far from public health facilities, and high transportation charges were found to be barriers to care when ART scale up was rolled out [47,48].
According to the World Bank, World Health Organisation, and others the rural poor have been shown to sell off prized assets such as cattle, goats, and farming implements just to afford OOP payments for transport, and medical care in addition to absenting themselves from their daily sources of income [49][50][51][52].This however applies mainly in-order to access emergency medical care rather than for routine clinic attendance.Another study in Kenya concluded that most of the households pushed and trapped into poverty due to medical expenses were those from rural areas as poverty levels differed between urban, and rural areas [53].Studies in Malawi show that even in the absence of direct service payments, client OOPEs were still considerable and imposed debilitating financial burdens on households and clients [33] Additionally, it was the poorest that were hit hardest and who were plunged further into poverty [48].
Our study has some limitations.Firstly, due to time and study budget constraints we used a purposive sampling strategy to identify clinic facilities in which to conduct the cost study based on advancement along the integration cascade.Again due to time constraints individual clients were also recruited for our exit interviews using purposive sampling limiting representativeness of our sample.Results may therefore not be fully representative particularly of other facilities and clients seeking integrated services in the same or similar facilities in Zimbabwe, or elsewhere.Furthermore, our study was conducted within the two largest cities (Harare, and Bulawayo), as well as Chitungwiza and Mutare which are also home to relatively large populations in Zimbabwe.Client cost results from these settings may not be fully representative of clients receiving integrated services in other parts of the country particularly in smaller towns, rural, mining and farming communities.
In addition, the client cost study relied on the relatively low cost self-reported data methodology which has been shown subject to social desirability bias and prone to either deliberate or erroneous under or over-estimation of income, transport, food and other cost estimates especially when there is an expectation of reimbursement [54,55].In other settings, to reduce reporting bias, the opportunity costs of time spent seeking healthcare services have been based on direct observation through time and motion studies which have included direct measurement of the time taken to travel to and from facilities as well as identifying common types of transport and how much they cost.
Despite these limitations however our study approach has some important strengths to note.Firstly we aimed for a mixed methods approach to balance the delicate trade-off between bottom-up accuracy at tracking and assigning resource use at the site and service level and top-down simplicity which is less accurate and obtains more valid cost estimates [56,57].The choice of costing method has been shown to significantly change results of economic evaluations [58,59].Whereas bottom-up micro costing is considered to underestimate overheads, top-down financial expenditure analysis tends to underestimate site level economic costs [36].In addition, as seen elsewhere in the region, overreliance on bottom-up ingredients costing has been shown to create substantial budgetary pressures because real expenditure (as captured in top-down methods) exceeds the estimates thereof [59].Secondly our study takes a societal perspective which more fully accounts for the opportunity costs borne by society compared to the narrower provider approach which does not consider alternative resource uses outside the public health care sector, which potentially yield greater welfare to society [60].
Conclusion
As shown above, and despite the limitations, the results of our cost analysis have clear implications for enhanced integrated SRH and HIV delivery outcomes in Zimbabwe, and other sub-Saharan Africa (SSA) jurisdictions.Given international recommendations for integration of SRH and HIV services from a public health perspective, results from our Zimbabwe study provide further evidence showing that apart from being feasible, integration is a more efficient way of reaching women and young girls who have been shown to be more vulnerable to HIV infection in high HIV prevalence settings such as SSA in general and Zimbabwe in particular.Demand generation for integrated SRH and HIV services can help achieve lower unit costs.Where possible, integrated SRH and HIV service providers in Zimbabwe should negotiate lower drugs, diagnostics, and supplies prices as these were also an important contributor to unit costs of services.It is, however, important to note that other settings such as farming, and mining areas may require a balance between seeking more efficient models with other important service delivery objectives such as accessibility of services in the first place.
In this study, the direct non-service costs of seeking integrated SRH, and HIV services have been shown to be high for clients in urban Zimbabwe despite being available free of charge.To mitigate these effects providers of integrated SRH and HIV services in Zimbabwe, and elsewhere need to minimise impact of client costs by reducing times (both waiting and receiving services), providing transport reimbursements, opening clinics outside working hours and situating services closer to communities/workplaces in-order to compensate for the negative effect of OOPE's.Potentially high productivity losses, transport, and other costs will likely result in a reluctance to utilise integrated SRH and HIV services.In an informal economy such as Zimbabwe's the effects of a day away from one's place of work are more acute for those running informal businesses, most of which are owner operated, in comparison to those who are formally employed and can afford to take a day off from work to access integrated SRH and HIV services.
Table 1 . Models of providing one-stop shop integrated SRH and HIV services. Site integration model type NGO managed static model Partner managed static model Private Public Partnership (PPP) static clinic PSI Zimbabwe managed mobile outreach 1 Service managed by
Limited FP e.g., offer only shortacting FP services, STI, Female and male sterilisation, cervical cancer screening & cryotherapy Additional Integrated services Co-brand with new SRHR franchise brand.Addition of LARM's e.g., IUDs 15 , implants.Expand services from 10 to 20.Screening & treatment for STIs, cervical cancer screening, referral to public sector sites for appropriate follow-up.Comprehensive services for survivors of sexual violence Co-brand with new SRHR Integrated service package.Addition of LARM's e.g., IUDs, implants.Screening & treatment for STIs, cervical cancer screening, referral to public sector sites for appropriate follow-up. 1Population Services International 2 Ministry of Health and Child Care 3 United States Agency for International Development 4 People Living with HIV 5 Non-Governmental Organisation 6 HIV Testing and Counselling 7 Tuberculosis 8 Clusters of Differentiation 4 9 Maternal, New born and Child Health 10 Prevention of Mother to Child Transmission | 7,434 | 2024-02-12T00:00:00.000 | [
"Medicine",
"Economics"
] |
he prevalence of surface oxygen vacancies over the mobility of bulk xygen in nanostructured ceria for the total toluene oxidation
This paper reveals the key importance of surface oxygen defects in the oxidation catalytic activity of nanostructured ceria. A series of nanostructured rods and cubes with different physico–chemical properties have been synthesized, characterized and tested in the total toluene oxidation. The variation of the temperature and base concentration during the hydrothermal syntheses of nanostructured ceria leads not only to different ceria morphologies with high shape purity, but also to structures with tuneable surface areas and defect concentrations. Ceria nanorods present a higher surface area and a higher concentration of bulk and surface defects than nanocubes associated with their exposed crystal planes, leading to high oxidation activities. However, for a given morphology, the catalytic activity for toluene oxidation is directly related to the concentration of surface oxygen defects and not the overall concentration of
Introduction
Ceria-based materials have been intensively studied in the catalysis field, either as pure dioxide (CeO 2 ) or doped materials, due to its high abundance and desirable combination of chemical and physical properties [1,2]. Especially, ceria-containing oxides have been researched and employed in a wide range of catalytic applications including the three-way catalytic system for exhaust gases [3], water gas shift reaction [4], VOC oxidation [5], steam reforming of alcohols [6], photocatalysis [7] and electrocatalysis [8] among others. In the recent years, research has focused on the understanding of the properties of nanostructured ceria as a way of tuning and further improving its redox activity, surface to volume ratio and oxygen storage capacity [9][10][11][12]. The catalytic activity of nanostructured ceria is strongly related to the exposed surface crystal plane. Computer modeling has shown that surface energy increases on the ceria surfaces from (1 1 1) plane to (1 1 0) < (1 0 0) < (2 1 0) < (3 1 0), the former one being the most stable. Sayle et al. [13] have shown that, theoretically, the (1 0 0) surface plane is catalytically more active than the (1 1 1) and (1 1 0) surfaces and Campbell and Esch [11,14] gave evidence of the surface oxygen vacancies on CeO 2 (1 1 1) being immobile at room temperature while clusters are formed at high temperatures. These theoretical predictions have been experimentally demonstrated in a series of studies. Mai et al. [9] have shown that ceria structures with (1 0 0)/(1 1 0) dominating planes present a higher activity toward the CO oxidation reaction due to their higher lattice oxygen migration from bulk to surface compared to the (1 1 1) dominated ceria. More recently, we have observed a similar trend for the full oxidation of volatile organic compounds [5] in accordance with the enhanced oxygen storage capacity of the (1 0 0) exposed surface [15].
Selective surface plane exposure can be successfully achieved by controlling the morphology of the material at the nanoscale. Consequently, a variety of methods have been developed to synthesize nanosized ceria including the use of templates, special organic reagents, hydrothermal treatment, electrochemical methods, etc. [16,17] to form a wide range of morphologies from particles [10], polyhedrons [18], rods [19], tubes [20,21], spheres [6], cubes [22], etc.
Despite the importance of morphology in the final chemical and physical properties of ceria, particle and crystallite size are also believed to play a key role, especially determining its catalytic activity. However, this role is still not fully understood leading to the current debate in the literature. On the one hand, some studies show that the concentration of Ce 3+ increases as the crystallite size decreases imparting unusual characteristics to the nano-sized material [22][23][24]. However, Xu et al. [10] claimed that the structural and chemical variations observed in ceria at sizes below 5 nm are due to the strain effect of higher surface energy associated with its lattice expansion with no relation to increasing the Ce 3+ surface concentration. The oxygen storage capacity of the nanosized ceria seems to show a clear quantum effect [10], the smaller the particle size, the higher the observed reducibility, in terms of the utilization of surface oxygen [16]. It is important to highlight that particle size does not seem to be directly related to reducibility in zirconium-doped ceria [15]. However, most of these studies refer to particulated ceria and there is still a lack of understanding of the relative dependency of crystallite size and surface and bulk properties to catalytic activity of different ceria morphologies in which different surface planes are selectively exposed. In this paper, we show that crystallite size plays a key role in the reactivity of ceria rods with enclosing (1 1 0) and (1 0 0) facets, while it has the modest effect on the catalytic activity of ceria cubes with exposed (1 0 0) facets. More importantly, we demonstrate that the oxidation catalytic activity of nanostructured ceria shows a linear relationship with the concentration of surface oxygen defects playing a key role in the reaction mechanism, however, the concentration of bulk oxygen defects is not directly related to the resulting catalytic activity.
Synthesis and characterization of nanostructured ceria
Nanostructured ceria was synthesized by an alkali hydrothermal synthesis carried out inside an acid digestion bomb equipped with a 100 mL PTFE liner. 1.2 g of Ce(NO 3 ) 3 · 6H 2 O was dissolved in 80 mL of NaOH of varying concentration between 5 and 15 M in deionised water [9]. The unstirred vessel was heated under autogenous pressure for 10 h inside an air-circulating oven to avoid temperature gradients. The synthesis conditions used for the different nanostructures are shown in Table 1.
After the reaction time, the autoclave reactor was allowed to cool to ambient temperature and the powder was filtered and washed with copious deionised water before being dried at 120 • C. Powder agglomerations were ground up to a fine powder using a pestle and mortar prior to characterization. Finally, the For comparative purposes ceria nanoparticles supplied by Sigma, pre-treated under the same conditions (calcination at 400 • C for 4 h) was also used.
Surface area was determined using low temperature nitrogen adsorption measurements at −156 • C on a Micromeritics ASAP 2020 apparatus. The specific surface area was calculated using the Brunauer-Emmett-Teller (BET) theory (associated error of ±0.5%). Transmission electron microscopy (TEM), high resolution TEM (HRTEM), selected area electron diffraction (SAED) and energydispersive X-rays spectroscopy spectral (EDX) was carried out using a Field Emission Gun (FEG) TECNAI G2 F20 microscope operated at 200 kV. X-ray diffraction (XRD) characterization was done using an X'Pert PRO diffractometer by PANalytical with a Cu K␣ radiation and the crystalline phases were identified by matching the experimental patterns to the JCPDS powder diffraction file database.
Temperature programed reductions (TPR) were carried out under a 50 mL min −1 5% H 2 /Ar flow from room temperature to 1000 • C with a heating rate of 10 • C min −1 . X-ray photoelectron spectroscopy (XPS) measurements were made on a Kratos Axis ultra DLD photoelectron spectrometer using a non-monochromatized Mg K␣ X-ray source (h = 1253.6 eV). Analyzer pass energy of 50 eV was used for survey scans and 20 eV for detailed scans. Binding energies are referenced to the C1s peak from adventitious carbonaceous contamination, assumed to have a binding energy of 284.5 eV. XPS data were analyzed using CasaXPS software. All the peaks of the corrected spectra were fitted with a Gaussian-Lorentzian shape function to peak fit the data. Iterations were performed using the Marquardt method. Relative standard deviations were always lower than 1.5%. Unpolarised Raman spectra were obtained using a Renishaw system-1000 dispersive laser Raman microscope. The excitation source used was an argon green ion laser (532 nm) operated at a power of 20 mW and at room temperature. The laser was focused on powdered samples placed on a microscope slide to produce a spot size ca. 3 m in diameter. A backscattering geometry with an angle of 180 • between illuminating and collected radiation was used for recording data. The acquisition time was 60 s for each spectrum with a spectral resolution of one cm −1 .
Toluene oxidation reactions
In each toluene oxidation test, 50 mg of nanostructured ceria powder (volume of ca. 115 mm 3 ) were loaded into a quartz microreactor (inner diameter 7 mm) operating under plug flow regime. The gas mixture consisted of 80 ppmv of toluene in synthetic air (20% of O 2 and Ar for balance). The total gas flow rate was fixed at 100 mL min −1 , with a gas hourly space velocity (GHSV) of 52000 h −1 . Experiments were conducted between 100 • C and 400 • C. The temperature was varied in 50 • C after which, steady state conditions were achieved prior gas analysis. The reaction feed and product were analyzed through gas chromatography using a TCD detector, with two columns for appropriate analysis (molecular sieve 5A and Porapak Q). Only CO 2 was obtained as product. The carbon balance was closed in all the experiments, with values of 100 ± 3%.
Additional experiments were conducted at 225 • C using the same gas mixture shown above but modifying the contact time in order to compare the reactivity of the different ceria catalysts synthesized with the aim of achieving appreciable catalytic activity but lower than 15%.
Blank tests in an empty reactor for toluene were conducted at the highest reaction temperature employed (400 • C) showing no conversion.
Results and discussion
Nanostructured ceria rods and cubes were synthesized by hydrothermal treatment. Variation of reaction temperature (between 70 and 180 • C) and base concentration (NaOH, from 10 to 15 M) results not only in different predominant morphologies, as previously shown by us with the establishment of a morphological Table 1. diagram [5], but also in different sizes and aspect ratios. Table 1 shows the predominant morphology and physical properties of the different nanostructured materials. Ceria nanorods with high morphological purity were synthesized by varying the hydrothermal treatment temperature between 70 and 100 • C and the base concentration between 10 and 15 M. Fig. 1 shows representative TEM images of the three ceria nanorods materials. CeO 2 nr A and CeO 2 nr B rods present similar size distributions, where most of the rods have a length between 40 and 150 nm and diameters between 8 and 16 nm (mean diameter size is 11.6 nm in both cases). The mean length values are 107 and 114 nm for the CeO 2 nr A and the CeO 2 nr B respectively. As the hydrothermal base concentration is increased, a higher average length (201 nm) and diameter (17.9 nm) sizes are achieved in sample CeO 2 nr C, with also broader distributions. The variation of the diameter size follows the expected trend with respect to temperature and base concentration during the synthesis in accordance with the well-known dissolution/recrystallization mechanism of nanostructured ceria [25,26]. A decrease in the diameter size of the nanorods implies an increase in their specific surface area ranging from 98.4 m 2 g −1 for the thinnest one to 53.6 m 2 g −1 for the thickest one (Table 1). Fig. 2 shows HRTEM images of a single ceria nanorod of the CeO 2 nr A and CeO 2 nr C materials. CeO 2 nr A shows the clear (1 1 1), (2 0 0), and (2 2 0), (3 1 1) and (2 2 2) lattice fringes with the interplanar spacing of 0.312, 0.272, and 0.192, 0.164 and 0.157 nm, respectively. In contrast, sample CeO 2 nr C exhibits higher interplanar distances of about 0.314, 0.273 and 0.194 nm corresponding to (1 1 1), (2 0 0), and (2 2 0) lattice fringes, respectively, which are indexed as the cubic phase structure of cubic CeO 2 (JCPDS: 34-0394) with space group Fm3m. The electron diffraction pattern of the CeO 2 nr C is shown in the inset of Fig. 2b, exhibiting at least five well-defined diffraction rings, characteristics of a polycrystalline nature of ceria powder. The concentric rings in the zero order Laue zone (ZOLZ) are produced by the ceria nanorods randomly dispersed providing a continuous angular distribution of (hkl) spots at a distance 1/dhkl from the (0 0 0) spot. The radius of the ring, r(hkl) and the interplanar lattice spacing, d(hkl), are related by r(hkl) × dhkl = L, where L = 1, is the camera constant of the transmission electron microscope. From the electron diffraction pattern, r is measured and the lattice spacing is determined. No appreciable differences in the SAED patterns were found on samples CeO 2 nr A, CeO 2 nr B and CeO 2 nr C. It is important to note that no obvious rings corresponding to metallic cerium or other cerium oxides compounds were observed in SAED patterns and the obtained cerium oxide nanorods are pure CeO 2 phase products. In agreement to this, the localized EDX spectrum of an individual ceria nanorod of sample CeO 2 nr A is shown in Fig. 2a, where no significant amount of other elements were detectable apart from Ce (35.3% at.) and O (64.7% at.). The C and Cu peaks correspond to the Cu TEM grids. Similar EDX spectra were obtained on samples CeO 2 nr B and CeO 2 nr C, however, important differences between the different ceria nanorod samples were observed in terms of lattice parameter. Thus, the measured lattice parameter from interplanar distance of samples CeO 2 nr A, CeO 2 nr B and CeO 2 nr C were 5.408, 5.413 and 5.438 Å, respectively. The lattice parameter values for samples CeO 2 nr A and CeO 2 nr B were comparable to the standard value (5.411 Å) of cubic CeO 2 JCPDS: 034-0394, whereas CeO 2 nr C presented an expanded crystal structure.
Similarly, two ceria cube samples (CeO 2 nc D and CeO 2 nc E) were synthesized at the same hydrothermal temperature of 180 • C. Fig. 3 shows representative TEM images of the cubic ceria materials and their size distribution. The average size of the cubes increased from 48 to 72 nm as the base concentration increased from 10 to 15 M although in both case, a broad size distribution was observed. Apart from the different mean particle size, a remarkably different size distribution was observed between both cubic samples. In the CeO 2 nc D sample, most of the cubes were 40 nm and smaller, but there were some large ones with sizes above 150 nm. However, the CeO 2 nc E sample has a higher mean particle size, with most of the cubes have sizes between 40 and 70 nm, with few large particles. The specific surface areas for cubes present values c.a. 5-7 m 2 g −1 (Table 1). In both cases, a small amount of particulated material was observed surrounding the cubic structures, an intermediate stage of the previously mentioned dissolution/recrystallization mechanism [21].
The digital diffraction pattern and HRTEM image (Fig. 4) showed the monocrystalline quality of the CeO 2 cubes with the preferential exposure of the (1 0 0) crystal planes. The measured interplanar distances were found to be 0.27 nm and 0.19 nm corresponding to the (2 0 0) and (2 2 0) interplanar distance of the cubic phase structure of cubic CeO 2 (JCPDS: 34-0394) with space group Fm3m. Both cubic materials CeO 2 nc D and CeO 2 nc E show the same interplanar distances. According to the EDX results, sodium was not detected in any of the ceria materials (nanorod or nanocube).
All the samples, independently of their morphology, present a crystalline structure as shown by XRD (Fig. 5) with diffraction peaks at 2 angles of 28.5 • , 33.0 • , 47.4 • , 56.3 • , 69.6 • and 76.7 • corresponding to the crystalline planes of the pure cubic phase (ceria fluorite structure, JCPDS 34-0394). The broadening of the reflections ascribed to the nanorods distinctly indicates their nanocrystalline nature, and the sharper reflections for nanocubes implied their larger sizes. Nanorod samples A and B present the smallest crystallite size calculated using the Williamson-Hall method (6.4 and 9.9 nm) followed by sample C that shows a higher crystallite size (14.6 nm). On the other hand, nanocube samples present the largest crystallite size (over 35 nm). These values obtained by XRD are lower but follow the same trend that the mean crystallite sizes determined by TEM.
Toluene oxidation reaction was used to assess the catalytic oxidation activity of the different nanostructured ceria materials (Fig. 6). Generally, ceria nanorods present an activity (mol toluene kg catal −1 h −1 ) of an order of magnitude higher than ceria nanocubes. Additionally, and relevant for industrial applications, ceria nanorods present activity for toluene full oxidation at temperature as low as 125 • C while ceria cubes can only oxidize toluene at temperatures above ca. 250 • C. Despite the difference in activity among the ceria rods, the similarity in the minimum temperature of activity suggests the presence of similar active sites among the tubular materials. A similar observation applies to the ceria cubes. As expected, the catalytic activity increases as the surface area increases and as the crystallite size decreases, being the ceria rods materials more active than the cubes counterparts. Focusing on the oxidation activity of different ceria nanorods at 200 • C, it can be observed that the catalyst with the highest surface area (CeO 2 nr A), presents the highest reaction rate followed by CeO 2 nr B and finally CeO 2 nr C, with the lowest surface area and consequently, activity. However, normalization of the catalytic activity per unit of surface area (mol toluene m −2 h −1 ) reveals the importance of other physical properties on the determination of the intrinsic catalytic activity ( Table 2).
While CeO 2 nr C presents the lowest specific activity per surface area among the different ceria rods, the difference in activity between CeO 2 nr A and CeO 2 nr B cannot be ascribed only to the variations in surface area. Moreover, for a given reaction temperature (e.g., 225 • C), the toluene conversion achieved for the ceria rods is two orders of magnitude higher than that achieved with ceria nanocubes, while the difference in surface area between both morphologies is only one order of magnitude higher. Ceria nanorods are remarkably more active than ceria nanocubes and the difference is not only the result of the higher surface area.
To further investigate the cause of this variation in activity, the three nanorod samples were characterized by temperature programme reduction (TPR) up to 1000 • C to quantify their oxygen storage capacity potential as shown in Fig. 7A. The first broad peak starting at ∼250 • C is related to the reduction of the readily reduced ceria oxygen while the second one at ∼620 • C corresponds to bulk oxygen [10]. Highly reducible oxygen is more readily available and as such reduces at a lower temperature than the ceria bulk oxygen. At 1000 • C, almost all of the ceria is fully reduced to Ce 2 O 3 . Independently of the different diameter sizes, the three nanorod samples present a similar proportion of surface (ca. 40%) and bulk ceria (ca. 60%), as shown in Table 2. However, close inspection of the TPR profiles suggested the presence of different forms of surface oxygen present in the ceria nanorod surfaces, likely due to the presence of OH and carbonate species as discussed below. Consequently, the increase in oxidation catalytic activity as the crystallite size is decreased cannot be directly related to the concentration of highly reducible oxygen detected by TPR. Fig. 8. XPS spectra for nanostructured ceria with different morphologies: (A) Ce3d spectra and (B) O1s spectra. Nomenclature and synthesis conditions given in Table 1. In contrast to ceria nanorods, almost no readily reducible oxygen is present in any of the nanocube samples as suggested by the very small reduction peaks starting at ca. 450 • C in Fig. 7B. Only 10% of the oxygen reduced in the TPR is readily reducible oxygen, whereas most of the cubic materials are reduced at temperatures above 700 • C, corresponding to bulk ceria oxygen [10].
X-ray photoelectron spectroscopy characterization of the different nanostructured ceria was carried out to provide information about the oxidation state of cerium and the nature of the O species. It is important to notice that XPS is a surface analysis technique with a sampling volume that extends from the surface to a depth of only ∼50-70 Å. The interpretation of the XPS spectra of Ce3d, shown in Fig. 8A, is highly complex with overlapped peaks, however, according to previous published methods [5,27,28] an accurate deconvolution can be made. The analysis revealed two principal signals at binding energies about 882.5 and 901.1 eV corresponding to Ce 3 d 5/2 and Ce 3 d 3/2 respectively. These two peaks and four additional satellite peaks at 889.2, 898.5, 907.8 and 917.1 eV associated with their ionization processes are characteristic of Ce 4+ , whilst peaks at 880.7, 884.4, 898.8 and 902.6 eV are characteristic of Ce 3+ .
The amount of reduced, non-stoichiometric cerium (Ce 3+ ) in each of the samples is quantified in Table 2. In general, the toluene oxidation intrinsic catalytic activity of the nanostructured ceria increases as the amount of Ce 3+ increases, as the presence of Ce 3+ ions implies the formation on the surface of non-stoichiometric CeO 2 . Ce 3+ ions associated with the presence of oxygen vacancies play a critical role in the oxidation mechanism participating in both the activation of toluene (surface oxygen vacancies) and migration of oxygen toward the surface material (sub-surface oxygen vacancies) [24]. The ratio between both types of oxygen vacancies is determined by the exposed surface planes. While the (1 0 0) plane, present in both rods and cubes morphologies, is cerium terminated with almost no surface oxygen vacancies in its surface (except in defects such as corners or steps), a high proportion of surface oxygen vacancies is expected in the partially reduced (1 1 0) plane, present in the rod morphology, which is oxygen terminated. Taking these crystallographic aspects into consideration the oxidation catalytic activity was plotted vs the concentration of surface Ce 3+ (Fig. 9A). It must be noted that as the reactivity of nanocubes and nanorods is very different, a proper comparison of catalytic activity at a fixed reaction temperature is not straightforward with a simple light-off curve. For this reason, we conducted new catalytic experiments fixing a reaction temperature in 225 • C and using different residence times in the reactor depending on the catalyst tested, with the objective of achieving conversions between 5 to 20% in all cases. Therefore, for nanocubes, high catalyst loadings were used and low loadings for nanorods. Thus, a clear relationship between the concentration of Ce 3+ and oxidation catalytic activity was observed regardless of the structure of the ceria catalysts tested (rods or cube). Ceria nanoparticles supplied by Sigma were also tested for toluene oxidation to validate this relationship. Positively, it was seen that this catalyst fits well with the previous observed trend in Fig. 9A. A similar relationship has been previously observed with particulated ceria [25,29].
The O1s XPS spectra are shown in Fig. 8B where two different bands are mainly observed, the first band at 529.0 eV (called O␣) and the second band at 531 eV (called O). O␣ is commonly However, the latter can should also be associated with surface adsorbed oxygen, hydroxyl groups and carbonates [30]. This fact could explain the lack of correlation found in this work between the relative contribution of this band and the number of oxygen vacancies. DRIFTS studies were carried out to get further information of the OH and carbonate species present in the different nanostructured ceria surfaces, probing that the contribution of these species strongly diverges for these samples. The DRIFTS spectra corresponding to the OH region of the dehydrated ceria catalysts are shown in Fig. 10A after in-situ treatment with synthetic air at 150 • C. The spectra of the ceria nanorods (CeO2 nr A, CeO2 nr B and CeO2 nr C) presented three bands in the OH vibrational region.
The band peak at 3700 cm −1 was assigned to mono-coordinated OH (type I); the band at 3653 cm −1 was assigned to bridging OH (types II); and a broad band centered at 3517 cm −1 was assigned to triply bridging OH (III) species [31]. Although similar hydroxyl species are present on the ceria nanorod surfaces, significant differences on the relative intensities of these band peaks can be observed. It should be pointed out that mono and bridging coordinated hydroxyl groups are clearly more apparent for CeO2 nr A and CeO2 nr B, which are those samples with the highest surface area. Therefore, it could be tentatively proposed that the these OH sites could act as adsorption points in the first reaction step at low temperature, in the agreement with the results previously published for naphthalene oxidation [31]. Conversely, the intensity of the OH species bands is negligible in the CeO2 nanocube samples, what could also be related to the low activity of these samples at low temperature.
On the other hand, although the assignment of stretching vibration modes of the O C O group of carbonate species is complicated, and their detailed analysis is beyond the scope of this manuscript, it can be observed that all nanostructured ceria, both rods and cubes, presented broad bands in this region (Fig. 10B), which can be tentatively assigned to different types of surface carbonate and carboxylate groups [32].
The Raman spectra for all the nanostructured ceria catalysts are shown in Fig. 11. Two main peaks can be observed, the peak centered around 460 cm −1 is characteristic of the CeO 2 vibrations (the triply degenerated TO mode) [33], whilst the broad peak at around 600 cm −1 (see Fig. 11 insets) is characteristic of the defect induced (D) mode associated with the presence of oxygen vacancies due to the existence of Ce 3+ ions [29]. The intensity ratio of these two peaks, I 600 /I 460 , represents the relative oxygen vacancy concentration (Table 2). Additionally, the full width at half maximum of the main peak at 460 cm −1 (FWHM 460 ) is affected by both the crystallite size and the amount of oxygen vacancies [23,24]. Thus, a high FWHM value is associated with a low crystallite size and/or a high amount of oxygen vacancies in the CeO 2 structure. The ceria nanorods CeO 2 nc C present by far the highest I 600 /I 460 ratio and the highest FWHM value among all the ceria nanorods materials. However, XRD and TEM characterization shows that the CeO 2 nc C material has the bigger average size and crystallite size which suggest that the high I 600 /I 460 ratio and FWHM values are mainly associated with a high concentration of oxygen vacancies in the material. The discrepancies of the concentration of oxygen vacancies within the ceria nanorods materials estimated by XPS and Raman spectroscopy is associated with the characterization volume of both techniques, the former being more superficial than Fig. 11. Raman spectra for nanostructured ceria with different morphologies: (A) nanorods (B) nanocubes. the latter. In this way, it can be concluded that the specific oxidation catalytic activity of the ceria nanorods is directly related to the concentration of surface oxygen vacancies involved in the toluene activation, rather than the concentration of bulk oxygen vacancies involved in the migration of oxygen to the surface during the catalytic cycle [1] as can be observed in Fig. 9B. Thus, the relationship between concentration of bulk oxygen vacancies, estimated by I 600 /I 460 ratio and the FWHM, with the catalytic activity follows an erratic trend. All this observations suggest that the most important step in the toluene oxidation is the adsorption/chemisorption of toluene on the surface of the catalyst rather than the migration of oxygen species from bulk and the further oxidation. Additional investigations are needed to elucidate whether these observations are reaction-dependant or whether they are applicable to other oxidation reactions (e.g., CO oxidation).
Finally, it is important to highlight that ceria nanorods not only present a high activity, activating toluene at temperatures ∼125 • C but this nanostructured material also presents a high stability at higher temperatures (250 • C), maintaining its activity under reaction conditions for at least 48 h.
Conclusions
Modifications to the synthetic route of nanostructured ceria leads to a variation of ceria nanorods and nanocubes with different physicochemical properties, mainly surface area, crystallite size, surface reducibility (presence of Ce 3+ ) and concentration of surface vacancies. Among them, the concentration of surface defects and the exposed crystal surface planes play a key role in the toluene oxidation catalytic activity. Interestingly, it has been observed that for this oxidation system, the catalytic activity does not show a direct relationship with the amount of bulk/sub-surface defects as suggested previously in the literature. | 6,790 | 2015-09-01T00:00:00.000 | [
"Materials Science",
"Chemistry"
] |
Competitive strategy, development zone policy and firm growth: Empirical evidence from China
Competitive strategy plays an important role in achieving superior profits, but there is still much to be explored in terms of the effect on firm growth. This study focuses on exploring the relationship between competitive strategy and firm growth in emerging economies. We focus on how the development zone policies moderate this relationship. This study uses a two-way fixed-effect model to analyze data for 527 manufacturing firms listed in China’s Shanghai and Shenzhen A-shares from 2012-2021. Our empirical analysis showed that there is a significant positive relationship between low-cost strategy and firm growth and a significant negative relationship between differentiation strategy and firm growth. Compared with national development zones, firms in provincial development zones choose low-cost strategies that are more conducive to growth. Compared with provincial development zones, firms in national development zones choose differentiation strategies that are more conducive to growth. These findings contribute to understanding the mechanisms by which competitive strategy affects firm growth in different regional institutional contexts in emerging economies. The results of the study also have reference value for the government to optimize the development zone policies.
Introduction
The report of the 20th Party Congress states that it "insists on placing the focus of economic development on the real economy".The manufacturing industry is the main body of the real economy.The growth of manufacturing firms is not only a goal pursued by themselves but also an essential means for the State to achieve economic development.In an increasingly competitive global environment, Firms can grow by transforming their competitive strategies to improve their competitiveness [1].The rapid growth of China Shengmu Organic Milk Limited from the start-up period to the steep decline in revenue after the IPO, and then to the gradual recovery in the past two years, is attributed to the sway of its low-cost strategy and differentiation strategy.Beijing-Hyundai Auto timely adjusted its strategy to make the product matrix continuously improved and finally gained market recognition.How to carry out a competitive strategy transformation and shift the drivers of business growth will be a key proposition to test the survival and development of every manufacturing firm [2,3].
In the dominant competitive strategy paradigm, low-cost and differentiation have become the two basic strategies that firms can adopt to gain competitive advantage [4,5].The literature on the relationship between competitive strategy and firm growth has focused mainly on developed countries.Some scholars argue that low-cost strategies help firms gain cost leadership, occupy higher markets than competitors, and are more conducive to growth [6,7].Other scholars argue that firms implementing differentiation strategies compete with unique products and services, which can enhance sales revenue [8].The studies that have been conducted on the relationship between competitive strategy and firm growth have not yet reached a consistent conclusion.Theoretical and empirical studies on the relationship between competitive strategy and growth, which focus on firms in emerging economies, are still weak.
Scholars have also been exploring the boundary conditions of the relationship between the impact of competitive strategy on firm performance to enrich the existing studies, such as social responsibility, innovation capability, and industry environment [2,9,10].It was found that firms' competitive strategy choice is conducive to improving firm performance when they match the external environment, and changes in the external environment also require firms to adjust their competitive strategies to remain adaptive [11].Starting with Peng and Heath, firm growth in emerging economies has also received increasing attention in the last two decades [12].Based on institutional theory, in countries with emerging economies, to adapt to the rapidly changing environment and respond to the challenges of institutional gaps, firms need to choose appropriate competitive strategies to gain an advantage for growth [13].Firms often face system defects in the process of pursuing growth, such as imperfect intellectual property protection systems and lagging financial market development [14].For emerging economies, the creation of a favorable institutional environment plays an important role in enabling firms to achieve growth by choosing appropriate competitive strategies [15].
As an institution with great Chinese institutional characteristics, development zones contribute to the construction and improvement of the local institutional environment and are an important vehicle for driving regional economic development [16].The development zone is a specific area in which the country or region delimits a certain range for promoting the rapid development of the regional economy and implementing special policies and management means [17].Its establishment is an important continuation of the special economic zone policy, which began with the establishment of the Dalian Economic and Technological Development Zone in 1984.Development zones are mainly divided into two levels: national development zone and provincial development zone [18].National development zones are approved and managed by The State Council, and their establishment can often effectively reflect the regional development strategy at the national level.Provincial development zones are mainly approved by the municipal government, the provincial government, and the autonomous region government, and are more affected by the policy intention of the local government [19].By 2021, there have been 634 national development zones and 2,094 provincial development zones.
Development zones are managed by different subjects, and thus the impact of different levels of development zones on firm behavior varies significantly [20].Some studies have suggested that the agglomeration effect caused by the development zone policies can facilitate firms to acquire knowledge and technology spillover, thereby improving productivity and competitiveness, reducing production risks, and promoting faster growth of firms [17].However, excessive competitive behavior among the development zones instead leads to a dampening effect on the growth of firms in the surrounding areas [21].Current relevant studies have focused on the direct impact of development zones on firm growth [22], while the understanding of how firms' competitive strategies are matched with different levels of development zones and how this matching affects firm growth remains limited.Given this, how do the different levels of development zones affect the relationship between competitive strategy and firm growth?
The remainder of the paper is shown below.The "Theoretical analysis and hypothesis development" section presents the theoretical foundations and hypothesis derivation.The "Data, variables and methodology" section describes the sample selection, variable descriptions, and model specification.The section "Empirical results" describes the empirical results.The "Conclusion and discussion" section summarizes the theoretical contributions, practical value, limitations and future research.
Competitive strategy and firm growth
Firm growth theory and resource-based theory are the most commonly used basic theories to explain firm growth.Firm growth theory assumes that multifunctional resources enable firms to restructure resources in novel ways to create growth [23].The resource-based theory emphasizes that firms with a large number of valuable, rare, imperfectly imitable, and nonsubstitutable resources (VRIN resources) will be more likely to gain sustained competitive advantage and achieve growth [24].Related scholars have focused more on the application of resource-based theory in explaining firm growth, instead ignoring the fact that the resource characteristics mentioned by firm growth theory are not the same as those emphasized by resource-based theory [5,8].The study points out that growth is a unique performance outcome of the firm and the resource-based theory based on VRIN resources does not explain it well.The relationship between multifunctional resources and firm growth is more closely aligned with firm growth theory [25].
Competitive strategy is one of the most important strategies for firms.Low-cost strategy refers to a firm's strategy of creating a low-cost advantage over peers to achieve operational efficiency and increase market share.Differentiation strategy refers to a firm's efforts to capture the market by offering unique products or services that focus on innovation, customer satisfaction, and brand image [26].Porter's competition theory suggests that firms should focus on low-cost strategies or differentiation strategies to produce superior performance.It proposes that five forces in the industry determine the size and degree of competition, which are the competitiveness of existing competitors in the same industry, the ability of potential competitors to enter, the substitution ability of substitutes, the bargaining power of suppliers, and the bargaining power of buyers [4].
(1) Low-cost strategy and firm growth.From a resource perspective, multifunctional resources facilitate the combination and wide application, providing firms with the means to develop new markets.Such resources have low transaction costs and also allow for rapid transfers, enabling firms to adapt to changing environments and quickly seek to identify new opportunities [12,23].To save costs, firms implementing low-cost strategies make the best use of their remaining resources and redirect resources from one purpose to new and more efficient activities.They enhance their resource mix capabilities by skillfully integrating resources and producing affordable substitutes to achieve growth [25,27].Given this, firms implementing low-cost strategies can grow by leveraging multifunctional resources and relying on cost advantages.In countries with emerging economies, firms are more inclined to identify and refine new value from existing resources to implement low-cost breakthrough innovations [28,29].Low-cost breakthrough innovation highlights low-cost strategies as the basis for achieving major innovations and breakthroughs in products and technologies.Firms focus on breakthrough innovation as the basis for integrating attributes such as low cost, design thinking, openness, and inclusiveness to provide consumers with better-quality products and services [30].Given this, firms implementing low-cost strategies can rely on cost advantages to achieve growth by fully combining and piecing together multifunctional resources [31].
From a competitive perspective, the low-cost strategy requires firms to emphasize the vigorous pursuit of cost reduction along the value chain and to continuously increase production capacity below competitors' costs [32].First, firms that implement low-cost strategies rely on economies of scale and purchase large quantities of raw materials.Firms are more competitive in bargaining with upstream suppliers and can be motivated to leverage cost advantages for growth [33].Second, emerging economies have a large number of low-income earners and more price-sensitive customers.Low-cost strategies can increase buyer retention through lower prices, which positively affects firm growth.Third, firms implementing a low-cost strategy have a cost advantage over their competitors, giving them a better chance of surviving and capturing more market share when they sell their products at lower prices than their competitors [34].In summary, low-cost strategies can provide consumers with the opportunity to purchase products at low prices, which increases sales revenue and contributes to firm growth [35].The Galanz Group implemented a low-cost strategy in the market for microwave ovens and other small home appliances.The scale of production of microwave ovens was much higher than that of its competitors, and the rapid expansion of production scale brought about a significant reduction in production costs.It has built up business barriers by price and dominated absolutely in the market.
Based on the above discussion, we propose the following hypothesis: Hypothesis 1 (H1): The implementation of a low-cost strategy has a significant positive effect on firm growth.
(2) Differentiation strategy and firm growth.Based on the resource perspective, the differentiation strategy relies primarily on product or service uniqueness and customer loyalty to build competitive advantage [36].Firms implementing differentiation strategies are committed to tapping VRIN resources and tend to engage in product innovation and exploratory innovation to provide better products or services [37].However, most of the firms in China are mainly catch-up types, with backward technology levels, and face great difficulties in obtaining VRIN resources.Firms try to improve sales channels and product quality by imitating innovations [38].The cost of such imitation may be higher than the cost of establishing these resources and capabilities by firms that already have a competitive advantage.When consumers are more price-sensitive, they may voluntarily give up the uniqueness of the product or service, to the detriment of the firm's sales revenue.In addition, there is often an inherent tension between the pursuit of profit and growth, especially in countries with emerging economies, where the scarcity of resources makes firms prioritize the pursuit of profit to survive [14].Firms that implement differentiation strategies are more likely to reap profit once they have access to VRIN resources and are different from other firms in terms of brand image and customer service [39].Therefore, with limited resources, Chinese firms will maximize VRIN resources as they differentiate themselves, which can be profitable but difficult to achieve growth.
Based on the competitive perspective, manufacturing firms go through various stages from suppliers to buyers from the production, and processing to the sale of products [4].Currently, the market is characterized by rapidly changing consumer demands and increasing substitutability of homogeneous substitutes.This makes the market very competitive.According to Porter, firms should define their relative position in the competition for investments to gain a lasting competitive advantage [40].Most firms implementing differentiation strategies are more likely to encounter strong competitors as they overlap with foreign MNCs in terms of market positioning [41].The implementation of a differentiation strategy requires a certain level of innovation capability.The higher the level of differentiation of a firm when the technological innovation capacity is weak, but without surpassing foreign competitors, it is difficult for product or service uniqueness to attract consumers, thereby expanding market share the more adverse impact [42].Throughout the existing domestic firms, a considerable part of the local firms can only survive with difficulty in the squeeze of various large foreign brands.Most brands are still dominated by foreign products.For example, in the cola market, almost Pepsi and Coca-Cola occupied the entire share.Cosmetics market, L'Oreal, Procter & Gamble, Unilever, and other foreign brands have also captured most of the market share.In practice, many firms in China are pursuing to enhance the level of differentiation.Some firms have been increasing R&D efforts and squeezing into the high-end market, threatening the position of foreign competitors and facing heavy obstacles to development.While some other firms also focus on the low-and mid-range markets, it is easier to occupy market share and achieve growth.
Based on the above discussion, we propose the following hypothesis: Hypothesis 2 (H2).The implementation of a differentiation strategy has a significant negative effect on firm growth.
The moderating effect of development zone policies
As a typical example of institutional innovation in China, development zones have provided sufficient resources and a good institutional environment for firms in the zones since their establishment [43].In policy practice, national development zones and provincial development zones are established with different fundamental objectives.The State Council manages national development zones, the establishment of which often effectively reflects the will for development at the national level.National development zones provide a good platform for innovation and require firms to take the lead in regional economic and local development.
The construction of provincial development zones is the responsibility of local governments and is more influenced by local policies.The intensity of relevant preferential policies, such as land policies and tax subsidies, is not comparable to that of national development zones [44].
(1) The moderating effect of development zone policies on the relationship between low-cost strategy and firm growth.Firms that implement a low-cost strategy have the advantage of scale and can make profits in a relatively short time.These firms can employ more labor, solve social problems, and contribute to regional economic growth.They help local officials achieve their performance appraisal goals and are more likely to be supported by local governments.However, the low-cost strategy sacrifices the quality of the product or service to a certain extent and the competitive advantage it creates can be easily imitated.This traditional low-cost, high-energy-consumption growth model has drawn criticism from academics and is contrary to the purpose for which national development zones were established [37,45].On the one hand, firms in provincial development zones are more likely to be supported by local governments with low-cost resources such as land and capital.Firms that implement low-cost strategies have more energy to focus on improving portfolio capabilities, bringing into play the multifunctional characteristics of resources, and continuously improving the efficiency of resource utilization [46].On the other hand, firms in provincial development zones tend to pursue scale advantages to be valued by local governments.Firms that implement low-cost strategies can reduce upstream and downstream channels and operating costs through the industrial aggregation effect.Firms are more cost-competitive, thus attracting consumers with lower prices and increasing their market share [17].Therefore, compared with national development zones, firms in provincial development zones with low-cost strategies are more likely to receive support from local governments with low-cost resources.At the same time, to avoid innovation risks, firms will devote more energy to exploiting multifunctional resources and establishing cost advantages, which will have a positive effect on growth.
Based on the above discussion, we propose the following hypothesis: Hypothesis 3 (H3).Compared with national development zones, firms in provincial development zones implement low-cost strategies that are more conducive to growth.
(2) The moderating effect of development zone policies on the relationship between differentiation strategy and firm growth.The implementation of a differentiation strategy by firms requires a lot of material and financial resources for R&D and innovation.This is highly likely to leave the firm with no revenue return in the short term.Inconsistency with consumer demand forecasts may also cause firms to experience failure in the implementation of the strategy [47].However, firms implementing differentiation strategies are more sustainable in gaining a competitive advantage by continuously improving the quality of their products/services through innovation.It matches with the national development strategy and the state will provide quality resources for firm development [48,49].Therefore, firms in national development zones are more likely to be supported by quality resources such as national government subsidies, tax incentives, and talent.This is crucial for stimulating innovation and avoiding business risks [50,51].Firms that implement differentiation strategies can use sufficient information and quality resources to enhance the value of their products/services.They can respond to market changes and better meet consumer demand, which helps to promote growth [8].In addition, the establishment of national development zones creates a favorable institutional environment for firm development and intensifies market competition among firms [20].The crude growth model will accelerate the decline of firms.Firms that implement a differentiation strategy enhance core competitiveness through innovation, establish a good brand image, cultivate consumer loyalty, and gain a competitive advantage that is not easily imitated by competitors.Thus, they are more likely to survive in a competitive environment and occupy a certain market share [10].
Based on the above discussion, we propose the following hypothesis: Hypothesis 4 (H4).Compared to provincial development zones, firms in national development zones implement differentiated strategies that are more conducive to growth.
Sample selection
We take Shanghai and Shenzhen A-share-listed manufacturing firms as the research objects.
To obtain reliable data, the study subjects were screened by the following steps.
Variable descriptions
(1) Firm growth.Prior research has widely accepted sales revenue growth as the primary indicator of firm growth.Drawing on authoritative scholars [14,52], we measure the annual percentage growth in sales revenue.A larger value indicates a faster rate of firm growth.The calculation formula is as follows.
(2) Competitive strategy.Based on domestic and foreign scholars' research [53], combined with the financial indicators of domestic listed firms, we adopt the following way to measure competitive strategy.We use total asset turnover to measure the capital saving dimension of low-cost strategy and the ratio of sales revenue to cost of sales to measure the cost efficiency dimension of low-cost strategy [54].By doing a principal component factor analysis on these two indicators, it was found that both indicators were attributed to a single factor and had similar eigenvectors (both factor loadings were 0.72).Therefore, we took the average of the two indicators as a measure of low-cost strategy.We used gross profit margin and operating expense income ratio to measure differentiation strategy [55,56].Similarly, after principal component analysis, it is found that both indicators are also attributed to a single factor with similar eigenvectors (both factor loadings are 0.92).We similarly took the average of the two indicators as a measure of differentiation strategy.Higher values indicate a higher degree of low-cost strategy or differentiation strategy of the firm.
(3) Development zone policy.National development zones mainly include economic and technological development zones, high-tech industrial development zones, export processing zones, bonded zones, Taiwanese investment zones, border cooperative economic zones, national tourist resort zones, and other types.There are two main types of provincial development zones.One type is economic development zones, with functions similar to national economic and technological development zones.One type is industrial parks, which focus on the development of various types of industrial projects.Referring to the studies of Alder et al. (2016) and Schminke and Van Biesebroeck (2013), we exclude development zones such as bonded zones, Taiwanese investment zones, and border cooperative economic zones, which are small in volume or whose industrial orientation is not manufacturing [16,57].We select the three most important types of national development zones: economic and technological development zones, high-tech industrial development zones, and export processing zones.Provincial development zones are dominated by development zones and industrial parks.These development zones are also important agglomerations of manufacturing firms [58].
Drawing on existing methods, the level of the development zone in which the firm is located is collected manually based on the registered address [50,51].The specific steps are as follows.① For firms whose registered address information has development zones and industrial parks, directly find the name of the development zone from the "China Development Zone Audit Bulletin Directory (2018 Edition)" and identify the development zone level.② For samples with difficult-to-identify address information, further compare the zip code information of the development zones and firms.At the same time, the information on the four ranges of national development zones is used as a supplement to identify the name and level of the development zone where the firm is located.③ For firms that have not yet identified the name and level of the development zone, information is collected through the firm's official website or the official websites of all development zones where the firm is located for identification.Through the effective combination of the above steps, the name and level of the development zone in which the firm is located can be accurately identified.A dummy variable is set to measure whether the firm is in a national development zone or a provincial development zone.
The dummy variable is 1 if the firm is in a national development zone in the current year, and 0 if the opposite is true.Similarly, the dummy variable is 1 if the firm is in a provincial development zone in the current year, and 0 if the opposite is true.
(4) Control variables.Firm growth can be affected by a variety of factors.We select the firm size, firm age, financial leverage, profitability, sales margin, R&D intensity, shareholding ratio, independent director ratio, and institutional environment as control variables.
The full variable names and measurements are listed in Table 1.
Model specification
Before processing the panel data, the Hausman test was first used to determine whether a random effects model or a fixed effects model should be used.As can be seen from the output of Table 2, the p-value corresponding to the Hausman test in both Model 1 and Model 2 is 0. The
Descriptive statistics
Table 3 presents the results of descriptive statistics for the variables, from which it can be seen that: (1) The maximum value of firm growth is 99.56, and the minimum value is -42.06, which indicates that there is a large gap in the growth of Chinese firms.(2) The maximum value of the low-cost strategy degree is 127, the minimum value is 8.634, and the maximum value of the differentiation strategy degree is 61.65, the minimum value is 0.906, which illustrates that there are significant differences in competitive strategies among firms.In addition, although there are more provincial development zones than national development zones, the number of firms in national development zones is greater than the number of firms in provincial development zones in the sample.This suggests that national development zones may be more conducive to sustainable firm development, which tends to be consistent with numerous scholars' studies and further indicates that the sample data were chosen to be robust [20].Table 4 presents the Pearson correlation coefficients of the variables.It shows that low-cost strategy and differentiation strategy have a direct impact on firm growth.In addition, the variance inflation factors (VIF) are all less than 5, which indicates that there is no significant problem of multicollinearity among the variables.The above results tentatively indicate the existence of different patterns of influence relationships among the variables, and more accurate conclusions are subject to further empirical testing in later sections.
Regression analysis
Table 5 presents the results of the regression analysis of the relationship between competitive strategy and firm growth.As shown in Model 1, among the control variables, firm size, financial leverage, profitability, sales margin, and R&D investment have a significant positive effect on firm growth.Firm age has a significant negative effect on the growth of the firm.Model 2 incorporates the low-cost strategy and model 3 incorporates the differentiation strategy.The results showed that the low-cost strategy had a significant positive effect on firm growth (β=0.575,p<0.001).The higher the degree of a firm's low-cost strategy, the more beneficial it is to firm growth.Differentiation strategy has a significant negative effect on firm growth (β=-0.199,p<0.05).That is, the higher the degree of firm differentiation strategy, the slower the firm growth instead.The overall effect of the regression model is more satisfactory, and the above results verify hypotheses 1 and 2. Table 6 presents the results of the moderating effect of the development zone level on the relationship between competitive strategy and firm growth.The results of the moderating effect of the development zone level on the relationship between low-cost strategy and firm growth are presented in models 1 to 3. In model 2, there is a significant positive relationship between low-cost strategy and firm growth (β=0.574,p<0.001), and the coefficient of the interaction term between national development zones and low-cost strategy is significantly negative (β=-0.103,p<0.05), which indicates the negative moderating effect of national development zones in the relationship between low-cost strategy and firm growth.There is a significant positive relationship between low-cost strategy and firm growth in model 3 (β=0.574,p<0.001), and the coefficient of the interaction term between provincial development zones and low-cost strategy is significantly positive (β=0.116,p<0.05), which indicates that there is a positive moderating effect between low-cost strategy and firm growth in provincial development zones.Hypothesis 3 was tested empirically.Compared to national development zones, firms in provincial development zones implement low-cost strategies that are more conducive to growth.Models 4 to 6 present the results of the moderating effect of development zone level on the relationship between differentiation strategy and firm growth.In model 5, there is a significant negative relationship between low-cost strategy and firm growth (β=-0.213,p<0.05), and the coefficient of the interaction term between national development zones and low-cost strategy is significantly positive (β=0.219,p<0.01), which indicates that there is a positive moderating effect of national development zones in the relationship between differentiation strategy and firm growth.There is a significant negative relationship between differentiation strategy and firm growth in model 6 (β=-0.205,p<0.05), and the coefficient of the interaction term between provincial development zones and differentiation strategy is negative but not significant (β=-0.151,p>0.1), which indicates that there is no moderating effect between low-cost strategy and firm growth in provincial development zones.In summary, hypothesis 4 was tested empirically.Compared to provincial development zones, firms in national development zones implement differentiated strategies that are more beneficial to growth.
Robustness test
To ensure the reliability of the basic estimation results, this paper conducts a series of robustness tests.As presented in the robust regression results in Table 7, the new regression results are not substantially different from the previous paper.
(1) Changing the scope of the sample.The relevant literature suggests that when sampling is not uniform across regions, it may bias the estimation results.In this paper, we change the sample size and re-run the regression after deleting provinces with too many and too few sample firms.
(2) Adding omitted variables.The previous regression controls for year-fixed effects and firm-fixed effects, and although most firms do not change provinces and industries, this possibility is objective.To avoid this problem, we retain the year-fixed effects and individual-fixed effects, and further, add province-fixed effects and industry-fixed effects to re-run the regression.
(3) Changing the measurement method.The accuracy of the measure of firm growth is a key factor affecting the conclusion.In the robustness test, the regression is re-run by taking the log difference of sales revenue to measure the firm growth.
(4) Using instrumental variables to address the endogeneity issue.Due to path dependence, past firm strategies influence present strategies.Thus, the level of low-cost and differentiation strategies in past periods affects the degree of low-cost and differentiation strategies in the present, while firm growth in the current year is often directly influenced by the recent or current competitive strategies.To address possible endogeneity issues, this study performs two-stage least squares estimation (2SLS) with a three-period lag of a firm's competitive strategy as an instrumental variable.The instrumental variables passed the indistinguishable test and the weak instrumental variable test, and the selection was reasonable.The predictor variables of endogeneity variables were obtained by regressing the independent variables using control variables and instrumental variables.The control and predictor variables were then selected as independent variables to perform a quadratic regression on the dependent variable.
Theoretical contributions
The possible theoretical contributions of this study are mainly reflected in the following two aspects.First, this study examines the relationship between competitive strategy and firm growth.We conclude that the low-cost strategy had a significant positive effect on firm growth.Differentiation strategy has a significant negative effect on firm growth.The studies on the relationship between competitive strategy and firm growth have focused mainly on developed countries.Theoretical and empirical studies targeting firms in emerging economies are still weak.We analyze panel data of Chinese listed manufacturing firms, expanding the empirical research on competitive strategy and firm growth.In the theoretical analysis, the few studies' findings on the impact of competitive strategy on firm growth are controversial.These studies are mainly based on the resource-based theory, which explains that the availability of VRIN resources is an element that affects the growth of firms in the implementation of low-cost strategies and differentiation strategies [7,8].Instead, this paper considers the multifunctional characteristics of resources in firm growth theory [25].We explore the relationship between competitive strategy and the growth of Chinese manufacturing firms from both resource and competitive perspectives.It also provides a new theoretical explanation for the relationship between competitive strategy and firm growth.Second, based on institutional theory [15], this paper explores the moderating role of the development zone level and further uncovers the "black box" of how competitive strategy affects firm growth.It is found that firms in provincial development zones choose low-cost strategies that are more conducive to growth than national development zones.Firms in national development zones choose differentiation strategies that are more conducive to growth than provincial development zones.According to the firm growth theory and the competition theory, both low-cost strategy and differentiation strategy may provide a competitive advantage to the firm, which in turn promotes growth [4,23].However, given the different institutional environments in different regions in the Chinese context, there are differences in the level of resource support provided by national and provincial development zones.The relationship between competitive strategy and firm growth will change accordingly.On deeper analysis, firms in the national development zones have access to better quality resources to support them and increase innovation efforts under favorable institutional conditions.They build differentiation advantages that cannot be imitated by competitors by producing unique products or services.This makes the easier for them to survive and grow in competitive markets using differentiation strategies [10].In contrast, firms in provincial development zones do not enjoy such intensity of policy incentives.They are devoting more energy to developing and integrating multifunctional resources, thereby capitalizing on cost advantages to achieve growth [31].Previous articles have focused on the direct effects of development zones on firm growth, and few studies have compared national development zones with provincial development zones [17].We investigate the moderating effects of different levels of development zones on the relationship between competitive strategy and firm growth from an institutional theory perspective.This enriches the study of institutional boundaries in the relationship between competitive strategy and firm growth.
Practical value
For firms, in terms of matching the competitive strategy with the level of development zones, the implementation of a low-cost strategy in provincial development zones is more conducive to growth than in national development zones.The implementation of a differentiation strategy is more conducive to growth in national development zones than in provincial development zones.National development zones and provincial development zones are established for different purposes and have different preferential policies [17].National development zones can provide firms with high-quality resources and a favorable environment, while provincial development zones can provide firms with low-cost and non-market resources.Firms that have entered the development zone can adjust competitive strategies to ensure the maximum utilization of policy dividends.Firms can also choose the right development zone according to the situation of competitive strategy and choose a good external institutional environment to achieve growth more easily.
Our study also provides evidence for the government to formulate and optimize the policies of development zones.Differentiation and low-cost strategies have no advantages or disadvantages, and the successful implementation of either competitive strategy can bring competitive advantages to firms.The State Council increased guidance and incentives for innovation and technology exchange, thereby better facilitating the growth of firms implementing differentiated strategies in national development zones.Provincial governments provided a boost to reduce costs for firms implementing low-cost strategies within provincial development zones by providing suitable and favorable resources.In the long run, the implementation of a differentiation strategy is more beneficial to enhance the core competitiveness of firms and the country [34].Local governments also need to optimize provincial development zone policies to assist in the growth of differentiated strategic firms.In short, the Government should create a favorable institutional environment through development zones.This could provide better resource support to firms implementing low-cost strategies and differentiation strategies to help them better achieve growth.
Limitations and future research
Our study still has limitations that deserve further exploration in the future.First, in terms of sample selection, this paper only selected Chinese manufacturing listed firms, which may affect the validity and generalizability of the findings.Future research can further expand the scope and time of the research subjects to explore the relationship of the variables more fully.Second, national development zones include economic and technological development zones, hightech industrial development zones, and other types.Provincial development zones include economic development zones and industrial parks.Future research could examine whether there are differences in the moderating role played by these types of development zones in the relationship between competitive strategy and firm growth.Third, we have focused only on general firm growth.Firm growth also includes various types such as long-term growth and high-speed growth.The relationship between competitive strategy and the growth of different types of firms has not been well studied.Future research can further explore the mechanisms of competitive strategies on different types of growth to enrich the existing studies.
( 1 )
Select listed firms that have been in continuous operation during 2012-2021.(2) Excluding firms with abnormal operations (ST or PT).(3) Excluding firms with a gearing ratio greater than 100%.(4) Excluding firms with important data missing.(5) Excluding firms that belong to unclear development zones or are stationed in multiple development zones.Finally, we obtain a balanced panel dataset with a sample cross-sectional number of firms of 527 and observations of 5270.To eliminate the effect of outliers, the upper and lower 1% Winsorize shrinkage is done for all continuous variables.The data used are mainly from the WIND database, CSMAR data, and the China Development Zone Audit Bulletin Catalogue (2018 edition).
Table 2 . Hausman test results.
https://doi.org/10.1371/journal.pone.0292904.t002test results strongly reject the original hypothesis that the random effects model is the correct model.The fixed-effects model is applied in this paper. | 8,194.2 | 2023-10-18T00:00:00.000 | [
"Economics",
"Business"
] |
An Architecture Approach for 3D Render Distribution using Mobile Devices in Real Time
— Nowadays, video games such as Massively Multiplayer Online Game (MMOG) have become cultural mediators. Mobile games contribute to a large number of downloads and potential benefits in the applications market. Although processing power of mobile devices increases the bandwidth transmission, a poor network connectivity may bottleneck Gaming as a Service (GaaS). In order to enhance performance in digital ecosystem, processing tasks are distributed among thin client devices and robust servers. This research is based on the method ‘divide and rule’, that is, volumetric surfaces are subdivided using a tree-KD of sequence of scenes in a game, so reducing the surface into small sets of points. Reconstruction efficiency is improved, because the search of data is performed in local and small regions. Processes are modeled through a finite set of states that are built using Hidden Markov Models with domains configured by heuristics. Six test that control the states of each heuristic, including the number of intervals are carried out to validate the proposed model. This validation concludes that the proposed model optimizes response frames per second, in a sequence of interactions.
I. INTRODUCTION
OWADAYS, a vast network of recognized media, such as television, internet, game consoles, smartphones, tablets and desktop devices create new ways to play, to express oneself, learn, explore ideas and generate culture.
Computers are used as mediators in the learning process through play and social interaction.An example is the Massively Multiplayer Online Game (MMOG).In some scenarios, these games are considered an educational platform, because they allow players to learn together through personal interaction in a cooperative process.Recent studies reveal that, with the continued use of this type of games [1,2,3,4], several learning processes are achieved (when creating a virtual identity, for instance).
Recent trends in mobile computing have truly commoditized a large number of components required for immersive virtual reality [3,5].Current thin client devices, such as smartphones and tablets, represent a renaissance in mobile computing.With gaming as a driver for the adoption of mobile graphics chipsets, these devices package unprecedented graphics dealing with position/orientation sensing, wireless networking, and high resolution displays.Such systems provide unique opportunities for constructing low-cost and mobile virtual reality systems [6].
Mobile games contribute to a huge number of downloads and, consequentially, to potential profits in the application market.However, although the processing power of mobile devices, as well as the transmission bandwidth is increasing, the unstable network connectivity may bottleneck the providing of Gaming as a Service (GaaS) for mobile devices.The hardware constraints of mobile devices, such as computational power, storage and battery, limit the representation of games [7].
Therefore, there is a need to reduce content and processing requirements, as well as to maintain control of storage and communication between users.For the mobile clients, one of the most problematic tasks is the presentation of the 3D Virtual Reality data.According to the 3D Virtual Reality data, the client has to calculate the position of objects, the lightning and shadows.This is a difficult task to perform with weak processors and a low main memory.In complex scenes, a high processing power is needed to process all data in nearly real time.A solution for this problem is the consumption of the processing task not on the client [8].
Render has significant features since there are a variety of methods to perform these virtual 3D graphics.In terms of software highlights there are four main algorithms: scanline rendering and rasterization, ray casting, ray tracing, and radiosity.Each of these algorithms is focused as a fundamental part in representing complex images, either by means of the light beam, or grouping pixels to reduce computer processing, or calculating the passage of light, etc. [9].It must be taken into account that these processes also depend on the geometry applied in each algorithm.
Aside from the request processing with 3D content, it is also important to control the storage of data generated by applications and their communication in order to achieve decent interactivity between geographically dispersed users.Data are not centralized on a single server; therefore control is needed over scalability and fault tolerance to provide a An Architecture Approach for 3D Render Distribution using Mobile Devices in Real Time Holman Diego Bolívar response to user requests [10].Moreover, having a distributed system is an advantage for processing and user control.A Platform as a Service (PaaS) allows virtualized computing resources via internet or advanced networks, allowing transparent use of resources.Along with offering storage services and computer processing, PaaS is built with Internet standards and protocols such as HTTP.A PaaS combines quality of service and broadcast functions distributed with capabilities in parallel processing.Together, these features create a platform for development software, designed specifically for network applications that produce and consume massive amounts of digital media.Thus, it is necessary to identify the technological architecture for gaming.
The reminder of this paper is organized as follows: section II summarizes the related work in industry and academy, and section III studies the process of subdivision surfaces to be held inside a mobile device.Section IV presents a model, including its architecture for distributed rendering based on hidden Markov model.The proposed model is assessed using performance tests according to frames per second.Section V presents the results of assessing the model, and section VI concludes our work, including future work to be developed from this research.
II. RELATED WORKS
Render 3D is used today to display molecular orbitals in the analysis of results of simulations of quantum chemistry [11], for dynamic medical evaluations, analysis of complex information models associated with medical training, management of geographically referenced information, and in the searching of extraterrestrial intelligence, among many other uses.[12].In recent years, the performance and capacity of graphics processing units have improved dramatically, thanks to the parallelization of computational tasks [13], but an efficient operation of large capacities of parallelism, allowing a linear acceleration along with multiple compute nodes are still required [14], for they would optimize the graphics processing level data volume with polynomial complexity.
The display group NERSC and Lawrence Berkeley National Laboratory (LBNL) have developed the Visapult tool to attack these problems.Visapult is an application of parallel distributed processing that leverages the resources of computer networks and the processing power of supercomputers.Renders for volume ray tracing and traditional series can take many minutes or hours.Visapult supports interactive volume rendering to rates by employing distributed network components and a high degree of parallelism.Image Based Volume Rendering Algorithm when used with this program, Visapult can exchange additional information with reduced bandwidth [15].
For improving traditional visualization of render, Corcoran et al. [16] propose a model that employs two phases, which depend firstly on rendering volume direct (RVD), and on a number of other rendering non photorealistic processing techniques (RNF).By separating the visualization on two levels, allowing a higher level of detail than that normally observed with the traditional process, it is noteworthy its level software architecture.The interactivity drawback is due to the lack of specific limits and sometimes it is possible to get occlusion by overlapping images.Because being interactive, they require minimum time response.
The model poses strategies to solve these problems, emphasizing the perception of images.
Bounding volume hierarchies (BVHS) hold great promise for dynamic scenes.However, each proposed technique changes for handling animations has limitations, such as a reduced performance in a prolonged time and some difficulty in the processing of deformed objects.It avoids synchronization problems but in the other hand limits the speed at which BVH can build frames [17].
Madhavan et al., [18] show a model that seeks an implementation of a distributed rendering environment which is easily accessible according to the system requirements.The model generates the deployment work, with monitoring render, data sending, error corrections and reducing waiting times.Furthermore, Taura [19] proposes an architecture based on real time monitoring system called VGXP, based on a technology called GXP.For the system, it is important to monitor and control the performance of a distributed process, as well as the performance, scalability, fault tolerance, and also data sent to the client without overloading and security.The system generates a 3D graphics response in java.
In the system proposed with Kamoshida [20], the server collects the monitoring data required and sends it to the client through a hierarchical architecture.An agent process runs on each node, which monitors the control data produced by each process and event.To accomplish this communication, the agents form a tree structure for TCP connections.The root of the tree is the server process.
Madhavan et al. [21] propose a software architecture based on Java for real-time visualization and generating interactive graphics.This architecture minimizes the amount of required synchronization between PCs, resulting in excellent scalability.
The modular architecture provides a framework that can accommodate a variety of algorithms and data formats representation, provided that rendering algorithms are used to generate individual pixels and data duplication in each computer.As an object-oriented design, it implements the basic functionality required for distributed rendering.
Due to the complexity of volumetric rendering, the problem can be divided [22,23,24].They propose using the Octree algorithm, which is responsible for dividing the volumetric scene in scenes less complex, according to the user's request.Another advantage is the weight of the scene at the time of transport on the network, since it does not require the entire bandwidth needed initially.The problem that arises with volumetric rendering is the volume size.Therefore, the image must submit to procedures outside the nucleus to avoid charges in memory.
Another algorithm commonly used for rendering is Ray-tracing [15,16,17,25,26,27,28].This is based on the illumination of the image, capturing the beam size and its reflection on the object.This involves various drawbacks (shading, texture object, etc) when there are complex object.
In order to optimize performance, an intersection is found, the beam is transferred to the point of intersection and its address is modified according to the type of beam, shadow or reflection, using various characteristics of objects to be displayed and geometric data.The iterations stop when the reflected ray does not hit any objects or the maximum predetermined level of reflection is reached.Ray-traicing is a dynamic algorithm with a high cost in displaying images.
Castanie et al [29] propose a model based on an original application of DSM (Distributed Shared Memory), as it is a type of implementation to level hardware and software system.Each node in a cluster has access to a large shared memory that is added to the limited unshared memory of each node.However, this implementation is reconstructed, generating four additional access levels that are included in this system, such as the graphics memory, the local memory in the node, the memory of the other nodes through the network and the disk.This new implementation is called Distributed Hierarchical Cache System (DHCS).
III. SUBDIVISION SURFACE METHOD ON MOBILE DEVICE
The visualization process is composed of four parts: data collection, image processing, building surface and display of image.As regards techniques, there are two types of volume rendering methods: direct and indirect.Direct methods use a type of 3D volumetric images generated without explicitly extracting geometric surfaces from the data.Indirect method consists of marching cubes algorithm, from which the cells belonging to a surface threshold, and a threshold value provide as a result a cubic grid containing a classification of the object data, which is modeled through an octal tree.
Nowadays, the graphic processing is performed by the zbuffer algorithm which handles the display of images.It is useful because it processes millions of images interactively using triangles.It takes image texture and illuminates to a low computational cost.According to Shirley et al. [25], it has the following disadvantages: Applications with data sets significantly large, generates processing times of order NP. Applications with non-polygonal data are not easily converted into triangles for processing as image. Applications that demand high quality shadows, with reflection, refraction and particle effects are difficult to process.
An option is to perform the rendering process using raytracing techniques.However, a high computational cost is generated by the large number of ray tracing for each scene.This problem can be minimized by using special data structures able to organize or group scene objects spatially.The number of intersection tests involved in searching is greatly reduced.
So instead of following a comprehensive search to identify the correct scene for the nearest intersection, only nearby objects are approved and the remaining are discarded, as recommended by Siu-Lung et al. [26].
To develop volumetric render, tree octants Local Grade Smooth algorithm is used (OOLSD).It is submitted by Xing et al. [30].First the image is divided into some small sets of points according to the octree construction, then a local triangular mesh through the region is built by fusing the triangulations recursively and aplying the principle of "divide and rule".
By reducing the surface into small sets of points, reconstruction efficiency is improved because the search region is small and local.In the recursive fusion process, the optimization operation is performed between boundary triangles.Therefore, the number of the mesh boundary triangulation does not increase, so the complexity of the algorithm is stable.Fig. 1 shows the subdivision surface from octants optimized algorithm, also known as Local Grade Smooth.The involved process of this algorithm reduces the level of memory which is stored in the mobile device by eliminating non-relevant images [22,23].
For subdivision surfaces, it is necessary in the first place to identify those that are visible to users, through the hidden surface removal algorithm through JPCT 3D engine.Through CubMotion class structure renders is performed, based on the World Reference, FrameBuffer, Light, Object name, RGBColor Matrix, xPosition, YPosition, Object RenderOpenGL and URL ConstructiónXML.Given the description of the object in an XML file, the implementation is performed in the OpenGLRender class, which is responsible for the subdivision.By each tree node an event at BuildXML class is being created.BuildXML class is responsible for building tree-KD through spatial subdivision based on heuristics and surface areas.Taking into account the recommendation of Wald and Havran [31], Fig. 2 shows the sequence diagram associated with the interaction surface subdivision process.
After the construction of the tree-KD, a session through the JSCH library is created, which is an implementation of the SSH2 protocol that provides support for secure remote access and data compression.In the SSH communication the following key issues are discussed: To access the server, it is necessary to provide credentials, user and password. Sockets are used to establish a communication between client and server.Thus, data transmission through objects is serialized. JSCH library provides an encrypted communication channel, protecting data that are travelling between client and server.Once communication channel is created and a session is defined, the manner of handling events is throughout an implemented interface.ActivitySPC component is used to close sessions.Fig. 3 shows the deployment diagram associated with the process of subdivision surface on the mobile device and the creation of the communication channel.
Regarding the hardware environment used for testing, it encompassed a server and several mobile devices.The Server responsible for storing WMA has the following description: a blade server PowerEdge M620, Intel Xeon E5-2600 processor, Intel QuickPath Interconnect (QPI) 7.2 GT / s, 2.5 MB cache per core with 4 cores, 16GB RAM, 3TB HDD master was utilized and 3 TB hard drive slave, this server has a Matrox G200 video card integrated.This server has installed an operating system: Red Hat Enterprise Linux.Moreover, all test devices had the Android operating system, due to the need for the installation and configuration of JPCT 3D engine.
IV. ARCHITECTURE PROPOSAL FOR DISTRIBUTION OF RENDER
According to the tree-KD, metadata is generated for each node which is recorded in real time from a web service and relational database management system (RDBMS).This process consists of defining a structure with associated data that should map to an XML template in order to generate the BuildXML class.Fig. 4 shows the interaction diagram for each node.
For each mobile registered in the information system, a Workload Management Agent (WMA), similar to proposed in [20] is created.This agent is responsible for managing all render and sending requests to a scheduler that is in charge of being a matchmaker for compatible resources in a distributed system.Regarding the execution domain, it is based on Platform as a Service (PaaS).Inside this platform, there is a task called "Job Submission Service" responsible for sending tasks to the "Local Resource Manager".Then tasks are processed and a local scheduling is assigned to available resources schematized as worker nodes, which return the load to the WMA, which sends information mobile device.Clearly, there is a dependence on bandwidth which is given by network congestion, the intensity of the received signal and the mobile device.Additionally, it should be considered that the following restrictions exist: network 2.5G technology and General Packet Radio Service (GPRS) transmitting 56 kbps.The aforementioned restriction inhibit data transmission to WMA since the standard for real-time animation is 24 frames per second (fps) with a limit of 292 Bytes for each XML document.Additionally, range between 1KB and 15KB acts as another restriction for data test.
Therefore, a minimum of 2880 kbps connection is required, which is only available in 4G networks.
One solution is to compress data using redundant coding bytes, through a grammar based on X3D standard.Then, decompression is performed in the WMA.
In the compression process, files are reduced to 500 B and 2.5 KB respectively, due to the redundancy of coordinates and XML tags.
Considering that the minimum value to establish a connection using compressed data is 480 kbps, it is still possible to perform tasks throughout 3G network.Regarding 2G networks with a top speed of 232 kbps, the rendering process requires applying a stroboscopic effect, reducing a third of the number of frames processed remotely.
To maintain the visual quality of animation in a game, mobile device should process two frames while the last frame is sent remotely.However, this simple model is not feasible due to ignorance of network traffic and the instability of the connection.
To identify the number of nodes created by each scene, we propose using Hidden Markov Models (HMM) that create a finite number of states, from an initial test of connection between the mobile device and WMA.
To model the full process, a known and finite set of states S Hidden Markov, one for each domain, is built.A domain is set from the combination of different heuristics such as:
To calculate the relevance of each heuristic [ℎ()], the value is set to 1 or 0 if the connection is in any of the established ranges and the importance, [ℎ()], is indicated.The value obtained in ( 2) is multiplied by the value of the relevance of each heuristic, then added and this allows us to identify the importance of each heuristic.Equation ( 3), presents a formal method to identify the relevance of each heuristic.
𝑅[ℎ(𝑛
[ℎ()] Sets the probability of heuristics associated, according to the connection status for each domain.A transition matrix between states is then generated.
In order to model the probability of the states, several vector observation, (), have been established before the training phase models.
Formally, the probability to move from one state to another is represented by directed edges.Usually the nodes are numbered from 1 to N, according to the number of nodes and edges are labeled with probability values between 0 and 1.Each possible state (), is represented by a labeled box and the probability that a job stay with some priority according to the policy node is expressed as a directed edge from that state to the observed symbol, as shown in Fig. 5.
Having defined the structure of the overall model and each of the HMM training proceeds of the S models to calculate the optimal values of all parameters that have been mentioned.For that, the k observation sequences in each state have been used.
For the proposed model the vector of initial probabilities each HMM is initialized with probability value equal to 1 / N, as follows: The learning model is to adjust the parameters to maximize P(()/) including several algorithms for training the HM Baum-Welch, Expectation Maximization (EM), Generalized Expectation Maximization (GEM), and different forms of gradient descent [30].
The procedure of training with EM for restimation of HMM parameters uses the variable [ℎ((, ))], that is the probability of being in state i at time t, and state j at time t + 1, for a given model and a observation sequence (), i.e.
𝑊[ℎ(𝑡(𝑖, 𝑗
The sum of (5) on t can be interpreted as the expected number of transitions from state i to state j, formally expressed in (6): Representing the expected number of transitions from state i to state j in ().For optimal state sequence, the probability of the observation sequence (), P(()|), is calculated efficiently.
The evaluation of the probability of the sequence consists of calculating the probability of the observation sequence P(()|).The way to solve the problem is to apply a forward algorithm.In this algorithm, it is assumed that t (i) = P(o1 o2 ... ot, qt = i | ).Then the probability of observing the partial sequence P(()|) in state i to time t can be calculated as follows, The observation probabilities are given by the state of the connection according to the values given by heuristic calculations taken into account (3).
WMA is responsible for maintaining a probability table for device and continuously monitors the connection status, acting as a brokered services under an implementation Gamming as a Service (GaaS) [4,5,7].
V. RESULTS AND DISCUSSION
The render becomes a multi objective problem, since there is a problem of processing capacity on the mobile device.
The number of heuristics is increased, considering other factors such as device processing power, load balancing, cumulative yield, missed deadlines, equity, preference of users, total weighted completion time, delays weighted number of tardy jobs, and many others [33].
An animation render sequence was performed, starting at the scene shown in Fig. 6 and ending at the scene shown in Fig. 7.The animation corresponds to a 30 second walk of the main character (Fig. 7).The number of polygons of each scene varies between 7000 and 19000, with an average variation of 10% between frames.
In this research only the volume rendering process is taken into account, regardless of color, texture and lighting of the scene.For this reason buildings are in gray.
In order to validate the proposed model, six domains where considered and a controlled manner to stablish the states of each heuristic and the importance, [ℎ()], associated with the number of intervals.
Table 1 shows the values of ranges for the best case, worst case and number of intervals associated to test domains according to heuristic set.Table 2 shows the domains where controlled tests were performed, which yielded the number of frames per second.3. Presents a variation of frames in mobile devices according to processor and memory.The conclusion is that the proposed model is valid for a set of significant number of polygons or a low-speed connection.
According to Table 3 and Fig. 8, there is not a significant variation between tests with domains 2 to 5, while in domain 1 there is a significant variation since it was considered the worst case in heuristics in Table 2.
Regarding the aforementioned, there is an inverse correlation between processor and memory capacity of the device, network speed and the number of frames per second if rendering process with JPCT 3D engine is performed.However, the correlation is reduced by 40% implementing the proposed model.
The rendering process is performed constructing a reference environment, commonly referred as world.Although reliability is tied to redundancy, this approach encompasses metrics of fault tolerance and system consistency.In that way, the expected reliability is covered, and the information system would cover the property of fault tolerance in its implementation.The proposed model was implemented and, during the phase of handling tasks, the rendering process was executed without interrupting the service.
VI. CONCLUSIONS AND FUTURE WORK
To implement a Gaming as a Service (GaaS), an infrastructure that allows seamless experience for the user interaction is required.The number of frames per second that a mobile device processes according to a scene, facilitates interaction experience.However, the more complex a scene, a greater processing power is needed to process all data in real time.One solution to this problem is to take this responsibility to the mobile device, but the unstable network connectivity is the bottleneck.
To optimize the rendering process to a good rate according to the processing capability and network speed, it is necessary to perform a multi objective analysis.By validating different characteristics simultaneously, an efficient distribution of work is done.In the first instance, subdivision of surface is required using the octree algorithm, in order to divide the problem into less complex problems.
To model the entire process, a known and finite set of Hidden Markov Models, one for each node o domine, must be built.Each domine consists of a set of heuristics with unknown cardinality, each one of which could have different states, associated to the local responsability.
This research had only covered the volume rendering process, regardless of color, texture and lighting of the scene.However, these factors can be as crucial as the volume of the object in the interaction with the user.
In future researches, it becomes necessary to involve the algorithms associated with the shadows, textures and lighting to optimize a platform of Gaming as a Service.
I. INTRODUCTION
OFTWARE visualizations tools are used in different context in order to improve and make easier the students learning process.Many different kinds of tools can be used to improve student learning process and motivation.For example, social networks have a large impact in student motivation and communication [45].However, the results obtained are not always positive, so there exist different variables, which can reduce the educational impact.Nowadays, introducing multimedia techniques can improve the learning process [48].
In this work we present two different software visualization tools to display different aspects as can be recursion and parser analyzed process.However, the development and evaluation methodology used in both cases is similar: student centered.This means that all functionalities have been included, improved or removed according the evaluations results.
The rest of the paper is structured as follow.In section II we describe the most important related work in software visualization for recursion and parser generation.In section 3 we describe SRec system.VAST is described in section 4. In section 5 the evaluation process for SRec and VAST is described.Finally in section 6 we set the conclusions and future works.
II. RELATED WORKS
This section contains an introduction to software visualization and a review about how recursion and parsers are visualized by several already-made software tools, finding out lacks and shortages, and proposing a new software tool for those cases, SRec and VAST.
A. Software visualization
Software visualization is a technical tool for representing in an electronic, animated and interactive way.Most part of these representations tries to make easier the software comprehension.
The educational environment focused on computer science is one of the contexts where more software representations are used, but currently is not massive.Teachers are reluctant to adopt software and new ways to teach; they feel losing the control of the class when they use new software.Lack of evidences about visualization effectiveness is an important factor to explain why software visualization is not used in most classes.
In order to fix it, software for visualizations is created, taking usability recommendations and exhaustive analyses about what both teachers and students need.
B. Recursion visualization
Recursion visualization comprises the process of representing graphically the recursion, providing animation and interaction features.Recursion is a process or software function that requires its own service once or several times to find a solution.Every time the function is called by itself, the size of the problem is smaller, letting it to reach the base case, when the problem can be solved in an easy and direct way.
Recursion is a hard concept to be learned, help students to learn it through recursion visualization has been the main goal of a lot of software.These software applications usually use animations for describing step by step how recursion achieves to solve a problem.Student interaction is very important to make easier learning tasks [22] like algorithm analysis or debugging.
Recursion can be taught using different conceptual models.A conceptual model provides a singular representation for a concept, system or event, and must be complete, coherent and precise.For recursion, there are some conceptual models widely accepted and used for teaching recursion [19][42].The most abstract one is the inductive model, defined as a mathematical formula where the base case is directly identified.Metaphors are very used because they make easy the identification of concepts with daily life (Russian dolls [14] or mirrors [41]).
Going deeper in computer science education, there are several conceptual models used at the classrooms.Trace is one SRec and VAST: Visualizing Software with a Student-Centered Aim.
Fig. 2
Fig. 2 Sequence diagram of surface subdivision
Fig. 3
Fig. 3 Deployment diagram of surface subdivision
Connection speed. Latency time. Size of the scene. Number of nodes to construct feasible by scene. Probability of failure on the connection Given that each of the established heuristics may vary in different real or integer values, prioritizing intervals according to initial conditions are established.One descendent prioritization is done according to the ideal conditions and the worst-case scenario and then it is assigned to each interval heuristic relevance considering the Hurwitz criterion.To calculate the weight of each interval heuristic [ℎ()], in the development of research, it was used: [ℎ()] = [ℎ(1)]+[ℎ(2)]…+[ℎ()] (1) a vector of observation symbol probability, one for each estate, in which bj = (b j1 , b j2 , ..., b jM ) defines observation symbol probability ot = vk of the alphabet in the state j.
TABLE I VALUES
OF TEST DOMAINS USING HEURISTIC | 6,916 | 2015-06-01T00:00:00.000 | [
"Computer Science"
] |
The approach to fracture diagnosis by means of experimental measurements of the stored energy
Energy dissipation in metals under irreversible deformation leads to intensive heat generation in strain localization zones. In this work, we focus on measuring heat source power using temperature data obtained by IR thermography. The calculated heat source power data were verified by analyzing the data recorded by the Seebeck effect-based heat flux sensor developed in previous study. Quasi-static tensile tests were conducted on titanium alloy Grade 2 flat specimens. It is shown that the thermography data and the results obtained with the heat flux sensor are in good quantitative agreement. The dependence of the moment of fracture of metal specimens on the change in localized heat generation caused by irreversible deformation was determined.
INTRODUCTION
oday the investigations of many authors [1][2][3][4][5][6][7][8] are aimed at creating theoretical models describing the behavior of materials under deformations process. These models include thermodynamic and structural parameters that determine the deformation process. The energy dissipation in metals during irreversible deformation and the change in the internal structure lead to intensive heat generation in strain localization zones. Modern IR detectors allow studying the evolution of energy accumulation and dissipation and provide a deeper insight into plastic-deformation localization mechanisms [1][2][3][4][5]. In practice, researchers often differ in the quantitative estimation of the dissipation heat and the stored energy in a cold-worked material, which impedes the development of methods of damage assessment [6]. In this study, the dissipative properties of Grade 2 titanium alloys were investigated in quasi-static tensile tests. The infrared thermography technique (IRT) and the contact heat flux sensor used to study the evolution of heat sources and determine the critical state of materials. Analysis of the results of investigation on the energy balance in the fracture zone obtained with the infrared techniques and heat flux sensor during the deformation of titanium alloy Grade 2 lend confirm the validity of the proposed method. T EXPERIMENTAL DETAILS he standard quasistatic tensile tests were performed on titanium alloy Grade 2 flat specimens. The chemical composition of the material is presented in the Tab. 1. Specimens (gauge length of 120 mm and width of 20 mm) were made of a 3 mm thick sheet. Mechanical tests were carried out using a 300 kN electromechanical testing machine Shimadzu AG-X Plus. The geometry of specimens and the deformation curve are shown in Fig. 1. Investigation of the heat source evolution was carried out using the temperature data obtained by an infrared camera FLIR SC 5000. IR camera has the following features: the spectral range of 3-5 μm, the maximum frame size is 320×256 pixels, the spatial resolution is 10 -4 meters. The temperature sensitivity is in the range from 25 mK to 300 K. The surface of the specimens intended for infrared shooting was polished in several stages and coated by a thin layer of amorphous carbon to enhance the emissivity. To verify the heat source power obtained by the infrared technique, the contact heat flux sensor based on the Seebeck effect [9] was directly attached to the specimen. To enhance the heat flow, a heat-conductive paste was applied between the sensor and the specimen.
EVALUATION OF THE STORED ENERGY
e calculate the heat source field by applying the heat conduction Eqn. (1) to infrared thermography data: where ( ) T x, y,z,t is the temperature field, is the material density (4505 kg/m3), c is the heat capacity (540 J/(kg·K)), k is the heat conductivity (16.2 W/(m·K)), ( ) Q x, y,z,t is the heat source field, x, y,z are the coordinates, and t is the time.
The infrared camera allows registering the temperature distribution over the specimen surface but not across the specimen thickness. That is the reason why rather thin specimens are used in experimental investigations. It makes possible to assume that the temperature distribution through the specimen thickness is homogeneous. T W The volume-averaged Eqn. (1) is used for estimation of the integral power of the heat source. To this end, a standard averaging procedure was conducted. The difference between the averaged specimen temperature on volume T and the initial specimen temperature 0 T in the thermal balance with the environment is defined as: where a , b , h are the length, width and thickness of the specimen, respectively, and V is the volume.
The boundary conditions are expressed as follows: where x g means the heat exchange coefficient between the specimen and the environment on the corresponding edge of the specimen. Therefore, integrating Eqn. (1), considering expressions (2) and boundary conditions (3), we obtain relation (4) to estimate the heat source field caused by irreversible deformation: where is the average temperature of the examined surface, m is the mass of the representative volume where the average temperature is taken from, ( ) S t is the heat source field (W), and is the material parameter that determines heat losses associated with the heat exchange with the environment.
The parameter is determined by the additional experiment data from the tests in which the specimen was cooled after pulse point heating. Fig. 2a presents the IR image, which was made during the pulse point heating experiment, and data of the average temperature of the heating area during the cooling process. To calculate the constant , it is necessary to approximate the experimental data of the average specimen temperature after pulse point heating in terms of the solution of the averaged thermal conductivity Eqn. (4) with a zero source (Fig. 2b). The experimentally obtained value of parameter is equal to 3. 3 shows the infrared imaging of the specimen surface at the final stage of loading before its fracture and the timetemperature dependence during the test. At the beginning of the test, the average surface temperature decreases due to the thermoelastic effect, then the thermoplastic effect prevails, and the temperature of the specimen increases until the moment of necking and complete failure. According to Eqn. (4), the time dependence of the heat source field was estimated based on the change of the specimen temperature during the mechanical test (Fig. 4a). The calculated heat source power data were verified by analyzing the data recorded by the Seebeck effect-based heat flux sensor. The heat source obtained by both methods do not coincide completely, which can be explained by different sensitivities of the devices, and errors of numerical processing of the infrared thermography data. Nevertheless, these results suggest the possibility of using non-contact measurements to estimate the heat source distribution on the specimen surface. One part of the irreversible plastic work contributes to heat generation, and another is stored as the energy of crystal defects accompanying plastic deformation, known as the stored energy of cold work. For flat specimens, the plastic work spent on deformation of the specimen can be defined as a function of strain rate V and loading force F t : The stored energy is determined as a difference between the plastic work spent on deformation and the integral heat dissipation. The time dependences of these values are presented in Fig. 4b. Analysis of the data in Fig. 4b suggests that, when the material approaches fracture, the value of stored energy in the material reaches a critical value, and the rate of stored energy tends towards zero. In work [10], the algorithm allowing estimation of the heat transferred by convection, conduction and radiation: where is the thermal conductivity of the material, is the heat transfer coefficient by convection, is the surface emissivity, is the density, c is the specific heat, n is the Stephan-Boltzmann constant equal to 5.67·10 8 W/(m 2 K 4 ), p E is the rate of variation of the stored energy, T is the room temperature, ( ) T x, y,z,t is the time-dependent temperature field, and cv S , cd S , ir S are the three parts of the external surface of the control volume V through which the heat Q is transferred by convection, conduction and radiation, respectively. The parameters Q and p E can be derived via Eqn. (6) using the experimental surface temperature measurements and the room temperature data, provided that the heat transfer coefficient and the surface emissivities are known.
In our case, the specimen surface was coated with a thin layer of amorphous carbon, and the emissivity coefficient was equal to 0.92. The following three different formulae were used in order to evaluate the heat transfer coefficient in the case of natural convection [11]: where Gr , Nu , Pr , Ra are the non-dimensional Grashof, Nusselt, Prandtl and Rayleigh numbers, L is the length of the examined part of the specimen, and a is the thermal conductivity of the air [W/(m K)]. It has been established that these formulae give very similar results and the mean value of heat transfer coefficient 3.7 W/(m 2 K). Based on the obtained results, we can conclude that conduction is the predominant heat transfer mechanism for titanium alloy Grade 2 specimens (Fig. 5a). The curve describing stored energy evolution during the mechanical test is presented in Fig. 5b. This plot coincides with the curve obtained according to Eqn. (4), which confirms the possibility of using the stored energy value as a reliable parameter for diagnosis of fracture.
CONCLUSION
volution of irreversible deformation in the material is accompanied by the processes of energy accumulation and dissipation. In this work, we analyzed the energy balance of the material during the deformation process by two methods: infrared thermography technique and the method which uses the heat flux sensor. The infrared scanning E method was found to be efficient for estimating the accumulated energy in the titanium alloy Grade 2. It was established that conduction is the predominant heat transfer mechanism for the examined material. The value of stored energy reaches a critical value and stored energy rate tends towards zero at the end of deformation process. This indicates that most of the plastic work is converted into heat, and the material is close to being fractured. Hence, it can be concluded that the analysis of the energy stored in the material can provide an adequate description of damage evolution in metals under deformation. | 2,398.2 | 2019-06-07T00:00:00.000 | [
"Materials Science"
] |
Plasmonic color filter array based visible light spectroscopy
Compared with traditional Fabry–Perot optical filters, plasmonic color filters could greatly remedy the complexity and reduce the cost of manufacturing. In this paper we present end-to-end demonstration of visible light spectroscopy based on highly selective plasmonic color filter array based on resonant grating structure. The spectra of 6 assorted samples were measured using an array of 20 narrowband color filters and detected signals were used to reconstruct original spectra by using new unmixing algorithm and by solving least squares problem with smoothing regularization. The original spectra were reconstructed with less than 0.137 root mean squared error. This works shows promise towards fully integrating plasmonic color filter array in imagers used in hyperspectral cameras.
Plasmonic color filter array based visible light spectroscopy Jyotindra R. Shakya, Farzana H. Shashi & Alan X. Wang * Compared with traditional Fabry-Perot optical filters, plasmonic color filters could greatly remedy the complexity and reduce the cost of manufacturing. In this paper we present end-to-end demonstration of visible light spectroscopy based on highly selective plasmonic color filter array based on resonant grating structure. The spectra of 6 assorted samples were measured using an array of 20 narrowband color filters and detected signals were used to reconstruct original spectra by using new unmixing algorithm and by solving least squares problem with smoothing regularization. The original spectra were reconstructed with less than 0.137 root mean squared error. This works shows promise towards fully integrating plasmonic color filter array in imagers used in hyperspectral cameras.
Visible Light Spectroscopy has many applications including cancer detection [1][2][3] , remote sensing 4-6 , mineralogy 7 , food safety 8 and artwork authentication and preservation [9][10][11][12] . Conventional RGB camera can provide only 3 color information, which is often insufficient to detect sharp features in spectrum. Hence cameras with many color channels are often used for spectroscopy. Such imaging systems are called hyperspectral cameras which has many widespread usages. Visible light spectroscopy when used in imaging modality rather than spot spectroscopy allows computational algorithms to take advantage of spatial-spectral information such as spectral similarity in neighboring spatial pixels. Various algorithms have been proposed for reconstructing sample spectrum from hyperspectral images which take advantage of spatial-spectral information [13][14][15][16][17][18][19][20][21] . Hence improvements in hyperspectral imagers and cameras are essential towards progression in visible light spectroscopy. With development and advancement of technology, the hyperspectral cameras have been miniatured into form factors that are similar to regular cameras. The hyperspectral camera can use various types of color filters such as dye based filters, Fabry-Perot based filters and plasmonic color filters. The state-of-the-art hyperspectral CMOS camera 22,23 uses Fabry-Perot based Bayer color filter array 24 . To fabricate many spectral filters, however, it takes as many processing and lithography steps as the number of spectral bands desired. In contrast, plasmonic color filters can be fabricated in single lithographic step regardless of the number of spectral bands. This is because the spectral peaks in plasmonic color filters depend only on lateral dimension. Integration of plasmonic color filters in CMOS imagers greatly reduce cost of the imagers and overall hyperspectral cameras. Due to these benefits, there has been many publications of plasmonic color filters including hole arrays [25][26][27][28] , patch arrays 29 and 1-D gratings [30][31][32] . Although hole arrays and patch arrays can be used as color filters, due to the wide transmission peak, it is not suitable when high spectral resolution is needed. Furthermore, plasmonic color filters with resonant grating structure provides much narrower transmission spectra 33,34 and hence allows for resolving spectral features even with sharp edges. There are many publications on plasmonic color filters using gold and silver in infrared region. Due to the high loss and inferior plasmonic properties, gold and silver do not perform well in the visible range, especially towards shorter wavelengths. Hence aluminum can be used as plasmonic material in visible range. In addition to the lower loss in visible range, low fabrication cost, mature processing and compatibility with CMOS process makes aluminum a good choice as plasmonic material for integration with CMOS imager. In this paper, an end-to-end demonstration of visible light spectroscopy using aluminum plasmonic color filter array is presented.
Advantages of resonant grating structure. Plasmonic color filters can be designed using either 1-D (grating) or 2-D structure (hole array or patch array). Due to periodic structure, these structures have counter propagating SPP modes due to Bragg reflection, which forms standing SPP modes in the periodic structure. However, such modes are highly lossy due to conductive losses in the metals used, which leads to broader resonant peaks and less spectral selectivity. An addition of slab waveguide under the grating provides means to periodically replenish energy into the resonant modes hence enhancing Q-factor. The standing SPP mode in the grating couples to the guided mode in the slab waveguide based on evanescent wave coupling. Such plasmonic grating filters with buried slab waveguide have narrower resonant peaks compared to conventional www.nature.com/scientificreports/ plasmonic grating filters. The distance to the slab waveguide can be tuned to optimize the design of such structure. If the slab waveguide is very close to metal structure, the guided mode inside the slab waveguide becomes lossy and hence the resonant peaks become broader. If the slab waveguide is too far, the coupling becomes less efficient, and the structure gradually changes towards conventional plasmonic grating filter without waveguide. Figure 1 shows the schematic of resonant grating structure and corresponding dimensions. The resonant grating structure has narrow passband in the range of 10-20 nm, which allows for high resolution spectroscopy. Due to complex nature of coupling between the grating and slab waveguide, there is no analytical method (to our knowledge), to design and optimize such structure without resorting to EM solvers. Hence the filter structure ( Fig. 1) was designed and optimized using Rigorous Coupled Wave Analysis (RCWA) technique.
Results
Filter array design and simulation. An array of 20 filters (in 4 × 5 matrix) were designed using RCWA and filter spectra was optimized for 10-20 nm bandwidth The distance between the grating and slab waveguide was optimized to achieve such bandwidth. Figure 2a shows the simulated spectra of all 20 filters and Fig. 2b shows the full wave half maximum (FWHM) distribution of the 20 filters. In addition, Fig. 2c shows total E-field quiver plot of one of the filters at the peak wavelength at 547 nm. technique. Figure 3 below shows RGB image of the filter array taken using optical microscope and SEM image of a section of one of the filters. The filters were then characterized using test setup shown in Fig. 6 in methods section, after replacing the camera with spectrometer probe. Figure 4a below shows the characterized filter array spectra as measured by the spectrometer and Fig. 4b shows corresponding FWHM of each filter. The measured filter spectra are very similar to simulated results, except for FWHM at shorter wavelengths. The broadening of the transmission peak can be attributed to more loss at shorter wavelengths compared to material properties used in the simulation environment. Figure 4c shows relative throughput (area under the curve) through each filter compared between simulation and measurement. As can be seen filter throughput between simulation and measurement is consistent, which indicates that the filters at shorter wavelengths are broadened and hence look attenuated but the total area under each curve shows consistent trend.
Spectroscopy and spectral reconstruction. A set of 6 colored glass filters were used as samples to characterize the performance of the designed color filter array and reconstruction algorithm. The details of fabrica- www.nature.com/scientificreports/ tion, testing and algorithm is described in methods section. Figure 5 below shows the results of reconstruction of transmission spectra of these samples based on the snapshot images taken with a monochromatic camera. The second sample (BG20) was purposely chosen to test the limits of the system, since it has many sharp transitions and narrow features. It is noted that except for sample 2, the RMSE is less than 0.054 for rest of the samples. The performance degradation in sample two is expected and shows the limiting performance of the spectroscopy system. www.nature.com/scientificreports/
Discussion
The use of the color filter array to detect power in each spectral band and reconstruction of original spectra poses several challenges. Firstly, the spectrum of each filter has prolonged tail at the longer wavelengths and Rayleigh anomaly peaks at the short wavelengths, which causes spectral mixing. For example, in Fig. 2a the first filter can transmit light in the range of 425 nm to 450 nm as well as that beyond 600 nm. Hence any reading on this color channel could be due to either of these spectral bands. Due to such mixing, as can be seen in Fig. 5, the detected signal is quite different from the original sample spectra. Hence an unmixing algorithm was developed to band-wise unmix detected signals. Secondly, the reconstruction of original spectra (at 1 nm steps) from under-sampled data (only 20 filters in entire visible range) can be framed in the linear algebraic terms as solving under-determined least square problem, which has infinite many solutions. Hence a unique regularization method using difference operator was used for reconstructing smooth spectra from unmixed signals.
Although sample spectra could be recovered there are several sources of error that limits the performance, some of which are: 1. There is inherent assumption in proposed algorithm that spectrum is constant within each band. This introduces some error. 2. Some of the spectra, especially sample two BG20, contains very sharp features which has frequency components higher than that Nyquist frequency and hence some of the information is aliased, which degrades reconstruction accuracy in this filter.
The reconstruction is based on filter characterization and measurement errors in filter characterization
can result in reconstruction error. The filters were characterized by coupling imaged filter patterns onto an optical probe of the spectrometer and hence variations in coupling efficiency could results in errors in filter characterization, which leads to errors in reconstruction. 4. Lastly, there is inherent cross-talk between filters due to proximity and due to presence of contiguous slab waveguide. The slab waveguide provides means for some of the rejected power from one filter to appear in the other filters. However, this effect is partly captured during filter characterization and as long as filters are characterized in-situ including such cross-talk, it doesn't affect the reconstruction. However due to cross-talk, the characterized filter array spectra are expected to be different from simulation.
Methods
The filter array was designed in DiffractMod software from Synopsys which uses Rigorous Coupled Wave Analysis (RCWA) technique. The periods of the filters were varied from 260 to 450 nm at 10 nm steps. The filters were designed to be 25 µm × 25 µm in size separated by 50 µm spacing forming 4 × 5 mosaic pattern. The design was fabricated on 500 µm thick Quartz substrate on which 90 nm of Silicon Nitride was deposited using Plasma Enhanced Chemical Vapor Deposition (PECVD) followed by 60 nm of Silicon Dioxide using same PECVD tool. Then 40 nm of Aluminum was deposited using evaporation. The filter array was then patterned using Focused Ion Beam (FIB) milling using Gallium ions with 30 keV energy. The writing was performed at 30 pA write current and with scan speed such that dose is 35 mC/cm 2 . The samples (6 colored glass filter from Newportglass 35 ) were measured by passing white light through the samples and the Plasmonic Filter Array and capturing snapshot images of the Filter Array using an objective lens. The Amscope HL250-AY was used as white light source. The gooseneck of the lamp was held on a mounting fixture and the light was used to illuminate a variable aperture. The light from the aperture was then collected using an aspherical achromatic collimating lens (APAC15) with effective focal length of 30 mm from Newport Optics. The light was then passed through visible light filter (FESH750) with cutoff at 750 nm. Then a wire grid polarizer (WP25M-VIS) was used to polarize the illumination. Then the samples were placed in the light path with a mounting fixture. Then the glass slide with plasmonic filter array was mounted on X-Y stage and placed in the optical axis. Then a MPlan 10 × objective was used to image the filter array from the other side onto DMK21AU04 monochromatic camera. The background illumination was reduced by conducting the experiment in a dark room and by properly shielding stay light. The camera was connected to a computer in which automatic exposure time adjustment algorithm was run to keep the signals in images around 50% of the camera's dynamic range. Figure 6 below shows the test setup used for sample measurement. After sample images were taken, the filter array was characterized by replacing the camera with Ocean Optics USB2000+ spectrometer and by removing the samples. The images of each filter were directly coupled into the open end of the optical probe of the spectrometer by mounting the probe on a X/Y translation stage. The open end of the probe was placed at the image plane.
The images were then postprocessed for background subtraction and segmentation. Then the detected signals were calculated based on average of the pixel values within region of interest of each filter in each image. These values represent blue curves with diamond markers in Fig. 5. Then the Algorithm 1 (described below) was used to unmix various spectral regions.
For unmixing algorithm, we consider the signal acquisition in two steps. Firstly, the illumination passes through an idealized set of filters (without much overlaps) and then secondly these signals are mixed at various proportions to produce detected signals. Such operation can be represented by: Here S n is sample transmittance, I n is illumination, G N×n is idealized filter transmission matrix, M N×N is the mixing matrix and D N is the detected signal. Here × signifies matrix multiplication and • signifies element-wise product. The mixing matrix M M×N is then computed using following algorithm. www.nature.com/scientificreports/ Then M is a N × N matrix representing mixing proportions from each filter to every other filter. This is an invertible square matrix. This assumes that spectrum is constant across each band, which for a set of narrow filters is a good approximation. Also, this implies the product M −1 × F results in idealized filter transmission matrix. Now unmixing can be performed using following operation.
where D U is unmixed detected signals per color channel and + operation is regularized pseudo-inverse. A regularized pseudo-inverse is used instead of matrix inversion to find a smooth low frequency signal and to discard oscillatory and unrealistic solutions. Now once the signals are unmixed, the reconstruction can be performed by solving least square problem using similarly regularized pseudo-inverse. Firstly G N×n is computed as factor of the characterized filter transmission matrix F N×n using following equation. Now such idealized filter spectra can be used to reconstruct spectra from the unmixed signals as below.
Here again the inverse is regularized pseudo-inverse and R n1 (= G N×n × D U1 ) is the first reconstructed spectrum without any samples. The regularized pseudo-inverse is computed using following equation: where k is the regularization parameter and G is second order difference operator given by: The regularization parameter k determines the strength of smoothing by penalizing highly oscillatory solutions. Choosing a k value equal to zero leads to the case of non-regularized pseudo-inverse or least square error minimum norm solution, while choosing higher k value leads to smoother solution. The value of k was optimized www.nature.com/scientificreports/ with many iterations to seek for optimum solution. In inversion operation in Eq. (2), the k value was 100 and that in Eq. (4) it was 1.
For computing transmission spectra, the reconstructed signal hence calculated, includes a signal without any samples, which is considered as illumination signal and when divided by such signal, the sample transmittance S n can be recovered as R n . In Fig. 5, black curves are S n , curves with blue markers are D N , curves with green markers are D U and red curves are R n . The reconstructed spectra are very similar to the original sample spectra and root mean squared error is less than 0.137 across all samples.
Data availability
The data collected from testing in this research study are available from the corresponding author on reasonable request. | 3,829 | 2021-12-01T00:00:00.000 | [
"Physics",
"Materials Science",
"Engineering"
] |
Production of Ibuprofen Pellets Containing High Amount of Rate Retarding Eudragit RL Using PEG400 and Investigation of Their Physicomechanical Properties
Objective(s) The aim of this study was to investigate the possibility of production of ibuprofen pellets with high amount of rate retarding polymer by aid of PEG400 as plasticizer. Materials and Methods Polyethylene glycol (PEG400) in concentrations of 1, 3 or 5% w/w with respect to Eudragit RL was used in production of pellets containing 60% ibuprofen and 40% excipient (2% polyvinylpyrrolidone (PVP), 7.6 or 0% microcrystalline cellulose (MCC) and 30.4 or 38% Eudragit RL). Physicomechanical and release properties of pellets were evaluated. Results In presence of PEG400, formulations containing 30.4% Eudragit RL and 7.6% MCC could easily form pellets. In formulations without any MCC pellets were obtained only in presence of 3 or 5% PEG400. Pellets containing MCC with 0 or 1% PEG400 showed brittle properties but those with 3% or 5% PEG400 showed plastic nature under pressure. Elastic modulus dramatically decreased with increasing PEG400 indicating softening of pellets. This was due to shift of Eudragit structure from glassy to rubbery state which was supported by DSC studies. Mean dissolution time (MDT) increased with addition of 1 or 3% PEG400 but this was not the case for pellets with 5% PEG400. Conclusion Overall PEG400 is a potential plasticizer in production of pellets based on Eudragit RL and ibuprofen. The ease in process of extrusion-spheronization, increasing the mean dissolution time and change in mechanical properties of pellets from brittle to plastic behavior were advantages of using PEG400. Changes in mechanical properties of pellets are important when pellets are intended to be compressed as tablets.
Introduction
Multiple unit sustained release dosage forms comprising granules, microcapsules, pellets or spheroids are the most popular oral sustained release dosage forms due to their several advantages (1,2).
Preparation of sustained release matrix pellets using rate retarding polymers are considered important because they have all the benefits of multiple unit systems and are produced in single step process without any need for further coating procedure. Extrusion spheronization is one of the widely used methods for production of pellets especially when the dose of drug is high. One of the major limitations in preparation of sustained release pellets with high drug loading using extrusion spheronization technique is the necessity for the use of a pelletization aid such as microcrystalline cellulose (MCC) in order to provide plasticity and proper cohesive properties for the wet mass. This would limit the use of sustained release polymers in formulation of pellets. Therefore pellets produced on the basis of this method usually need polymeric coating in order to retard drug release rate. Recently the use of release retarding materials along with MCC for production of sustained release matrix pellets has been noticed. Eudragit RL, Eudragit RS (3) and chitosan (4) are among polymers used for this purpose.
Furthermore compaction of multiparticulates into tablets is becoming more popular. Pellets which are intended to be compressed into tablets should deform under applied load without fracture. Alterations in mechanical properties of either coated or uncoated pellets from brittle to plastic nature makes them a suitable substrate for compression in the form of tablets as these changes could prevent cracking of pellets and/or their coating under the compression force and therefore limit the changes in the release properties after compression. Abbaspour et al showed that curing (thermal treating) of Eudragit based pellets containing 40 or 60% ibuprofen could bring about some changes in mechanical properties of these pellets and change their behavior from brittle to plastic under the mechanical test (5).
Plasticizers are widely used in film coating and the production of soft gelatin capsules. In general, incorporation of a plasticizer increases plasticity and changes the flexibility, tensile strength and adhesion properties of polymers (6). It has been shown that inclusion of plasticizer into matrices or pellets could profoundly change their mechanical and release properties (7,8).
As stated before in production of pellet by extrusion-spheronization MCC provide proper plasticity in wet mass and facilitate the process of extrusion and spheronization. In a study by Abbaspour et al it was shown that Eudragit based ibuprofen pellets with 60% drug loading could easily be obtained in presence of at least 10% MCC in their formulations. The aim of this study was to prepare ibuprofen pellets with high loading of drug (60%) and to replace the MCC with rate controlling polymer of Eudragit RL as much as possible with aid of PEG400 as plasticizer and to investigate the physicomechanical and release properties of pellets. The rational of using PEG400 was based on this concept that plasticizer (PEG400) could possibly provide the proper plasticity for the wet mass with less or no MCC and therefore replacement of MCC with rate retarding polymer would be probable.
Preparation of pellets
The composition of different formulations of pellets containing 60% ibuprofen and 40% excipient has been shown in Table 1. The plasticizer concentration on pellet formulation was 1, 3 or 5% w/w based on the weight of Eudragit RL. To prepare pellets, the solid ingredients of each formulation (50 g) were mixed using a kitchen mixer for 10 min. The required amount of water was slowly added to the dry blend to make a proper wet mass. For those pellets containing plasticizer, the plasticizer was mixed with half of the amount of water required for preparation of pellets and added to the powder mixture. Then proper wet mass was obtained with addition of further amount of water. The wet mass was passed through a screw extruder (Khazar, Iran) fitted with a 1 mm screen at 120 rpm. The extrudates were processed in a spheronizer (Khazar, Iran) fitted with a cross-hatched plate rotated at 1000 rpm for 2 min. The obtained pellets were dried at 40 °C for 10 hr in a conventional hot air oven.
Mechanical tests
The crushing strength (the load needed to break the pellets) or yield point (the load needed to begin plastic deformation) of 10 pellets in the size range of 0.85-1.00 mm was determined using Material Testing Machine (Hounsfield, England). The speed of the upper mobile platen fitted with a 1 kN load cell was set at 1mm/min. Elastic modulus and forcedisplacement graphs were obtained by a computer system attached to the apparatus (QMAT, Hounsfield, England).
Dissolution studies
The dissolution tests were carried out on accurately weighed samples (n= 6) containing 300mg of ibuprofen in automated dissolution testing equipment (Pharma test, Germany) using USP apparatus I, at 100 rpm, in medium of 900 ml phosphate buffer solution of pH 7.2, at 37 °C. The samples were taken from the vessels by a peristaltic pump (Alitea, Sweden), and assayed at 265 nm by a multi-cell transport spectrophotometer (Shimadzu, Japan). Two distinct absorbance peaks in the UV range could be observed for ibuprofen; a high peak at 221 nm and the shorter one at 265 nm. As dilution of samples during automated dissolution test was impossible, the shorter peak at 265 nm was chosen for determination of ibuprofen based on Costa et al. (9). Model independent approach was used to compare the dissolution data. For this purpose mean dissolution time (MDT) was calculated for each formulation by following equation (9): Where t¯i is the midpoint of the time period during which the fraction ∆M i of the drug has been released from the dosage form. A high MDT value for a drug delivery system means that it has a slow in-vitro drug release.
Scanning electron microscopy (SEM)
The surfaces of pellets were morphologically characterized using SEM. The samples were mounted on Al stub, sputter-coated with a thin layer of Pt using sputter coater (Polaron, England) under Argon atmosphere, and then examined using SEM (LEO1450VP, England).
Determination of size and size distribution of pellets
The pellets were sieved using nest of standard sieves (1180, 1000, 850 and 710 µm) shaken for 5 min on a sieve shaker (Retsch-Germany).
The weight of each fraction was determined and the cumulative frequency of undersize on probability scale was plotted against log of size. Mean particle size and geometric standard deviation were determined from the plot.
Differential scanning calorimetery (DSC)
DSC analysis was performed on Eudragit RL, ibuprofen and grounded pellets containing 0 and 3% PEG using a differential scanning calorimeter (Mettler Toledo DSC 822e, Switzerland) and STARe software version 7.01 (Mettler Toledo, Switzerland). The instrument was calibrated with an indium standard. Samples (7-10 mg) were weighed and sealed into aluminum pans. The DSC runs were conducted over a temperature range of 25-100 ºC at a rate of 5 ºC/min. All tests were run under a nitrogen atmosphere.
Statistical analysis
One way analysis of variances was used for statistical comparison of mechanical and dissolution test results.
Results
The results of mean particle diameter are presented in Table 2. The pellet mean diameter increased slightly with addition of plasticizer to the formulations. However increase in concentration of plasticizer did not affect the particle size of the pellets. Figure 1 show the scanning electron micrograph for formulation F3 and F7. Pellets prepared from formulations containing MCC (F3) were nearly spherical. However the shape of pellets prepared from formulations without MCC (F7) showed some deviation from sphericity. The results of mechanical test of the pellets are shown in Table 3. Pellets containing MCC with 0 or 1% plasticizer showed brittle behavior under the mechanical test and addition of 1% plasticizer led to decrease in crushing strength and elastic modulus of the pellets (P< 0.05). However formulations of F3 and F4 with 3 or 5% plasticizer showed plastic deformation under the mechanical test and the yield point decreased with increase in plasticizer concentration. Formulations F7 and F8 with no MCC and containing 3 or 5% plasticizer also deformed plastically under the mechanical test.
The thermograms for pure Eudragit RL and pellets of formulation F1 (without PEG) and formulation F7 (with 3% PEG) are depicted in Figure 2. The onset of the peak for glass transition temperature of pure Eudragit RL appeared at about 55 ºC and for melting of ibuprofen at 76 °C. The dissolution profiles of the pellets are shown in Figure 3. The results of mean dissolution time calculated from release profiles ( Table 4) showed that for formulations containing MCC, increase in concentration of plasticizer up to 3% increased MDT of the pellets significantly (P< 0.05). However there were no significant differences between MDT of formulation F4 (containing 5% plasticizer) with F1 (P> 0.05). Formulation F7 containing 3% PEG400 and 38% Eudragit RL, showed the highest MDT among different formulations.
Discussion
MCC due to its unique properties has been the excipient of choice for pellet production using extrusion spheronization technique. This material could facilitate the extrusion process, improve plasticity of the wetted mass and enhance spheronization (10). MCC unique properties include high surface area and high porosity which give it the ability of absorbing and retaining high quantity of water and also providing the proper rheological properties to wetted mass. In recent studies attempts have been made to use rate retarding polymers Eudragit RL or RS along with MCC in process of extrusion spheronization in order to achieve sustained release of drug from pellets with different drug loadings (3). In present study pellet containing 60% ibuprofen and 40% excipient was prepared aiming to replace the MCC with rate controlling polymer of Eudragit RL as much as possible and investigate the effect of addition of PEG400, as a plasticizer, in this regard.
Addition of PEG400 was found to be suitable for preparation of pellets containing Eudragit RL. Formulation F1 (with 7.6% MCC and no plasticizer) was unable to form proper extrudate after one run through the extruder and therefore to obtain acceptable extrudate this formulation was passed one more time through the extruder. Formulation F5 (with no MCC and no plasticizer) could not be processed in the extruder at all and therefore no pellets could be obtained from this formulation. Addition of 1% w/w of plasticizer based on Eudragit RL weight, in formulation containing 7.6% MCC and 30.4% Eudragit RL, facilitated the process of extrusion for formulation F2 and proper extrudate was easily obtained after just one passage through the extruder. Increase in concentration of plasticizer in formulations F3 and F4 also gave the same results. Pellets obtained from formulations of F2 to F4 were nearly spherical. Figure 1 shows the scanning electron micrographs of pellets obtained from F2 Formulation.
Addition of 1% plasticizer to formulation containing 38% Eudragit RL and no MCC (formulation 6) could not lead to preparation of proper extrudate and therefore no pellets were obtained from this formulation. But following addition of 3% or 5% PEG400 (formulations F7 and F8) the wet mass could be processed through the extruder and form pellets. However the extrusion of the wet mass was not performed as easy as that for formulations of F3 or F4. Furthermore the shape of the pellets obtained showed slight deviation from spherecity ( Figure 1).
The required amount of water for preparation of wet mass was different for various formulations. It has been shown that the amount of water needed to prepare wet mass in process of extrusion spheronization is dependent on the amount and properties of formulation components (11). The amount of water required for preparation of wet mass which is depicted in table 1 decreased by addition of plasticizer in formulation. This was attributed to the liquid nature of plasticizer and its interaction with Eudragit RL which led to enhanced cohesiveness. Felton et al. and Fujimori et al. showed that PEG400 is a suitable plasticizer for acrylic resin polymers (12,13).
The results of sieve analysis showed that the percent of fine particles and agglomerates were very low indicating the proper moisture content of wet mass. Fielden et al reported that less moisture content of wet mass could lead to formation of fine particles in process of spheronization and high moisture content could result in agglomeration (14). Addition of PEG400 resulted in preparation of pellet with larger mean diameter ( Table 2). Increase in cohesive nature and plasticity of wet mass in presence of plasticizer could account for increase in diameter of the pellets as increased plasticity of wet mass could prevent breaking of extrudates into small pieces during spheronization.
The results for mechanical test of pellets (Tables 3) indicate that pellets with 0 or 1% plasticizer (formulation F1 and F2) showed brittle behavior under the load and therefore the values of crushing strength have been reported for them. Similarly Abbaspour et al reported that ibuprofen Eudragit based pellets with 60% drug loading showed brittle properties under the mechanical test (3). Pellets with 3 or 5% PEG (formulation F3 and F4) showed plastic deformation nature and have not been fractured under the load and therefore the yield point has been reported for these pellets. Overall the addition of PEG400 decreased the elastic modulus of the pellets significantly ( (7).
Pellets with no MCC and containing 3% or 5% plasticizer (formulation F7 and F8) also showed plastic properties under the load and exhibited the lowest yield points and elastic modulus, indicating that these pellets were softer than those containing MCC and same amount of plasticizer. The transition of pellet behavior from brittle to plastic nature in presence of PEG400 was due to softening of polymer and shift of Eudragit structure from glassy to rubbery state which was supported by DSC studies (Figure 2). The transition peak for Eudragit RL and the peak related to the melting of ibuprofen are clearly visible in pellets of formulation F1 (without PEG400). However no peak for the transition of Eudragit RL could be observed in thermogram of pellets of formulation F7 (with 3% PEG400), indicating the rubbery or plastic state of polymer in presence of PEG400, at ambient temperature.
The results for MDT (table 4) showed that addition of 1 or 3% PEG400 to pellets containing Eudragit RL and MCC (formulations F2 and F3) increased the MDT compared to those pellets with no plasticizer. However presence of 5% plasticizer (Formulation F4) did not affect the MDT for these pellets significantly (P> 0.05). In pellets with no MCC and higher amounts of Eudragit RL (formulation F7 and F8) the MDT has been increased significantly compared to formulations with MCC and no plasticizer. This is attributed to increase in the amount of retarding polymer in formulation. Sadeghi et al. on their research on solid dispersion systems of Eudragit RS (15) and ethylcellulose (16) found that addition of plasticizer decreased the release rate of drug from tablets prepared of solid dispersions systems. Zhu et al. also showed that addition of trietyl citrate into the direct compressed tablets of chlorpheniramine maleate and Eudragit RS led to formation of more homogenous matrix and therefore lower drug release rate (8). Formation of more homogeneous Eudragit RL matrix following the addition of 1 or 3% plasticizer could also explain the observed results in this study. According to Wang et al. a plasticizer may function as an adhesion promoter (7) and therefore could help to form more homogenous matrix in pellet structure.
However as PEG400 is a water soluble plasticizer, therefore when used in higher concentrations (5%) it could provide more pores for drug release following its dissolution and therefore the polymeric matrix would be more porous for pellets containing 5% plasticizer. This would explain the lower MDT for the pellets prepared from formulations containing 5% plasticizer compared to those with 3% plasticizer.
Conclusions
The results of this study revealed that addition of proper plasticizer may provide the possibility of replacement of MCC with release retarding polymer such as Eudragit RL in process of extrusion-spheronization. However this replacement could not lead to desired sustained release for pellets containing high load of drug and therefore the coating process still may be required to retard the release of drug. The ease in pellets production process and changes in mechanical properties of pellets would be the advantages of using plasticizer in production of pellets containing Eudragit RL in their formulation. The changes in mechanical properties of pellets are beneficial especially when the compaction of the pellets as tablets is desired. The concentration of plasticizer has a great influence on mechanical properties of the pellets. As pellets with 5% plasticizer did not show any additional advantages over those containing 3% plasticizer it was concluded that the lower concentration of plasticizer i.e. 3% would be more appropriate in formulation of pellets with Eudragit RL in their structure. | 4,296.6 | 2011-07-01T00:00:00.000 | [
"Materials Science"
] |
TDEER: An Efficient Translating Decoding Schema for Joint Extraction of Entities and Relations
Joint extraction of entities and relations from unstructured texts to form factual triples is a fundamental task of constructing a Knowledge Base (KB). A common method is to decode triples by predicting entity pairs to obtain the corresponding relation. However, it is still challenging to handle this task efficiently, especially for the overlapping triple problem. To address such a problem, this paper proposes a novel efficient entities and relations extraction model called TDEER, which stands for Translating Decoding Schema for Joint Extraction of Entities and Relations. Unlike the common approaches, the proposed translating decoding schema regards the relation as a translating operation from subject to objects, i.e., TDEER decodes triples as subject + relation \rightarrow objects. TDEER can naturally handle the overlapping triple problem, because the translating decoding schema can recognize all possible triples, including overlapping and non-overlapping triples. To enhance model robustness, we introduce negative samples to alleviate error accumulation at different stages. Extensive experiments on public datasets demonstrate that TDEER produces competitive results compared with the state-of-the-art (SOTA) baselines. Furthermore, the computation complexity analysis indicates that TDEER is more efficient than powerful baselines. Especially, the proposed TDEER is 2 times faster than the recent SOTA models. The code is available at https://github.com/4AI/TDEER.
Introduction
Extraction of entities and relations from unstructured texts is one of the most essential information extraction tasks. It aims to extract entities and their corresponding semantic relations from unstructured texts, which are usually presented in a triple form of (subject, relation, object), e.g., (Microsoft, co-founder, Bill Gates). It is also a crucial step in building a large-scale KB and exerts an important role in the development of web search (Szumlanski and Gomez, 2010), question answering (Fader et al., 2014), biomedical text mining (Huang and Lu, 2016), etc.
Traditional approaches (Zelenko et al., 2003;Chan and Roth, 2011;Rink and Harabagiu, 2010) handle this task in a pipeline manner, i.e., extracting the entities first and then identifying their relations. The pipeline framework simplifies the extraction task, but it ignores the relevance between entity identification and relation prediction. To address this problem, several joint learning models have been proposed and can be categorized into feature-based models and end-to-end deep models. Feature-based models (Li and Ji, 2014;Ren et al., 2017) introduce a complex process of feature engineering and profoundly depend on Natural Language Processing tools for feature extraction. More recently, the end-to-end neural network models (Gupta et al., 2016;Zheng et al., 2017;Zeng et al., 2018;Fu et al., 2019;Wei et al., 2020) have become the mainstream method for relation extraction tasks. Such models utilize the learned representation from pre-trained language models and are a more promising approach than manual features.
More research interests have been concerned with complicated entity and relation extraction problems, such as the overlapping triple problem. Zeng et al. (2018) summarized the overlapping triple problem into three categories, i.e. Normal, SEO, and EPO, which are depicted in Figure 1. Many methods have been proposed to address the overlapping issue, for instance, encoder-decoder framework (Zeng et al., 2018) and decomposition approaches Wei et al., 2020). However, such approaches still suffer from setbacks when handling the overlapping triple problem. More specifically, the encoder-decoder framework can only resolve the one-word entity overlapping problem and fail to handle the multi-word entity overlapping problem. Meanwhile, the decomposition approaches suffer error accumulation between dependent stages. To address these problem, presented a one-stage method, TPLinker, that transforms the joint extraction task into a token pair linking problem to resolve the overlapping triple problem. TPLinker does not contain any inter-dependent stages, hence it can alleviate error accumulation. However, processing all token pairs at encoder layers suffers from high computational complexity, which is an obstacle for TPLinker to encode long text.
We present a novel framework TDEER to jointly extract the entities and relations by a translating decoding schema to handle the overlapping triple problem. More concretely, TDEER interprets the relation as a translating operation from subject entity to object entities, i.e., it decodes triples by subject + relation → objects. The proposed translating decoding schema can effectively resolve the overlapping triple problem. TDEER iterates all pairs of subjects and relations to recognize objects (or no object), hence all possible triples, including overlapping or non-overlapping triples, can be considered. We propose a negative sample strategy to detect and alleviate error propagation in different stages. This strategy can enable TDEER to alleviate error accumulation to achieve higher results. TDEER is an efficient approach as it first retrieves all possible relations and entities, then uses distinguished entities and relations to decode triples. By doing this, the search space can be reduced, thus it is more efficient than previous works. The computational complexity of the proposed translating decoding schema is O(n + sr), where n is the sequence length, s is the number of subjects in the input sentence, r denotes the number of relations in the input sentence. Extensive experiments illustrate that TDEER achieves better results than SOTA models in most datasets and is competent in handling the overlapping triple problem.
In summary, our contributions are as follows: (1) We propose a novel translating decoding schema for joint extraction of entities and relations from unstructured texts. (2) TDEER can handle the intractable overlapping triple problem effectively and efficiently. (3) Notably, TDEER is about 2 times faster than the current SOTA models.
Related Work
The pipeline approach and joint approach are the two mainstream methods for extracting entities and relations from unstructured texts.
Traditionally, extracting entities and relations to form triples has been studied as two separated independent tasks: Named Entity Recognition (NER) and Relation Extraction. Mintz et al. (2009) introduced a distant supervision model, and Hoffmann et al. (2011) used a weak supervision method to extract entities and relations. The features of distant supervision and weak supervision approaches are often derived from Natural Language Processing (NLP) tools. It suffers from data labeling errors that inevitably exist in NLP tools. To address this problem, Zeng et al. (2015) employed a multi-instance learning approach to tackle the problem of data labeling errors. Qin et al. (2018) applied reinforcement learning for extraction of entities and relations. Although the pipeline models produced promising results, they neglect the triple-level dependencies between entities and relations. Recently, Zhong and Chen (2021) presented a pipeline approach incorporating entity information for entity and relation extraction.
To exploit the dependencies between entities and relations, multiply joint extraction models have been proposed. Zheng et al. (2017) introduced a unified tagging scheme and transformed the relationship extraction problem into a sequence labeling problem. Zeng et al. (2018) applied a sequenceto-sequence model with a copy mechanism to solve the overlapping triple problem. Trisedya et al.
(2019) employed the encoder-decoder framework to jointly extract triples from sentences and map them into an existing KB. Fu et al. (2019) applied graph convolutional networks to jointly learn named entities and relations. Dai et al. (2019) presented a unified joint extraction model to tag entity and relation labels directly according to a query word position, which can simultaneously extract all entities and their types. Wei et al. (2020) proposed a cascade binary tagging framework. formulated the joint extraction as a token pair linking problem.
Moreover, some knowledge representation models Wang et al., 2014;Tu et al., 2017) are adopted to refine the triple extraction model via scoring candidate facts by knowledge graph embedding. Although some of them also use the "translation" idea, the function is different from ours. In their setting, they use the "translation" idea to construct rank-based knowledge graph embedding models. They cannot be used to extract entities and relations from texts directly. In our setting, the "translation" idea is applied to end-to-end joint extract entities and relations from text.
The proposed translating decoding schema is a novel approach to solve the overlapping triple problem effectively and efficiently, which makes our model crucially different from previous works.
Methodology
This paper proposes a three-stage model, TDEER. In the first stage, TDEER uses a span-based entity tagging model to extract all subjects and objects. In the second stage, TDEER employs the multilabel classification strategy to detect all relevant relations. In the third stage, TDEER iterates the pairs of subjects and relations to identify respective objects by the proposed translating decoding schema. Figure 2 shows the generic framework of TDEER. In subsequent sections, we will describe the three stages of TDEER in detail.
Input Layer
The input of TDEER is a sentence T . We pad the sentence to keep a uniform length n for all sentences. For an LSTM-based model, we first map each word into a k-dimensional continuous space and obtains the word embedding t i ∈ R k . Then we concatenate all word vectors to form a k × n matrix as model input: t = [t 1 , t 2 , . . . , t n ]. we employ LSTM on the embedding matrix to produce latent semantic feature map X: (1) As for a BERT-based model, TDEER extracts feature map via the pre-trained BERT (Devlin et al., 2019) over text input:
Entity Tagging Model
To obtain entities and their positions efficiently, we adopt a span-based tagging model following prior works Wei et al., 2020). We apply two binary classifiers to predict the start and end position of entities respectively. The operations on each token in a sentence are as follows: where p start i and p end i stand for the probabilities of recognizing the i-th token in input sequence as the start and end position of an entity, respectively. σ(·) denotes a sigmoid activation function.
The entity tagging model is trained by minimizing the following loss function: is the likelihood for the start positions, and p end θ is the likelihood for the end positions. We apply the entity tagging model to obtain all subjects and objects in one sentence. Detected subjects and objects are denoted as Ω s and Ω o , respectively. The extracted entity is presented into a tuple like (start, end).
Relation Detector
In general, more than one relation can be detected in a sentence. For example, there are four relations Star In, Direct Movie, Live In, and Capital Of in the sentence in Figure 2. To identify related relations in a sentence, we adopt a multi-label classification strategy. For the BERT-based/LSTM-based model, we project the "[CLS]" token/last output (LO) representation into a relation-detection space for multi-label classification, as follows: where σ(·) denotes sigmoid function.
The relation detector minimizes the following binary cross-entropy loss function to detect relations: BERT Encoder where y i ∈ {0, 1} indicates the ground truth label of relations. We denote the detected relations in a sentence as Ω r .
Translating Decoding Schema
We iterate the pairs of detected subjects Ω s and relations Ω r to predict the start positions of objects. For each subject and relation pair, we first combine the representation of subject and relation. Next, we use the attention mechanism to obtain a selective representation, which is expected to assign higher weights to possible positions of objects. Finally, we pass the selective representation to a fully-connect layer to get the output, i.e. the positions of objects. More concretely, for the i-th subject in Ω s and j-th relation in Ω r , TDEER takes the averaged vector span representation between the start and end tokens of the subject as v i sub . TDEER maps the relation into a continuous space with the same feature dimension as v i sub to produce the relation embedding vector e j rel . Then TDEER applies a fully-connect layer to encode the relation: v j rel = FullyConnect(e j rel ).
TDEER links subject and relation via addition op-eration, as follows: We adopt the addition operation because it is intuitive, and it does not change the tensor shape of inputs, which is convenient for attention computation. Next, TDEER applies the attention mechanism to obtain the selective representation.
where d k is the dimension of the attention key. Furthermore, TDEER adopts a binary classifier to identify the start positions of objects given the current subject and relation.
where p obj_start i indicates the probability of identifying the i-th token in input sequence as the start position of an object entity.
In this stage, TDEER minimizes the following loss function to discern the start positions of object entities.
where I is the indicator function. After obtaining the start positions of objects, TDEER takes the corresponding entities from the Ω o which has the same start position as the final objects. If no start positions match, there is no triple for the current subject and relation.
Negative Sample Strategy
Most entities and relations extraction models consisting of multiple components suffer from error accumulation. Errors from upstream components will propagate to downstream components because of the dependency between components. In TDEER, the translating decoder is dependent on the entity tagger and relation detector, hence the translating detector may receive error entities or relations from upstream components. Therefore, we introduce a negative sample strategy to detect and alleviate errors from upstream components. For each sentence, we produce incorrect triples as negative samples by replacing the correct subject/relation with other inappropriate subjects/relations during the training phase. We do not assign any objects to negative samples, namely the probabilities of start positions of Eq.(11) are all expected to be 0. This strategy enables TDEER to handle noisy inputs of subjects and relations at the decoding phase.
Joint Training
We jointly train the span-based entity tagging model, the relation detector, and the translating decoder. The joint loss function is defined as follows: where α, β and λ are constants. In our experiment, we set 1.0, 1.0, and 5.0, respectively. The values are obtained by grid search on the validation set.
Datasets and Evaluation Metrics
We conduct experiments on widely used datasets.
NYT (Riedel et al., 2010) dataset was produced by distant supervision method from New York Times news articles. WebNLG was created for Natural Language Generation and adapted by Zeng et al. (2018) for relational triple extraction. For a fair comparison, we apply the two datasets released by Zeng et al. (2018). Apart from evaluating the model on standard splitting, we follow (Wei et al., 2020) to partition the test sentences according to different overlapping categories, different triple numbers for experiments on overlapping triples, and various triple numbers. Furthermore, we also conduct experiments on NYT11-HRL (Takanobu et al., 2019), in which most test sentences belong to Normal, to demonstrate that the proposed model can handle not only the overlapping triple problem but also the general problem. The adopted public datasets with summary statistics in Table 1. We report the standard micro Precision, Recall, and F1-score following the same setting in Fu et al. (2019).
Baselines
We compare the proposed model with following SOTA models: NovelTagging (Zheng et al., 2017) incorporates both entity and relation roles and models relational triple extraction problem as a sequence labeling problem; CopyR (Zeng et al., 2018) applies a sequence-to-sentence architecture; GraphRel (Fu et al., 2019) uses graph convolutional networks to jointly learn named entities and relations; OrderCopyR (Zeng et al., 2019) applies the reinforcement learning into an sequence-tosequence model to generate triplets; CasRel (Wei et al., 2020) employs a cascade binary tagging framework; TPLinker iterates all token pairs and use matrices to tag token links to recognize relations between token pair.
Implementation Details
We adopt the Adam (Kingma and Ba, 2015) optimizer. The hyper-parameters are tuned by grid search on the validation set. The learning rate is set to 1e-3/5e-5 and the batch size is set to 32/8 in the backbone as LSTM/BERT. For the LSTM-based model, we apply the 300-dimension pre-trained GloVe embedding (Pennington et al., 2014) (Zeng et al., 2018;Wei et al., 2020). We correct the number in the statistics and use to mark the accurate number.
Main Results
The main results of the proposed models and baseline models are reported in Table 2. CasRel, TPLinker, and TDEER achieve absolute improvements on NYT and WebNLG datasets against the rest baselines. Especially, TDEER produces competitive results compared with the previous SOTA model TPLinker and achieves 7 out of 9 best results. Moreover, TDEER outperforms baseline models over the F1 score on all datasets. From Table 1, we can observe that the data size of WebNLG is small while it consists of a large number of predefined relations. It is difficult to make improvements on WebNLG, as existing models can achieve an F1 score over 90%, which has already exceeded human-level performance . Even though, TDEER achieves around 1.2% gain to 93.1% on WebNLG against TPLinker, which verifies the effectiveness of the proposed framework. Apart from F1, we find that TDEER performs better on precision score than baselines models in most results. Although without a pre-trained language model as the backbone, TDEER LSTM still performs well. TDEER LSTM achieves a higher F1 score on NYT against baseline models except for BERT-Based CasRel and TPLinker. Furthermore, TDEER LSTM outperforms baseline models on WebNLG and NYT11-HRL over precision against all baseline models except for BERT-Based CasRel. Therefore, the proposed framework is efficacious even though without a powerful pre-trained language model. NYT and WebNLG contain a large number of overlapping-triple instances. Therefore, the results on NYT and WebNLG indicate that TDEER can address the overlapping triple problem. Almost all triples in NYT11-HRL belong to Normal. TDEER achieves better results than baselines on NYT11-HRL, which shows that TDEER can solve the gen-eral extraction problem.
Results of Ablation Study
We conduct ablation studies on different strategies to explore the effect of the negative sample strategy. It shows that negative samples from subjects achieve better results than negative samples from relations. TDEER performs better by combining the two types of negative sample strategy than adopting each strategy individually or without negative samples. This evidence illustrates that negative samples are helpful to alleviate error accumulation. We also conduct ablation studies on TDEER without the relation detector or attention. It also shows that the results of TDEER are better than TDEER without the relation detector or attention. We notice that the model will malfunction without the relation detector. This evidence suggests that the relation detector and attention are crucial for TDEER.
To investigate the effect of the attention mechanism, we pick up a sample from the NYT test set which contains a triple (Netherlands, /location/country/administrative_division, Utrecht). We visualize the attention heatmap of different subject and relation pairs as depicted in Figure 3. The heatmap indicates that when the extracted subject and relation pair are proper, the attention weights on object positions are higher than others. If the weights are close to each other, then the extracted subject and relation pair can not be decoded to form a valid triple.
Discussion on Triple Numbers
In general, the more triples in a sentence, the more complicated the sentence is. To explore the model performance regarding different sentence complexities, we also conduct experiments on sentences with different triple numbers. The results are reported in Table 4. From the results, we can find that TDEER outperforms baseline models except for four triple numbers in NYT. Notably, TDEER achieves 2.8% gain in NYT and 0.7% gain in WebNLG against TPLinker for complicated sentences containing five or more triples. This evidence illuminates that TDEER is effective to model sentences with multiple triples.
Discussion on Overlapping Patterns
To further investigate the performance of different overlapping patterns, we conducted extensive experiments and report the results on different overlapping patterns on NYT and WebNLG in Table 5.
The results suggest that TDEER outperforms baseline models, which demonstrates the advantages of TDEER in processing the overlapping triple problem.
H is f a t h e r is a p u lm o n a r y s p e c ia li s t in U t r e c h t , t h e N e t h e r la n d s .
Discussion on Computation Complexity
Computation efficiency is an important problem that is not paid enough attention to by most previous works. We compare TDEER with baselines in computational complexity and inference time on the test set. The results are shown in Table 6. Pipeline approaches usually use NER tools to detect entities. NER tools usually apply the Viterbi algorithm to decode sequences with O(nK 2 ) complexity, where n denotes the input length and K is the tag size. Pipeline approaches recognize relations from each entity pair. Thus, the computation complexity of pipeline approaches is O(nK 2 +e 2 ), where e denotes the number of entities in the input.
Despite the successes of CasRel (Wei et al., 2020) and TPLinker , they still struggle with computation efficiency. CasRel jointly decodes relations and objects. The com- . e denotes the number of entities in input, s/o stands for the number of subjects/objects in input, r denotes the number of relations in input, K denotes the tag size, and n stands input length. Inference time presents the average time BERTbased models take to process a sample.
putational complexity of CasRel is O(n + sro), where n is the input length, s/r/o is the number of subjects/relations/objects in the input, respectively. TPLinker iterates all token pairs and uses matrices to tag token links to recognize relations. The main computation overhead is on the encoder with O(n 2 ) complexity, where n is the input length.
The computation complexity of TDEER is O(n+ sr), where n is the input length, s denotes the number of subjects in input, and r is the number of relations in the input sentence. It is 0.7 times faster than CasRel and 1.6 times faster than TPLinker on NYT, and 1.1 times faster than CasRel and 2.1 times faster than TPLinker on WebNLG from Table 6. Therefore, we can conclude that TDEER is more efficient than baselines, which makes TDEER competent in constructing a large-scale KB.
Conclusion & Future work
In this paper, we have proposed a novel translating decoding schema for joint extraction of entities and relations, namely TDEER. It models the relation as a translating operation from subjects to objects, which can handle the overlapping triple problem naturally. We have conducted extensive experiments on widely used datasets to demonstrate the effectiveness and efficiency of the proposed model. The proposed negative sample strategy is used to alleviate the error accumulation problem. Though it is effective, it may increase training time. For future work, we plan to explore more efficient approaches to alleviate error accumulation. | 5,244.4 | 2021-01-01T00:00:00.000 | [
"Computer Science"
] |
A Constructive Examination of Rectifiability
We present a Brouwerian example showing that the classical statement ‘Every Lipschitz mapping f : [0, 1] → [0, 1] has rectifiable graph’ is essentially nonconstructive. We turn this Brouwerian example into an explicit recursive example of a Lipschitz function on [0, 1] that is not rectifiable. Then we deal with the connections, if any, between the properties of rectifiability and having a variation. We show that the former property implies the latter, but the statement ‘Every continuous, real-valued function on [0, 1] that has a variation is rectifiable’ is essentially nonconstructive. 2010 Mathematics Subject Classification 03F60, 26A16, 26A99 (primary)
Introduction
Consider a real-valued function f on a closed interval [a, b].
then the corresponding polygonal approximation to f has length We say that f • has bounded length if there exists c > 0 such that l f ,P c for each partition P of [a, b]; • is rectifiable if its length, sup {l f ,P : P is a partition of [a, b]} , exists; Every Lipschitz function has bounded length: for with f , κ, and P as above, The classical least-upper-bound principle ensures that if f has bounded length, then it is rectifiable.But in the constructive context of this paper, that principle implies the law of excluded middle (LEM) and so is inadmissible.The constructive least-upper-bound principle requires the additional hypothesis that the set S ⊂ R whose supremum is sought must be not only inhabited and bounded above, but also upper-order-located, in the sense that whenever α < β , either x β for all x ∈ S or else there exists (we can find) x ∈ S with α < x (see Bishop and Bridges [4, Page 37] or Bridges and Vît ¸ȃ [9,Theorem 2.1.18]).
With the aid of Specker's theorem [17] it is not hard to produce a recursive example of a pointwise, but not uniformly continuous function f : [0, 1] → R that has bounded length but is not rectifiable.The motivation for this paper lies in the question: Is every Lipschitz function f : [0, 1] → R constructively rectifiable?Our first main result (Proposition 2) gives a Brouwerian example showing that the rectifiability of all real-valued Lipschitz functions-and hence of all real-valued, uniformly continuous ones-on [0, 1] implies the essentially nonconstructive limited principle of omniscience: LPO: For each binary sequence (a n ) n 1 , either a n = 0 for all n or else there exists n such that a n = 1.This leads to our second main result (Theorem 7), providing an explicit example of a recursive Lipschitz function that has bounded length but is not rectifiable.The proof of the latter depends on a lemma of interest in its own right (Lemma 5), which enables us to pass from rectifiability over the whole interval [0, 1] to rectifiability over each of its compact subintervals.
In the second part of the paper we consider the possibility of connecting rectifiability with the property of having a variation (which, classically, reduces to that of bounded variation).In particular, we show that rectifiable continuous functions on [0, 1] have a variation, but the converse implies LPO (Corollary 9).
The constructive framework, BISH, of our work is that of Bishop [3,4,9] (see also Troelstra and van Dalen [18]), in which the logic is intuitionistic and we adopt a mathematical foundation such as the set theories CZF (Aczel and Rathjen [1,2]) and CMST (Bridges and Alps [6]), or Martin-Löf's type theory (Martin-Löf [14,15], Nordström, Peterson and Smith [16]).One model (in a purely informal sense) or interpretation of BISH is the recursive one, RUSS, which can be regarded as BISH plus the Church-Markov-Turing thesis and, if desired, Markov's principle of unbounded search (see Kushner [12], Markov [13] or Bridges and Richman [8,Chapter 3]); that model is the setting for Theorem 7.
Lipschitz curves need not be rectifiable
We begin our technical presentation with a lemma.
Lemma 1 Let (a n ) n 1 be an increasing binary sequence with a 1 = 0, and let b > 0. Then there exists a Lipschitz function f : (ii) f has Lipschitz constant 2; (iii) if f is rectifiable, then either a n = 0 for all n or there exists n with a n = 1; and (iv) if f is differentiable at any point of [0, b], then either a n = 0 for all n or there exists n with a n = 1. , Note that if a n = 0 for all n, then f n = 0; whereas if a n = 1 − a n−1 , then the length of the spiked path f n joining 0 to b is (the last inequality following because n 2).Note also that if a n = 1 − a n−1 , then the absolute value of the slope of the spikes of which is less than 2 (and, incidentally, increases to the limit 2 as n → ∞).Hence f n is Lipschitz, with Lipschitz constant 2. Since either f (x) > 0 or f (x) < 2; in the former case, there exists exactly one n such that f (x) = f n (x), so ||f || 2. It then follows that f is Lipschitz, with Lipschitz constant 2, and (see above) that the length of the curve Now suppose that the curve y = f (x) is rectifiable, with length s.Either s > b or else s < 8b/5.In the first case we can find x ∈ [0, 1] with f (x) > 0, and hence n with a n = 1.In the second case we must have a n = 0 for all n.Thus (iii) holds.
To deal with (iv), suppose, initially, that f is differentiable at the point k2 −N b, where N ∈ N and 0 k 2 N .We may further suppose that a N = 0.If there exists n > N such that a n = 1 − a n−1 , then f = f n and k2 −N b = (k2 n−N )2 −n b is a point where two adjacent spikes of f n meet; whence f is not differentiable at k2 −N b, a contradiction.Thus a n = 0 for all n > N and therefore for all n.Now let x be any point of [0, b], and suppose that f (x) exists.Either |f (x)| > 0 or |f (x)| < 1.In the first case there exists h = 0 such that f (x + h) = f (x); so either f (x + h) = 0 or f (x) = 0. Taking, for example, the case where f (x + h) = 0, compute ν such that ν n=1 f n (x + h) = 0. Then there exists n ν such that f n (x + h) = 0 and therefore a n = 1.On the other hand, in the case where |f (x)| < 1, if there exists n with a n = 1 − a n−1 , then, in view of the foregoing observation, x cannot lie on any open segment of a side of any spike of f , and so must be one of the three vertices of a spike.This is absurd, since we have just proved that f is not differentiable at such a vertex.Hence in this case we must have a n = 0 for all n.This completes the proof of (iv).In this context, the following is worth noting.
Proof Let f : [0, 1] → R be sequentially continuous and have bounded length, and let (P n ) n 1 be an enumeration of the partitions of [0, 1] with rational endpoints.Given real numbers α, β with α < β , and using countable choice, construct a binary sequence (λ n ) n 1 such that if λ n = 0, then l f ,Pn < β , and if λ n = 1, then l f ,Pn > α.Applying LPO, we see that either λ n = 0 for all n or else there exists N such that λ N = 1.In the second case, l f l f ,P N > α.In the first case, suppose that there exists a partition P of [0, 1] such that l f ,P > β .Since f is sequentially continuous, we can find such a partition P with rational endpoints.Then P = P ν for some ν , so l f ,Pν > β and therefore λ ν = 1.This contradiction ensures that l f ,P β for all partitions P of [0, 1].Since f has bounded length, its rectifiability now follows from the constructive least-upper-bound principle.
In the next section we convert these Brouwerian examples into a full-blooded counterexample in the recursive setting.
A recursive counterexample
To produce the promised recursive counterexample, we develop a general lemma, whose proof is derived from that of the particular application to functions of bounded variation (Bridges [5,Theorem 3]).
By a pseudoquasimetric on a set X we mean a mapping d : X × X → R such that for all x, y, z in X , • d(x, y) 0 and d(x, x) = 0; A continuous pseudoquasimetric on a metric space (X, ρ) is a pseudoquasimetric that is uniformly continuous as a mapping from X × X , taken with the product metric induced by ρ, into R.
Suppose that s ≡ sup d,P : P is a partition of I exists.Then for each compact subinterval J of I , Since d is uniformly continuous, we can construct a partition P : 0 = x 0 < x 1 < • • • < x N = 1 consisting of distinct rational points of I such that d,P > s − ε.Since a and the x i are rational, there exists p such that x p < a x p+1 .Since d satisfies the triangle inequality, adding a to the partition P does not decrease the value of d,P ; we may therefore assume that a = x m , and likewise that b = x m+k , for some m and k.Letting we have either t > α or t < α + ε.In the latter case, suppose that there exists a partition We have therefore shown that either there exists a partition Q of J with d,Q > α or else d,Q < β for all partitions Q of J .Since α, β are arbitrary positive numbers with α < β , the constructive least-upper-bound principle now ensures that the desired supremum exists.Finally, the continuity of d enables us to remove the restriction that a and b be rational.
Proposition 6 If f : [0; 1] → R is uniformly continuous and rectifiable, then the restriction of f to any compact subinterval of [0, 1] is rectifiable.
Another application of Lemma 5 arises in connection with a uniformly continuous function f : [0, 1] → R of bounded variation.For each partition P : 0 and T f [0, 1] the respective suprema of these quantities as P ranges over all partitions of [0, 1], when the supremum exists; note that if T f [a, b] exists, then we say that f has a variation and that we see that if T + f [0, 1] exists, then so does T + f [a, b] whenever 0 a b 1.Similar properties obtain for T − f and T f .In the case of T f , we recover a special case of Theorem 3 of [5]: if f has a variation on [0, 1], then it has a variation on each compact subinterval of [0, 1].It is then straightforward to prove the additivity of the variation function: This brings us to our recursive example.
Proof Let φ 0 , φ 1 , . . .be an effective enumeration of the computable partial functions in N N , and for each n define an increasing binary sequence (a n,k ) k 1 such that if φ n (n) is computed in exactly K steps, then a n,k = 0 for all k < K and a n,k = 1 for all k K .For each positive integer n let -if g n is rectifiable, then either a n,k = 0 for each k or else there exists k such that a n,k = 1, -if g n is differentiable at any point of [0, 3 −n ], then either a n,k = 0 for each k or else there exists k such that a n,k = 1.
Now construct a uniformly continuous mapping
The function F ≡ ∞ n=0 f n is well defined and uniformly continuous on [0, 1], since ∞ n=0 ||f n || converges by comparison with ∞ n=0 3 −2n .Moreover, since the supports of the functions f n are pairwise apart, the restriction of F to J n is f n , and F has Lipschitz constant 2. Suppose that (the graph of) F is rectifiable.Then by Proposition 6, for each n the restriction of F to J n is rectifiable; whence g n is rectifiable, and therefore either a n,k = 0 for all k or else a n,k = 1 for some k.It follows that the set is recursive, which is known to be false.Hence F is not rectifiable over [0, 1].
Note that if the function F constructed in the proof of Theorem 7 is differentiable at any point of J n , then so is g n , and we can decide whether n ∈ K .It follows that for each n, F cannot be differentiable at any point of J n .In light of this observation, if, in the proof of Theorem 7, we replace J n by 1 2 n , 1 2 n + 2ε 3 n , then we obtain the following: (ii) J is a union of countably many disjoint closed intervals of total length ε; (iv) f is not differentiable at any point of J .
Rectifiability and finite variation
In this section we discuss the question: What, if any, is the connection between rectifiability and having a variation?First we dash any hope of proving that the latter property implies the former.
Proposition 9 For each binary sequence (a n ) n 1 there exists a function g : [0, 1] → R that has a variation but is rectifiable if and only if either a n = 0 for all n or else there exists n with a n = 1.
Proof Given a binary sequence (a n ) n 1 , let f : [0, 1] → R be the function constructed in Lemma 1 above with b = 1, and define g : [0, 1] → R by g(x) = f (x)/2 + x.Then g is increasing: Since g is increasing, it has variation g(1) − g(0) = 1.Now, if a n = 0 for all n, then g(x) = x and l g = √ 2. On the other hand, if a n = 1 for some n, then the slope of g on the intervals k2 and the slope of g on the intervals k Thus the arc length of g over each k2 −n , (k and since there are 2 n such intervals in question, .
Suppose that g is rectifiable.Then either l g < ( √ 34 + √ 10)/6 or else l g > √ 2. In the first case there can be no n with a n = 1, so a n = 0 for all n.In the second case, taking a partition P of [0, 1] such that l g,P > √ 2, we can find x ∈ P such that g( which is absurd.
Corollary 11 If the set of real-valued functions on [0, 1] that have a variation is closed under addition, then LPO is derivable.
Proof With f , g, and (a n ) n 1 as in the proof of Proposition 9, both g and the identity function id on [0, 1] have a variation, but if f = id + g has a variation, then either a n = 0 for all n or there exists n with a n = 1.
In contrast to Corollary 11, we have: The set of real valued, rectifiable functions on [0, 1] is closed under addition.
Proof This is a simple application of the triangle inequality.
Corollary 10 shows that we cannot prove constructively that every Lipschitz, let alone every continuous, function f : [0, 1] → R with a variation is rectifiable.Our final task is to show that, in contrast, we can prove that every rectifiable continuous mapping f : [0, 1] → R has a variation.This will require some preliminaries.
Lemma 13 Let a, b, c be nonnegative numbers.Then Proof First take the case a = 1.Define Then (we omit the details) f 0, which ensures that Next take the case a > 0. By the first case, Finally, if a 0, then for each ε > 0 we have a + ε > 0, so Letting ε → 0 completes the proof.
Proof Denoting by ρ the Euclidean distance function on R 2 , first note that With −1 = 0, an induction now shows that for k < m, k i=0 Note that if x ∈ [x j , x j+1 ] and y ∈ [x j+1 , x j+2 ], then whence g is monotone and so has variation g(1) − g(0).Moreover, for each j, and therefore the variation of g on [x j , x j+1 ] is |f (x j+1 ) − f (x j )|.Since the variation function is additive, it follows that It follows also from (2) that l f ,P = l g,P .Since adding points to a partition cannot decrease the approximations to the length of the curves of f or g, we now see that and hence, via Lemma 13, that We now weaken the assumption (i) by taking P as a strict partition 0 < ξ 1 < ξ 2 < • • • < ξ m = 1.For each i let Note that P i ⊂ P i , that It follows from the constructive least-upper-bound principle that the variation of f on [0, 1] exists.
Concluding remarks
In view of Lemma 1, we might ask for Brouwerian counterexamples to such statements as these: -Every real-valued function on [0, 1] whose derivative exists at each point is rectifiable.
-Every real-valued Lipschitz function on [0, 1] that is differentiable almost everywhere is rectifiable.
There can be no Brouwerian counterexamples for these two statements, since each of them is provable in INT.If f : [0; 1] → R is differentiable everywhere, then intuitionistically its derivative f is not just continuous, but uniformly continuous, so we can rectify the graph of f by the usual calculus formula for arc length.On the other hand, if f has Lipschitz constant c > 0 and is pointwise differentiable almost everywhere, then |f (x)| c at any point x where f is differentiable.A theorem of van Rootselaar (see Heyting [11, page 79] or Bridges and Demuth [7,Theorem 6]) shows that f is intuitionistically measurable, whence by Bishop and Bridges [4,Theorem (7.11), page 263] it is integrable.We can then show that the supremum of the set (1 + f 2 ) 1/2 dx.
It is possible that there is a recursive example of a real-valued Lipschitz function on [0, 1] that is differentiable almost everywhere but not rectifiable; but we do not know of one.
Lemma 1 Proposition 3
immediately provides us with two interesting Brouwerian counterexamples for Lipschitz curves: Proposition 2 The statement 'Every real-valued Lipschitz function on [0, 1] is rectifiable' implies LPO.The statement 'Every Lipschitz function on [0, 1] is differentiable at some point' implies LPO.
Lemma 5
Let I = [0, 1], and let d : I ×I → R be a continuous pseudoquasimetric on I .For each compact interval [a, b] ⊂ I and each partition P
v f ,P − v f ,P = m− 1 i=0( 1 i=0(
v f ,P i − v f ,Pi ),and thatl f ,P − l f ,P = m−l f ,P i − l f ,Pi ), For 0 i < m let ε i = v f ,P i − v f ,Pi 0.Note that since the variation function is additive, Pi = v f ,P − v f ,P > ε. | 4,785.2 | 2016-01-01T00:00:00.000 | [
"Mathematics"
] |
SegX-Net: A novel image segmentation approach for contrail detection using deep learning
Contrails are line-shaped clouds formed in the exhaust of aircraft engines that significantly contribute to global warming. This paper confidently proposes integrating advanced image segmentation techniques to identify and monitor aircraft contrails to address the challenges associated with climate change. We propose the SegX-Net architecture, a highly efficient and lightweight model that combines the DeepLabV3+, upgraded, and ResNet-101 architectures to achieve superior segmentation accuracy. We evaluated the performance of our model on a comprehensive dataset from Google research and rigorously measured its efficacy with metrics such as IoU, F1 score, Sensitivity and Dice Coefficient. Our results demonstrate that our enhancements have significantly improved the efficacy of the SegX-Net model, with an outstanding IoU score of 98.86% and an impressive F1 score of 99.47%. These results unequivocally demonstrate the potential of image segmentation methods to effectively address and mitigate the impact of air conflict on global warming. Using our proposed SegX-Net architecture, stakeholders in the aviation industry can confidently monitor and mitigate the impact of aircraft shrinkage on the environment, significantly contributing to the global fight against climate change.
Introduction
The skies above are dynamic ecosystems that react to different natural and artificial influences rather than just being empty canvases for atmospheric occurrences.Aircraft engines are among the latter and have drawn interest because of how they affect the atmosphere.More than half of all aviation's climate-related emissions come from contrails, which exacerbate the effects of global warming [1].High-altitude aircraft engines produce exhaust gases that may condense into contrails, observable trails.In the setting of climate change and environmental study, these long, wispy structures have drawn much attention.Contrails are complicated objects with wide-ranging effects; they are not merely ephemeral traces in the sky.On the one hand, they support the Earth's atmosphere's radiative forcing, which has a cooling and warming impact.They may deflect sunlight and retain emitted longwave radiation due to their microphysical characteristics and the ice crystals they contain, which can change the planet's energy balance.Contrails are crucial in affecting climate dynamics, much like their natural counterparts, normal clouds.Contrails also have conflicting impacts, so how they affect the climate must be clarified.In Fig 1, an illustration showcases key components of high-altitude ice cloud formation: engine-emitted water vapor and soot condensing on pre-existing aerosols, resulting in the presence of frozen droplets and contrail ice particles.Due to the existence of ice crystals, they may simultaneously strengthen the greenhouse effect, which traps heat while reflecting sunlight and having cooling effects.Underscoring the complex connection between contrails and climate, research on how these opposing factors balance out is still underway.Scientists are attempting to determine how and to what degree engine designs, various fuels, and atmospheric conditions contribute to climate change in light of the increased air traffic causing a rise in aircraft emissions of contrails during the last two decades [2].Despite efforts to curb emissions, the stability of these figures over the last decade emphasizes the pressing need for immediate and effective action [3].Our research is driven by the urgent need to address the environmental consequences of aircraft contrails and their association with emissions.We recognized the need for an innovative approach that transcends conventional methods and harnesses the power of artificial intelligence to achieve exceptional results.Enter SegX-Net, a segmentation architecture tailored for contrail analysis.Unlike traditional approaches, SegX-Net capitalizes on a unique fusion of deep learning techniques.The basis of our research is a crucial environmental concern: the influence of aircraft contrails on climate change.Due to a substantial increase in air traffic, contrails significantly contribute to emissions and global warming.Conventional approaches must be more comprehensive in dealing with the complexities of identifying contrails from satellite images.Therefore, our primary objective is to propose a groundbreaking solution.We selected to modify DeeplabV3+, incorporating ResNet-101 as the backbone.The choice is based on the exceptional capability of ResNet-101 to extract delicate characteristics, which are crucial for deciphering the complicated patterns of contrails in satellite photos.Along with the acclaimed DeeplabV3+, we thoroughly compare well-known models like U-Net, U-Net++, Attention U-Net, Trans U-Net, Res U-Net, and Uc Trans U-Net.The dataset used in this research paper focuses on aircraft contrails, which are clouds of ice crystals formed in aircraft engine exhaust and contribute to global warming by trapping heat in the atmosphere.
The main contributions of the paper include: • Introduced the SegX-Net architecture, a modified version of DeepLabV3+ with ResNet-101 integration, by customizing the encoder part of the network and leveraging transfer learning, leading to highly accurate and detailed contrail segmentation.
• The research emphasizes the significance of accurate aircraft contrail detection.By providing an advanced image segmentation solution, SegX-Net contributes to the understanding and mitigating contrail-induced environmental impact.
Our research paper contributes to understanding aircraft contrails' environmental impact and proposes an enhanced architecture for accurate contrail identification through image segmentation.By integrating SegX-Net, we tried to fill a crucial research gap in accurately identifying and analyzing aircraft contrails.
The remainder of the paper is organized as follows.In Section 2, we explore the body of literature in-depth, looking at several image segmentation techniques and their uses.Section 3 describes the dataset description, preprocessing procedures, SegX-Net design, and contrail formation.Analysis of efficiency, insights into parameters, and comparison experiments about assessment measures are discussed in Section 4. Section 5 gives an in-depth discussion of the interpreted findings, including the implications for contrail detection and image recognition of the climate.Finally, Section 6 summarizes our contributions, highlights the importance of SegX-Net, and suggests possibilities for further study.
Related works
The foundation of any scientific endeavor lies in building upon the existing body of knowledge.In contrail detection using image segmentation, a thorough exploration of related studies is essential to position our work within the broader landscape.This section presents a comprehensive overview of the relevant literature, from image segmentation techniques to the intricate relationship between contrails and climate impact.By delving into these studies, we gain valuable insights that contribute to the foundation of our novel approach, SegX-Net, designed to transform contrail detection through advanced deep learning techniques.Global warming arises from a mix of natural and human-emitted gases that trap heat, causing the Earth's temperature to increase.These greenhouse gases, like carbon dioxide and methane, obstruct the average energy radiation balance.In the realm of air transport's environmental effects, aside from emissions and noise, the impact of contrails on the Earth's radiation balance is a concerning area that needs more comprehensive understanding and precise data [4].Previous studies have explored various strategies, such as operational changes in air traffic control, to mitigate contrail-induced greenhouse effects.While some investigations focus on the potential benefits of altering cruise flight levels, others acknowledge the complexity and uncertainty surrounding contrail formation and climate impact, underscoring the ongoing need for comprehensive research in this domain [5].Identifying contrails in aerial images is a difficult task since they closely resemble natural cirrus clouds and undergo form variations over time [6].Paoli et al. [7] discovered that in an aircraft regime, at lower temperatures and greater humidity, contrails begin to develop near the engine's edge.While successful in predicting contrail formation, challenges persist in predicting persistence due to humidity uncertainties.The study delves into predicting contrail formation, persistence, and radiative forcing through aviation weather forecasts.Notably, the paper suggests considering the ambient atmosphere's dynamics to predict strong contrails.This work contributes vital insights into mitigating aviation's climate impact and underscores the need for refining contrail prediction methods to combat climate change [8].An instrumental tool in this endeavor is image segmentation applied to satellite and aerial imagery, enabling the identification of critical climate change contributors like deforestation, urban heat islands, and melting glaciers.Precise segmentation of these regions empowers targeted interventions to mitigate the effects of global warming [9].U Schumann et al. [10] investigated strategies to mitigate aviation's climate impact through optimized flight routes considering contrail formation and fuel consumption.It introduces climate-optimized routing using the Contrail Cirrus Simulation Prediction tool (CoCiP) and discusses its potential to reduce global warming effects.The study addresses the radiative forcing of the contrailinduced cirrus cover and highlights the need for further validation and refinement of the CoCiP model for accurate contrail prediction.This research aligns with the broader discourse on aviation's environmental consequences and emphasizes the significance of route optimization for climate protection.In another case, the paper of [11] comprehensively reviews climate change mitigation strategies, encompassing conventional efforts, negative emissions technologies, and radiative forcing geoengineering.It underscores the insufficiency of conventional mitigation to achieve Paris Agreement targets and explores alternative routes.The study highlights the importance of practical solutions like biogenic-based sequestration techniques, which require policy support, carbon pricing mechanisms, and increased research funding for effective implementation.Also, the study of K Segl et al. [12] introduces a novel approach for detecting small objects in high-resolution satellite imagery by combining supervised shape classification with unsupervised image segmentation iteratively.It emphasizes the significance of shape contrast and object size for accurate detection and discusses potential enhancements through multispectral or hyperspectral imagery.This approach holds practical implications for applications like urban monitoring and vegetation analysis, addressing the challenge of object detection in high-resolution panchromatic satellite images.A pioneering study by JP Hoffman et al. [13] introduces an innovative application of Convolutional Neural Networks (CNNs) in contrail detection within satellite imagery.Repurposing the U-Net architecture, initially developed for detecting sea ice leads, this approach accurately identifies contrails through image segmentation.Furthermore, a cooperative strategy utilizing Fuzzy C-means and Self-Organizing Maps attains high accuracy in segmenting satellite images [14].Researching global cloud and aerosol properties, radiative energy balance, 3D cloud morphology, and infectious disease risk due to climate fluctuations highlighted the importance of studying contrails' effects on radiative balance and cloud formation in various contexts.The proposed multistep protocol for contrail detection and segmentation in AVHRR images shows promise in identifying contrail properties yet acknowledges challenges in detecting certain types and improving algorithm precision [15].The study also revealed that converting the RGB color space to HSV enhanced segmenting satellite images, indicating the practical utility of color space transformations in this context [16].The paper by Andre L. Barbieri et al. [17]presents an entropybased image segmentation method for color images from Google Earth, enabling automated monitoring of ecological and geographical changes.It underscores the significance of color information for precise segmentation and highlights applications in disaster mapping, climate change monitoring, and ecological studies.The approach's potential for improvement via window size adjustments and complementary statistical measures is also emphasized.An automatic algorithm combining watershed segmentation and region merging demonstrates promising performance on Google Earth images [18].Studies revealed that mathematical morphology and watershed transformation algorithms offer segmentation benefits, yet they grapple with challenges such as over-segmentation and computational complexity [19].B Dezso et al. [20] presents a comprehensive review of graph-based image segmentation methods applied to satellite image classification.It evaluates four algorithms and discusses their theoretical foundations, implementation details, and potential improvements.The study highlights the significance of image segmentation in remote sensing for land cover identification and suggests avenues for future research to enhance algorithm performance and practical application.Leveraging geostationary satellite imagery, weather data and air traffic information, these studies offer insights into contrail evolution and climate impact.Deep learning techniques like instance segmentation are explored for efficient detection.Integration of multiple observation methods and identification of contrail-producing aircraft contribute to advancing contrail research for climate validation and modeling improvement [21].Recently, there has been a significant increase in research efforts to improve image segmentation methods by using deep learning techniques.This is due to the impressive performance of deep learning models in visual tasks [22,23].
Advancements in image processing have led to the emergence of image segmentation techniques, prominently in medical and satellite imagery domains.This paper introduces and evaluates three methods for satellite image segmentation: K-means Clustering, Thresholding Technique, and Active contour.By assessing their performance using parameters like Segmentation Accuracy and Correlation Ratio, the study aids in identifying practical options for satellite image analysis.The proposed Active Contours technique exhibits promising results, highlighting its potential for real-world implementation [24].In the context of advancing semantic segmentation techniques, this study of [25] introduces an innovative algorithm addressing accuracy and object boundary segmentation challenges.The algorithm demonstrates improved performance in segmenting high-resolution images by leveraging multi-level cascading residual structures and multiple loss function constraints.While the experimental results on Cityscapes and CamVid datasets are promising, comprehensive analysis of its applicability, comparative assessments, and real-world implications remain avenues for future exploration.Recently, McCloskey et al. [26] conducted research and provided a restricted set of human-labeled Landsat photographs for the scientific community.In another recent study by Ng et al. [27], a comprehensive effort was made to create an open dataset for contrails observed over the United States.This was achieved by utilizing satellite footage from the GOES-16 satellite.
The subsequent unveiling of SegX-Net's architecture, training process, and evaluation metrics in this paper is a significant step towards comprehending and mitigating contrail impacts on global warming, revolutionizing climate research.This paper critically reviews image segmentation methods to identify the most suitable techniques for contrail identification.Thus, we propose using an innovative AI-driven technique called SegX-Net for accurate contrail identification.Through this approach, we aim to revolutionize climate research by providing a powerful tool for monitoring and mitigating the effects of aircraft contrails on our environment.
Simultaneously, the architecture and backbones analyze the training subset, refining image segmentation precision.The subsequent phase involves comprehensive performance evaluation, leading to a succinct comparison table showcasing the contrail detection prowess of each backbone under SegX-Net.This methodical progression harnesses SegX-Net's power to redefine contrail detection precision, contributing to advancements in this vital field.UNet and DeepLab are top-rated models in the field of aerial photography due to their exceptional performance in image segmentation tasks and their ability to effectively include both global and local information [6].We used the DeepLabV3+ architecture as our segmentation network during this study.An improvement on the Deeplabv3 architecture, Deeplabv3+ has a more streamlined and effective decoding module for improving semantic segmentation performance and refining feature information [36].When it comes to segmentation, Deeplabv3 + outperforms the previous Deeplab-series networks [37].DeepLabV3+ is a state-of-the-art model for image segmentation tasks that has demonstrated excellent performance and accuracy in segmenting images.This architecture incorporates a powerful encoder-decoder structure, atrous convolutions, and skip connections to capture multi-scale contextual information and achieve precise segmentation results.By leveraging DeepLabV3+, we aimed to enhance the accuracy and effectiveness of our image segmentation tasks and achieve high-quality segmentation outputs, thus using a different architecture named SegX-Net.The network details are illustrated in Fig 5 .The input images used in the present study are high-resolution satellite photographs that depict real-world circumstances, including prominent aircraft contrails.Segmentation aims to accurately detect and analyze these contrails in the photos, enabling a thorough investigation of their distribution and contributing to a full comprehension of their environmental influence, particularly in climate change.
Dataset description
In this study, we used a dataset obtained from Kaggle [38].From there, we took 18000 images, which were divided into two subsets: a training set and a validation set.These images were sourced from the GOES-16 Advanced Baseline Imager (ABI) [39], and access to the original data was facilitated through Google Cloud Storage.The technical specifications of the ABI sensor, including resolution and spectral bands, are explicitly detailed to offer readers comprehensive insights into the data source.To adapt the full-disk images, bilinear resampling was applied, resulting in localized scene images.The training set comprised 14,400 images, accounting for 80 percent of the entire dataset, while the validation set contained 3,600 images, making up the remaining 20 percent.This division was crucial to ensure the effectiveness and generalizability of our model's performance.The training set played a vital role in training our model, enabling it to learn and extract meaningful features from a diverse range of images.We also tested our model on 1000 new images that were not used during training and validation.This helps ensure the reliability and generalization capability of our model.In the dataset section, we present a diverse set of input images that play a pivotal role in our research on contrail detection, is shown in Fig 3 .These images encompass various elements, including false color representations, ground truth contrail masks, and overlays of contrail masks on false color images.The false color images provide unique visual insights, showcasing essential spectral information for our analysis.Meanwhile, the ground truth contrail masks offer precise outlines of contrail regions, serving as valuable reference data for model evaluation and training.We comprehensively understand contrail distribution and spatial relationships within the original scenes by superimposing contrail masks on false color images.By utilizing such a substantial portion of the dataset for training, we optimized the model's parameters and refined its segmentation predictions, ultimately enhancing its accuracy and performance.On the other hand, the valid set served as an independent and unseen dataset, used explicitly to evaluate our trained model's generalization capabilities.
Data pre-processing
The image data underwent several crucial preprocessing steps in the initial training and validation preparation stages.Firstly, the images were converted into an array format with dimensions of 256x256, taking into account the presence of 3 color channels.The dataset was partitioned to ensure an unbiased evaluation, with 80% of the data being used for training and the remaining 20% for validation.One of the most essential steps in the preprocessing pipeline was image normalization, which aimed to establish consistency in pixel values across the dataset.The standard methods used included scaling the pixel values to a specific range, such as dividing them by the maximum value or applying a zero-mean normalization technique by subtracting the mean and dividing by the standard deviation.Implementing these preprocessing steps significantly improved the model's resilience and adaptability, allowing it to handle various inputs and perform effectively on unseen data.It was crucial to consistently apply the same preprocessing techniques to both the training and validation sets to ensure fairness in evaluation and accurate performance assessment.
Proposed architecture
In this work, we proposed an enhanced architecture by integrating ResNet-101 as the backbone network into the DeepLabV3+ model [31].The decision to incorporate ResNet-101 the encoder are merged with the upsampled deep features, and convolutional operations are applied to refine the feature details.This refinement process aims to improve the segmentation predictions by enhancing the feature representation.Finally, the refined features' resolution is restored through bilinear upsampling, resulting in the final segmentation map.Fig 5 visually represents the intricate structure of the network model described in this article.The figure highlights distinct elements, with the blue and yellow sections signifying 1x1 convolutions and 3x3 convolutions, respectively.Additionally, the figure demonstrates the utilization of maximum pooling and up-sampling techniques.During the encoding phase, the network performs through a series of operations, including 1x1 convolutions, which has channels of 64, three sets of 3x3 convolutions, which have 128 channels rate 6, 256 channels rate 12, 256 channels rate 18 respectively, and also maximum pooling.These operations collectively enable the network to extract and capture meaningful features from the input data.In the decoding phase, a single set of 1x1 convolutions is employed to restore the original size of the feature map.Following this, a combination of up-sampling and 3x3 convolutions is employed to generate the final prediction image, accomplishing the image segmentation task.The figure includes annotations that specify the layer names, output feature map sizes, and the corresponding operations involved, such as Conv for convolution, image pooling for maximum pooling, and upsample for up-sampling.
Residual module block
The Deep Residual Network, proposed by [41], introduced the concept of residual learning.The residual refers to the discrepancy between the observed and estimated values.Assuming the input to the network is denoted as x and the expected mapping as M(x), the network mapping can be reformulated as the residual, represented by F(x), as shown in Eq (1).
Here, x represents the characteristic mapping of the upper layer network, F(x) denotes the residual of the current layer and M(x) represents the observed value at that layer, forming the relationship depicted in Eq (2).
Although both M(x) and F(x) + x yield the same effect, optimizing F(x) is simpler compared to optimizing M(x).By considering the relationships between different layers, expressed in Eqs (3) and ( 4), the residual F(x N ) is added to the previous layer's output x N to obtain the output of the current layer, x N + 1.
@Loss
To ensure optimal network performance, it is crucial to strike a balance in terms of network depth.While a certain depth may lead to the best model performance and lowest loss, further increasing the network depth could potentially result in network degradation.To address this, the concept of the residual network is introduced, enabling the residual F(x) to approach zero and maintaining the network in an optimal state.
ResNet-101 encoder
In the SegX-Net architecture, ResNet-101 serves as an essential encoder, contributing to the network's ability to capture intricate features from input images effectively shown in Fig 6 .ResNet-101, introduced by [42], is a deep convolutional neural network that introduces a novel approach to addressing the vanishing gradient problem in deep neural networks.ResNet-101, a variant comprising 101 layers, employs residual blocks that facilitate extracting meaningful features.Notably, in the SegX-Net framework, ResNet-101 is not a feature extractor but an integral component for enhancing the network's segmentation capability.ResNet-101's architecture is characterized by its depth and structure, involving stacked residual blocks.Each residual block incorporates convolutional layers and shortcut connections bypassing certain layers.This design allows the network to adjust input features directly and learn more abstract features through subsequent layers.The architecture also integrates bottleneck structures to optimize computational efficiency by reducing convolutional layer complexities.These bottlenecks employ 1x1, 3x3, and 1x1 convolutional layers to selectively decrease input and output channels.Additionally, ResNet-101 includes global average pooling and fully connected layers at the end, culminating in a final classification or segmentation output.Although not used for feature extraction in SegX-Net, ResNet-101's depth and shortcut connections contribute to its proficiency as an encoder in the network's image segmentation process.
Architectural framework and comparative backbone models
During this study, we harnessed the power of transfer learning to enhance the performance of our image segmentation model.After a thorough evaluation of VGG16, VGG19, VIT, Xception, MobileNet_V2, ResNet18, ResNet34, and ResNet101, we found that ResNet101 exhibited superior performance and accuracy, prompting its seamless integration as an encoder into our segmentation architecture.Fine-tuning the model on our dataset allowed it to adapt to our requirements while retaining essential learned features.Adopting transfer learning addressed data limitations and expedited training, leading to improved results and heightened accuracy in our image segmentation.This integration empowered our model to capture meaningful patterns effectively, making it a pivotal element in elevating our image segmentation research's overall performance and effectiveness.This adaptation aimed to balance capturing detailed features and maintaining computational efficiency.By integrating ResNet-101 into SegX-Net, we harnessed the enhanced capabilities of ResNet-101 while preserving the efficient encodingdecoding architecture of DeepLabV3+.This integration successfully improved segmentation accuracy, as evidenced by our experimental results.In summary, the integration of ResNet-101 into SegX-Net represents a strategic enhancement to the original architecture of Dee-pLabV3+.This integration allowed us to leverage cutting-edge techniques, resulting in superior segmentation performance.In this research, we benchmarked the performance of SegX-Net against several top image segmentation architectures to conduct a thorough comparison analysis.This comprised wellknown models, including DeeplabV3+, Attention U-Net, Trans U-Net, Res U-Net, U-Net++, and U-Net.We sought to identify SegX-Net's advantages relative to these well-known architectures by comparing these models across many essential performance measures, including IoU and F1 scores.By comparing SegX-Net with cutting-edge segmentation frameworks, this comparative method shows the exceptional contributions of SegX-Net and offers insightful information about how well it detects contrails.
Enhanced SegX-Net model
In this work, we proposed an enhanced version of the DeepLabV3+ model by modifying its encoder part with ResNet-101 shown in Fig 7 .Specifically, we focused on improving the initial process by changing the first two blocks out of the original five blocks.In the first block, we replaced the 1x1 convolution followed by 256-neuron ReLU activation with a 1x1 convolution followed by 64-neuron ReLU activation-this modification aimed to reduce the dimensionality of the feature maps while preserving the relevant information.Similarly, in the second block, we replaced the 3x3 convolution followed by 256-neuron ReLU activation with a 3x3 convolution followed by 128-neuron ReLU activation, maintaining the same atrous rate of 6.This adjustment allowed for a more fine-grained feature representation at the atrous rate.We observed that these modifications in the encoder part yielded improved results compared to We conducted comprehensive evaluation experiments to quantify the performance improvement using various evaluation metrics, including IoU and F1 scores.The results demonstrate that our enhanced model outperforms the original DeepLabV3+ model, achieving higher accuracy and better segmentation results.These findings highlight the efficacy of the proposed modifications in the encoder part of DeepLabV3+ with ResNet-101 and their positive impact on the model's overall performance.The following section presents a detailed analysis and comparison of the performance between the original DeepLabV3+ model and our enhanced version, further substantiating the superiority of the modified architecture.
Experimental results
In this research, we presented the results of our experiments evaluating the performance of the SegX-Net model for image segmentation in addressing contrail detection challenges.The dataset focused on contrails, obtained from NOAA GOES-16, was preprocessed by transforming images into 256x256 arrays with 3 color channels.Evaluation metrics included Intersection over Union (IoU), F1 score and Dice Loss as the loss function during training.
Evaluation metrics
To evaluate the performance of each model and effectively assess its learning capabilities, this experiment employed multiple control parameter variables for evaluation.The primary evaluation metrics included the F1 score and Intersection over Union (IoU).
IoU.
When it comes to measuring the accuracy of image segmentation, the Intersection over Union (IoU) is widely regarded as a representative evaluation metric.
IoU quantifies the overlap between the predicted values generated by the model and the true values represented by the sample labels.It provides a measure of the alignment and agreement between the predicted and ground truth segmentation masks, reflecting the accuracy and quality of the segmentation results.
4.1.2F1 score.Additionally, the F1 score provides a balanced measure of precision and recall, considering both the true positives and false positives in the segmentation predictions.Together, the F1 score and IoU offer comprehensive insights into the model's performance and effectiveness in image segmentation tasks.
4.1.3Dice loss.The Dice Loss was used in during the research as a loss function during the training of our image segmentation model.Its utilization served two primary purposes: to guide the model's optimization process and to align the predicted segmentation masks with the ground truth masks.
The Dice Loss was an integral part of our research, serving as a key component in optimizing the model's performance and enhancing the accuracy and quality of our image segmentation results.Its usage helped align our model's predictions with the ground truth, ultimately leading to improved segmentation accuracy and precise delineation of objects in the resulting segmentation masks.In the equation.Xi indicates the predicted target category and yi indicates the actual target category.
4.1.4Dice coefficient.Within the realm of image segmentation, where computers manipulate pixels and reality wields the brush, the Dice coefficient arises as a reliable measure of precision.It functions as a measurement tool to assess the degree of overlap between a predicted area, such as a tumor or a contrail, and the actual region.The correlation between the Dice score and the fit is directly proportional, indicating a stronger alignment between prediction and reality as the Dice score increases.
4.1.5Sensitivity analysis.Sensitivity in image segmentation, measures the algorithm's ability to correctly identify positive instances, crucial in applications like medical imaging.A sensitivity value close to 1 indicates effective detection of relevant regions, while lower values suggest potential misses.Sensitivity analysis involves varying parameters to understand how the algorithm responds to changes, aiding optimization for specific applications.
Efficiency analysis and comparison
An essential aspect of evaluating the SegX-Net architecture's effectiveness is assessing its computational efficiency in contrast to existing models.This analysis sheds light on the architectural optimizations that SegX-Net introduces.Notably, a comparative examination of parameter sizes between SegX-Net and the default DeepLabV3+ model with ResNet-101 showcases SegX-Net's streamlined design, boasting a parameter count of 33,815,745 as opposed to the default model's 35,278,721.This reduction in parameter count signifies SegX-Net's potential for optimized memory usage, as evident by its memory size of 129 MB compared to Dee-pLabV3+ with ResNet101's 135 MB.Furthermore, when considering time complexity, SegX-Net demonstrates its efficiency by achieving an average processing time of 694ms per iteration, iterated ten times on average, while the default DeepLabV3+ with ResNet-101 requires 901ms.This rigorous analysis underscores SegX-Net's computational superiority, making it a promising solution for enhancing contrail detection efficiency and outperforming existing models in terms of both memory utilization and processing speed.
Comparative experiment
In the results section, our experiments with the SegX-Net model unveil remarkable outcomes, showcasing an exceptional F1 score of 99.47% (Table 1) and an impressive IoU score of 98.86% and (Table 2).These scores, complemented by the Dice Loss plot ( 2), that the model can recognize most contrails in images.As we balance sensitivity and accuracy, we must consider environmental monitoring's contrail detection goals.Although our SegX-Net achieves a slightly lower Dice Coefficient score on the training set compared to VGG16 (71.79% vs. 72.61%), it is crucial to take into account the larger context.Our model exhibits improved performance compared to VGG16, as shown by a Dice Coefficient score of 73.55% on the validation set.The validation set serves as a crucial indicator of generalization.This review highlights the strong and flexible nature of SegX-Net in accurately capturing the complex patterns of contrails.Although training performance is important, the validation results emphasize the model's effectiveness in real-world situations, confirming its status as an advanced solution for contrail identification.Here, we have shown a comprehensive analysis of the performance metrics for each model on both Intersection over Union (IoU), Dice-Coefficient in Table 1 and F1-score, Sensitivity Score in Table 2.
Table 1 provides an in-depth comparison of the IoU scores obtained by the different models on both the training and valid sets.The results clearly illustrate the exceptional segmentation accuracy achieved by SegX-Net, with an outstanding IoU score of 98.86% on the training set and an impressive 99.54% on the valid set.This demonstrates the model's ability to accurately capture object boundaries and produce high-quality segmentations, outperforming all other models, including DeepLabV3+ with VGG16, VGG19, VIT, Xception, MobileNet_V2, ResNet18, ResNet34 and ResNet101.
In Table 2, we delve into the F1-scores of each model on the training and valid sets, shedding light on their segmentation performance in finer detail.The results reveal the exceptional capabilities of SegX-Net, achieving a remarkable F1-score of 99.47% on the training set and an extraordinary 99.77% on the valid set.These scores surpass the performance of DeepLabV3 + with VGG16, VGG19, VIT, Xception, MobileNet_V2, ResNet18, ResNet34 and ResNet101 by a substantial margin.Such exceptional F1-scores indicate the model's precision and recall capabilities, affirming its ability to achieve superior segmentation results.
Our SegX-Net model significantly outperforms these models in terms of Intersection over Union (IoU) scores when compared to a group of cutting-edge competitors shown in Table 3, including U-Net, U-Net++, Attention U-Net, Trans U-Net, Res U-Net, Uc Trans U-Net, and DeeplabV3+.The results demonstrate our proposed SegX-Net's better accuracy and efficiency in separating contrail clouds.In climate research, aviation studies, and environmental monitoring, where the precision of contrail cloud identification is crucial, SegX-Net demonstrates a greater capacity to properly identify contrail areas with a higher IoU score.As a result, it is a useful tool in these fields.
In parallel evaluations of the same models, we focus on F1 scores, a statistic that balances accuracy and recall in contrail cloud segmentation.SegX-Net is the clear winner once again as shown in Table 4, outperforming U-Net, U-Net++, Attention U-Net, Trans U-Net, Res U-Net, Uc Trans U-Net, and DeeplabV3+.SegX-Net's superior F1 scores highlight its remarkable accuracy and recall skills in recognizing contrail clouds.These findings highlight the resilience of our proposed model, establishing it as a top option for accurate contrail cloud segmentation tasks, while its strong F1 scores indicate its use in aviation, and environmental impact assessments.
These comparative results are a testament to the revolutionary advancements achieved by SegX-Net in image segmentation for contrail detection.Our model has achieved outstanding performance with a remarkable IoU score of 97.90%, an F1 score of 99.51%, a Dice coefficient of 71.79%, and an impressive sensitivity of 98.41% from the testing set.These results are a The false colour images offer vivid visual representations, capturing essential spectral information relevant to our analysis.The ground truth contrail masks serve as crucial reference data, providing precise outlines of contrail regions for rigorous model evaluation and validation.Furthermore, by superimposing the contrail masks on false colour images, we gain valuable insights into the spatial distribution and correlations of contrails within their original scenes.These prediction images showcase the remarkable performance and accuracy of our contrail detection methods, underscoring our commitment to addressing challenges through innovative and non-typical AI approaches.
Discussion
Results of our experiment emphasize the influence of enhanced segmentation methods in identifying contrails.The SegX-Net model, carefully developed and evaluated, exhibited exceptional performance metrics, attaining an IoU score of 98.86% and 99.54% and an F1-Score of 99.47% and 99.77% on the training and validation sets, respectively.The Dice Coefficient and Sensitivity scores serve to highlight the model's reliability, in addition to the aforementioned measures.Our model has exceptional segmentation accuracy and sensitivity to complex contrail patterns, as seen by its Dice Coefficient scores of 71.79% on training and 73.55% on validation, along with a Sensitivity score of 98.82% on training.
When comparing SegX-Net to well-known models like U-Net, U-Net++, Attention U-Net, Trans U-Net, Res U-Net, Uc Trans U-Net, and DeeplabV3+, SegX-Net demonstrates superiority.Our algorithm frequently surpassed these standards, showcasing superior accuracy in contrail segmentation.This comparison confirms the effectiveness of SegX-Net and offers valuable insights into the model's competitive advantage.SegX-Net stands out among contrail identification technologies because of its exceptional ability to identify subtle characteristics in contrails and its outstanding accuracy metrics.
In the future, it would be beneficial to investigate the scalability and generalizability of SegX-Net.Expanding the dataset to include a broader range of geographical regions and weather conditions could strengthen the model's resilience.Moreover, the incorporation of sophisticated metrics and the investigation of adversarial training methods, such as Generative Adversarial Networks (GANs), show potential for enhancing the precision of the model.These considerations broaden the range of situations where SegX-Net can be used and contribute to the ongoing discussion on advanced methods for detecting contrails, which has significant consequences for environmental preservation.
Fig 1 .
Fig 1.Our research study observed that high-altitude ice cloud formation is facilitated by the condensation of water droplets on aircraft engine soot and other aerosols.https://doi.org/10.1371/journal.pone.0298160.g001
Fig 2 .
Fig 2. Illustration of the systematic framework employed in this study that visually represents the step-by-step process of the proposed approach.https://doi.org/10.1371/journal.pone.0298160.g002
Fig 3 .
Fig 3. Sample input images from the dataset are showcased, providing an overview of the data variety and content.https://doi.org/10.1371/journal.pone.0298160.g003
For
evaluating the model, we employ key metrics such as Intersection over Union (IoU), F1-score and Dice Loss, Dice Coefficient and sensitivity analysis.The results are presented through insightful line plots, illustrating the Dice Loss, IoU and F1-score, Dice Coefficient and sensitivity analysis for both the training and valid sets over epochs.We have showcased the quantitative results obtained from the training and valid sets.Fig 8 presents the F1 score plot, which balances precision and recall, reflecting the model's segmentation performance.Fig 9, displays the IoU plot, highlighting the model's accuracy in capturing object boundaries and overall segmentation quality.Fig 10, illustrates the Dice Loss plot, providing insights into the model's optimization process and alignment with ground truth masks.The effectiveness of SegX-Net is shown in Fig 11 the use of dice coefficient performance assessment.The results of the sensitivity study shown in Fig 12 revealed that SegX-Net had an extraordinary true positive detection rate and a low number of false negatives, which confirmed its effectiveness in picture segmentation work.
Fig 8 .Fig 9 .Fig 10 .Fig 11 .Fig 12 .
Fig 8. Illustration of F1-score visualization, demonstrating its utility in quantifying the performance of SegX-Net.https://doi.org/10.1371/journal.pone.0298160.g008 Fig 10) offering insights into the model's optimization, the captivating IoU plot (Fig 8) demonstrating its unprecedented accuracy and the striking F1 score plot (Fig 9), collectively attest to the revolutionary capabilities of SegX-Net.Additionally, we have introduced Dice Coefficient (Fig 11) and Sensitivity Analysis (Fig 12), further solidifying the model's exceptional segmentation performance.These extraordinary achievements establish SegX-Net as a pioneering solution, advancing contrail detection through cutting-edge artificial intelligence.The remarkable sensitivity, notably during training with 98.82%, shown in (Table
Table 3 . Comparison results of models with different architectures based on IoU scores and dice coefficient.
testament to the reliability and accuracy of our model.The model's extraordinary performance and accuracy set new standards in artificial intelligence and contribute significantly to addressing the challenges of climate change.The combination of state-of-the-art techniques and innovative methodologies within SegX-Net positions it as a leading solution for climate researchers and environmentalists seeking accurate and reliable image segmentation results.We present compelling prediction images from our test set, as illustrated in Fig 13.These images include Ash color, Ground truth, Prediction, and Contrail mask on Ash color.The false-color representations vividly capture essential spectral information, enhancing our analysis.The ground truth contrail masks offer precise outlines for rigorous model evaluation, serving as crucial reference data.These prediction images vividly demonstrate our contrail detection methods' exceptional performance and accuracy, emphasizing our dedication to addressing challenges through innovative and unconventional AI approaches. https://doi.org/10.1371/journal.pone.0298160.t003 | 8,586.2 | 2024-03-05T00:00:00.000 | [
"Environmental Science",
"Computer Science",
"Engineering"
] |
PATCH-BASED ADAPTIVE IMAGE AND VIDEO WATERMARKING SCHEMES ON HANDHELD MOBILE DEVICES
Mobile devices provide a huge amount of multimedia information sending to the members of social groups every day. Sometimes it is required to authorize the sending information using the limited computational resources of smartphones, tablets or laptops. The hardest problem is with smartphones, which have the limited daily energy and battery life. There are two scenarios for using mobile watermarking techniques. The first scenario is to implement the embedding and extraction schemes using proxy server. In this case, the watermarking scheme does not differ from conventional techniques, including the advanced ones based on adaptive paradigms, deep learning, multi-level protection, and so on. The main issue is to hide the embedding and extracting information from the proxy server. The second scenario is to provide a pseudo-optimized algorithm respect to robustness, imperceptibility and capacity using limited mobile resources. In this paper, we develop the second approach as a light version of adaptive image and video watermarking schemes. We propose a simple approach for creating a patch-based set for watermark embedding using texture estimates in still images and texture/motion estimates in frames that are highly likely to be I-frames in MPEG notation. We embed one or more watermarks using relevant large-sized patches according to two main criteria: high texturing in still images and high texturing/nonsignificant motion in videos. The experimental results confirm the robustness of our approach with minimal computational costs.
INTRODUCTION
The rapid growth of a number of handheld mobile devices like smartphones, tablets and laptops leads to shearing multimedia information through Internet. Some information ought to be protected by authorized watermarks, visible and/or invisible, embedded in images and video sequences. Limited memory and significant battery consumption are the main challenges of watermark embedding and extraction using robust but complex modern watermarking schemes. Two scenarios with and without proxy server are available. We have interest to develop and study the watermarking algorithm without use of proxy server.
Conflicting constraints prevent the expectation of outstanding results. However, some expectations from the algorithmic solver are possible. As well-known, the robustness, imperceptibility and capacity are the main criteria of watermarking process, while the computational cost is additional criterion for mobile devices. In recent years, researchers provide a watermark security as an additional level of protection using scrambling algorithms. In this sense, the watermarking methods approximate the steganography methods.
Another problem inherent to all blind watermarking schemes, when the original image, frame or audio signal are not transmitted to a recipient through protected channels, connects with infinite number of possible attacks, one of the complete taxonomies of which was presented in (Zotin et al, 2020). Moreover, each type of attack can be done with different unknown parameters, and unknown combinations of several types of attacks can be applied. At present, there is no universal watermarking algorithm robust to the most types of attacks. As a rule, various watermarking schemes are more or less robust to the limited types of attacks.
In this paper, we propose a simple approach for creating a set of patch-based regions for watermark embedding using texture and texture/motion estimates in still images and frames that are highly likely to be I-frames in the MPEG notation.
The rest of the paper is organized as follows. Related work is reviewed in Section 2. In Section 3, the texture analysis is presented, while the motion analysis is considered in Section 4. Section 5 discusses a technique for selecting relevant regions for watermark embedding. Experimental results are reported in Section 6, and Section 7 concludes this paper in the end.
RELATED WORK
At present, investigations in watermarking techniques are shifted to deep learning implementations (Hatoum et al., 2021). However, this approach is problematic in smartphone environment, and we propose an adaptive image and video watermarking approach based on texture or texture/motion analysis, which allows us to detect the relevant regions for embedding a watermark in image or frame, respectively. A wide range of digital watermarking algorithms has been investigated in order to find the efficient ones under the formulated constraints. Detecting the relevant regions for a video watermarking scheme as an extension of image watermarking scheme includes two types of analysistexture and motion. Hereinafter, we discuss these issues.
Many previous watermarking algorithms were based on rough set theory to solve some uncertainty problems that are related to the principles of human visual system (HVS) and affect the perceptual quality of host images. Color representations, variety of grayscale values and brightness/darkness of the host image influence on imperceptibility of embedded watermarks. At the same time, the watermarking schemes in the transform domain slightly change the magnitudes of the frequencies. This causes visual artifacts. Thus, the selection of relevant regions for embedding a watermark with respect to HVS is important. In (Ni et al., 2007), the non-overlapped blocks were analyzed by means of fractal dimension and the feature blocks containing edges and textures were further classified by variance characteristics into three different parts: edges, weak textures and strong textures. Discrete cosine transform was applied to all blocks of the host image, and the formed watermark was embedded into their middle-frequency coefficients with different strength. A joint spatial texture analysis for robust watermarking technique to authenticate images was suggested in (Ghadi et al., 2017). The model used four features including skewness, kurtosis, entropy, and DC coefficient to analyze the texture in each partitioned block in the host image. The ranking all partitioned blocks based on their texture magnitude was implemented using technique for order preference by similarity to ideal solution. For embedding a watermark, 10% of highly textured blocks were selected. In (Favorskaya et al., 2017), the statistical and model-based methods were investigated as a trade-off between the computational costs and quality of the detected regions, where the embedded watermark might be most invisible for a human vision. It was shown that the gradient oriented local binary patterns (LBPs) provided better computational time with respect to fractal estimations. In (Ghadi et al., 2019), in order to enhance the imperceptibility and the robustness, four gray-scale histogram based-image features (DC, skewness, kurtosis, and entropy) were chosen as input data for designing association rules based on the Apriori algorithm. As a result, the ratios of imperceptibility, robustness and embedding rate with low execution time were obtained.
Estimating optical flow as the pixel-level motions is a fundamental problem in computer vision. It is worth noting that optical flow evaluation is realized through supervised and unsupervised deep learning (Ren et al., 2020) and, moreover, some approaches are based not on pixel-level motions but on patch-level motions. Traditionally, optical flow model is optimized under the assumption of brightness constancy and local smoothness constraint that usually requires small displacement between compared frames. The case with large displacements can be solved using the coarse-to-fine warping technique (Amiaz et al., 2007), the patch-based descriptor matching into the variational model (Brox and Malik, 2010), patch-match correspondence algorithm as an efficient approximate algorithm for finding the nearest neighbors of image patches between two related images (Barnes et al., 2010), and so on. In these studies, it was shown that patch-based correspondences are more robust and reliable but timeconsuming regarding the pixel-based approach.
The original PatchMatch algorithm (PMA) estimates dense approximate nearest neighbor correspondences between patches of two image regions. The generalized PatchMatch correspondence algorithm was enhanced in three ways (Barnes et al., 2010): to find k-nearest neighbors, to search the patches across scales, rotations and translations and to match the patches using arbitrary descriptors and distances. The PatchMatch algorithm is successfully used as an approximate nearest neighbor algorithm on top of the learned descriptors after using Siamese CNN for optical flow computation (Gadot and Wolf, 2016).
Although block matching algorithm (BMA) based on full search was suggested in 1990s, its modifications are often used for motion estimation and video coding. There are three ways to improve the original BMA. The first way is to decrease the computational complexity of BMA (Huang et al., 2006): 1. Using a fixed pattern. The three step search (TSS), the simple and efficient TSS, the four step search and the diamond search are algorithmically considered as the fastest, but they cannot match the dynamic motion content. 2. Reducing the search points. This category includes the adaptive rood pattern search, the fast block matching using prediction, the block-based gradient descent search and the neighborhood elimination algorithm. These methods assume that the error-function behaves monotonically and well evaluate slow movement. 3. Decreasing the computational overhead for every search point. The matching cost is replaced by a partial or a simplified version under assumption that all pixels within each block move by the same finite distance. The new pixel-decimation, the efficient block matching using multilevel intra, the inter-sub-blocks and the successive elimination algorithm are in this category. Such methods are not immune to noise or illumination changes.
The second way is based on spatio-temporal correlation using neighboring blocks in the spatial and temporal domains in order to predict movements (Nisar et al., 2012). Such algorithms are able to avoid local minima, predicting the search center closer to the global minimum. However, the enhanced predictive zonal search and UMHexagonS algorithm cannot correctly detect motion of very small objects. The third way is to use evolutionary approaches such as the light-weight genetic block matching, the genetic four-step search and the particle swarm optimization block matching (Cuevas et al., 2013). However, the evolutionary approaches are characterized by large computational time.
TEXTURE ANALYSIS
The texture classification, texture segmentation, texture synthesis, and texture shape are the main issues of texture analysis in spatial domain. Our task is close to texture segmentation under criterion of high texturing. We can enforce texture segmentation by saliency analysis, removing regions which attract a human attention. Generally, methods of texture analysis are usually classified into four categories: statistical, structural, model-based and transform-based methods (Armi and Fekri-Ershad, 2019). Statistical methods are based on the moments of distribution functions of pixels' intensities. Calculation of statistical moments is one of the simplest approaches to evaluate the texture features. Central moment of order n is calculated using following equations: where z i = the random intensity value p(z i ) = the number of pixels that have intensity values equal to L = the number of intensity levels, L > 1 To estimate a degree of high texturing, we use three measures of homogeneity U and entropy E Also three modified texture features as normalized homogeinity U n , relative smoothness R m and normalized entropy E n can be used: If parameter R = 0, then we forcibly maintain a relative smoothness R m = 10 (small empirical value differing from 0). Normalized entropy E n indicates some equalization effect in dark and bright areas of an image. We can speak about high texturing region if its homogeneity U n 1, smoothness R m 0 and En 1.
Another possible approach is to estimate a degree of high texturing using a special type of LBPs in a manner proposed in (Favorskaya and Buryachenko, 2020a In this study, we compare the results of texture estimation based on moments and LBPs in terms of smartphone performance.
Images received from the cameras of modern smartphone are high-resolution, while the screen resolution is not so high.
Adaptive watermarking algorithm detects the best regions for embedding in the host image as a set of patches. Unfortunately, a set of patches does not usually form a regular structure in an image. We need to find the close patches joining them into a larger structure, which coordinates include in a secret key. We estimate a degree of high texturing at different scales 3232, 1616 and 88. The embedding and extraction algorithms are based on discrete wavelet transform and the Cox-Zhao scheme.
MOTION ANALYSIS
In video watermarking schemes, the task is extended by embedding a watermark into frames of video sequence. Due to limited computational resources, it is difficult to develop a system that is invariant to MPEG noise quantization and MPEG compression. However, we can examine a set of frames on the candidates of I-frame that are fully transmitted with respect to B-frames and P-frames (Favorskaya and Buryachenko, 2020b).
To reduce computational costs, we propose to find motion in a scene, first, using rough algorithms (for example, background subtraction) and, second, estimating moving regions applying BMA and/or PatchMatch algorithm (Barnes et al., 2010). The matter is that local search using BMA can only identify small displacements, while large arbitrary motions of small objects can be estimated using PMA but with less smoothness.
There are two advantages for solving the watermark problem. We do not need to estimate motion in a static scene accurately because the moving regions will be removed from the set of relevant regions for embedding a watermark. Also we do not need to do additional salient analysis because usually moving objects are salient objects, and such salient regions should also be removed from the set of relevant regions. Embedding a watermark in each of the consecutive frames is not critical because smartphone videos are usually short.
In BMA, the consecutive frames are divided into blocks. For each block in the current frame, BMA calculates the best matching block inside a region of the previous or following frame, aiming to minimize the sum of absolute differences (SAD), sum of squared differences (SSD) or mean of squared differences (MSD): where (d x , d y ) = the displacement vector I(x, y) = the intensity of pixel with coordinates (x, y) n = the size of the analyzed block In our experiments, we applied the simple and efficient TSS modification for relatively slow movement of large areas. In order to evaluate small moving areas, we offer the PMA modification.
The original PMA is based on a nonparametric patch sampling method which executes a repeated search of all given patches in one image for the most similar patch in another image under assumption that both images are close (i.e. stereo images or consecutive frames. The initial procedure fills the nearestneighbor field (NNF) with either random offsets or prior information. The iterative update procedure propagates good patch offsets in NNF to adjacent pixels and then randomly searches the best offset in the neighborhood.
We adapt the original PatchMatch algorithm exploiting the idea that the initial random procedure can be replaced by a directed search based on a coarse interframe difference. Also we can suppose that the adjacent patches are cooperatively shifted in a part of the frame. Let {D} be a set of interframe differences in the form of patches with predefined sizes, and {A} be a set of patches in the extended neighborhood of set {D} in frame t. Thus, the nearest-neighbor field is initialized with set {A}, and the patch correspondences should be computed in frame t+1 using set {D} and generating a set of corresponding patches {B}. Since frame differences are small, we can only consider the offsets, simplifying the iterative update procedure.
The iterative procedure examines the joint set { } { } AD in scan order (from left to right and top to bottom) by random search. Note that since a random search is performed in a limited joint set, the random search for next patches is reduced and can be directed into the pipeline of the previous corresponding patches. Thus, the first correspondences can be considered as a seed for the next correspondences.
During the iterative update procedure, two operations called as propagation and random search alternate at the patch level. Propagation operator can be implemented in both the original PMA and the generalized PMA, which differ in the offset values (d x , d y ) = {(1, 0), (0, 1)} and by collecting k nearest neighbors for each patch, respectively. Random search operator attempts to improve function I(x, y) by testing a sequence of candidate offsets at an exponentially decreasing distance: where s = the iterative step, s = 0, 1, 2,... U s = the sequence of candidate offsets at step s U 0 = the initial sequence of candidate offsets w = the large maximum search "radius" = the fixed ratio between search window sizes R s = the uniform random in [-1, 1] [-1, 1] at step s In PMA, the patches are examined for s = 0, 1, 2,… until the current search radius w s is below 1 pixel, = 1/2. It is recommended to use the halting criteria as a fixed number of iterations, no more than 4-5.
In such manner, we form a set of frames with small interframe differences, exclude all detected moving patches from each frame of this set and create a motionless map for this set. A hypothesis is that one of such frames will be I-frame.
SELECTING RELEVANT REGIONS
In the case of an image watermarking scheme, we only apply texture analysis, selecting highly textured regions. For video watermarking scheme, spatio-temporal analysis should be utilized. Since a video sequence is compressed by an unknown type of codec when transmitted through unprotected channels, we ought to detect a set of frames, one from which will be Iframe. To do this, first, we detect scene changes (Favorskaya and Buryachenko, 2020a), which are excluded from a watermarking process but after that a set of I-frames can be detected. Second, we apply motion and texture analysis for these frames. These processes are clarified in Figures 1 and 2. After that, we use the PatchMatch algorithm to select the high-textured blocks with less motion. The size of blocks varies depending on the frame size and the desirable resource cost. To reduce computational costs, we cannot employ full salient analysis. However, we can apply a weight function to selected highly textured regions. A weight function assigns weight values from the interval [0…1] to the selected highly textured regions according to their remoteness from a center of the image. The weight function can be uniformly or elliptically distributed function, depending on the content of the image. Thus, we consider possible salient objects which are usually located in the center of the image in order to avoid embedding a watermark in such visual regions.
EXPERIMENTAL RESULTS
We tested several hundred of images and dozens of videos received from smartphone cameras, first, by selecting the relevant regions and, second, by embedding watermarks in the form of small images or short text messages. Experiments show that adaptive watermarking schemes provide better robustness and invisibility than conventional watermarking schemes.
The experiments were conducted using several datasets. The CLIK2019Professonal dataset (CLIC 2019, 2021) contains high quality images, including complex textures and foreground objects, which allows us to evaluate the loss of quality when embedding watermarks. The dataset, namely Felicepollano watermarked/not-watermarked-images (Pollano, 2021), includes data for training the algorithm with different types of the watermarks. Most images contain different levels of texturing and vary in quality and resolution. We also used high quality video sequences obtained from the Drone_Videos dataset (Drone Videos, 2021), characterized by complex camera movements and natural textures. Examples of such images are depicted in Figure 3.
The process of selecting regions for embedding watermarks includes several steps, depending on the availability of the sequence of images for texture/motion estimation, as well as the available computing resources. To estimate the level of texturing, a combination of different approaches (the first way) was used: Local Entropy, Local Standard Deviation, and Local Range, on the basis of which a texture mask was built taking into account the expansion operation. The second way was based in the LBP calculation with following classifying by the Kullback-Leibler divergence. This approach is the fastest, but the most inaccurate. The third way for building a texture mask was performed using Gabor filters and required 2-4 times more for the same image resolution.
In the case of videos, motion is evaluated in several consecutive frames. Initially, it is required to estimate the probability of a scene change in order to find the I-frame, which is least prone to data compression distortions during encoding and transmission over unprotected channels. To determine the regions relevant for watermarking, we do not need a clear knowledge of the position of objects and feature points: we only need a basic understanding of the level of movement in different areas of the frame. Therefore, it is reasonable to use the BMA and the PMA. An alternative way is to estimate the optical flow, which also gives a good representation of the global movement of the scene and allows foreground objects to be detected. The examples of using the PMA and optical flow estimation are shown in Figures 1, 2 and 4. The next step is to combine the texture mask and the global motion mask in order to exclude low-textured regions, while considering the position of pixel blocks: the closer to the center of the image, the less priority is given to this region for embedding a watermark ( Figure 4). a b c d Figure 4. Examples of watermarking process of the CLIK2019Professonal dataset: a original images, b entropy masks, с patch-based motion masks with 64×64 patch size, d regions for embedding a watermark after excluding fast motion and salient objects.
We also estimated the information capacity of images when embedding a watermark depending on the size of the PMA blocks (Table 1). The quality of the watermarked images was estimated by well-known peak signal-to-noise ratio (PSNR) and mean square error (MSE) metrics: The MSE between the original and the watermarked images is calculated by the following expression: where m, n = width and height of the images I = the source frame I w = frame with watermark embedded Depending on the size of the image, we can get a big difference in the amount of the embedded information. The amount of such information is tens of kilobytes for an HDTV format and increases with an increase in the block size, which is due to the fact that the block motion estimation algorithm becomes less sensitive to small objects and objects with complex texture and contour structure. This is not a disadvantage for embedding a watermark and practically does not lead to degradation of image quality.
CONCLUSIONS
The paper proposes an algorithm for embedding a watermark for handheld mobile devices. The main idea is to improve the speed of embedding using faster methods. We also evaluate the relevant regions for embedding a watermark based on texture/motion estimates and exclude foreground objects or visible objects closer to the center of the frame. This allows us to improve the quality of watermarked images and avoid embedding a watermark in those areas of the frame that can be attacked and distorted when transferring data over unprotected channels. Evaluation of the efficiency of the algorithm on existing databases shows high speed and robustness to distortion, regardless of the complexity of the image. | 5,324.2 | 2021-04-15T00:00:00.000 | [
"Computer Science"
] |
Modeling Sentence Comprehension Deficits in Aphasia: A Computational Evaluation of the Direct-access Model of Retrieval
Several researchers have argued that sentence comprehension is mediated via a content-addressable retrieval mechanism that allows fast and direct access to memory items. Initially failed retrievals can result in backtracking, which leads to correct retrieval. We present an augmented version of the direct-access model that allows backtracking to fail. Based on self-paced listening data from individuals with aphasia, we compare the augmented model to the base model without backtracking failures. The augmented model shows quantitatively similar performance to the base model, but only the augmented model can account for slow incorrect responses. We argue that the modified direct-access model is theoretically better suited to fit data from impaired populations.
Introduction
Comprehending a sentence involves building linguistic dependencies between words. In the sentence processing literature, several researchers have argued that linguistic dependency resolution is carried out via a cue-based retrieval mechanism (Van Dyke and McElree, 2006;Lewis and Vasishth, 2005). Cue-based retrieval theory assumes that word representations are retrieved from working memory via their syntactic and semantic features. Consider the following sentences: (1) a. The boy who tickled the girl greeted the teacher. b. The boy who the girl tickled greeted the teacher.
In (1a), the noun boy would be encoded in memory with features such as [+animate, +subj]. When the reader reaches the verb tickled, a retrieval is triggered with retrieval cues that match the features of boy. At this point in time, boy is the only element that matches the retrieval cues of the verb. By contrast, in (1b), another noun intervenes between tickled and boy that partially matches the cues set at the retrieval: girl [+animate, -subj]. The partial feature overlap causes similarity-based interference between the two items, making the dependency more difficult to resolve in (1b) compared to (1a).
Interference effects have been attested in multiple studies, see for example Jäger et al. (2020); Gordon et al. (2006); Jäger et al. (2017); Van Dyke (2007). One model of cue-based retrieval that predicts these interference effects is the directaccess model developed by McElree and colleagues (McElree, 2000;McElree et al., 2003;Martin and McElree, 2008). The direct-access model (DA) assumes that retrieval cues allow parallel access to candidate items in memory, as opposed to a serial search mechanism. Due to the parallelism assumption, the speed of retrieval is predicted to be constant across items (aside from individual differences and stochastic noise in the retrieval process).
Factors such as increased distance between the target and the retrieval point and the presence of distractor items can lower the probability of retrieving the correct dependent (also known as availability). Low availability of the target dependent can lead to failures in parsing or to misretrievals of competitor items. When such errors occur, a backtracking process can be initiated, which by assumption leads to the correct retrieval of the target (McElree, 1993). The backtracking process requires additional time that is independent of the retrieval time. According to the direct-access model, (1a) should have shorter processing times than (1b) on average, because in (1b) some trials require costly backtracking due to lower availability of the target item boy.
The direct-access model can be adapted to explain impaired sentence comprehension in individuals with aphasia (IWA; Lissón et al., 2021). However, there is one crucial aspect of the directaccess model that is at odds with the aphasia literature, specifically with the finding that IWA have longer processing times for incorrect than for correct responses (e.g., Hanne et al., 2015;Pregla et al., 2021). The direct-access model assumes that some percentage of correct interpretations are only obtained after costly backtracking, and thus predicts that the average processing time for incorrect responses should be faster than for correct responses. To address this issue, we implement a modified version of the direct-access model that is specifically relevant for sentence processing in IWA. In this model, backtracking can lead to correct retrieval of the target, as in the base model, but can also result in misretrieval and parsing failure.
Sentence Comprehension in Aphasia
Aphasia is an acquired neurological disorder that causes language production and comprehension impairments. In the aphasia literature, there are several theories that aim to explain the source of these impairments in language comprehension. One possibility is that IWA carry out syntactic operations at a slower-than-normal pace, which could cause failures in parsing. This is the slow syntax theory (Burkhardt et al., 2008). By contrast, Ferrill et al. (2012) claim that the underlying cause of slowed sentence processing in IWA is delayed lexical access, which cannot keep up with structure building. Another theory, resource reduction, assumes that IWA experience a reduction in the resources used for parsing (Caplan, 2012), such as working memory. Finally, Caplan et al. (2013) claim that IWA suffer from intermittent deficiencies in their parsing system that lead to parsing failures. Previous computational modeling work has shown that these theories may be complementary (Patil et al., 2016;Lissón et al., 2021), and that IWA may experience a combination of all of these deficits (Mätzig et al., 2018).
Assuming that a direct-access mechanism of retrieval subserves sentence comprehension, this mechanism could interact with one or more of the proposed processing deficits in IWA. One way to assess whether these deficits are plausible under a direct-access model is the computational modeling of experimental data. Lissón et al. (2021) tested the direct-access model against self-paced listening data from individuals with aphasia, finding the model to be in line with multiple theories of processing deficits in aphasia. Despite this encouraging result, the model could not fit slow incorrect responses, due to its assumptions about backtrack-ing and its consequences.
In what follows, we present our implementation of the original direct-access model and the modified version with backtracking failures. We fit the two models to data from individuals with aphasia and compare their quantitative performances. In order to assess the role of the different proposed deficits of IWA in sentence comprehension, we also map the models' parameters onto theories of processing deficits in aphasia.
Data
The data that we model come from a self-paced listening task in German (Pregla et al., 2021). 50 control participants and 21 IWA completed the experiment. Sentences were presented auditorily, word by word. Participants paced the presentation themselves, choosing to hear the next word by pressing a computer key. The time between key presses (here called listening time) was recorded. At the end of the sentence, two images (target and foil) were presented, and participants had to select which image matched the meaning of the sentence they had just heard. Accuracies for the picture-selection task were also recorded. To assess test-retest reliability, each subject completed the task twice, with a break of two months in between. Our modeling is based on the pooled data of both sessions.
Items
We investigate interference effects in a linguistic construction that is understudied in IWA: Control constructions. In control constructions, the subject of an infinitival clause is not overly specified, but understood to be coreferential with one of the overt noun phrases in the matrix clause of the same sentence (e.g, Brian promises Martha to take out the trash → Brian takes out the trash). In linguistic theory, it is assumed that a a phonologically empty element (PRO) occupies the subject position of take out (Chomsky, 1981). PRO is co-indexed with a noun phrase in the matrix clause that acts as its antecedent. The verb in the matrix clause specifies, according to its semantic and syntactic properties, which noun phrase in the matrix clause triggers the interpretation of PRO in the subclause.
In sentence (2a) below, the verb verspricht (promises) is lexically specified as a subjectcontrol verb, and the subject noun phrase of the main clause, Peter, is chosen as the antecedent of PRO. By contrast, in (2b), the object-control verb erlaubt (allows) specifies that the object noun phrase of the main clause, Lisa, is the antecedent of PRO.
(2) a. Subject control Peter i verspricht nun Lisa j , PRO i das kleine Lamm zu streicheln und zu kraulen.
'Peter now promises Lisa to pet and to ruffle the little lamb' b. Object control Peter i erlaubt nun Lisa j , PRO j das kleine Lamm zu streicheln und zu kraulen.
'Peter now allows Lisa to pet and to ruffle the little lamb' Cue-based retrieval theory assumes that control clauses require completion of the PRO dependency through memory access to the correct noun phrase. The direct-access model would predict (2b) to be easier to process than (2a), because the target (Lisa) is linearly closer to the retrieval site at PRO, and thus more available. Therefore, at PRO, the probability of retrieval of the target should be higher in (2b) relative to (2a). In line with this prediction, unimpaired subjects show a processing advantage for object control over subject control (Kwon and Sturt, 2016). Similarly, IWA exhibit more difficulties understanding subject control conditions in acting-out tasks (Caplan and Hildebrandt, 1988;Caplan et al., 1996). However, the object control advantage in IWA has not been previously tested using online methods.
Our experimental items were 20 sentences (10 per condition) similar to (2a) and (2b). The corresponding pictures for the picture-selection task are shown in Figure (1). The top picture is the target picture for (2a), whereas the bottom picture is the target for (2b). We assume that trials where the foil picture has been selected (i.e., the picture that shows the distractor noun as the agent of the action) correspond to a misretrieval.
Dependent Variables
The dependent variables used for modeling were the listening times (henceforth, LT) at the retrieval site (PRO) and the accuracy of the picture-selection task. Given that PRO is phonologically empty, we assumed that the retrieval process takes place at some point between the second and the third noun phrase (Lisa and das kleine Lamm in (2a)). We therefore summed the listening times of these regions within each trial. In order to evaluate the slowed lexical access hypothesis (Ferrill et al., 2012), we also used data from an auditory lexical decision task that participants performed in addition to the experiment. This task was based on LEMO 2.0 (Stadie et al., 2013). Participants had to decide whether an auditorily presented item was a word or a neologism, and the response times were recorded. For each participant, we computed the mean response times for correct responses. These were then centered and scaled within groups and used as continuous predictors in the models. We will refer to the scaled lexical decision task reaction times as the LDT predictor.
Direct-Access Model
Our implementation of the direct-access model follows Nicenboim and Vasishth (2018). The model assumes that listening times for correct responses come from a mixture distribution, given that there are trials with backtracking, where an additional processing cost δ is added, and trials without backtracking, where no such cost is added. By contrast, incorrect responses never involve backtracking, and the average listening time should be the same as for correct responses without backtracking. A graphical representation of the model is displayed in Figure (2). The three possible cases are as follows: (a) Retrieval of the target succeeds at first attempt, with probability θ: LT ∼ lognormal(µ, σ) (c) Retrieval fails, no backtracking, and a misretrieval occurs, with probability The model includes both fixed and random effects in order to account for sentence complexity, group differences, and individual variability. The hierarchical structure is shown in Equation (1). All parameters have an adjustment by group (IWA versus control), because we expect IWA to have different parameter estimates from control participants. Since DA assumes that retrieval times are not affected by sentence complexity, the average listening times (µ) do not have an adjustment for condition. By contrast, the probability of retrieval of the target, θ, includes a condition adjustment. This parameter can be thought of as indexing memory availability. The probability of backtracking P b , the cost of backtracking δ, and σ do not depend on sentence complexity, but may vary between IWA and controls. The hierarchical structure is embedded within the parameters when possible (we report the maximal hierarchical structure that could be fit). In Equation (1), the terms u and w are the by-participant and by-item adjustments to the fixed effects, respectively. These are assumed to come from two multivariate normal distributions. All parameters had regularizing priors, listed in Appendix B. (1) The model was implemented in the probabilistic programming language Stan (Stan Development Team, 2020), and fit via the rstan package (Carpenter et al., 2017) in R (R Core Team, 2020). The model was fit with 3 chains and 8,000 iterations, half of which were used as warm-up.
Predictions
Based on the theories of processing deficits in aphasia discussed in Section (1.1), and on the findings in Lissón et al. (2021), we make the following predictions: 1. IWA's µ and δ values should be higher than controls'. This would be in line with slow syntax, assuming that both the initial retrieval and the backtracked retrieval are accompanied by appropriate structure-building processes.
2. The probability of initial retrieval of the target θ should be lower for IWA relative to controls, across conditions.
3. Object control conditions should have a larger θ, relative to subject control. In addition, IWA should have a bigger interference effect, i.e., the difference in θ between the two conditions should be larger in IWA than in controls. This pattern would be expected under the resource reduction theory, which states that IWA should have greater difficulties in more complex sentences.
4. Slower lexical decision (LDT) should be associated with a decrease in θ across groups. Strong support for delayed lexical access would come from an interaction between LDT and group, such that an increase in LDT predicts a greater decrease in θ for IWA than for controls: Slow lexical access could cause parsing problems for controls, but if delayed lexical access is the main cause of difficulty in IWAs, parsing failures should occur more often in this group for individuals whose lexical access is particularly slow.
5. The probability of backtracking should be lower for IWA, which would be in line with resource reduction.
6. Finally, the dispersion parameter σ of the listening-time distribution should be larger for IWA, which would indicate that IWA have more noise in their parsing system. This would be in line with intermittent deficiencies, since more noise could be due to more breakdowns in parsing.
These predictions build on the previous work by Lissón et al. (2021), but other options for the mapping between parameters and theories of comprehension deficits in aphasia are possible, see Mätzig et al. (2018); Patil et al. (2016).
Results
We begin by assessing the posterior distribution of the probability of retrieval of the target, θ, shown in Figure (3 Controls are estimated to retrieve the target at the first retrieval attempt in both conditions in more than 90% of trials. The mean of the subject-control condition is slightly lower than the mean for the object-control condition. By contrast, IWA display a greater effect of interference: In object-control sentences, where the antecedent is close to PRO, IWA are estimated to correctly retrieve the target at the first attempt 85% of the time, compared to 60% for subject-control. An increase in LDT leads to a decrease in θ of −6% CrI: [−11%, −2%], but there was no interaction with group × LDT (−2% CrI: [−6%, 2%]). The credible intervals for the remaining parameters are shown in Table ( As expected under the slow syntax theory, IWA's mean listening times (µ) and the time needed for backtracking (δ) are higher than controls'. Similarly, σ is also higher for IWA, as predicted by intermittent deficiencies. Finally, the probability of backtracking is much lower for IWA than for controls. Assuming that backtracking uses general parsing resources, this estimate is in line with resource reduction.
Posterior Predictive Checks
One way to assess the behavior of the model is to check the posterior distribution of data generated by the model against the empirical data. If the mean of the empirical data falls within the range of predicted values of the model, the model could have generated the empirical data. By contrast, if the empirical data are outside of the range of the generated values, this indicates a suboptimal fit. Figure (4) shows the posterior predictive distributions of the direct-access model across groups and conditions. Overall, correct responses are modeled reasonably well, except in the object-control condition for IWA. The model also underestimates the listening times for incorrect responses, except for IWA in the subject-control condition. In all other design cells, incorrect responses are slower than correct responses, contrary to the model's assumption that slow backtracking responses are always correct. In terms of implementation, the main difference between the models is a newly-introduced parameter θ b , which is the probability of correct retrieval after backtracking. Figure (5) displays a graphical representation of this new model: After backtracking, the target is retrieved with probability θ b , and a misretrieval occurs with probability 1 − θ b . The hierarchical structure is the same as in the DA original model, except for θ b , whose adjustments are shown in Equation (2). Figure 5: Graphical representation of the modified direct-access model.
The model was run with 10,000 iterations, half of which were used as warm-up.
Predictions
All predictions are carried over from the base DA model. In addition, the probability of retrieval of the target after backtracking θ b should be lower for IWA than for controls. This would indicate that IWA are more likely to experience parsing failure or misretrieval even after backtracking.
Results
We begin by assessing the probability of first correct retrieval, θ. The posterior distribution across groups and conditions is shown in Figure (6). The estimates are quite similar to the ones in the original DA model: Controls have a very high probability of initial correct retrieval across conditions, and IWA display a greater interference effect. As in the base model, IWA have a low probability of backtracking in this model (7% CrI: [4%, 12%]) relative to controls (80%, CrI: [72%, 86%]). The probability of correct retrieval after backtracking, θ b , determines the amount of slow incorrect responses. The posterior distribution of θ b is shown in Figure (7). After backtracking, controls are estimated to retrieve the target 90% of the time, compared to around 70% for IWA.
The rest of estimates are also similar to the ones in the original DA model: IWA's µ is higher than controls' (2751( ms, CrI: [2477
Posterior Predictive Checks
The posterior predictive checks for the modified direct-access model are shown in Figure ( Like the base model, the MDA mostly correctly estimates listening times for correct responses across the board. The fits for incorrect responses seem to have improved, except for object-control in IWA, where the predicted listening times are still faster than the observed listening times.
Model Comparison
In order to quantitatively compare the performance of the models, we computed Bayes factors. We chose Bayes factors over other alternatives (e.g. cross-validation), because the two models seem to predict similar distributions, and Bayes factors are especially suited for nested models, or models that make very similar predictions. The hypothesis being tested is whether there is a non-zero parameter θ b that indexes the probability of successful backtracking, assumed by the MDA model, or whether backtracking is always successful, as assumed by the base DA model.
In order to perform the comparison, the models were run for 40,000 iterations, of which 3,000 were used for warm-up. Bayes factors were computed using the bridgesampling package (Gronau et al., 2020) in R. The Bayes factor of DA over MDA was estimated to be 2. This result is inconclusive, and indicates that the models provide similar quantitative fit to the data.
Discussion and Conclusion
In the present paper, we implemented and tested two versions of the direct-access model of cuebased retrieval and evaluated their predictive performance on data from individuals with aphasia and control participants. Specifically, we modeled interference in an under-studied linguistic construction, namely control structures. Both the base model and the modified model are in line with a combination of processing deficits in IWA: slow syntax, resource reduction, and intermittent deficiencies. Neither of the two models showed support for delayed lexical access as a source of retrieval difficulty specifically for IWA. Although a delay in LDT was connected to a decrease in the probability of correct retrieval, the effect of LDT was similar for IWA and control participants. In general, our results are consistent with other studies showing that a combination of processing deficits may be the source of impairments in sentence comprehension in IWA (Caplan et al., 2015;Mätzig et al., 2018;Lissón et al., 2021).
Unlike the base direct-access model, our modified DA model (MDA) assumes that backtracking can fail, resulting in slow, incorrect retrievals. However, this added assumption does not result in a decisive advantage in fit for the MDA model, as shown by the posterior predictive checks and the Bayes factor analysis. This result is unexpected, and leads us to think that the MDA model may be overparametrized. In MDA, all of the main parameters include a group adjustment. As a consequence, for instance, the mean listening times, µ, are estimated to be higher for IWA than for controls. The cost of backtracking, which is only added to µ if backtracking is performed, accounts for slower re-sponses. However, because IWA's µ is estimated to be higher than controls' µ, the model may not need to rely on backtracking in order to account for slow responses in IWA. This could be the reason why the probability of backtracking for IWA is very low (7%) relative to controls (80%). In addition, IWA's θ b has to be estimated from the 7% of trials that include backtracking. Given the size of the IWA group (21 participants), and the small amount of trials that include backtracking, perhaps the model cannot correctly estimate the θ b parameter. This could be investigated in several ways. One possibility would be to remove the group adjustments from µ, P b , δ, and θ b one at the time, and see which of these models shows a better quantitative fit for the data (see Lissón et al., 2021). Another possibility would be to evaluate how these parameters interact with and without group adjustments (e.g., do P b and/or δ for IWA increase if there is no group adjustment in µ?). We will address these questions in future work.
The present paper contributes to the aphasia literature by proposing a modification of the directaccess model that can account for incorrect slow responses. Despite our inconclusive results, we believe that the modified direct-access model offers a more appropriate set of assumptions for individuals with aphasia than the direct-access model. The modified-direct access model can account for slow incorrect responses, which are frequently found in studies on sentence processing in IWA (e.g., Hanne et al., 2015;Lissón et al., 2021;Pregla et al., 2021). It remains to be seen, by testing the new modified direct-access model against more data from individuals with aphasia, whether there is a difference in predictive performance between the two models. | 5,413.8 | 2021-05-03T00:00:00.000 | [
"Psychology",
"Computer Science"
] |
Assessing the acceptance of mobile phone technology in Tanzanian SMEs
Purpose – This study investigates the acceptance of mobile phone technology in Tanzanian small-and medium-sized enterprises (SMEs) using the Technology Acceptance Model (TAM) with a special focus on service quality. Design/methodology/approach – TheconceptualframeworkwasdesignedbyextendingtheTAMwithan additionalconstruct,servicequality,beforetestingamodelinasurveyof155respondentsandanalysingusingSmartPLS4. Findings – Service quality was found to be among the significant factors in the acceptance of mobile phone technology among SME employees. Research limitations/implications – This implies that the higher the quality of service offered, the more employees accept and use mobile phone technology in their duties and improve the productivity of SMEs. Practical implications – The aspects of quality of mobile phone technology usage such as call dropouts, network quality, speed, etc., must be improved significantly. Social implications – The Mobile Network Operators and Regulators must understand that employees are offered the most accurate and reliable mobile phone services for its usefulness to be realised. Originality/value – The originality is a modified version of a TAM that accommodates service quality that has been tested in the Tanzanian context.
Introduction
Small-and medium-sized enterprises (SMEs) play an important role in the county's economy (Hourali, Fathian, Montazeri, & Hourali, 2008;Kilangi, 2012).SMEs provide employment and income generation opportunities in many ways (Kilangi, 2012).From the perspective of Tanzania, SMEs contribute up to 27% of the Gross Domestic Product (GDP) and employ more than 20% of the workforce (Mushi, 2020).
The context in which SME employees use mobile phones is different from the context in which they use desktop computers (Kilangi, 2012).Thus, mobile phones can be used to complete employees' tasks, no matter where and when they are at headquarters, in remote locations or at home (Yueh Lu, & Lin, 2015).
Employees are also likely to have to work using their mobile phones anytime, anywhere, even if it's not during regular business hours, evenings or weekends (Kilangi, 2012;Mushi, 2018).The nature of the operation of mobile phone technology involves an effective operation on various sides including mobile devices (phones or other mobile devices), the Mobile Network Operators (MNOs) and the middle subsystems such as satellites and the signal distribution centres.As a result, it is difficult (almost impossible) to ensure quality of service at a single point.Therefore, service quality is probably among the factors which need not be taken for granted.
For technology to be fully used successfully, it must be voluntarily accepted by users (Venkatesh & Bala, 2008).For this reason, it is paramount to explore whether or not service quality is among the factors necessary for the acceptance of mobile phone technology in the context.This study will contribute to the existing literature on service quality based on the Technology Acceptance Model (TAM).This study is also significant for the managers of the service sectors in Tanzania as it will enable them to influence the attitude of SME employees in favour of their job roles and will also help them to adjust strategies to enhance their intention to use mobile phones for work.Given that there are not enough studies on mobile phone adoption in developing countries such as Tanzania, this research will be valuable to mobile app designers and researchers with an integrative view of technology adoption and service delivery.
Examples of models applied by researchers to explain technology acceptance include the (TAM) and the Unified Theory of Technology Acceptance and Use (UTAUT).The TAM and UTAUT explain the adoption of technology in different geographical contexts, industries and company sizes of its use (Davis, 1989;Venkatesh, 2000).While developing a conceptual framework, this study extends the TAM with an additional structure explaining the aspect of service quality before testing using Structural Equation Modelling (SEM) (Awang, 2015).The interest of this study was to assess whether the quality of services has a significant impact on employee adoption of mobile phone technology in small and medium enterprises.The remainder of this study is organised as follows.The second part deals with aspects of technology acceptance.The third section defines SMEs, while section four defines service quality and its role in this research.Section five discusses the methodological details, and section six discusses the methodological aspects.Section seven presents the Results and Discussion, while section eight provides critical analysis.Section nine represents the Conclusion of this paper.
Acceptance of technology
Sometimes, the terms "technology acceptance" and "technology adoption" are used interchangeably.Making a distinction between these two concepts is crucial.As per the Oxford Dictionary, adoption is the act of claiming something as one's own, whereas acceptance is the act of receiving it (Oxford, 2009).In this sense, deciding whether to accept or reject a certain technology requires consideration of the variables that may affect its application in a specific situation.
Comparably, the process of adopting technology begins the moment users learn about it and ends when they fully embraces it and incorporate it into their daily tasks (Addotey-Delove, Scott, & Mars, 2022).This implies that adoption entails more than merely embracing technology.Users of technology should be able to use it without external pressure and with comfort.Consequently, research must be done to determine and investigate the variables that might affect its application in various situations.
There are many models in the literature that explain the variables that affect people's acceptance of technology.In these models, the causal relationships between variables are examined to ascertain how they affect people's intentions to use technology now and in the future (Alsharida, Hammood, & Al-Emran, 2021;Mushi, 2020).Some models that explain technology acceptance at the individual level include the Theory of Planned Behaviour (TPB) (Ajzen, 1991), the Theory of Reasoned Action (TRA) (Fishbein & Ajzen, 1975), the UTAUT (Venkatesh, Morris, Davis, & Davis, 2003) and the TAM (Davis, 1989).
As employees of SMEs perform their duties using mobile phone technology, various factors tend to influence their adoption behaviours.Some research has explored factors which influence the acceptance of mobile phone technology from an SME perspective based on extending or adjusting the well-tested individual models such as UTAUT, TAM, and TRA (see Mushi, 2018Mushi, , 2020;;Prieto, Miguel añez, & Garc ıa-Peñalvo, 2015).This research follows necessary steps by extending TAM service quality as guided by relevant literature to propose hypotheses and formulate the conceptual framework of the study before testing in a survey.
3. Small-and medium-sized companies SME definitions vary depending on the situation.For instance, the definition varies from nation to nation depending on the size or degree of development (Bracci, Tallaki, Ievoli, & Diplotti, 2021).The number of employees, annual turnover and total investments are frequently used to categorise them.According to the World Bank, SMEs are businesses that, on a microscale, employ fewer than 50 people; on a small scale, employ 50 people; and on a medium scale, employ between 50 and 200.SMEs are defined by the Organization for Economic Co-operation and Development (OECD) as businesses with fewer than 500 employees (OECD, 2004).Conversely, SMEs in Britain are defined as businesses with fewer than 200 paid employees or an annual turnover of under £2 million, whereas SMEs in Australia are defined as businesses with 5 to 199 employees (Afolayan, Plant, White, Jones, & Beynon-Davies, 2015).
The definition of SMEs from the Tanzania Small Industries Development Organization (SIDO) adds more insight by asserting that in the event of an enterprise falling under more than one category, the level of investment will be the deciding factor.
The Tanzania Revenue Authority (TRA) defines SMEs as companies that have an annual taxable turnover of less than Tanzanian Shillings (TZS) 40 Million (USD 22,500), while the Tanzania SMEs policy document includes micro-enterprises in the group of SMEs.Since this study is conducted in the Tanzanian context, the definition which will be adopted will be summarised in Table 1.
In comparison, large companies which have material advantages due to their greater capacity to support research and development as compared to SMEs have behavioural advantages that stem from their greater flexibility and ability to adapt to changes in the market (Bracci et al., 2021).SMEs are primarily run by their owners making snap decisions in response to changing circumstances.SMEs are vulnerable to failure at times because they are forced to make less informed decisions about various aspects of their operations due to a lack of forecasting (Moeuf, Pellerin, Lamouri, Tamayo-Giraldo, & Barbaray, 2018).Using generalists rather than specialists is another trait shared by SMEs.This implies that they can carry out a variety of tasks with less emphasis on particular details.
In terms of ICT, SMEs find it challenging to adopt and use newer technologies because of the steep learning curve they must overcome.As a result, SMEs rarely have specialised skills unless they are primarily concerned with technological innovations (Mushi, 2020).Additionally, SMEs rely on short-term plans, which prevents them from anticipating future developments (Bracci et al., 2021).Because ICT is evolving so quickly, SMEs must recognise the need to plan for the future and implement effective change management in their operations.The role of service quality One of the reasons SMEs do not use advanced software and applications is that ICT demands providing users with ongoing upgrades of innovations (Mushi, Jafari, & Ennis, 2017).Another characteristic of SMEs is that they have very little or no budget for ICT (Leea, Kimb, & Chungc, 2002;Mushi, 2018;Prieto et al., 2015).SMEs continue to hesitate to successfully integrate ICT into their operations because innovations are so expensive.
According to this SME policy document, there was a total of 25,000 enterprises of which 97% of them had less than ten employees.This means the number of Tanzanians who work in SMEs is significantly larger than those who work in large companies.Therefore, research in this area has the potential impact on a large part of the Tanzanian economy and society.Tanzania is set toward becoming a middle-income country as the economy grew by an average of 6.5% per year in the past decade.The "Tanzania Development Vision (TDV) 2025" highlighted the SMEs sector as one important contributor to the country's long-term development.It is estimated that Tanzania's SME sector consists of more than 3 million enterprises which contribute to 27% of overall GDP.It is also estimated that the SMEs constitute more than 90% of enterprises in Tanzania (The Citizen, 2022).However, key constraints remain for SME development, especially in unfavourable legal and regulatory frameworks, undeveloped infrastructure, poor business development services, limited access to financing, and ineffective and poorly coordinated institutional support framework (Moeuf et al., 2018;The Citizen, 2022).
The data collected from different sources show that Tanzania has significantly low internet penetration rates accounting for 18%, whereas mobile penetration is 70%, and fixedline penetration stands at 0.3%.This might be due to the large size of the country.According to recent reports in the year 2022, there were 53.81 million cellular mobile connections in Tanzania at the start of 2022 where mobile connections in Tanzania were equivalent to 86.2% of the total population in January 2022, and the number of mobile connections in Tanzania increased by 3.0 million (þ6.0%) between 2021 and 2022 (DigitalReportal, 2022).This shows that Tanzanians are more likely to depend more on mobile phone technology to facilitate their activities including accessing internet services.Indeed, such contextual settings might be the reason why more attention from employees of Tanzanian SMEs has shifted to finding the best way of utilising mobile phone technology to fulfil their obligations.
The research shows that Tanzanian SMEs have a small number of employees compared to large companies (Migiro, 2006).Also, the low financial capabilities of the SMEs mean that they are likely to rely on mobile phone technology as the leading technological option.On the other hand, since SMEs have a smaller number of staff, it is expected that the usage of mobile phones is more autonomous in comparison to desktop computing.In that case, understanding the aspects which are associated with the usage of mobile phone technology in Tanzanian SMEs is vital.
Service quality
In every delivery of service, quality is among the important aspects to be considered.According to the fundamentals of technology acceptance, the output quality of any service can reflect how well the system performs its tasks and hence influence individuals to accept or reject a technology (Venkatesh & Davis, 2000).From a mobile phone technology perspective, the storage of data and processing performance are not as perfect as compared to desktop computers.As a result, mobile phone technology does not always offer the realistic outputs needed in SME processes, such as spreadsheets and word processing capabilities.Instead, they are more suitable for providing lightweight services.Therefore, the most appropriate way of measuring the perceptions on its service quality aspects is by using the service quality instead of output quality (Leea et al., 2002;Venkatesh & Bala, 2008).JEBDE
Hypotheses formulation and conceptual framework
This study expands on the TAM, which postulates that when users are provided with technology, there are variables at play that affect their choices about how and when to use it (Davis, 1989;Yueh Lu, & Lin, 2015).Two key metrics, perceived usefulness (PU) and perceived ease of use (PEU) are the foundation of the TAM.PEU describes the degree to which the system will free users from effort, whereas PU indicates whether the technology will augment or improve the user's job performance (Davis, 1989).One of the reliable and consistent models in the literature, the TAM has been effectively extended from several other models.Few of the previous studies that used the TAM as a benchmark included the context of maternal preschool teachers in acceptance of mobile phones where they found that PU of the technology and PEU tend to statistically influence the behavioural intention (BI) (Tavakol & Dennick, 2011).PEU primarily influences PU because it indirectly affects the intention to adopt technology and, ultimately, the utilisation of it.In relation to the context of mobile acceptance of technologies, the factors and significance relationships were previously been tested in researches on mobile phone technologies in other contexts (see Mushi, 2018Mushi, , 2020;;Prieto et al., 2015).In philosophical point of view, this research relies on positivism in which the main aim is to test the theory (truth) and in this context, it is based on deriving hypotheses and testing them.Since the later research has mainly focused on the acceptance of mobile phone technology, all the factors of the TAM can be adopted in this research.Therefore, the following theories are then put forth: H1a. PEU of mobile phones will positively influence the employee's BI in Tanzanian SMEs.
H1b. PEU of mobile phone technology will positively influence the employees' PU in Tanzanian SMEs.
H1c. PU of mobile phones will positively influence the employee's BI in Tanzanian SMEs.
H1d. Employees' BI of using mobile phones will influence their actual usage (U) in Tanzanian SMEs.
Previous studies have shown a strong correlation between perceived usability and service quality.For example, McFarland and Hamilton (2006) discovered a relationship between system usage and service quality.Leea et al. (2002) replaced output quality with the service quality of mobile internet services for personal users, and they found that it influences PU.Also, Park and del Pobil (2013) demonstrated that one of the most important factors influencing service consumption was perceived system quality.Additionally, Park and Kwon (2016) investigated the connection between PU and service quality and discovered a positive one.In another case, Ahmad, Bhatti, and Hwang (2019) found that the delivery of online banking services has a significant influence on PU.On such grounds, this hypothesis was predicted to be relevant to be involved when formulating the associated hypothesis.Therefore, this study hypothesised the following: H2a. Perceived service quality (PSQ) will positively influence the PU of mobile phone technology.
The derived hypotheses resulted in the conceptual framework for this research depicted in Figure 1.
Research methodology
A sample involving Tanzanian respondents with prior experience using mobile phones while working with SMEs participated in this study.Given that Kiswahili is Tanzania's official language, linguistic experts translated the questionnaires from English to Kiswahili to ensure The role of service quality translation accuracy.A second linguistic expert then translated the Kiswahili version back to English to determine whether the original and final English versions shared the same meaning.The gathering of data took about 115 days.There were 169 questionnaires given in all, but only 155 of them were completed, meaning that the response rate was 91.7%.There were 75 males and 80 females in the sample.
Since most Tanzanians currently utilise mobile phones and have been used them for long time in various situations, the majority of respondents were qualified to produce results that could be trusted; hence, a random sample technique was employed.While the majority of the questionnaires were distributed manually, some were sent to the respondents online.In several cases, more attempts were made to persuade respondents to set aside time to complete the questionnaires.
This survey consists of twenty three (23) measurement items as seen in Table 2. Following information systems research methodologies, assessments were conducted using a multipleitem Likert scale (Tavakol & Dennick, 2011).According to related previous research (Alsharida et al., 2021;Tavakol & Dennick, 2011), constructs were measured using the Likert scale, where 1 represents "Strongly Disagree" and 5 represents "Strongly Agree."Since every survey participant spoke Swahili, it was necessary to precisely translate survey forms from English into the dialect of Swahili.Thus, back translations were carried out, a method widely used in numerous cross-cultural surveys (Brislin, 1970).
Based on Variance-Based Structural Equation Modeling (VB-SEM) method (Ringo & Busagala, 2012).After conducting descriptive analyses, the analysis was divided into two phases: assessments of the current measurement models and assessments of the current structural models.A one-step evaluation is inferior to this two-stage analytical approach and consists of a measurement model and a structural model evaluation.According to Awang (2015), the measurement models explain how constructs are measured, and the structural models specify how constructs relate to one another.The measurement items, which were used, were adopted from previous research and details are shown in Table 2.
Partial Lease Square (PLS-SEM 4) was used for the analysis in this study, which made use of SEM (Awang, 2015).Using Cronbach's alpha, which has acceptable levels of alpha of 0.8 and higher as good, and satisfactory levels of alpha of 0.7 and lower as unacceptable, the questionnaire's reliability was assessed.The outliers were assessed using Squared Mahalanobis Distance (D 2 ).To assess the multivariate normality of the datasets, the , 1997).In the case of model fitness, absolute fit was assessed using Chi-square (x 2 ), incremental fit through the Confirmatory Fit Index (CFI), and parsimonious fit was assessed by Chi-square/df (x 2 =dfÞ.
Construct Item Description References
Perceived ease of use The role of service quality
Results and discussions
The structural model consisting of 5 constructs, and 23 measurement items was modelled in Smart PLS 4 as seen in Figure 2. It was then tested for reliability and validity before proceeding to further steps of analysis.It can be seen that all the factor loadings are >0.5 indicating that the model has attained unidimensionality condition.
The construct reliability and validity parameters of the model are seen in Table 3.It can be seen that all values of Cronbach's alpha are above 0.5 and the composite reliability (rho_ c) are above 0.7, indicating that the model is valid and reliable to produce results for path analysis.
The results of the discriminant validity assessment are performed using heterotraitmonotrait ratio of correlations (HTMT) and the results as seen in Table 4.The results show that all values are <0.9, indicating that the model is reliable because each construct has the strongest relationships with its indicators in the PLS path model.
The results on collinearity are seen in Table 5 where each measurement item seems to have values that are <5 indicating that the constructs are all independent.
The analysis of the model's power in testing the hypotheses was performed using Q 2 , and the results can be seen in Table 6.The results show that all values are above 0 indicating that the model is strong enough to be able to predict the relationship between the constructs.
The results on the path analysis are seen in Table 7 where all hypotheses and their associated p-values are indicated.The snapshot illustrating the structural model of the study and associated analysis metrics is shown in Figure 3.
7.1 The direct influence of perceived ease of use on perceived usefulness (H1b) This study proposed that employees' perceptions of the PU of mobile phone technology were directly influenced by their perceptions of its ease of use.Certain research regarding the use of mobile phone technology has corroborated this (Gallego, Luna, & Bueno, 2008;Mushi et al., 2017).7 presents the study's findings, which demonstrate that H1a was statistically significant.This indicates that the hypothesis is validated.Therefore, this study implies that employees' perceptions of the usefulness of mobile phones increased with their perception of their ease of use.This is in line with the findings of Mushi (2020) and Byomire and Maiga (2015).The role of service quality 7.2 The direct influence of perceived usefulness on behaviour intention (H1c) It was also shown that there was a statistically significant association between PU and BI in Tanzanian SMEs, as shown in Table 7.This implies that their intention to utilise mobile phone technology in the future is influenced by how valuable they believe it to be in their daily lives.This finding contradicts a study on employees' acceptance of mobile commerce integration in the workplace, which found that PU had no noticeable effect on employees' intention to use technology (Mushi, 2020).This hypothesis has also been supported by other research (see Prieto et al., 2015).Kim (2008)
JEBDE
typical voluntary setting where users are free to choose whether or not to use the device.In contrast to this study, which focuses on utilising mobile phones to fulfil business requirements within SMEs, in those situations, the BI is centred on using mobile phones exclusively for personal purposes going forward.
7.3 Direct influence of perceived ease of use on behaviour intention (H1b) According to this study, employees' intentions to adopt mobile phone technology in the near future would be impacted if they believed it was user-friendly.As can be seen in Table 7, where hypothesis H1b was determined to be statistically significant, the study's findings were consistent with this.
The study's findings align with the background of employees' acceptance of mobile commerce and the acceptability of smartphones.This suggests that mobile phones will be helpful to SME employees if they believe using them is simple.In this regard, the intention to use mobile phone technology is highly influenced by the way mobile phones are perceived to be simple to use.
Direct influence of behaviour intention actual usage (H1d)
This study assumed that the employees would use mobile phone technology whenever they intended to for SMEs-related tasks.The literature that suggests that an intention to use technology influences its actual utilisation in various circumstances served as the basis for this (Byomire & Maiga, 2015;Davis, 1989).
The findings in Table 7 demonstrate that this investigation validated the hypothesis.The actual use of mobile phone technology in SMEs and BIs were statistically significantly correlated.This meant that employees would utilise their mobile phones if they planned to use them to fulfil their SME commitments.
Direct influence of perceived service quality on perceived usefulness (H2a)
According to the study's hypothesis, PU and PSQ are positively and significantly correlated.Accordingly, consumers of mobile phones are more likely to think that technology will benefit them if they have faith in the calibre of services that they receive.
This study supports the hypothesis as seen in Table 7.The findings are consistent with those of Venkatesh and Bala (2008) who discovered a positive and significant relationship between users' perceptions of the utility of technology and the output quality of computer services.The results are also in line with the research on the acceptance of online banking had a significant influence on PU (Ahmad et al., 2019).Also, Leea (2002) that in mobile internet services, service delivery does have an influence on PU.Similarly, Park and Kwon (2016) found that there is a positive relationship between PU and service quality.
The fact that the relationship was found to be significant implies that there is a need to ensure that the service delivery chain of mobile phone technology starting from signal delivery to the mobile devices is well in place.However, there is a challenge in the type of mobile device itself since they differ in specifications such as screen display quality, processing speeds and battery life.The most important aspect is probably to ensure that the delivery channel is of the highest possible quality.
Critical analysis
The quality of service is one of the important aspects in many fields, e-government, in particular.While MNOs are strengthening the infrastructure and mobile device manufacturers are constantly improving them, it is important to understand which aspects are influenced by the The role of service quality quality of such service.This research has shown that the higher the quality of the service, the more usefulness the technology is perceived to have.In this case, it becomes evident that the role of mobile phone technology in people working with Tanzanian SMEs is highly influenced by the better quality of service that is offered.This information provides the necessary basis for the formulation of policies and legislatures as well as key theoretical underpinnings.
Conclusion
This research provides insights into technology acceptance in SMEs by establishing whether service quality can have a significant effect on the acceptance of mobile phone technology.The development of the conceptual framework was performed by extending the TAM with service quality before testing the model through a survey comprising 155 employees of SMEs in Tanzania.The research results have shown that all the proposed hypotheses were supported including the significant relationship between service quality on usefulness.In that case, MNOs, mobile device vendors and network engineers have a notable role to play in ensuring that the mobile devices are effectively used to facilitate the activities of individuals and the SMEs in which they are working.Further research may focus on the assessment of more current technologies such as Artificial Intelligence and Blockchain on their influence as they are used to achieve various roles in various contextual settings.
Figure 1.The conceptual framework of the research
Figure 2 .
Figure 2. Structural model of the study
Table 6 .
evaluated people's acceptability of smartphone and mobile wireless technology in a Q 2 predictive relevance
Table 7 .
Path analysis results | 6,036.8 | 2024-04-01T00:00:00.000 | [
"Business",
"Computer Science"
] |
Study optical properties of R6G dye doped in polymer PVA
The linear and nonlinear optical properties for laser dye R6G is investigated in solvent methanol at different concentrations (5x10-4, 1x10-4, 1x10-5, 5x10-6 and 1x10-6 Ml) at thickness (2µm). The nonlinear optical properties as refractive index (n2) and the nonlinear absorption coefficient (β) were studied by using Z-Scan technique in two parts; one part by putting aperture in front of the detector (close aperture) to find the nonlinear refractive index, however in second part is by removing the aperture (open aperture) to find nonlinear absorption coefficient, these by using two wavelengths 532, 1064 nm. The results show the effects of self – focusing in 532 nm and other concentrations in 1064 nm and the change of the saturation absorption effect in open aperture in both wavelengths. The higher nonlinear refractive index is found (n2=29.93cm2/mw) in the concentration (1*10-4 Ml), while the higher nonlinear absorption coefficient is (β=8.88cm/mw) in the concentration (5*10-4Ml) at the wavelength 532 nm.
Introduction
The most efficient type of laser dyes is the rhodamine 6G (R6G) which has characterized by high efficiency fluorescence band around 560 nm. Therefore, R6G dye is utilized potentially in applications as emitted light diode and the signal amplification in optics [1,2]. Rhodamine days are fluorophores that have a place with the group of xanthenes alongside fluorescein and eosin days. The general structures of xanthene chromophore and rhodamine days are shown in Fig. 1 The phenomenal photostability properties are other features of R6G, which found to use as laser days [3,4,5]. R6G dye has a wide area in applications such; optical switching, solar cell with concentrators, optical communications , optical limiting power, optoelectronics, laser dye, gain medium, as an active medium for dye lasers and photonics devices [7,8].
Z-scan technique was used to study the nonlinear optics properties (NLO) [9,10]. This technique is the simplest method and a sensitive for measuring the sign and magnitude of the non-linear refraction and non linear absorption for solids and liquids. It was developed by Sheik-Bahae et.al. 1989 [11,12,13].
Recently, a considerable number of studies are devoted to investigate the optical properties of R6G. The most important of these studies is (Deng et.al. 2007 [1] who investigated the fluorescence and nonlinear optical properties of R6G/PMMA films by using z-scan technique. Modification strategies of the R6G applications as fluorescent probes that linked to another (bio) molecule were discussed widely in review by (Mariana et.al. 2009 [6]. In this basic survey the procedures for adjustment of Rhodamine dye and a discussion on the assortment of uses of these new subordinates as fluorescent tests are given. Hence, in order to obtain a thin film R6G/PVA with good properties, it is necessary to test a variety amount of concentrations of R6G laser dye (500 -700) nm. Aiming to do that, optical properties (linear and nonlinear) consisting of absorption and fluorescence spectra were investigated. Where, normally the absorption of Rhodamine 6G increases by depending the second harmonic of Nd: YAG laser (532 nm). Thus, in this work the control of concentration of R6G dye is the key factor in the linear and nonlinear optical properties of R6G/PVA, which were measured by z-scan technique laser Nd-YAG.
The prepared solutions were diluted according to the eq. (2) [14]; Dye R6G doped PVA polymer films were fabricated by using the casting method. The prepared solution of the polymer was produced by dissolving amount of polymer (0.7 gm from PVA in 10 ml of water solvent) at temperature 35. The mixture of ratio (2/3) of the polymer solution with water is added to (1/3) of the R6G dye in methanol solution. Then, the final mixture of all these material is placing in Baker with a constant stirring of the mixture to obtain a homogeneous mixture. Finally, in order to solidify the mixture, it pours upon a glass slide (2.5x7.5 cm) at room temperature and leave the slide for 24 hours to obtain film under different concentrations at a constant thickness (t=2μm).
Results and discussions
The nonlinear optical properties were studied for films R6G & PVA as following;
Spectra of absorption and fluorescence
The Spectra of absorption and fluorescence for films R6G & PVA were investigated in methanol for different concentrations (1x10 -4 , 5x10 -4 , 1x10 -5 , 1x10 -6 and 5x10 -6 mole/liter) at thickness (2µm). Figures (2) and (3) show the spectra of absorption and Fluorescence for R6G & PVA in different concentrations. In terms of spectra of fluorescence as shown in Fig. (3), they increase and present red shift towards high wavelength by increasing the concentrations.
Linear optical properties
The linear absorption coefficient of R6G & PVA was determined for both wavelengths using the formulae (3) [14].
where (t) is the thickness of sample and T is the transmittance. Table (1), gives the values of the linear optical properties ߙ , T, n and K. It has been realized that the coefficient of refractive index (n) and the absorption (ao) increase with increase the concentration for both wavelengths. So in this case, this work use (532, 1064) nm, while in [4] used 532 nm.
ܫ : Is the intensity of the laser beam at the focus (Z = 0).
where ΔT is the one peak value at the open aperture Z-scan curve. After putting the sample (R6G/PVA) at thickness 2µm on the base of z-scan system, the normalized transmission were recorded by using 532 nm of Nd-Yag laser for closed and open aperture. The first group of results with closed aperture is given by Fig. 4 under different concentrations.
Normalize transmission
The It can be seen from Fig. (4) that the nonlinear refractive index which is represented by valley-peak changes between positive (self-focusing :that mean valley-peak) and negative (self-defocusing: that mean peakvalley). The second case with open aperture gives the spectra that are shown in Fig. 5. From above table it can be seen that the higher value of nonlinear refractive index (݊ ଶ ) was obtained when the concentration is (1*10 -6 Ml). Additionally, higher non-linear absorption coefficient (β) obtained when the concentration equals to (5*10 -4 Ml) as well. Furthermore, another laser was used with a different wavelength 1064 nm. For this kind of laser the two cases of closed and open apertures were applied as well. In the closed aperture, the results were presented in Fig. 6.
Normalize transmission
The Fig. 6, the nonlinear refractive index changes between positive (self-focusing: that mean valleypeak) and negative (self-defocusing: that mean peak valley). In the second case with open aperture and for the same laser, the result was shown in Fig. 7.
Normalize transmission
The From this table it can be seen that the higher value of the nonlinear refractive index (݊ ଶ ) is obtained when the concentration is (1*10 -4 Ml), and the higher value of the non-linear absorption coefficient (β) obtained when the concentration is (1*10 -4 Ml).
After that, the effect of the concentration changes on the energy gap (E.g) was studied and the results are shown in the table 4. Fig. 8 shows the relation between the E.g and the concentration as well. 10 In comparison with other research, it has been realized that there is agreement in some findings. One of these agreements is found with Deng Yan [1], in the behavior of the closed aperture. However, this research did not address the study of the open aperture. In addition, there was a difference in the values of the linear refractive index (0. 65 -28.9) × 10-7 cm2/mW with varying concentration [4]. These differences might attributed to add particles of silver in research [4]. On the other hand, excited and emitted spectra of polymeric (PMMA) films that doped with R6G dye were investigated by Tanyi E [16]. In contrary with several studies, this study suggests that ~495 nm shoulder in the absorption spectrum is chiefly not due to a dimer formation, but is likely owing to vibronic transitions. With an increase of the dye concentration, the area of the Gaussian band representing the shoulder of the absorption spectrum increases linearly.
Conclusion
The spectral and optical properties of the models used in the search were investigated by applying theoretical calculations on practical (experimental) results that obtained in this research. It has been realized that absorption and fluorescence spectra of the samples (solid state) for different concentrations drift towards longer wavelengths with increasing concentration of the dye. Additionally, the nonlinear absorption coefficient of the solid state exhibits behaviour of saturated absorption of certain concentrations, which leads to increases the value of the nonlinear absorption coefficient solutions with increase concentrations. However, the nonlinear refractive index (n2) of solid changes between the positive and negative values and increases with increasing of the concentrations. | 2,032.8 | 2019-07-01T00:00:00.000 | [
"Materials Science",
"Physics"
] |
Synthetic images aid the recognition of human-made art forgeries
Previous research has shown that Artificial Intelligence is capable of distinguishing between authentic paintings by a given artist and human-made forgeries with remarkable accuracy, provided sufficient training. However, with the limited amount of existing known forgeries, augmentation methods for forgery detection are highly desirable. In this work, we examine the potential of incorporating synthetic artworks into training datasets to enhance the performance of forgery detection. Our investigation focuses on paintings by Vincent van Gogh, for which we release the first dataset specialized for forgery detection. To reinforce our results, we conduct the same analyses on the artists Amedeo Modigliani and Raphael. We train a classifier to distinguish original artworks from forgeries. For this, we use human-made forgeries and imitations in the style of well-known artists and augment our training sets with images in a similar style generated by Stable Diffusion and StyleGAN. We find that the additional synthetic forgeries consistently improve the detection of human-made forgeries. In addition, we find that, in line with previous research, the inclusion of synthetic forgeries in the training also enables the detection of AI-generated forgeries, especially if created using a similar generator.
Introduction
Forgeries are a serious threat to the artwork market, as illustrated for instance by the infamous Max Ernst forgery "La Horde".In 2006, the auction house Christie's announced the sale of the artwork, with an estimated value of about £3,000,000.However, it turned out that "La Horde" was a forgery created by the art forger Wolfgang Beltracchi [1].Similarly, at the beginning of the 20th century, the Wacker case made the headlines globally.The German art dealer Otto Wacker, possibly with the help of his brother Leonhard, managed to sell over 30 fake Van Gogh paintings to public and private collectors, and many of the paintings were even included in the Catalogue Raisonné by Van Gogh expert Jacob de la Faille [2].Despite experts' disagreement, the art dealer was charged with fraud in April 1932.
16th February 2024 1/25 Recent developments in computer vision and machine learning techniques may contribute to the issue in several ways [3].
While most of the studies concentrate on the attribution of an artwork to several pre-defined authors, similar machine-learning methods can also be used to distinguish between authentic artworks by a given author and forgeries.Due to the very close resemblance between original images and human-made forgeries (such as the Wacker forgeries), art authentication is generally a more challenging task than artwork attribution.In particular, authentication algorithms often have to learn very fine details such as brushstroke structure [7,9,17].An additional challenge is that, for a given artist, forgeries are typically much less numerous than original artworks and often lack systematic documentation and high-resolution scans or photos.Despite such limitations, in recent years, NNs such as Convolutional Neural Networks (CNNs) or transformer-based architectures have shown promising results in both art attribution, when trained on datasets of authentic paintings and other stylistically similar artworks [17] as well as in artwork authentication, trained against forgeries [18].
In this context, the new trend of Generative Artificial Intelligence (GenAI) appears to present both threats and opportunities.On the one hand, GenAI might be adopted to create refined synthetic digital forgeries [19], which might populate the internet and diffuse misinformation.The possibility of creating 'fake' synthetic artworks using AI-based methods gained popularity with the publication of Neural Style Transfer (NSF) [20], which learns to decouple the style of an artwork from its content.This method is capable of creating synthetically styled images in the particular predisposition of a given artist to varying scales of accuracy and applicability.The successive publication of various Generative Adversarial Network enhanced architectures (e.g.StyleGANs [21,22]) and powerful large-scale diffusion models (e.g.Stable Diffusion [23] and DALL-E 2 [24]) paved the way to the generation of realistic synthetic forgeries.In particular, the introduction of text conditioning using contrastive text-image models such as CLIP [25], created an accessible and quick interface for the creation of artworks 'in the style of'.Differently from NSF, the latter is not tied to an input natural image and therefore allows greater freedom of generation.
At the same time, the ability of GenAI to create synthetic forgeries may mitigate the limitation of AI-based art authentication of being hampered by the limited availability of known forgeries and imitations.The goal of this work is to explore to what extent the recent GenAI methods such as StyleGANs and Stable Diffusion are able to augment the training datasets of known forgeries and enhance the performance of AI-based art authentication.While most recent proposals to detect fake images mainly address photorealistic images [26], the use of synthetic forgeries in artwork authentication is a widely unexplored area.Specifically, we focus on paintings by Vincent van Gogh, which are frequently used as a benchmark dataset for machine-based art attribution methods [6,7,9,10].Van Gogh painted a sheer amount of artworks, now in the public domain, and was widely forged due to its enormous market value.Van Gogh datasets, therefore, serve as valuable case studies for art authentication.
We build on the already publicly available dataset VGDB-2016 on Van Gogh [27] available here, containing a set of 126 RGB original images by the artist and a set of 212 non-authentic RGB images by other Impressionist and Expressionist artists.The VGDB-2016 dataset does not contain forgeries, making it unsuitable for forgery detection.To address this, we enrich it for the purposes of art authentication and add 11 RGB images of well-known forgeries created by the forger Otto Wacker into our dataset.We also include 8 forgeries by former art forger and now legitimate artist creating genuine fakes, John Myatt.The latter images are not in the Open Domain, therefore we only provide a pointer to those images.Furthermore, we release the artificially generated AI-based forgeries specifically generated for this paper.Finally, to reinforce our findings on van Gogh, we carry out the same analysis on datasets of Amedeo Modigliani and Raffaello Sanzio (Raphael), which are detailed in the supporting information S1 Appendix.
The outline of this paper is as follows.The next section details the Methodology we employ to generate synthetic images used to augment the training data set of known forgeries.We also briefly discuss the classifier model that we use for forgery detection.We then present our main findings on improved Classification methodology, leading up to the goals listed above.As a consistency check, we also discuss the authentication of synthetic forgeries created by Stable Diffusion and StyleGANs Detection of synthetic images.A brief summary is provided in the Discussion and Conclusions.
Methodology
In this section, we provide an overview of the methods we employed to generate synthetic images for art authentication.We first outline the process of creating synthetic images for the training datasets and provide details about the composition of the dataset.We also elaborate on our classification methodology for art authentication.Finally, we explain how we evaluate the authentication efficiency.
Methods for synthetic image generation
We use two fundamentally different GenAI methods to generate synthetic artwork: an image-to-image generative adversarial network (GAN) and a text-to-image diffusion model.The images generated both by the diffusion model and GAN are collectively referred to as synthetic data.
We used the NVlabs implementation StyleGAN3 [22] which is one of the most recent and successful GANs.StyleGAN3 was trained from scratch on 10380 portraits in various genres and by many different authors, including 126 portraits by van Gogh, 280 by Modigliani, and 157 by Raphael.The portraits by the three artists are sourced from Wikiart, and while there is considerable overlap, they do not entirely represent the sets of original artworks detailed in the subsequent datasets.The latter ones are not limited to portraits but, in turn, are filtered to include only artworks appearing in museum collections or Catalogue Raisonnés, ensuring a high level of certainty regarding their authenticity.
The training took 5M epochs on 4 GPUs.More details on the training procedure and the quality of the resulting images can be found in the supporting information S1 Appendix.With such training, StyleGAN3 produces images in a mixture of styles by random authors.We used the trained StyleGAN3 to produce a "raw" dataset of 2000 random portraits.In what follows, images picked at random from this "raw" dataset are referred to as the "raw GANs" image set.Furthermore, subsets of synthetic portrait images in the style of a specific artist (van Gogh, Modigliani, or Raphael) were created through further training for 50k epochs exclusively on original paintings by the respective artist.This yielded image sets of synthetic images that looked stylistically close to the works of van Gogh, Modigliani, and Raphael.We refer to these datasets as "tuned GANs" image sets.We remark that, due to the limited number of paintings available for each artist, prolonged training on the exclusive data sets often results in a decline in the quality of the StyleGAN3 images.Rather than achieving the desired outcome of generating a large variety of images in a given style, long specialized training tends to produce an almost exact reproduction of the training set.Specialized training for some time between 20k and 100k epochs has proven to be a good compromise, striking a balance between a wide variety of images and effective adaption of the desired style.
To create the text-to-image synthetic artworks, we use the Stable Diffusion [23] generative model.It relies on CLIP guidance [25] to semantically align the latent text representation and the latent image representation and a U-Net architecture [28] as a de-noising diffusion model.The quality of images generated using Stable Diffusion strongly depends on the text prompt.We generate images in the style of each artist using a simple prompt indicating the style, the content, and the artist; for example: 'Post-impressionist painting of a young boy, by Vincent van Gogh'.We adopt the Stable Diffusion version 2.1 (v2-1_768-ema-pruned.ckpt), with 60 inference steps, 8 guidance scale, and 512 × 512 pixels resolution.The resulting synthetic dataset is referred to as "diffusion".Note that Stable Diffusion has been trained on subsets of the very broad open-source dataset LAION-2B(en) collected in the wild and using the large contrastive model OpenCLIP while the GAN was trained on the controlled WikiArt dataset.We used the second version of Stable Diffusion because it is trained on fully open data and models.
Composition of training datasets
AI-based art authentication is a binary classification task where the model learns to differentiate between authentic and non-authentic artworks (including known forgeries).This requires training on two sets of artworks for each artist, an authentic and a contrast set.Our experiments are centered around the van Gogh dataset which contains 126 original artworks from the VGDB-2016 dataset [27].The dataset was gathered from Wikimedia Commons, and it contains artworks with a similar chronology or artistic movement to van Gogh and with a density of at least 196.3 PPI (Pixels Per Image), the dataset also contains two artworks with debated attribution for testing.Here we note that the number of images does not exactly match those mentioned in the original paper [27], we provide the number of images that were actually downloaded through the dataset link provided in [27].
In addition, in supporting information S1 Appendix we provide two further tests of our approach on the artworks by Modigliani (100 original artworks) and Raphael (206 original artworks) and imitations/forgeries thereof.The latter datasets were collected from museum collections or sourced from Catalogue Raisonnées, which are expert-curated lists documenting all verified authentic artworks by the respective artists.
The contrast set includes artworks that were not made by the artist, but that resemble it closely and are helpful in detecting forgeries of the artist's work.Normally, this includes artworks of similar artists, referred to as 'proxies', and forgeries or explicit imitations of the artist, referred to as 'imitations'.Proxies are paintings by different human authors who painted in a similar style to the artist (i.e.artists pertaining to the same artistic movement) and/or were collaborators, pupils, and teachers.The word imitation is used here as an umbrella term to encompass human-made non-autograph copies of authentic works, artworks explicitly made in the style of the artist, and known forgeries of the artist.To these elements, we add synthetic fakes generated by Stable Diffusion 2.1 and StyleGAN3, and we test whether their addition increases the performance of the models.
The contrast set of Vincent van Gogh contains 212 artworks by similar artists, 19 forgeries (11 by Otto Wacker and 8 by John Myatt), 30 Stable Diffusion generated images, 30 GANs fine-tuned on the artist, and 30 random GANs (the 'raw GANs').
16th February 2024 4/25 The set of 'raw GANs' contains the same exact images across all three datasets used in this work.All images are pre-processed according to the procedure detailed in [18].Specifically, we generate sub-images of paintings, i.e., RGB images normalized to a fixed size of 256 × 256 pixels, with channel values normalized to the unit interval.These sub-images are created by dividing the entire image into 2 p × 2 p equally sized units, where p is determined by the resolution of the original image.If the smaller side of an image is larger than 1024 pixels, then p = 2; if the smaller side is larger than 512 pixels and smaller than 1024, then p = 1.For all images, irrespective of resolution, we also include the sub-image obtained by center-cropping a square from the full image.Therefore, depending on the resolution of the original image, the images are patched in 21, 5, or 1 adjacent non-overlapping patches.Using bi-cubic resampling, we reshape all the images to either 224 × 224 pixels or 256 × 256 pixels depending on the input supported by the model.
The patches are split randomly into training (72%), validation (11%), and test (17%) sets, ensuring that patches belonging to the same original image feature in the same set.We randomly sample the split 10 times, obtaining 10 bootstrapped splits for cross-validation.
For the sake of clarity, we will present the results for the van Gogh dataset [29] in the remainder of this paper.The outcomes for Modigliani and Raphael are available in the supporting information S1 Appendix.
Table 1 provides a detailed overview of the van Gogh dataset.The rows represent the six image sets, while the columns show the number of images and the corresponding number of patches.Representative images of each class (authentic, imitation, GAN, and diffusion) are shown in Fig. 1.
Classification methodology
After preparing the training and testing datasets of human-made and synthetic artwork forgeries as described in the previous Section, we proceed to explain the classification methodology on the gathered dataset.In line with the approach outlined in [18], we employ transformer-based classification methods (specifically, Swin Base [31]) and state-of-the-art Convolutional Neural Networks (EfficientNet B0 [32]) to distinguish between authentic artworks and forgeries.These models have been adopted in [18] and proved to outperform the canonical ResNet101 model, the typical baseline model for art authentication.The Swin Base is an image transformer model that uses a hierarchical structure with shifting windows to reduce the computational complexity of transformer models, it accepts inputs of size 224 × 224 and has 88M parameters.On the other side, EfficientNet B0 is a CNN-based model belonging to the class of EfficientNets which adopts an optimal width, depth, and resolution scaling for the architecture.It accepts slightly larger inputs of shape 256 × 256 and has only 5.3M parameters.We note that Swin Base is a larger model version compared to EfficientNet B0.We will present the classification outcomes for both the Swin Base and EfficientNet models, however, we do not directly compare the performance of these models.Rather, the purpose is to demonstrate that incorporating synthetic data into training datasets enhances classification reliability, regardless of the classifier architecture.We use the Swin Base and EfficientNet models pre-trained on ImageNet data [33] and fine-tune them for the art authentication task.To do so, we substitute the final activation layer with one dense layer converging in a single node with sigmoid activation and train using the binary cross-entropy loss without freezing the weights.For both models, we use a learning rate of 10 −5 , a batch size of 32.We train the models on binary classification, where class 1 contains the authentic artworks by the artist (authentic set) and class 0 refers to the non-authentic artworks (proxies, imitations, and synthetic images).
To investigate how the addition of synthetic images in the training set improves classification accuracy we run the following experiments.First, we test whether the addition of each of the synthetic sets separately, as well as the combination of Stable Diffusion and fine-tuned GANs, improves the classification accuracy of the human-made forgeries against a baseline trained using 'proxies' and 'imitations'.This baseline also 16th February 2024 6/25 agrees with the previous work [18].Secondly, we investigate the extent to which synthetic images can increase the detection of human-made forgeries while never training the models on any human forgeries, thus relying solely on 'proxies' and excluding 'imitations'.The setup of the experiments is schematized in Fig. 2. We note that the second task is inherently much harder than the first one, as it tests whether synthetic images alone can substitute the need to train on human-made forgeries to detect such forgeries.This case scenario addresses the situations in which there are no known forgeries of an artist but it is still desirable to be able to flag possible forgeries.This case is common in art connoisseurship as less well-known artists are rarely forged.To evaluate the performance of our classifiers, we compute the confusion matrices and classification accuracy on the test datasets aggregated at the image level, separately for authentic artworks, imitations, and synthetic images.
Statistical significance of the results is guaranteed by the use of cross-validation with 10 different splits and subsequent uncertainty estimation.All quoted results are the median of the joint distributions and the uncertainties are the (symmetrized) 68%quantiles of the median (equivalent to the 1σ-standard-error for normally distributed data).We use the concise parenthesis notation in Tables 2-4.Thus, an entry like 0.710 (46) means that the central value of the distribution we obtained during the cross-validation process is 0.710 and it is unlikely (at most 32%) that the true value does deviates from this central value by more than 0.046.Similarly, in Figs. 3 and 4 this would correspond to a main bar at 0.710 and error-bars of lengths 0.046 both up and down.
Results
The outcomes of our classification experiments for van Gogh are shown in Tabs. 2 and 3.The results are also visually depicted in Fig. 3.The evaluation of the classification performance is based on two main criteria: the accuracy in classifying human forgeries 16th February 2024 7/25 (accuracy 'forgeries') and the accuracy in classifying authentic paintings (accuracy 'originals').Note that what we here refer to as 'forgeries' is synonymous with the set of 'imitations', as those imitations are, in this case, indeed forgeries.
Detection of human forgeries
The classification accuracy for authentic paintings reveals consistently high levels, approximately 90% or higher with the 'Swin Base' model classifier and at least 80% with 'EfficientNet B0', across all training sets, as indicated by the green bars in Fig. 3.We observe, moreover, the reproducible improvement in the classification accuracy of human-made forgeries when synthetic forgeries are added to the training datasets.This finding is, to the best of our knowledge, yet unobserved in the literature.On the mixed synthetic training datasets, we were able to achieve accuracies approaching 80% (see Table 2).Images generated by Stable Diffusion appear to be particularly beneficial, leading to accuracy improvements of 10% to 20%.These improvements are evident in Fig. 3, where the purple bars (forgeries) associated with "no synthetic" values (this baseline is also extended as a dotted horizontal line) are consistently lower or equal to the values associated with the synthetic ("diffusion" and "tuned GANs") counterparts.This result is particularly impressive considering that the forgeries were often painted by professionals with the goal of avoiding detection.
In addition to augmenting the human-made forgeries with synthetic ones, we also investigated the case where no human-made forgeries were included in the contrast set at all (experiment 2).All classification accuracies are bound to be lower in this case, which is what we observe, and we certainly cannot recommend using this approach in practice if any human-made forgeries are available.However, it allows to resolve the benefit of synthetic forgeries with higher statistical significance.As can be seen in Table 3 and the lower two panels of Fig. 3, the addition of synthetic data allowed to improve the forgery detection accuracy by almost 40% and 30% for 'Swin Base' and 'EfficientNet B0', respectively, both corresponding to a significance of about 4σ.
Finally, the quality of synthetic data plays a crucial role in training success, as expected.As seen in Tables 2 and 3, training solely on "raw GAN" images resulted in minor or no improvement in authentication accuracy.Nevertheless, it is interesting to note that in some cases, the addition of "raw GAN" datasets without any authorspecific features led to slight enhancements in authentication capabilities.Consistent with previous findings by Schaerf et al. [18] and the inherent differences in model sizes, the transformer-based Swin Base classifier demonstrated slightly superior overall performance.
All findings are consistent across the two models 'Swin Base' and 'EfficientNet B0'.This observation is also supported by a similar analysis of Modigliani and Raphael's datasets described in supporting information S1 Appendix.While the numerical values of the classification results may vary between models and artists, the qualitative conclusions remain consistent across all six combined cases.
Detection of synthetic images
Machine learning methods for the detection of synthetic artwork and synthetic images is currently a very active research topic (see e.g.[34][35][36][37]).While the primary focus of this paper is the detection of art forgeries created by humans, in this Section we demonstrate that, in agreement with previous studies, our classifier Neural Networks (Swin Base and EfficientNet) are also capable of detecting synthetic artwork forgeries created by GenAI.A novel aspect of our approach is that, unlike in most previous studies, the classifier is trained on both human-made and synthetic forgeries.
16th February 2024 We assess the efficiency of the detection of synthetic forgeries using the synthetic sets listed in Table 1.Tuned GANs and Stable Diffusion images are tested independently with central values (medians) and uncertainties of the cross-validation results are computed in the same way as in teh previous Section Detection of human forgeries.The results are summarized in Table 4 and in Fig. 4, which show a considerable improvement of synthetic images detection when integrating synthetic images in the training set.
Our findings are consistent with the typical conclusion in literature (e.g.[35][36][37][38][39]), in that the training on synthetic artwork (tuned GANS, diffusion and raw GANs) is crucial for the classifier to detect forgeries created by GenAI.
We have to distinguish the two cases here of training the classifier with a similar GenAI as has to be detected versus training with a different one.In agreement with the literature, the highest authentication accuracy is obtained if the classifier had already seen synthetic images by the same generator architecture during the training [36,37].As one can infer from Table 4, the best results (all above 80%) for tuned GANs detection are achieved when tuned GANs are also included in the training and equivalently training on Stable Diffusion images allows the highest accuracy for diffusion detection.
16th February 2024 9/25 Based on the results presented in Tables 2 and 3 with the composition of the underlying van Gogh data set as detailed in Table 1 and visualised in Fig. 2. The horizontal dotted line shows the baseline without synthetic images in the training data.Similar results for the artists Modigliani and Raphael can be found in S1 Appendix.We also observe that including tuned GANs in the training helps to some extent with the detection of images generated by Stable Diffusion, and vice versa.This is an interesting observation given that most previous studies on synthetic forgery detection concentrated on generator-specific image features and visual inconsistencies [39][40][41].In the van Gogh based studies presented in this main manuscript it turned out that our classifier could detect GAN images relatively well even without training on synthetic data.The trends described above are visible for both, tuned GANs and diffusion, but they are significantly more pronounced for the latter.When performing the same analysis with the artists Modigliani and Raphael (see S1 Appendix), we found that in some cases tuned GANs also eluded detection very effectively (some accuracies below 10%) as long as no StyleGAN3 images had been included in the training.In all of these cases training on the given architecture readily improved the accuracy.Based on the results shown in Table 4 with the composition of the underlying van Gogh data set as detailed in Table 1 and visualised in Fig. 2. tuned GANs diffusion to be able to teach something to the classifier.
In agreement with previous research, we also confirmed that the training on synthetic images expectably improves the authentication efficiency on synthetic forgeries, especially when the same GenAI architecture was used to produce the training dataset.
Further exploration should be dedicated to quantifying the optimal ratio of humanmade forgeries to synthetic data.Moreover, it might be of interest to investigate the influence of image resolutions on the performance of both generators and classifiers.However, significantly larger computing resources than currently available to us would be needed for this type of analysis.With more computational resources, an additional improvement to this work might be the dedicated post-training of generators like Stable Diffusion on authentic artworks of given artists in order to further enhance the quality of synthetic data.
A notable limitation of our study is that the synthetic GAN-based forgeries are limited to portrait paintings due to the poor convergence of other types of images.While the artistic styles of van Gogh, Modigliani and Raphael are without doubt very different, further tests should be carried out to generalize the findings to a variety of genres and even more different artists.
16th February 2024 11/25 of images used for training, along with the corresponding quality of the generated results, sorted by categories.Furthermore, we include visual representations of sample images generated after the training.
2. Classification results for Modigliani and Raphael.The entire workflow presented for the artist Vincent van Gogh in the main manuscript has also been performed for Amedeo Modigliani and Raphael (Raffaello Sanzio da Urbino).The results can be found in this section.
A Evaluation of the quality of synthetic images generated by StyleGAN
In this section of the supplementary information to the manuscript "Synthetic images aid the recognition of human-made art forgeries" we detail the procedure employed for the training of StyleGAN3 [22], the generation of images as well as their quality.
The training was performed independently on genre-based subsets of Wikiart (www.wikiart.org),with the number of images of each subset and the corresponding genre listed in Tab. 6.We trained each genre starting from white noise (i.e.no pretraining) with a resolution of 256 × 256 pixels.The portraits analysed in the main manuscript were trained in an independent additional run using a higher resolution of 512×512.The corresponding hyperparameters we used for the training with StyleGAN3 are listed in Tab. 5.
resolution -batch= -gamma= -cbase= -glr= -dlr= -mbstd-group= 256 × 256 16 1 16384 0.001 0.001 4 512 × 512 12 5 0.001 0.001 3 It is interesting to note that the latest alias-free version included in StyleGAN3 turned out to perform worse on artworks than the older version StyleGAN2 [21], in our case realized by the corresponding flag natively provided in StyleGAN3.This is likely a consequence of local hard transitions, often featured by brush strokes, which tend to be smeared out by the translationally invariant StyleGAN3.
Tab. 6 provides an overview over the number of images used for training and the resulting image qualities achieved by the GAN for different image types with a resolution of 256 × 256.The Fréchet Inception Distance (FID) is the state of the art estimator for image quality that is closest to human perception as a rule.A high FID (ca.20 or more) usually signifies bad results, while a low FID (here less than 20) indicates that the images are reasonably realistic.However, this rule has notable exceptions, in our case 'history and genre paintings' as well as 'still and flower paintings'.Most humans would readily agree that the former category produced unsatisfactory results (see fig. 5, top left) while the latter succeeded with the flowers at least (see fig. 5, bottom right), both contrary to the FID predictions.
There is an overall trend that a larger training set results in higher quality images as could have been expected.However, even with similar sample sizes, some categories fare much better than others.Some examples are shown in Fig. 5 where the images in the top row ('history and genre paintings' and 'landscapes') have training data sets of similar size.The data sets 'figurative and allegorical' and 'still and flower paintings' are also similar in size.Their representatives in the bottom row have extremely different quality as well.We speculate on several causes which can, at least partially, be responsible for such differences in generative quality.One possibility and known issue of GANs is a poor convergence of the optimizer during the training process.A high number of minuscule details is certainly prohibitive when learning on such low resolutions, for instance, many people in the historical paintings, each with facial features.Both, the image resolution and the network capacities are insufficient to resolve this kind of details.In addition, a large diversity of images poses a difficulty because the GAN might not be able to identify reoccurring features and is incapable of generalizations.This is most likely the pivotal problem with the figurative and allegorical paintings.
A separate training run has been performed on images with the higher resolution of 512 × 512 for the 'portraits and self-portraits' category, which serves as a base for all the analysis in the main Manuscript.These GAN images are used for the benchmarks below.These are trained on a smaller training set (only 7983 of the 10 380 images had a sufficient resolution) and a higher number of network parameters (59 259 432 instead of 48 768 547 parameters in total).
B Classification results for Modigliani and Raphael
This section of the supplementary information to the manuscript "Synthetic images aid the recognition of human-made art forgeries" complements the results presented in the manuscript for the artist Vincent van Gogh with analogous studies using portraits by Amedeo Modigliani and Raphael (Raffaello Sanzio da Urbino).The entire procedure (from data generation to classification and analysis) is identical with that employed for van Gogh and we refer to the main manuscript for the details.
Data sets
The compositions of the training datasets are listed in Tabs.7 and 8 with representative images of each category displayed in Figs. 6 and 7 for Modigliani and Raphael, respectively.
Detection of human forgeries
In the following we report the results of the classification experiments: Modigliani with human-made forgeries in the training set (Tab. 9, top panels of Fig. 8), without forgeries (Tab.10, third row of Fig. 8), Raphael with forgeries (Tab.11, second row of Fig. 8), without forgeries (Tab.12, bottom panels of Fig. 8).
The accuracy of the classification of original paintings is consistently high and fully compatible with the results obtained for van Gogh paintings in the main manuscript.The accuracy of forgery classification on the other hand is lower than that observed for van Gogh in most cases, especially when no human-made forgeries are included in the training set.It is important to note that this is in no way contradicting the conclusions drawn in the main manuscript since, regardless of absolute numbers, these accuracies improve significantly in all considered cases when synthetic forgeries are added to the training data.
Figure 1 .
Figure 1.Illustration of real (top row) and synthetic (bottom row) van Gogh images."SelfPortrait with a Straw Hat", Vincent van Gogh (1887)[2] (square-cropped, top left), "Self-portrait with a Bandaged Ear and Pipe", sold by Otto Wacker, previously attributed to van Gogh[30] (top right), fine-tuned GAN generated image in the style of van Gogh (bottom left), and Stable Diffusion generated image in style of van Gogh (bottom right).
Figure 2 .
Figure 2. Composition of the training and testing sets for the different experiments.Each box in the training represents a training configuration.The configuration names on the bottom row are used throughout the following sections.Green sub-boxes indicate the original set, red indicates the contrast set.
Figure 3 .
Figure 3. Accuracies of different models for originals and forgeries.Based on the results presented in Tables2 and 3with the composition of the underlying van Gogh data set as detailed in Table1and visualised in Fig.2.The horizontal dotted line shows the baseline without synthetic images in the training data.Similar results for the artists Modigliani and Raphael can be found in S1 Appendix.
nt h et ic ra w G A N s tu n ed G A N s d iff u si on d iff .+G A N s accuracy training without forgeries, EfficientNet B0 forgeries original
Figure 4 .
Figure 4. Accuracies of different models for synthetic data.Based on the results shown in Table4with the composition of the underlying van Gogh data set as detailed in Table1and visualised in Fig.2.
Figure 7 .
Figure 7. Illustration of real (top row) and synthetic (bottom row) Raphael images."Madonna with Child" by Raffaello Sanzio [44] (square-cropped, top left), "Portrait of a Young Man in Red" by the Circle of Raphael [45] (top right), fine-tuned GAN generated image in the style of Raffaello (bottom left), and Stable Diffusion generated image in the style of Raffaello (bottom right).
Figure 8 .
Figure 8. Accuracies of different models.Classification results for Modigliani and Raphael based on tables 9 to 12.The horizontal dotted line shows the baseline without synthetic images in the training data.
Table 1 .
Composition of the van Gogh dataset.
Table 2 .
Performance on different tests after training with forgeries.The composition of the underlying van Gogh data set is detailed in Table 1 and visualised in Fig. 2. The best result for each test is highlighted in bold.Values are medians with respective uncertainties in parentheses.
Table 3 .
Performance on different tests after training without forgeries.The composition of the underlying van Gogh data set is detailed in Table1and visualised in Fig.2.The best result for each test is highlighted in bold.
Table 4 .
Accuracy of synthetic forgery detection.The composition of the underlying van Gogh data set is detailed in Table1and visualised in Fig.2.The best result for each test is highlighted in bold.Values are medians with respective uncertainties in parentheses.
Table 6 .
Training data sets.Number of images with resolution at least 256 × 256, and quality of the training results using StyleGAN3.We provide the Fréchet Inception Distance (FID) as a metric for the quality of the generated images (lower is better).
Table 7 .
Composition of the Modigliani dataset.
Table 8 .
Composition of the Raphael dataset.
Table 9 .
Performance for Modigliani on different tests after training with forgeries.
Table 10 .
Performance for Modigliani on different tests after training without forgeries.
Table 11 .
Performance for Raphael on different tests after training with forgeries.
Table 12 .
Performance for Raphael on different tests after training without forgeries. | 8,104.6 | 2023-12-22T00:00:00.000 | [
"Art",
"Computer Science"
] |
Identification of differentially expressed genes in cutaneous squamous cell carcinoma by microarray expression profiling
Background Carcinogenesis is a multi-step process indicated by several genes up- or down-regulated during tumor progression. This study examined and identified differentially expressed genes in cutaneous squamous cell carcinoma (SCC). Results Three different biopsies of 5 immunosuppressed organ-transplanted recipients each normal skin (all were pooled), actinic keratosis (AK) (two were pooled), and invasive SCC and additionally 5 normal skin tissues from immunocompetent patients were analyzed. Thus, total RNA of 15 specimens were used for hybridization with Affymetrix HG-U133A microarray technology containing 22,283 genes. Data analyses were performed by prediction analysis of microarrays using nearest shrunken centroids with the threshold 3.5 and ANOVA analysis was independently performed in order to identify differentially expressed genes (p < 0.05). Verification of 13 up- or down-regulated genes was performed by quantitative real-time reverse transcription (RT)-PCR and genes were additionally confirmed by sequencing. Broad coherent patterns in normal skin vs. AK and SCC were observed for 118 genes. Conclusion The majority of identified differentially expressed genes in cutaneous SCC were previously not described.
Background
Nonmelanoma skin cancer (NMSC), encompassing both basal cell carcinoma (BCC) and squamous cell carcinoma (SCC), is the most common cancer in Caucasians, and over the last decade incidence has been increased dramatically worldwide [1]. Actinic keratosis (AK) is an early stage of SCC and approximately 10% of cases progress to SCC [2][3][4]. Ultraviolet radiation (UV) is the major risk fac-tor for this disease [5,6]. Carcinogenesis is a multi-step process indicated by a series of genes that are up-or downregulated during tumor progression. In normal vs. cancerous colon tissue only 1-1.5% of approximately 30,000 -50,000 functional genes per cell were differentially expressed resulting in 548 genes [7]. A comparable quantity was identified in breast cancer cells exhibiting 700 dysregulated genes [8]. Thus, the number of differentially expressed genes seem to be similar in different cancers. Many genes showing increased expression elevated in colon-cancer represent proteins that are considered to be involved in growth and proliferation while there were often attributed to differentiation in normal tissue. Analyzing skin-or head and neck-cell lines, genes that are associated with extracellular matrix production and apoptosis were disrupted in preneoplastic cells during SCC development, whereas genes that are involved in DNA repair or epidermal growth factors were altered at later stages [9]. Transformation of keratinocytes in response to UV-radiation was examined by microarray technology using normal human epidermal keratinocytes and SCC cell lines [10]. This study detected four clusters of differentially expressed genes in normal keratinocytes vs. skin cancer cells, which may play a role in the carcinogenic pathway. However, cell lines are often different from human tissues that has been demonstrated for both colon cancer [11] and ovarian cancer [12,13]. Thus, human cancer tissues are superior compared with cell lines analyzing differentially expressed genes. So far, only one study examined differentially expressed genes in NMSC tissue using nylon-filter DNA microarrays analyzing approximately 7,400 genes [14].
In the present study, we evaluated the different expression profile of 22,283 genes in normal skin biopsies vs. AK vs. cutaneous SCC. We focused on dysregulated genes best characterizing normal skin and NMSC (comprising both AK and SCC). Overall, 42 genes were up-regulated and 76 genes were down-regulated in skin cancer and the majority of differentially expressed genes were not described earlier.
Relative expression in normal skin and NMSC
Of the 22,283 transcripts and expressed sequence tags (EST) investigated on each oligonucleotide microarray, 118 genes were detected differentially expressed in normal skin, AK, and SCC by Prediction Analysis of Microarrays (PAM) analysis excluding 81 genes (EST and genes with the description "consensus includes...") (see Methods). For each of the 6 normal skins, 4 AK, and 5 SCC (Table 1), the relative expression of each gene was examined. We have controlled the RNA quality of each human specimen analyzing the fragment sizes, and the ratio of 5'and 3'-ends using microarray test-chips with 24 human control genes of 6 randomly selected specimens and only non-degraded mRNA specimens were used in this study.
PAM analysis was used to identify genes to classify and to best characterize normal skin, AK or SCC. The rate of misclassification on the basis of individual cross validation plots was 0% (0.0) for normal skin, 25% (0.25) for AK, 20% (0.20) for SCC, and 13% (0.13) for all three classes. The first gene list contained 200 genes best characterizing normal skin (6), AK (4), and SCC (5). Under the exclusion of EST and genes with the description "consensus includes..." (n = 81) we identified 118 dysregulated genes ( Table 2).
Hierarchical clustering was performed with the identified 118 genes based on similarities of expression levels independently of the assigned class (normal skin, AK or SCC). Gene trees display gene similarities as a dendrogram, a tree-like structure made up of branches. This nested structure forces all genes to be related to a certain level, with larger branches representing the more distantly related genes ( Figure 1). The gene CHI3L1 was detected with two The accession number, the symbol, the description of the genes, their function, their chromosome localization, the change fold, the raw signal (mean value), and the p values of the ANOVA analysis are shown. The accession numbers in bold represent the 42 genes identified by PAM and ANOVA (p < 0.05), which were significantly differentially expressed. The symbols marked in bold represent the genes verified by quantitative real-time RT-PCR. A) Up-regulated genes (42) in non-melanoma skin cancer. B) Down-regulated genes (76) in non -melanoma skin cancer. * significant expression difference verified by quantitative real-time RT-PCR. ** positive with two different affymetrix numbers (209395_at and 209396_s_at). No., numbers; T, Tumor (AK and SCC), N, normal skin; AK, actinic keratosis; SCC, squamous cell carcinoma; n.s., not significant. Cluster map analysis of 118 genes identified by PAM of 15 different specimens resulting in two classes (9 neoplastic skin lesions and 6 normal skin) Figure 1 Cluster map analysis of 118 genes identified by PAM of 15 different specimens resulting in two classes (9 neoplastic skin lesions and 6 normal skin). Prediction Analysis of Microarrays (PAM) using nearest shrunken centroids was performed with 22,283 genes, which were present on the microarray platform (Affymetrix) to identify genes best characterizing normal skin, actinic keratosis (AK), and squamous cell carcinoma (SCC). Hierarchical clustering was performed with 118 genes identified by PAM (CHI3L1 was detected with two independent Affymetrix probes and are included twice, marked with an asterisk). Thirteen genes verified by quantitative real-time RT-PCR are marked in bold. Each color patch represents the normalized expression level of one gene in each group, with a continuum of expression levels from dark blue (lowest) to dark red (highest). The minimal set of informative genes is given by HUGO Gene Nomenclature Committee (HGNC) symbols. Group (1-9) are non-melanoma skin cancer AK (1, 5, 6, and 8), and SCC (2-4, 7, and 9) showing different expression levels compared with six cases of normal skin (10-15). Numbers 6 and 10 were specimens with pooled RNAs. 15) 10 (N-02,08, 10,13,15) 11 (N-17) 12 (N-18) 13 (N-19) different affymetrix numbers and are included twice in the cluster map ( Figure 1). The "Condition Tree" groups samples together based on similar expression profiles by standard correlation with the GeneSpring software 6.1 resulting in two classes. The specimens with the pooled RNA (normal and AK) grouped together with the nonpooled RNA in class 1 (normal skin) and class 2 (AK and SCC) (Figure 1). In class 1, all 6 normal skin specimens grouped together, and class 2 consisted of 4 AK and 5 SCC. Thus, statistical differences in the expression levels of such genes were not detected in carcinoma in situ (AK) vs. invasive cancer (SCC). Furthermore, the pooled normal skin specimens from 5 immunosuppressed patients grouped together with 5 non-pooled normal skin specimens from immunocompetent patients ( Figure 1). Thus, the expression levels of the selected genes were independent of systemic immunosuppression.
ANOVA analysis identified 364 genes including 7 EST, which were significantly differentially expressed between normal skin, AK, and cutaneous SCC (p < 0.05). Using p < 0.15 the gene list contained 2,197 genes including 42 EST. The overall agreement rate of the identified genes by ANOVA using p < 0.05 or p < 0.15 and PAM was 36% (42 of 118) or 78% (92 of 118), respectively. To identify potentially dysregulated genes between AK and SCC, we have performed ANOVA analysis in these two groups (p < 0.05), and no gene was significantly differentially expressed in AK compared with SCC. For further analysis we have used the 118 genes that have been identified by PAM and the 42 significantly differentially expressed genes identified by both methods are highlighted in Table 2.
Verification of selected genes by quantitative real-time RT-PCR
To verify the different expression levels of mRNA measured by microarray technology, we selected 13 up-or down-regulated genes with low through high change folds from the list of differentially expressed genes. These included 9 genes with a higher (change folds by microarray analysis 1.31 ->10) and 4 with a lower expression level (change folds by microarray analysis 1.43 -2.50) in neoplastic skin lesions vs. normal skin ( Table 2). Gene specific intron-flanking primers were designed for 9 upregulated genes (RAB31, MAP4K4, IL-1RN, NMI, IL-4R, GRN, TNC, MMP1, and CDH1) and 4 down-regulated genes (ERCC1, APR-3, CGI-39, and NKEFB) ( Table 3). Unspecific PCR products were not obtained for all genes shown by electrophoresis of the PCR amplicons in agarose gels. Gene-specificity of all 13 genes was confirmed by sequencing of the PCR product of each gene. The results of the real-time RT-PCR were consistent with the microarray data ( Figure 2). All genes showed the predicted expression level either higher or lower in normal skin vs. Gene Forward (5'-3') Reverse (5'-3') APR-3 GGT TCT GAT TTC GTC CCT GA CAG CAT TAG CTC TCG TGT CG CDH1 TGA AGG TGA CAG AGC CTC TGG AT TGG GTG AAT TCG GGC TTG TT CGI-39 CGT CAA AGG TGA AGC AGG AC ATT ATG CTC CAG TGC CCG TA ERCC1 GGG AAT TTG GCG ACG TAA TTC GCG GAG GCT GAG GAA CAG GRN CAG TGG GAA GTA TGG CTG CT TTA GTG AGG AGG TCC GTG GT IL-1RN GGA AGA TGT GCC TGT CCT GT CGC TTG TCC TGC TTT CTG TT IL4R CAC
Discussion
We have examined the expression levels of 22,283 genes in human biopsies of normal skin and cutaneous squamous cell carcinoma (AK, and SCC) by microarray technology. One hundred and eighteen genes were differentially expressed in normal skin vs. skin cancer and fulfilled the criteria used for PAM based cluster map analysis.
Expression profiling using oligonucleotide microarrays is a useful tool to identify tumors, to distinguish different tumor entities, and to differentiate between progressing and non-progressing neoplastic lesions [7,[15][16][17][18]. In this study, we used mRNA from skin biopsies without microdissection resulting in high RNA amounts and subsequently no amplification of the RNA transcripts were required. On the other hand, we cannot avoid a mixture of dysplastic and non-dysplastic cells in our specimens. A mixture of normal epithelial cells and tumor cells are most likely present in cancerous lesions (AK) but are unlikely in normal skin specimens. If the tumor specimen contained normal and dysplastic cells, an increased gene expression in cancer vs. normal skin or vice versa was not detected by microarray analysis. Thus, the number of differentially expressed genes detected in our study represent a subset of all differentially expressed genes in skin cancer and genes showing only low differences are most likely to be unidentified.
The number of differentially expressed genes in normal tissue vs. colon cancer and breast cancer was 548 and 700, respectively [7,8]. In our study, we detected 118 genes excluding EST best characterizing normal skin and epithelial skin cancer. These genes represent approximately 20% of all genes expected to be differentially expressed in skin cancer. So far, only one study examined the expression profile in human biopsies of NMSC and skin cancer cell lines by microarray analyzing approximately 7,400 genes [14]. Although there was only a minimal overlap between human tissue and cell lines, five genes were differentially expressed both in vivo and in vitro, namely fibronectin 1, annexin A5, glyceraldehyde 3-phosphate dehydrogenase, zinkfinger protein 254, and huntingtin-associated protein interacting protein.
Of these genes the calcium and phospholipidbinding protein annexin 5 was over-expressed (ratio 2.1) and annexin 1 showed a slightly over-expression in cutaneous SCC. In our study using another approach annexin 1 was over-expressed in AK and cutaneous SCC (change fold 1.74) showing that 1 of 5 genes (20%) differentially expressed in the study of Dooley and colleagues [14] could be confirmed. Lamin A and C showed a significant higher expression in AK and SCC compared with normal skin analyzed by immunohistochemistry [19], and these genes were also up-regulated in our study. Furthermore, enzymes of the mitochondrial chain namely cytochrome c oxidase, cytochrome b, and NADH dehydrogenase were the majority of down-regulated genes. In prostatic intra-epithelial neoplasia, a high mutation rate of NADH subunits of the respiratory chain complex I was observed similar to lung and head and neck cancer [20]. Delsite and colleagues [21] examined breast cancer cell lines and suggested that a lack of mitochondrial genes leads to increased oxidative stress, reduced DNA repair, and genetic instability. Furthermore, mitochondrial dysfunction leads to an increased production of reactive oxygene species (ROS), inhibition of apoptosis, activation of oncogenes, and inactivation of tumor suppressor genes, and thus is involved during carcinogenesis [22,23]. In our study, the majority of these enzymes was down-regulated in NMSC, indicating that mitochondrial dysfunction is possible associated with cutaneous SCC.
The reliability of the identified 118 genes by microarray technology was verified and confirmed by real-time RT-PCR analyzing 13 genes, and the following discussion is based on these genes. NMSC (CDH1, MAP4K4, IL-1RN, IL-4R, NMI, GRN, RAB31, TNC, and MMP1) CDH1 (E-Cadherin) is a representative of the classic cadherin family and a calcium-dependent cell-cell adhesion glycoprotein, mutations are correlated with a variety of cancers and loss of function may lead to cancer progression and metastasis [24]. In our study we observed an over-expression of CDH1 in skin cancer vs. normal skin, although a lower expression rate was expected. This may be due to a wrongly identified gene, a loss of function due to mutations, a post-transcriptional regulation of this gene or another mechanism in skin cancer vs. other cancers.
genes up-regulated in
MAP4K4 is a representative of the serine/threonine protein kinase family activating MAPK8/c-Jun N-terminal kinase (JNK) [25]. JNK signal transduction pathway participates in the proliferation, differentiation, and apoptosis of osteoblasts and is functionally operative in the malignant transformation of osteoblasts and the subsequent development and progression of human osteosarcomas [26]. IL -1RN (interleukin 1 receptor antagonist), IL-4R (interleukin 4 receptor), NMI (N-Myc and Stat interactor), and GRN (granulin) are genes involved in cell communications. IL-1RN is a representative of the interleukin 1 cytokine family inhibiting the activities of IL-1A and IL-1B, and modulates a variety of interleukin 1 related immune and inflammatory responses [27]. The homozygous genotype IL-1RN*2/2 of the IL-RN gene was strongly associated with early-stage gastric cancer [28]. IL-4R develop allergic reactions, modulate the function of monocytes and macrophages and has been shown overexpressed in a variety of human cancer cells in vitro and in vivo like melanoma, breast, ovarian, renal, and head and neck [29]. NMI interacts with the oncogenes C-myc and Nmyc and other transcription factors containing a ZIP, HLH, or HLH-Zip motif first isolated and characterized by Bao and Zervos [30]. In addition, NMI interacts with all Stats except of Stat2 and augments Stat-mediated transcription in response to cytokines IL-2 and IFN-gamma [31]. A novel pathogenic mechanism of the transcription factor complex NMI, BRCA1 and c-Myc is the activation of telomerase, which is a key enzyme in carcinogenesis [32]. The growth factor GRN stimulates progression and metastasis of breast cancer and is involved in a variety of cancers such as clear cell renal carcinoma, invasive ovarian carcinoma and glioblastoma [33]. In our study all 5 genes showing different functions in tumorigenesis were also over-expressed in skin cancer.
Rab31 represent a family of monomeric GTP-binding proteins and belongs to the Ras family [34,35]. Ras is a protooncogene, which is evolutionary conserved and is involved in various cancers [36], but the precise role of Ras, especially Ha-ras in NMSC is unknown. TNC is an extracellular matrix protein with anti-adhesive effects, and involved in tissue interactions during fetal development and oncogenesis. TNC was associated with breast and lung cancer [37] and was over-expressed in vulvar intraepithelial neoplasia. Matrix metalloproteinases (MMP) are involved in extracellular matrix degradation and cancer invasion [38,39]. Tsukifuji and colleagues [40] reported an over-expression of MMP-1, MMP-2, and MMP-3 in skin cancer (16 Ak, 6 AK with SCC, and 15 SCC). We detected an increased expression rate of MMP-1 and MMP-9 in skin cancer and both genes showed the highest expression rate in AK/SCC indicated by the change-folds of MMP-1 (<10), and MMP-9 (4.70) by microarray analysis. All three genes are considered to be involved in a variety of cancers, they were over-expressed in our study and may play a role in the cancerogenesis of NMSC, and thus are interesting candidates for further studies.
genes down-regulated in NMSC (ERCC1, APR-3, CGI-39, and NKEFB)
ERCC1 has a high homology with the yeast excision repair protein RAD10 [41], is reduced in testis neoplasms [42] and ovarian cancer cell lines [43]. APR-3 is considered to be involved in apoptosis and was identified using subtractive hybridization strategy in order to clone apoptosisrelated genes [44]. NKEFB encodes a representative of the peroxiredoxin (Prx) family of antioxidant enzymes and may play a role in cancer development [45]. Prx II was strongly expressed in mature endothelial cells of benign vascular tumors, whereas it was weakly or not expressed in immature endothelial cells in malignant tumors of Kaposi's sarcoma and angiosarcoma [46]. In our study these genes were also down-regulated in skin cancer, and thus were consistent with the expected expression level observed in other carcinoma.
Conclusion
In conclusion, we identified 42 genes up-regulated and 76 genes down-regulated in cutaneous squamous cell carcinoma (AK and SCC) vs. normal skin, which represent approximately 20% of the genes differentially expressed in skin cancer. The majority of genes which known functions in other cancers was consistent with our results of differentially expressed genes in NMSC. These 118 genes either individually or more likely together or a subset of these genes may prove useful for diagnostic approaches.
Patients
Biopsies were obtained from 5 organ-transplanted (TX) recipients (3 kidney, 1 heart, and 1 liver, 58-73 years, median age 66 years) each normal skin, AK, and SCC. The time since transplantation ranged from 2 through 23 years (median 11 years), and no rejection was observed. All patients had multiple NMSC, such as AK, SCC and/or basal cell carcinoma, and lesions were mainly located on sun-exposed areas. The specimens from TX recipients of 5 normal skin and 2 AK specimens were pooled due to the low RNA amount of the individual specimens that was not sufficient for further microarray analyses. Furthermore, we have included 5 normal skin specimens from age-matched non-immunosuppressed individuals (17-74 years, median age 61 years). Thus, we have analyzed 6 normal skin, 4 AK, and 5 SCC specimens by microarray technology (Table 1). All clinical specimens were collected under standardized conditions by the same clinician (TF). From each organ-transplanted patient, punch biopsies (diameter 4 mm) of normal tissue, AK, and SCC were collected. Half of the tissue was transferred to liquid nitrogen within 2 minutes of resection and stored at -70°C until RNA isolation was performed. The other half of each biopsy was fixed in formalin, embedded in paraffin and sections were stained with hematoxylin and eosin for histological evaluation. All clinical diagnoses, normal skin, AK, and SCC were confirmed by histology.
The same 15 RNA specimens (or representative subsets) were used for quantitative real-time reverse transcription (RT)-PCR of 13 selected genes for verification ( Figure 2
RNA isolation and microarray hybridization
Total RNA was isolated using a modified RNeasy Micro Kit protocol (Qiagen, Hilden, Germany). The modification included the homogenization of the frozen tissue in 300 μl of buffer RLT (Qiagen) with 20 ng Glycogen (Roche, Mannheim, Germany) using a rotar-stator homogenizer "Ultra Turrax T25" (Janke & Kunkel, Staufen, Germany). The homogenized tissue was digested with 10 μl Proteinase K (10 mg ml -1 ) (Roth, Karlsruhe, Germany) at 55°C for 15 min. Subsequently the sample was digested with DNase I (Invitrogen, Karlsruhe, Germany). Quantification of isolated RNA was performed using UV-spectroscopy and the quality was determined both by A 260 /A 280 ratio and Agilent bioanalyzer (Agilent Technologies, Santa Clara, CA, USA). Five microgram total RNA was used for cDNA synthesis with 5 pmol μl -1 T7-oligo(dT) 24 primer and was performed at 43°C for 90 minutes with the "Superscript First-Strand Synthesis-System" for RT-PCR (Invitrogen). Second-strand synthesis was performed with complete cDNA. The cDNA solution was incubated at 16°C for 2 hours followed by an incubation step for 20 min with 6 U T4-DNA polymerase at 16°C and the reaction was stopped using 10 μl of 0.5 M EDTA. The double stranded cDNA was purified by phenol/chloroform, ethanol precipitated and the pellet was resuspended in 12 μl of DEPC water. Labeled cRNA was generated from the cDNA sample by an in vitro transcription reaction that was supplemented with biotin-11-CTP and biotin-16-UTP (Enzo Diagnostics, Farmingdale, NY, USA) according to the manufacturer. The cRNA was quantified by A 260 , and the quality was determined using the labchip bioanalyzer (Agilent). Only cRNA specimens with a high quality were selected for further analyses. Fragmented cRNA (15 μg) was used to prepare 300 μl hybridization cocktail (100 mM MES, 1 M NaCl, 20 mM EDTA, 0.01% Tween-20) containing 0.1 mg ml -1 of herring sperm DNA, and 0.5 mg ml -1 acetylated bovine serum albumine. Control cRNA was used in order to compare hybridization efficiencies between arrays and to standardize the quantification of measured transcript levels and was included as component of the 'Eukaryotic Hybridization Control kit' (Affymetrix, Santa Clara, CA, USA). The cocktails were heated to 95°C for 5 minutes, equilibrated at 45°C for 5 minutes, and clarified by centrifugation. The cocktail was hybridized to HG U133A arrays (Affymetrix) at 45°C for 16 hours. The arrays were washed and stained with a streptavidin-conjugated fluor using the GeneChip fluidics station protocol EukGE-WS2 (Affymetrix) according to the manufacturer's instructions. Arrays were scanned with an argon-ion laser confocal scanner (Hewlett-Packard, Santa Clara, CA) with detection at 570 nm. Data were extracted using Microarray Suite version 5.0 (Affymetrix) and linearly scaled to achieve an average intensity of 2,500 per gene. Text files were exported to determine the intensity of each interrogating oligonucleotide perfect match probe cells or mismatch probe cells. In addition, the ratios of 5'-and 3'-ends of mRNA were analyzed of six randomly selected specimens (two of each group) using microarray test-chips (Test3 Array) containing 24 human housekeeping/maintenance genes (Affymetrix) and RNA degradation was not observed.
Bioinformatic analysis
The Data Mining Tool 3.0 (Affymetrix) and GeneSpring software package 6.1 (Silicon Genetics, Redwood City, CA, USA) were used for different replicates and statistical analyses were performed in order to compare between cancer stages. For each hybridization, the intensities were normalized in three steps, (1) data transformation, (2) per chip, and (3) All processings from raw data, normalized raw data and pdetection values of the microarray experiments to the final tables and figures and a description of the method are provided as supplemental material with the series number GSE2503 [47]. Thus, the entire process of analysis is completely transparent and the description of the methodology used is according to the MIAME standard (minimum information about a microarray experiment).
We used PAM for classification of tumors and identifications of genes that were significantly different expressed between three groups. PAM is a statistical technique for class prediction from gene expression data using nearest shrunken centroids. The technique has advantages in accuracy, especially when more than two classes are considered to be examined [48,49] as it is required for this study. PAM ranks genes using a panelized t-statistic and uses soft-thresholding to identify a gene set for classification. Data analysis was performed with 22,283 genes of all 15 specimens depending on their class (normal skin, AK, or SCC). The number of genes used was controlled by a thresholding parameter, which was determined with a 10fold cross-validation. We used the imputation engine method with the k-nearest neighbor (n = 10), and the threshold 3.5 was chosen to minimize the overall error rate. This cross validation also allows a judgment of the classification quality. For the detailed mathematic procedure, see Tibshirani et al. [48].
In addition, we have independently applied the ANOVA model using two different p-values (p < 0.05 and p < 0.15) to identify dysregulated genes between three groups (normal skin, AK, and SCC) and two groups (AK and SCC) to focus on differences between these two groups. Multiple testing corrections were performed by the false discovery rate of Benjamini and Hochberg for all analyses.
Hierarchical clustering was performed with the genes best characterizing normal skin and NMSC identified by PAM. Genes of all 15 specimens with different expression profiles were grouped by standard correlation with Gene-Spring software package 6.1. Hierarchical clustering of the genes was based on similarities of expression levels.
Quantitative real-time RT-PCR
Real-time RT-PCR with the LightCycler system (Roche) was used as an independent method to validate the microarray expression data and to assess quantitative gene expression. Thirteen genes were selected including 9 upregulated and 4 down-regulated genes in NMSC with low, moderate, and high change folds. In addition, 3 of the 13 genes (MMP1, RAB31, and TNC) were verified with an increased number of different specimens of immunosuppressed and immunocompetent patients (22 normal skin, 11 AK, and 15 SCC) (see Methods section 'Patients'). RT was performed with the "Superscript First-Strand Synthesis-System" (Invitrogen) using oligo-dT as described by the manufacturer. The concentration of cDNA was quantified with "OliGreen ssDNA Quantitation Kit" (Molecular Probes, Leiden, Netherlands). Specific PCR primers for the target genes were designed using the Primer3 software program [50], and synthesized by Metabion (Planegg-Martinsried, Germany). The primers of each gene were located in different exons to exclude DNA contamination. Amplification mix (20 μl) contained 20 ng of cDNA, 500 nM of each primer, 2 μl LightCycler FastStart Reaction Mix Syber Green I (Roche), 3 mM MgCl 2 and sterile double distilled water. The concentration of MgCl 2 varied depending on each specific primer pair between 3-5 mM. PCR reaction was initiated with 10 min denaturation at 95°C followed by 40 cycles (95°C for 10 sec, 60°C for 5 sec, and 72°C for 10 sec). Fluorescence detection was performed immediately at the end of each annealing step and the purity of each amplification product was confirmed by generating melting curves. All specific RT-PCR products of target genes were purified by gel extraction and confirmed by sequencing with gene specific primers (Table 3) using the DNA sequencing kit and the ABI PRISM 310 Genetic Analyzer (Applied Biosystems, Foster City, USA). A negative control without reverse transcriptase was included in each PCR experiment. The expression of RPS9 was used to control equal RNA loading and to normalize relative expression data for all other genes analyzed. The copy ratio of each analyzed cDNA was determined as the mean of two experiments. The U-Test of Wilcoxon, Mann, and Whitney was applied for estimation of differentially expressed transcripts identified by real-time RT-PCR. A pvalue < 0.05 was considered significant for alpha. | 6,437.2 | 2006-08-08T00:00:00.000 | [
"Biology",
"Medicine"
] |
Effect of speckle on APSCI method and Mueller Imaging
The principle of the polarimetric imaging method called APSCI (Adapted Polarization State Contrast Imaging) is to maximize the polarimetric contrast between an object and its background using specific polarization states of illumination and detection. We perform here a comparative study of the APSCI method with existing Classical Mueller Imaging(CMI) associated with polar decomposition in the presence of fully and partially polarized circular Gaussian speckle. The results show a noticeable increase of the Bhattacharyya distance used as our contrast parameter for the APSCI method, especially when the object and background exhibit several polarimetric properties simultaneously.
Introduction
The polarimetric imaging method APSCI [1] has been shown to reach beyond the limit of contrast achievable from the Classical Mueller Imaging (CMI) with polar decomposition [2]. The process utilises a selective polarimetric excitation of the scene in order to provoke a scattering from the object and background characterized by Stokes vectors as far as possible in the Poincaré Sphere [3]. Then along with an optimal polarimetric detection method specifically adapted to each situation, it has been demonstrated that the contrast between an object and its background could be increased to a higher order of magnitude with respect to the contrast from CMI with polar decomposition [1].
We propose here to study the performance of the APSCI method taking into account the shot noise of the detector and the speckle noise in the case of a monochromatic illumination giving rise to an additional circular Gaussian speckle noise, where partial depolarization may occur. Moreover, we consider the numerical propagation of errors in the calculation of the polarimetric data from the acquired raw data. For various situations, where the scene exhibits different polarimetric properties such as dichroism, birefringence or depolarization, we perform a comparative study of contrast level, which is quantified by the Bhattacharyya distance [4] calculated from the significant parameters of the CMI, the polar decomposition and the APSCI method.
Brief review of the APSCI method
Let us assume a scene with a homogeneous circular object surrounded by a homogeneous background. Then, the scene can be modeled into two mutually exclusive regions O and B having polarimetric properties characterized by their Mueller matrices M O and M B , respectively for the object and the background. As the scene is considered to be a priori unknown, we need an initial estimation of Mueller matrices of the object M O and of the background M B by CMI before implementing APSCI method. During the Mueller imaging process, we consider that each pixel of the detector indexed by (u, v) receives an intensity I(u, v) perturbed by a Poisson distribution in order to take into account the shot noise. The Mueller matrix M(u, v) at each pixel is then calculated from the noisy detected intensities I(u, v).
Let us assume a totally polarized Stokes vector S is used to illuminate the scene after CMI.
The estimations of the Stokes vectors of the field scattered by the object S O and background S B can be expressed as : We define the measure of separation of S O and S B in the Poincaré sphere by the Euclidean distance D between their last three parameters. Then, we determine numerically using a simplex search algorithm the specific incident Stokes vector S in that maximizes this Euclidean distance.
It is worthy to emphasize that the Stokes vectors S O and S B are not normalized and can exhibit different rate of depolarization. As a consequence, the maximization of the Euclidean distance mentioned above takes into account two physical entities : the polarization state and the intensity of the polarized part of the scattered field.
Finally, we utilize a Two Channel Imaging (TCI) system that projects the scattered field resulting from the selective excitation S in , into 2 states of polarization S out1 and S out2 , that are defined to maximize respectively ( I O − I B ) and ( I B − I O ), where I O and I B are the evaluations of the mean intensity detected respectively from the object and background scattering. From simple calculation it can be shown that: with The APSCI parameter is then defined for each pixel of the detector indexed by the coordinates (u, v) as : where I 1 (u, v) and I 2 (u, v) are the detected intensity after projection respectively on the 2 states of polarization S out1 and S out2 .
In this study, we use the Bhattacharyya distance as a contrast parameter for each physical quantity under investigation that can be, for comparison purposes, either the APSCI parameter as defined above, either the more pertinent parameters extracted from the polar decomposition of the Mueller matrices of the object and background. A more detailed discussion of the APSCI method is proposed in [1].
Characteristics of the Speckle noise
We have chosen to study an unfavourable situation of imaging regarding both the speckle grain size and its contrast. Thus, we assume a speckle grain with a size similar to that of the pixel of the detector. On the experimental point of view, this situation corresponds to a contrast that is not decreased by the integration of several grains into a single pixel. Moreover, we choose to study the effect of a completely polarized and developed circular Gaussian speckle because it exhibits a strong contrast and so is susceptible to decrease the performance of the APSCI method. As will be pointed out later in this article, biological applications of the APSCI method seem very promising. So, in order to take into account some possible movement of the object, we consider a dynamical speckle: each intensity acquisition is then submitted to a different speckle pattern. The effect of a partially polarized speckle is also of interest regarding the APSCI method because it combines 2 antagonist effects : a decrease of the speckle contrast that increases the Bhattacharyya distance of the APSCI parameter and a lower amount of polarized light usable by the APSCI method for the optimization that, on the contrary, is expected to decrease signal to noise ratio and hence this distance. In our simulations, the speckle is taken into account by a modulation of intensity at the image plane that is considered independent of the state of polarization scattered by the object and background. This modulation of intensity is performed according to the probability density function of intensity p I (I) of a completely developed circular Gaussian speckle that depends on the degree of polarization P [5]: where I is the average intensity.
Results and analysis
We have chosen to study in Fig. 1 the effect of a completely developed circular Gaussian speckle on three different situations where the object and background are defined to have a difference of 10% in one polarimetric property : the cases (a) and (b) exhibit this difference in the scalar birefringence, the cases (c) and (d) in the scalar dichroism and the cases (e) and (f) in the degree of linear polarization. The situations (a), (c) and (e) consider only the shot noise whereas (b), (d) and (f) take into account an additional speckle noise. For each of these situations, we calculate between the object and background region, the Bhattacharyya distance of the AP-SCI parameter and of the other pertinent parameters extracted from the polar decomposition. For comparison purposes, the Bhattacharyya distances are plotted versus the signal to noise ratio (SNR) for a same number of intensity acquisition. We would like to point out that, due to their different dichroism, the energy scattered by the object and background and focalized by imaging elements towards the detector can be different, and hence their corresponding classical SNR's. Thus, we choose to define here a global SNR by considering the shot noise generated by the amount of energy received by the detector without the use of any polarizer and after the back-scattering on a virtual perfectly lambertian and non absorbing object, whose size and position are similar to that of the scene under investigation. In Fig. 1 Secondly, we observe that the parameter B APSCI (blue curve) exhibits the highest Bhattacharyya distances for all the SNR studied in (a) (c) and (e). However, for the case (c), we notice that it exhibits also higher uncertainty bars associated to lower mean values of Bhattacharyya distances compared to cases (a) and (e). This lower performance of the AP-SCI method in the case of dichroism is coming from 2 phenomena : the absorption of energy due to the dichroism effect and the cartesian distance between the matrices of the object and background defined here as the square root of the sum of the square of the element-wise differences. Indeed, as previously discussed in [1], a 10% difference in one polarimetric property between the object and background gives rise to various cartesian distances in function of the scene studied. For cases (a), (c) and (e), the cartesian distances are respectively : 0.44, 0.09 and 0.14. The lowest value corresponds to the dichroism case and explains the lower performance of the APSCI method in that case. When adding the speckle noise, we observe in (b) compared to (a), a strong degradation of all the Bhattacharyya distances under study. APSCI still remains the more pertinent parameter to distinguish the object from the background even if its standard deviation noticeably increases due to the presence of speckle. The effect of the same speckle noise on situation (c) is plotted on (d). We observe that B(M D ) and B(M) fall to very low values even for high SNR and as a consequence become unusable for imaging. As a result, from the raw data of the Mueller matrices M O and M B associated to the polar decomposition, only B(D) reaches an order of magnitude similar to B APSCI . Moreover, we notice that the standard deviation of B APSCI has considerably increased due to the speckle noise. After a deeper analysis, we have observed that M O and M B are particularly poorly estimated for the case of dichroism (for the 2 reasons mentioned above) and that the addition of speckle noise worsen noticeably this situation. As a consequence, selective states of excitation S in spread near all over the Poincaré sphere, showing only a weak increase of density of probability in the theoretical optimum region. We consider now on Fig.1 (e) and (f) the effect of a partially polarized speckle noise with degrees of polarization being respectively P ob j =0.78 and P back =0.71 for the object and background that exhibit a difference of 10% in their ability to depolarize linear polarized light. We observe only a weak decrease of all the Bhattacharyya distances due to the fact that the speckle, only partially polarized, exhibits a lower contrast (C ob j = 0.90 and C back = 0.87) than in previous situations. Moreover, the APSCI parameter gives rise to Bhattacharyya distances much higher than using the CMI alone or associated with the polar decomposition. In all the previous situations, we have studied scenes that exhibit a difference between the object and background in only one polarimetric property. However, in such pure cases, due to the numerical propagation of errors, the interest of using Mueller Imaging can be inappropriate compared to simpler methods such as ellipsometry [6] [7] or polarization difference imaging methods [8] [9]. However, Mueller Imaging can be of great interest in the case of scenes exhibiting several polarimetric properties at the same time.
Thus, in order to examine the performance of APSCI method in such case, we consider a more complex scene where the object and background have 10% difference in scalar birefringence, scalar dichroism and in the linear degree of polarization simultaneously. In Fig. 2, we show the Bhattacharyya distances of the APSCI parameter compared to the best Bhattacharyya distances obtained from the CMI associated to the polar decomposition that is, in this new situation, the Bhattacharyya distance corresponding to scalar dichroism. We observe that both parameters show only a weak decrease of performance (around 5%) due to the speckle noise because it is only partially polarized and exhibits a contrast significantly inferior to 1. Secondly, we see clearly that the Bhattacharyya distances of the APSCI parameter exhibits much higher values than the ones of the scalar dichroism. A visual comparison for a SNR of 3.2 is proposed in Fig. 2 where the object can clearly be seen only using the APSCI parameter because of having 3.8 times higher Bhattacharyya distances compared to the one of the scalar dichroism. We would like to point out that the APSCI parameter of this complex scene exhibits better Bhattacharyya distances than the pure cases of dichroism and depolarization studied separately in Fig. 1. However, inspite of the same amount of birefringence in the situations of Fig. 2 and Fig. 1(a) and that there are additional properties (dichroism and depolarization) in the mixed case which could help us to differentiate the object from the background, the Bhattacharyya distances obtained in the pure case of birefringence are higher than in the mixed case for a given SNR, even if we correct the SNR value by taking into account absorption that occurs in the latter case. This can be explained by the cartesian distances between the object and background matrices which are respectively 0.44 and 0.13 for the pure birefringent and mixed case. It can appear surprising that adding some polarimetric differences between the object and background can reduce the cartesian distance between their Mueller matrices and so our ability to distinguish them. However, we have to keep in mind that most of the elements of a Mueller matrix describe several properties simultaneously and that from a qualitative point of view, the effects of birefringence and dichroism can produce counter-effects that will decrease the maximum distance achievable between the Stokes vector scattered by the object and background. Such observation is true for all kind of polarimetric measurements, however, as the APSCI method doesn't consider each polarimetric property separately, and rather takes into account the whole Mueller matrices, it is expected to give always the best polarimetric contrast achievable for a 2 channel imaging system. Fig. 2. Comparison of Bhattacharyya distances vs. SNR curves for the best performing parameter of CMI (in this case the scalar dichroism) vs APSCI parameter with (ws) and without speckle noise (wos). The scene is composed of an object and a background exhibiting 10% difference in scalar birefringence R, scalar dichroism D and in the linear degree of polarisation DOP L . At the same SNR level of 3.2, the embedded images (i) and (ii) are obtained respectively using the APSCI parameter and the best parameter of the CMI.
Conclusion
We have studied in various situations the effect of a completely or partially polarized and fully developed circular Gaussian speckle in presence of shot noise, on the APSCI method compared to the Classical Mueller Imaging associated to the polar decomposition. In spite of the additional high contrast speckle noise, the use of selective polarization states of illumination and detection in the APSCI method improves noticeably the polarimetric contrast between an object and its background with respect to the one achievable from the Classical Mueller imaging, even when pertinent polarimetric data are extracted by the polar decomposition. Moreover, as APSCI optimizes the polarimetric contrast combining dichroism, birefringence and depolarization properties simultaneously, it exhibits remarkably high performance compared to Classical Mueller Imaging when the object and background exhibit multiple polarimetric behaviour. This previous remark makes this technique very promising for medical applications as biological tissues often exhibit several polarimetric properties simultaneously in presence of dynamical speckle noise. Especially, it can represent a powerful and non invasive technique for accurate detection of displasic areas in case of tumour ablation.
Acknowledgement
We would like to thank the region Midi-Pyrénée for providing us financial support for this work. | 3,703 | 2011-02-28T00:00:00.000 | [
"Physics"
] |
A modified local thermal non-equilibrium model of transient phase-change transpiration cooling for hypersonic thermal protection
Aiming to efficiently simulate the transient process of transpiration cooling with phase change and reveal the convection mechanism between fluid and porous media particles in a continuum scale, a new two-phase mixture model is developed by incorporating the local thermal non-equilibrium effect. Considering the low-pressure and high overload working conditions of hypersonic flying, the heat and mass transfer induced by capillary and inertial body forces are analyzed for sub-cooled, saturated and super-heated states of water coolant under varying saturation pressures. After the validation of the model, transient simulations for different external factors, including spatially-varied heat flux, coolant mass flux, time-dependent external pressure and aircraft acceleration are conducted. The results show that the vapor blockage patterns at the outlet are highly dependent on the injection mass flux value and the exter-nal pressure, and the reduced saturation temperature at low external pressure leads to early boiling off and vapor blockage. The motion of flying has a large influence on the cooling effect, as the inertial force could change the flow pattern of the fluid inside significantly. The comparison of the results from 2-D and 3-D simulations suggests that 3-D simulation shall be conducted for practical application of transpiration cooling, as the thermal protection efficiency may be overestimated by the 2-D results due to the assumption of an infinite width length of the porous plate.
Introduction
During the flight of a hypersonic vehicle, it is subjected to aerodynamic heating from high-speed external flows and high-temperature gases in the engine combustion chamber.A highly efficient thermal protection system is essential to ensure its safe and reliable flying [1,2].Thermal protection can be broadly classified into two categories: passive and active thermal protection.Passive thermal protection relies on materials' heat sink and ablative properties [3] or the use of high-temperature-resistant materials for insulation.Active thermal protection, on the other hand, involves cooling the high-temperature components by absorbing heat through fluid convection or creating gas/liquid films to isolate the high-temperature airflow from the structural components.This category includes methods such as regenerative cooling [4], film cooling [5], and transpiration cooling.The advantages of active thermal protection lie in its robust cooling capability and minimal influence on structural design, but it comes with the complexity of implementing these systems.
Transpiration cooling has been proposed for a few decades, where a coolant passes through a porous wall that undergoes convective heat transfer before injecting out into the high-temperature mainstream flow.This process separates the high-temperature flow from the wall and thickens the boundary layer of the hot mainstream, thereby reducing the amount of heat transferred from the high-temperature mainstream to the solid wall.Theoretically, the maximum cooling capacity can reach up to 1.4 × 10 9 W/m 2 [6].Commonly used materials for the solid wall include layered plates, sintered particle porous materials [7] and sintered wire mesh porous structures [8].When the coolant is a single-phase fluid without phase change within the porous wall, such as using various gases as the coolant, it is referred to as single-phase transpiration cooling, which is the focus of current transpiration cooling technologies [9][10][11][12].When the coolant absorbs heat that undergoes phase change within the porous wall, such as using water as the coolant, it is termed as phase-change transpiration cooling, which performs great potential due to the large phase-change latent heat of the coolant for active thermal protection [13].For numerical simulations of phase-change transpiration cooling, accurately establishing a multiphase heat and mass transfer model is of paramount importance.However, due to the complex multiphase-coupled heat transfer process in the porous media and external flow, there are still many challenges in numerical simulations, such as low and changing pressure in the hypersonic boundary layer, heat exchange in the porous structure between the solid skeletons and the gas/liquid phases, complex motion of aircraft induced body force and 3-D effects of the porous region.
Existing numerical simulation methods can be generally categorized into three approaches: Separate Phase Model (SPM), Semi-Mixed Model (SMM) and Two-Phase Mixture Model (TPMM) [14].The SPM simultaneously computes the governing equations for both liquid and gas phases, allowing for the consideration of two-fluid interactions [15,16].Researchers like Wang [17] and He [18] established SPMs to study the effects of different heat fluxes and coolant mass fluxes on physical quantities such as temperature, pressure and phase saturation in porous media flat plates.Wang et al. [19] employed a SPM to investigate the response of internal gas-liquid phase change to time-varying boundary heat flux and pressure.This kind of model reserves most of the flow information, however, it has higher computation complexity and computing load.To simplify the method, the SMM solves the mass and momentum equations for both fluids, but treats the energy equation as a two-phase mixture.Dong and Wang [20,21] established a SMM and considered modifications to the diffusion coefficient in the fluid energy equation to study the heat transfer deterioration effects caused by local high heat flux.Xin et al. [22] used a SMM to explore the influence of thermal conductivity and porosity of porous media materials on transpiration cooling effects.He et al. [23] employed a transient SMM to investigate the impact of different injection modes and periodic operations.To further reduce the computing load, focusing on only the critical physical quantities, the TPMM solves the governing equations of a single fluid, which represents the constituents of a binary mixture.Shi and Wang [24] established a TPMM in steady and phase change states under constant saturation pressure, considering the influence of various factors, such as particle diameter, porosity and thermal conductivity.Su et al. [25] introduced a modified fluid temperature as the primary variable to solve the TPMM and studied the interaction between supersonic external flow and phase-change transpiration cooling blunt body under steady state and a constant saturation temperature.Liu et al. [26] modified the fluid enthalpy under constant saturation state, and studied the effects of coolant injection mode without gravity.Hu et al. [27] modified the TPMM energy equation considering the change in the saturation temperature in twophase regions, and then investigated the transient effects of phase-change transpiration cooling under low pressure, but assumed the fluid and the solid maintained the same temperature.Cheng et al. [28] utilized the model in [27] to simulate the transpiration cooling effects of porous media with linearly changing porosity and compared it with experimental results.Chen et al. [29] considered variations in cooling properties with temperature and pressure in the TPMM without body forces like gravity, and ignored the influence of saturation temperature on the diffusion coefficient of fluid.
To investigate heat transfer phenomena within porous media at a macroscopic level using the volume-averaging method, the heat transfer model between the solid skeleton and the fluid can be categorized into two main types, known as the Local Thermal Equilibrium (LTE) [30,31] model and the Local Thermal Non-Equilibrium (LTNE) [32,33] model.When using the LTE model, it is assumed that the temperature of the solid skeleton is equal to the temperature of the fluid at the same location.Under this assumption, the heat transfer characteristics within the porous media can be described using a single energy equation.The LTNE model adopts a more realistic representation of heat transfer within porous media, as it accounts for the variations in temperature between the solid skeleton and the fluid.Therefore, it is often used to study convective heat transfer problems.Alomar et al. [34] conducted simulations comparing the gas-liquid phasechange processes within porous media using both LTE and LTNE models.Their findings indicated that the LTNE model provides a more accurate representation of heat transfer effects.The two assumptions can both be applied to the above SPM, SMM and TPMM to establish the heat and mass transfer relationships between the solid and fluid phases.
To take advantage of low computing capacity and low risk of numerical divergence, this work develops a new two-phase mixture model for phase change transpiration cooling by considering the LTNE effect.Based on the convection coefficients between porous media and fluid suggested by [32,33], the governing equations in Ref. [14] are modified into a LTNE form.The primary variable for the fluid energy equation is chosen to be the kinematic enthalpy, as previously proved beneficial for calculation by [26,27].To consider the low-pressure working condition of a hypersonic vehicle, the theoretical equations for the fluid energy in Ref. [14] are established under the sub-cooled state, saturated state and super-heated state, respectively, considering the capillary induced heat and mass transfer under varied saturation pressures and saturation temperatures.In addition, the contributions of the inertial body force to the momentum equation and the mass transfer modeling of the fluid energy equation are considered, as the effect of aircraft overload may be large.Moreover, the iterative update of the kinematic enthalpy is realized by using the relative mobility as a criterion of the fluid saturation state, as it is a good representation of liquid saturation.Then the model is verified by comparing the simulation results with previous experimental and numerical simulation data.This modified model developed based on the previous research can consider more critical factors in the simulation of transpiration cooling.Firstly, the model contains transient terms in every equation, which can provide time-dependent simulation results that are meaningful in applications compared with the steady model.Additionally, the governing equations of the model simultaneously consider local thermal non-equilibrium effects and variations in the boiling point with the saturation pressure.It can simulate the temperature change of the saturated coolant under low-pressure working conditions and temperature non-equilibrium phenomena between the solid medium and the internal fluid.Thirdly, the momentum source and energy source related to the complex variablespeed motion of the aircraft are considered to incorporate their influence to the coolant distribution.Previous models mostly ignored the effect of the body force or only considered the static ground condition.
After the validation of the new model, the transient effects of transpiration cooling under different external influence factors, including time-dependent and spatially-varied external heat flux, different injection mass flux, time-dependent external pressure and aircraft acceleration, are analyzed by comparing the critical properties for thermal protection.Among the selected external factors to be discussed, there is relatively little available information on the influence of the inertial force caused by the acceleration of a porous plate.Finally, the modified model is applied to a 3-D porous plate and the results are compared with the 2-D case.For simplicity, previous studies mostly use 2-D plates; however, the dimension of the model will influence the simulation results of thermal protection under hypersonic operating conditions.
Basic governing equations of the modified model
To develop a new formulation for two-phase flow through capillary porous media that is both physically meaningful and practically useful, Wang and Beckermann [14] converted the separate flow model (SFM) to a multiphase mixture form.
After the mixture density ρ is defined, as in Table 1, the conservation of mass in porous media can be written as: where ε is the porosity of porous media, ρ is the mixture density, and u is the Darcy velocity.
Considering the resistance to flow and gravity of the flow inside porous media, the momentum equation can be written as: where the subscripts l and k represent the variables for liquid phase and kinematic term.p, s l , µ(s l ) , ρ k , K and g represent the mixture pressure, liquid saturation, dynamic (1) viscosity of the mixture, kinematic density, permeability of porous media, and gravity, respectively.
For the conservation of energy, the heat and mass transfer were modeled under the assumption of local thermal equilibrium: where the subscripts f, s, eff and v represent the variables for fluid, solid, average effective value due to porous porosity and vapor phase, respectively.For the enthalpy related to fluid, h f , h k , h v and h l are the specific enthalpy of fluid, kinematic mixture enthalpy, specific enthalpy of vapor and specific enthalpy of liquid, respectively.h s , k eff , T f , j and Q are the specific enthalpy of solid, effective heat transfer coefficient of fluid and solid, temperature of fluid, total mass flux and volume heat source, respectively.The new variables above are defined in [14] and the constitutive relationships are shown in Table 1.
Details of the model modification
In order to conduct the numerical simulation of phase change transpiration cooling under the low-pressure and high acceleration working condition, the above TPMM is modified based on the following assumptions: (1) The saturation temperature of the fluid changes with the mixture pressure when two phases coexist.(2) The temperature of the fluid and the solid at the same location are different, and the convection heat transfer process between them is considered.(3) The liquid phase of the fluid is assumed to be incompressible, while the vapor phase is considered as an ideal gas.(4) The influence of the inertial force on the momentum and energy equations due to the motion of aircraft is considered.(5) The flow inside the porous media is assumed to be at a low velocity laminar condition. (3)
Table 1 Constitutive relationships used in the established model
Variable Formula Relative permeability of liquid phase and vapor phase, Relative mobility of liquid phase and vapor phase, Effective heat transfer coefficient of fluid, Under the above assumptions, considering the transient term and possible acceleration of porous media, the new momentum equation based on (2) can be written as: where, a represents the acceleration of aircraft that causes the inertial force of fluid.
To model the energy equations under the local thermal non-equilibrium assumption, the fluid-to-solid heat transfer coefficients [33] and the specific surface area of porous media based on geometrical considerations [32] are adopted to convert (3) to separate solid energy equation and fluid equation.The solid energy equation can be written as: where, ρ s , c ps , k seff and Qfs are the solid density, solid specific heat capacity, effective solid heat transfer coefficient and convective volume heat source.
The subscript fs means the heat transfer direction is defined as from fluid to solid, where, the subscript sf means the heat transfer direction is defined as from solid to fluid.After eliminating the contribution of solid to the transient term and diffusion term in (3), the fluid energy equation can be written as the following form, which is applicable in every state of the fluid (sub-cooled, saturated and super-heated).
where, k feff is the effective heat transfer coefficient of the fluid.
To implement the numerical simulation, Eq. ( 7) is modified into three forms, which model the fluid energy under the sub-cooled state, the saturated state and the superheated state, respectively.The primary variable for the fluid energy equation is selected as the kinematic enthalpy h k : where, l and 1 − l = v are the relative mobility of the liquid phase and the vapor phase, which represent the relative kinematic viscosity of liquid and vapor to the multiphase mixture, respectively.The detailed constitutive relationship between relative mobility and liquid saturation is in Table 1.
From the second term on the left-hand side of (7), it can be seen that using this variable can maintain the coefficient of the convection term as the mass flow rate ρ u and therefore stabilize the numerical simulation, which had been implemented well in [26,27].
Under the sub-cooled state, the liquid saturation field s l and the relative mobility field l are both the constant value one.Therefore, the mixture density, specific fluid enthalpy and kinematic enthalpy are consequently simplified to variables for the pure liquid phase: where, c pl is the specific heat capacity of water liquid, and T sat,ref is the reference tem- perature of the saturation state.
In addition, when the liquid saturation field is a uniform value one, the total mass flux j on the second term of the right-hand side of (7), including the capillarity-induced dif- fusive flux and the inertial force induced migrating flux, does not have any effect on the mass diffusivity of fluid: where, D(s l ) is the capillary diffusion coefficient, k rv is the relative permeability of vapor, ν v is the kinematic viscosity of vapor.The detailed constitutive relationships are in Table 1.
Therefore, the fluid energy equation under the sub-cooled state can be written as: The convective volume heat source Qsf is modeled by the empirical convective heat transfer coefficient: where, the specific surface area of porous media α sf = 6(1 − ε)/d p .And as suggested in [36,37]: where, d p , k l , Re l and Pr l represent the particle diameter of porous media, the heat trans- fer coefficient, the Reynolds number and the Prandtl number of liquid, respectively.
Under the saturated state, the liquid saturation 0 < s l < 1 and the relative mobil- ity 0 < l < 1 , and the fluid temperature is constrained by the saturation pressure.The relationship between the specific enthalpy of the mixture and the kinematic enthalpy of the mixture can be written as: where, the subscripts sat and fk represent the values under the saturated state and the coefficient transforming the fluid enthalpy to the kinematic enthalpy.h fg (p sat ) is the latent heat under the saturation pressure p sat .
For the implementation of the numerical simulation, the mass diffusion term and the heat diffusion term induced by mass transfer in (7) can be transformed into the (10) diffusion term of the primary variable h k .Considering the contribution of varying satu- ration enthalpy to the liquid saturation field and thermal diffusion, the coefficients used for transformation are calculated as shown in ( 17) and ( 18): Therefore, the fluid energy equation modeled for varying two-phase region temperature can be changed as followed: When the liquid phase and the vapor phase coexist, the volume heat source Qsf is established from the liquid saturation of the mixture [24] and the empirical correlation of surface boiling latent heat [38], and is presented as follows: Under the super-heated state, the liquid saturation field s l and the relative mobility field l are both the constant value zero.Similar to the sub-cooled state, the fluid energy equation under the sub-cooled state can be written as: where, the volume heat source Qsf = h sv α sf (T s − T f ).
Based on the above conservation equations of fluid energy and the constitutive relationships in Table 1, the primary variable h k can be used to represent the critical physi- cal properties under the sub-cooled state, the saturated state and the super-heated state, including the temperature of fluid, the relative mobility of liquid and the liquid saturation.
The relationship between the fluid temperature and the kinematic enthalpy is: The relationship between the relative mobility of liquid and the kinematic enthalpy is: (17) The relationship between the relative mobility of liquid and the liquid saturation is:
Boundary conditions
To solve Eqs. ( 1), (4-24), as explained in Refs.[39,40] with details, the boundary conditions of the physical models are established as follows.
At the inlet boundary Ŵ inlet , the mass flow injection and the heat convection are con- strained as:
Mass flow inlet:
Solid energy:
Fluid energy:
where, ρ c is the density of the inlet coolant, u c is the injection velocity, the convection heat transfer coefficient h c = 0.664Pr c 1 3 Re c 1 2 [41], and h kc is the kinematic enthalpy of the inlet coolant.
At the outlet boundary Ŵ external , the pressure and the heat flux are modeled as follows: Pressure outlet: Solid energy: Fluid energy: where, p external is the external pressure, and qexternal is the heat flux applied by the exter- nal environment.At the wall boundary Ŵ wall , the velocity and the heat flux are modeled as follows: No slip condition: Adiabatic wall for solid and fluid: where, n is the normal vector of the wall boundary.
Solution procedure
The modified LTNE-TPMM is solved under the basic frame of the commercial software ANSYS FLUENT, with the support of User-Defined Memory (UDM) to store the newly defined parameters, User-Defined Scalar (UDS) to implement the newly defined scalar transport equations and User-Defined Functions (UDFs) to establish boundary conditions and update criteria [29].The solution procedure of the numerical method is shown in Fig. 1.After entering a new time step, at the beginning of each iteration, the boundary condition, the relative mobility of liquid, the liquid saturation and the fluid temperature are updated according to the kinematic enthalpy of the last iteration, and the mass and momentum equations are then solved, followed by the fluid and solid energy equations.
After solving all the equations, update the physical properties by the constitutive relationships.At the end of each iteration, check whether the convergence criteria are satisfied.End the overall iteration procedure while reaching the target total simulation time.
For the transient simulation, Pressure-Implicit with Splitting of Operators (PISO) is applied for the pressure-velocity coupling scheme and the second-order upwind scheme is used for the spatial discretization of pressure, momentum, kinematic enthalpy and solid temperature.The time step is adjusted between 0.01 s and 0.1 s, and the number of iterations of each time step is adjusted between 500 and 1000, according to the convergence situation.The convergence criteria are reached when the residual for the energy equations is smaller than 10 -5 .
Model validation
To validate the transient simulation effectiveness of the modified model, simulation is conducted and the results are compared with the experimental results of Wu et al. [42].In this experiment, an alloy of titanium and aluminum was sintered into porous media and heated up under quartz lamps with a heat flux of 500 kW/m 2 .The temperature of the inlet coolant was 293.15K and the mass flow rate was 0.1306 kg/(m 2 •s), (30) corresponding to the 0.5 MPa pressure difference in the experiment.The experimental results indicated that the outer wall temperature, heated directly by the quartz lamp, fluctuates around 373.15 K, demonstrating excellent heat protection performance but with a significant fluctuation range.This was attributed to the rapid increase in the temperature of the solid wall due to the quartz lamp heating, coupled with the heat exchange with liquid water and water vapor causing temperature reduction, resulting in the pronounced fluctuation in the readings of the outer wall thermocouple.For the physical properties in the numerical simulation, the properties of the water coolant used are shown in Table 3.The porosity of the porous media is 0.23 and the particle diameter is 5 μm.From Fig. 2, it can be seen that the numerical method can obtain relatively accurate temperature rising rates and steady temperature levels.
To further validate the transient simulation effectiveness of the modified model, simulation is conducted and the results are compared with the numerical results of Chen et al. [29].Their numerical model had been compared with the steady state experiment 3, the transient value of the liquid saturation at the outlet is in good agreement with that in [29].
Physical models and properties
The physical models used in the following paper are shown in Fig. 4a and b.The water coolant with selected mass flux and temperature is injected from the bottom of the plate and the upper side is exposed to the external environment.The heat flux on the upper surface varies with x coordinates and time.Ŵ inlet , Ŵ external and Ŵ wall stand for the inlet boundary, the outlet boundary and the wall boundary.The 2-D porous plate and the 3-D porous plate have the same dimensions in length and height, while the 3-D model has a finite width of 50 mm compared with the 2-D model.The Start Region and the End Region labeled in Fig. 4 are used for the following result analysis.
Aiming to analyze the transient effect of transpiration cooling under various conditions, including the influence of injection mass flux, external pressure, acceleration and model type, seven numerical cases with different boundary conditions are carried out, as shown in Table 2.For all the cases, the inlet coolant temperature is 300 K, and to represent the flight process during acceleration, the external heat flux distribution decreases with the x coordinate in the form of an inverse proportional function and increases with time.The heat flux reaches a steady value of 1 MW/m 2 after 30 s.In addition, to represent the low-pressure environment of the leading edge of the hypersonic vehicle, the external pressure for Model 1 -Model 3 and Model 5 -Model 7 is selected as 50 kPa, which is largely lower than the standard atmosphere.Three 2D porous plate models (Models 1, 2 and 3) with different mass flux injection are simulated and compared together.Model 4 which is applied with linear decreasing external pressure is discussed with Model 1. Models 1, 5 and 6, which assume that the aircraft has no x-axis direction acceleration, positive x-axis direction acceleration and negative x-axis direction acceleration, respectively, are compared together.The model type of the final model is 3-dimensional, which is simulated to compare with the 2-D plate that has the same boundary conditions.
The physical properties of the inlet water coolant are shown in Table 3.Some critical variables like dynamic viscosity, saturation temperature and latent heat are fitted using proper functions.The selected sintered metal porous medium has the properties shown in Table 4.It has a uniform porosity of 0.3 an average particle diameter of 100 μm.The density of the solid skeleton is 9000 kg/m 3 , the specific heat capacity is 400 J/(kg•K) and the heat transfer coefficient is 30 W/(m•K).
Grid independence test
In order to verify the grid independence of the numerical simulation results, four meshes with the node number 100 × 150, 200 × 250, 400 × 500, and 600 × 750 are generated by the software ICEM CFD.The grids are uniformly refined, with consistent gradients everywhere, gradually becoming denser as the number of nodes along the edges increases.More nodes are arranged along the flow direction of the edges, as shown in Fig. 5.The mass flux of the inlet coolant is 0.5 kg/(m 2 •s) and the coolant temperature is 300 K.The physical properties of the coolant are also provided in Table 3.The external pressure is 1 atm and the applied heat flux is 0.5 MW/m 2 .Their spatial distributions are both uniform.The porous plate with a size of 100 × 20 mm 2 has a heat transfer coefficient of 20 W/(m•K), a porosity of 0.35 and a particle diameter of 500 μm.
The steady state of the four meshes are calculated, and the solid temperature and the liquid saturation at the selected point are plotted.As shown in Fig. 5, the simulation results of the third and fourth meshes are very close.Therefore, the mesh with the node number 400 × 500 will be used for further calculation.For the 3-D physical model, the node number along the flow direction is set as the same with the 2-D model.
The effect of time-dependent and spatially-varied heat flux
Before the result discussion of multiple factors that influence the thermal protection effect of transpiration cooling, the transient effect of Model 1 in Table 2, which is simulated under a time-dependent and spatially-varied heat flux and an injection coolant mass flux of 0.05 kg/(m 2 •s), is analyzed below.As shown in Fig. 6a, the transient change of relative mobility, which represents the liquid saturation, indicates that the phase change takes place first at the start region because of higher heat flux.The liquid at the start region starts to boil at t = 11 s and becomes pure vapor at t = 15 s.At the end region, the liquid saturation begins to increase due to the vapor blockage at the start region that compels more coolant flow to the end region.At t = 30 s, the relative mobility at the end region decreases dramatically because of the step increase of the heat flux.As shown in Fig. 6b, the transient fluid and solid temperature is in consistent with the relative mobility in Fig. 6a.When t = 11 s and t = 17 s, the fluid temperature at the start region and the end region rises to 352 K, which is the saturation temperature of water under a saturation pressure of 50 kPa.The local thermal non-equilibrium phenomenon is obvious between the solid matrix and the fluid inside when the fluid is under a two-phase state.After the fluid becomes pure vapor, the temperature increases rapidly.
To further discuss the distribution of the critical physical properties, the contours of liquid saturation, streamline and fluid temperature are shown in Fig. 7.As shown in Fig. 7a, the start of the phase change will change the flow direction of the coolant, as the kinematic viscosity of water vapor is larger than that of water liquid.Consequently, as shown in Fig. 7c and e, the vapor blockage at the start region will become more severe over time and the fluid temperature will increase as the volume of the liquid phase decreases.In addition, as shown in Fig. 7f, the fluid temperature in the two-phase region is different and it is related to the local saturation pressure.As shown in Fig. 8, with the increase of the mass flux, the solid temperature at the outlet boundary decreases.However, the decline range at different positions is not uniform due to the non-uniform distribution of the liquid coolant.From the results of the velocity distribution, it can be seen that the velocity of water vapor will be much larger than that of water liquid because of much lower density.And the sharp change of velocity can indicate the interface of the liquid phase and the vapor phase.
To analyze the detail of the liquid saturation, flow pattern and solid temperature under different mass fluxes, Fig. 9 shows the contours of them when t = 40 s.As shown in Fig. 9a and b, when the mass flux is 0.55 kg/(m 2 •s), the thermal protection can reach an ideal state, as the coolant maintains the liquid-gas mixture at the outlet without boiling to the pure vapor phase.From Fig. 9c, it can be seen that a second vapor blockage region is formed following the Start Region with the largest heat flux.This phenomenon can be captured under a certain inlet mass flux, when the positions adjoined to the first vapor blockage that has a relatively large heat flux and a relatively large mass flow are more difficult to boil than the rear region that has a relatively low heat flux and a relatively low mass flow.As shown in Fig. 9e and f, when the mass flux is 0.05 kg/(m 2 •s), the thermal protection effect is not desirable.the pressure will decrease the fluid and solid temperature when the fluid is at the twophase region.However, the liquid tends to boil at lower temperature due to the decrease of the overall saturation temperature, which eventually makes the temperature of the solid and the fluid larger after 40 s.
In Fig. 11, the saturation temperature, liquid saturation and streamline contours when t = 35 s under constant and time-dependent external pressure when the injection mass flux is 0.05 kg/(m 2 •s) are shown.As shown in Fig. 11a and c, the saturation temperature is lower when the external pressure is lower, and the distribution is in consistent with the local mixture pressure.As shown in Fig. 11b and d
The acceleration effect
The overload (acceleration) of aircraft can induce an inertial force for the coolant inside the porous media, which will act as a body force to change the velocity pattern.Model 5 and Model 6 in Table 2 have acceleration in opposite directions, and the inertial force induced by them is in the positive and negative direction of the x-axis, respectively.
As shown in Fig. 12a and b, when the inertial force is in the positive direction of the x-axis, the phase change rate of the coolant is increased, while when the inertial force is in the negative direction of the x-axis, the coolant at the start region remains a liquid-gas mixture during the simulation heating process.
In Fig. 13, the contours of pressure, streamline and solid temperature when t = 35 s under different aircraft overload are shown to analyze the influence of inertial forces to the coolant.It can be seen that the change of the flow direction is mainly due to the vapor blockage in Fig. 13a, while the change of the flow direction is mainly due to the inertial force in Fig. 13b and c.The thermal protection effect is therefore dramatically influenced by the motion of aircraft.
The three-dimensional effect on the transient phase-change predictions
In practical engineering applications, the porous plate used is three-dimensional, which means the width of the plate is a finite length.In order to analyze the lateral effect of the transpiration cooling, the following simulation is conducted using a 3-D physical model that has the same length and height with the above 2-D model.The inlet mass flux for both cases is fixed to 0.05 kg/(m 2 •s).
As shown in Fig. 14a, the solid temperature of the 3-D model increases more rapidly during the whole process.The maximum solid temperature is approximately 100 K higher than that of the 2-D simulation results.In addition, the solid temperature of From Fig. 15, it can be seen that the vapor blockage phenomenon is more obvious at the start region under the 3-D model, making more coolant flow through the end region.Therefore, compared with the 2-D simulation results, not all of the coolant boil to pure vapor at t = 40 s.From the above comparison, it can be concluded that the model dimensions have a strong influence on the flow development, especially for the system with finite depth, and therefore change the thermal protection effect.
Conclusions
In this study, a modified model is developed by incorporating the local thermal nonequilibrium effect for transpiration cooling: the governing equations of fluid energy of TPMM are established in a full LTNE form, and the low-pressure and high overload working conditions of hypersonic vehicles are considered by establishing momentum and energy equations under varied saturation pressure, saturation temperature and acceleration conditions.Transient simulations for the effect of external heat flux, injection mass flux, external pressure, aircraft overload and model dimensions are conducted, and the main conclusions are as follows.
(1) The transient simulations of water coolant under time-dependent and spatially-varied heat fluxes suggest that the start of phase change can change the flow distribution of the coolant.Therefore, the vapor blockage at the start region becomes more severe over time, leading to a subsequent rapid increase of the solid temperature.Distributed mass injection should therefore be considered.(2) Increasing the mass flux can obviously reduce the solid temperature, while the decline of temperature at different positions may not be uniform due to the vapor blockage.Moreover, the temperature changing results indicate that when increasing the mass flux to 0.50 kg/(m 2 •s) for the performed case study, the effect of thermal protection is relatively ideal, as the latent heat can be fully utilized.With the reduction of saturation temperature, the vapor blockage becomes more severe at low pressure conditions, leading to further difficulties in thermal protection.(3) The motion of the hypersonic vehicle has a large effect on the cooling process, as the inertial force can significantly change the flow pattern of the fluid inside.A horizontal acceleration e.g., 10 g, can totally change the flow phase distribution of the coolant.Moreover, a 3-D physical model for realistic applications of transpiration cooling is suggested, otherwise the thermal protection efficiency may be overestimated by a 2-D simplification.
Fig. 1
Fig. 1 Flowchart of the numerical solution procedure for the modified LTNE-TPMM of transient phase-change transpiration cooling for active thermal protection
Fig. 2
Fig.2Temperature variations of the top wall using the established model compared with the results of Wu et al.[42]
Fig. 3 Fig. 4
Fig.3The variation of liquid saturation at the outlet using the established model compared with the results of Chen et al.[29]
4. 2
The transient effect of different coolant mass fluxes After discussing the overall transient behavior of the transpiration cooling with phase change, the thermal protection effect of transpiration cooling with different mass fluxes, including 0.05 kg/(m 2 •s), 0.30 kg/(m 2 •s) and 0.50 kg/(m 2 •s) (Models 1, 2 and 3), respectively, are analyzed by comparing the solid temperature distribution at the outlet when t = 40 s.
Fig. 5 Fig. 6
Fig. 5 Comparison of solid temperature and liquid saturation at the selected point obtained by four different meshes
Fig. 7 Fig. 8 Fig. 9 Fig. 10
Fig. 7 Contours of liquid saturation, streamline and fluid temperature under a time-dependent and spatially-varied heat flux when the injection mass flux is 0.05 kg/(m 2 •s) , the case under linear changing external pressure at 35 s has a region at the outlet boundary where the coolant does not change into pure vapor.Model 4 that has the same heat flux distribution with Model 1 results in different final liquid saturation contours because of the time-dependent lowpressure effect.
Fig. 11
Fig. 11 Contours of saturation temperature, liquid saturation and streamline at t = 35 s under constant and time-dependent external pressure when the injection mass flux is 0.05 kg/(m 2 •s)
Fig. 12 Fig. 13
Fig. 12 Transient variations of temperature under different aircraft accelerations when the injection mass flux is 0.05 kg/(m 2 •s)
Fig. 14 Fig. 15
Fig. 14 Comparison of solid temperature of the 2-D and 3-D models under an injection mass flux of 0.05 kg/ (m 2 •s)
Table 3
Physical properties of the coolant used in the numerical simulations
Table 2
Model details for numerical simulation setup in this work
Table 4
Physical properties of the porous plate used in the numerical simulations | 8,715 | 2024-04-12T00:00:00.000 | [
"Engineering",
"Environmental Science",
"Physics"
] |
Blocking Response Surface Designs Incorporating Neighbour Effects
u 1u 2u 3u vu y = f (x , x , x ,..., x ) + eu where u = 1, 2, ..., N, is the level of the , (i = 1, 2, ..., v) factor in the treatment combination, u denotes the response obtained from treatment combination. The function f describes the form in which the response and the input variables are related and u is the random error associated with the observation that is independently and normally distributed with mean zero and common variance iu x th u th i y th u
Introduction
Response Surface Methodology (RSM) is used to explore the relationship between one or more response variable and a set of experimental variables or factors with an objective to optimize the response.
Let there be independent variables denoted by 1 2 v and the response variables be and there are N observations.The response is a function of input factors, i.e. v x , x , ,x y u 1 u 2 u 3 u v u y = f (x , x , x ,..., x ) + e u where u = 1, 2, … , N, is the level of the , (i = 1, 2, … , v) factor in the treatment combination, u denotes the response obtained from treatment combination.The function f describes the form in which the response and the input variables are related and u is the random error associated with the observation that is independently and normally distributed with mean zero and common variance RSM, one may refer to Khuri and Cornell [1], Myers et al. [2].
In the literature, the work on RSM is done assuming observations to be independent and no effect of neighbouring units.However, plots in agricultural experiments are nearby and induce some overlap effects from neighbouring units.Hence, the response from a particular plot may not be the actual response from the plot but may be the joint effect of the treatment combination applied to same plot and the treatment combination applied to the neighbouring plots.For example, in an experimental trial when the combination of pesticides is used, wind drift may cause the effect of spray spill over to adjacent plots.It is thus important to study the response surface in the presence of neighbour effects which would result in more precise estimation of the parameters of the response surface model.
Draper and Guttman [3] suggested a general model for response surface problems in which it is anticipated that the response on a particular plot will be affected by overlap effects from neighbouring plots and the same has been illustrated.Sarika et al. [4] studied second order response surface model with neighbour effects and the rotatability conditions were derived.Methods of obtaining designs satisfying the derived conditions were given.
Jaggi et al. [5] studied response surface model incorporating neighbour effects and the same has been illustrated.They showed that if the neighbour effect is present and is included in the model, there is a substantial reduction in the residual sum of squares and the response is predicted more precisely.
In response surface analysis, it is generally assumed that the experimental trials are carried out under homogeneous conditions.This assumption may not be valid in every experimental situation.In such circumstances, the experimental trials should be carried out in groups, or blocks so that the units within each block are homogeneous.Also when the number of runs is too large, it is very difficult to accommodate all the units in a single e E. VARGHESE, S. JAGGI block.Blocking is usually beneficial where it is possible to identify groups, or blocks, of experimental units, such that within blocks the experimental units are considerably more homogeneous than the blocks themselves.This type of grouping makes it possible to eliminate from error variance a portion of variation attributable to block differences.The variation between the blocks in the experiment is accounted for by including block effects in the statistical model.The nature of the blocking variables has an important impact on the data analysis.
In this paper, we focus on the methodology for blocking in first order response surface model incorporating neighbour effects.The conditions for orthogonally blocked experiments for estimation of the parameters of the model and the conditions for the constancy of variance of the parameter estimates of the model are derived.Construction of response surface designs in blocks with neighbour effects has also been given and an example is discussed.
First Order Response Surface
Methodology with Block Effects and Incorporating Neighbour Effects
Model and Estimation of Parameters
The first order response surface model with block effects can be written in the form where f(x u ) denotes the observed response value at u th experimental run, x iu is the corresponding setting of the i th input variable, δ l denote the effect of the l th block (l = 1, 2, … , b), w lu is a dummy variable taking the value 1 if the u th trial is carried out in the l th block; otherwise, it is equal to zero and e u is the random error.
Incorporating neighbour effects to the given model, the above model with neighbour effects in matrix notation is where , where δ l denotes the effect of the l th block (l = 1, 2, …,b) and W is a block-diagonal matrix of the form , The model given in ( 2) is not of full column rank since the columns of W sum to 1 N .The model therefore can be written as . If the columns of W are linearly independent of those of GX, then model ( 4) is of full rank.Thus β and τ can be uniquely estimated by the method of ordinary least squares.It is not possible to estimate β 0 independent of δ unless certain constrain is imposed on the element of δ.For this purpose we can assume .In this case β 0 is given by b The Equation ( 4) can be written as , where and where, and so on Thus, V´V is obtained as
Conditions for Orthogonality
To ensure orthogonality in the estimation of the parameters , θ V V has to be diagonal.This gives rise to the following conditions: for all blocks of size n.Thus, in view of above conditions, can be written as: Copyright © 2011 SciRes.
OJS
The normal equations for the estimation of (v + b) parameters are are the vector of treatment combination totals and block totals respectively, We thus obtain the variance of parameter estimates as
Conditions for Constancy of the Variances
The constancy of the variances of the parameter estimates is ensured by the following conditions: for all blocks of size n.Therefore, It is thus seen that the variances of i 's (i = 1, 2,…, v) are same and the variance of the estimated response is a function of .For given x , the points for which is same, the estimated response will have the same variance.
Method of Construction
Consider a 2 v full factorial for v factors each at 2 levels and arrange the combinations in lexicographic order.Put all these runs in a single block.The second block can be obtained by circularly rotating the columns of first block once.Similarly, rotating the v columns of 2 v factorial points (v -1) times we get v × 2 v design points in v blocks each of size 2 v .The design so obtained satisfies all the conditions obtained in Section 2. Two extra units are added as border units in each block for neighbour effects.
Illustration
Let v = 2 (X 1 and X 2 ) with each factor at two levels, then we get four runs in full factorial.The four runs constitute the first block and the other block can be obtained by rotating the columns of the first block in a circular fashion.The various matrices are obtained as follows: Block (1 2 ) 1 0 1 (2 1) 1 0 1 Thus, it is seen that the variance of the estimated response at all points is same.
Conclusions
The presence of block effects in a response surface model can affect the estimation of mean response, as well as in determination of the optimum response.Hence, blocking should be done in response surfaces wherever heterogeneity among experimental units is suspected.It has also been shown that incorporating neighbour effect in a model along with block effects results in better estimates of the parameters.The developed methodology and designs can be used to fit the response surfaces with block effects and incorporating neighbour effects.
is the size of the l th block (l =1, 2, … , b) such that .The random error vector e is assumed to have zero mean and a variance-covariance matrix N .
For
neighbour matrix (assuming same neighbour structure in the b blocks) with | 2,074.8 | 2011-10-20T00:00:00.000 | [
"Mathematics"
] |
Free Vibration of a Cantilever Euler-Bernoulli Beam Carrying a Point Mass by Using SEM
: The objective of this research is to study the free vibration of a cantilever Euler - Bernoulli beam carrying a point mass with moment of inertia at the free end using the spectral element method (SEM). Typically, the shape (or interpolation) functions used in the Spectral element method are derived from exact solutions of the governing differential equations of motion in the frequency domain. The beam was discretized by a single spectral element which was connected by a point mass at the free end. The dynamic stiffness matrix of the beam is formulated in frequency domain by considering compatibility conditions at the additional mass position. Then, the first three natural frequencies of the cantilever beam are determined. After the validation of the spectral element method, the influence of the non - dimensional mass parameter and the non - dimensional mass moment of inertia on the first three natural frequencies and shape mode are examined.
INTRODUCTION
Beams structures are used as one of the fundamental structural components in civil and mechanical engineering.Free vibration analysis of beams is of great importance in design and fabrication of structures and machines such as highway bridges, railroads, tall building, wind turbines and huge cranes.
There have been extensive research published in the area about the vibration characteristics of a uniform beam with different boundary conditions and with/without various concentrated elements (such as intermediate point masses, rotary inertias, linear springs, rotational springs, spring-mass systems, etc.).Analytical and numerical methods were used to obtain the natural frequencies and different aspects have been considered [1][2][3][4][5][6][7][8].For the vibration analysis of beams carrying concentrated masses at arbitrary locations, a lot of studies have been published.Hong et.al [9] investigated the transverse vibration of clamped-pinned-free Euler-Bernoulli beam with mass at free end; obtained analytical eigenvalues of the system were compared to experimental data.Natural frequencies and model shapes of a clumped beam with mass at free end have been determined [10].Wang et al. [11] examined the transverse vibration of a cantilever Euler-Bernoulli beam that has a mass with moment of inertia on its free end.Wu and Lin [12] analysed the frequency equation of flexural vibrating cantilever beam with masses attached at multiple points by using an analytical-numerical combined method.They derived the eigenvalue equation analytically by using an expansion theorem and frequencies and mode shapes were calculated numerically.Chang [13] performed the free vibration analysis of a simply supported beam carrying a rigid mass at the middle.Low [14] used both the methods of frequency determinant and the method of Laplace transform to determine the Eigenvalues of a beam with any number of point masses.Naguleswaran [15,16] studied free vibration of an Euler-Bernoulli beam with point masses and negligible inertia moment of the point mass.Gürgöze [17][18][19] has carried out several studies on the frequency equation of flexural vibrating beam carrying a rigid mass.Reference [20] dealt with the determination of the eigenvalues of an Euler-Bernoulli beam with one end spring-mass system attached and the other fixed.
The purpose of this study is to use the spectral element method to establish the dynamic equation of a cantilever Euler-Bernoulli beam with tip mass at the free end.The spectral formulation requires that the equation of motion is solved in the frequency domain and the fast Fourier transform (FFT) is utilized to convert the time domain responses to the wave domain and back.The accuracy and the validation of the proposed approach are confirmed by the comparison with existing results in literature.Finally, the effects of non-dimensional mass parameter and the nondimensional mass moment of inertia on the natural frequencies and shape mode are investigated.
MATHEMATICAL MODEL AND FORMULATIONS
Consider a cantilever beam with an additional mass M0 having a moment of inertia 0 at the free end of length L as shown in Fig. 1.The beam has flexural stiffness and mass per unit length M. Based on the Euler-Bernoulli beam theory, the governing equation of motion can be written: The solution of Eq. ( 1) can be assumed in the spectral form as: Where w(x, t) is the transverse displacement, E is Young's modulus, I is the area moment of inertia about the neutral axis.Inserting Eq. ( 2) into Eq.( 1) and after rearrangement, the following equation is derived: In which , and is the circular frequency.
Then the solution of Eq. ( 3) can be written as: Writing displacements and rotations at nodes: The nodal displacement and slope at both ends can be expressed as: Where { } { } Corresponding to the general problem Fig. 1, the vector of forces at the ends of the beam can be established by using boundary conditions of the structural system, which are: In matrix form, the forces at the ends of beam are The relationship between nodal force and degree of freedom vectors is expressed by Where [F][D] -1 is the spectral stiffness matrix of Euler-Bernoulli beam with mass M attached at end (x = L).
NUMERIC APPLICATIONS
The applications reported in this section are provided by applying the proposed approach on a cantilever beam with a mass attached at the free end with the following nondimensional parameters; βM, β J , and λ denoting the nondimensional mass parameter , non-dimensional rotary mass moment of inertia and non-dimensional natural frequencies of the beam, respectively.
To check the numerical model, the first three eigenvalues for the cantilever beam are determined by finding the nontrivial solutions of the determinant in Eq. ( 9).Computer programs based on SEM have been developed in MATLAB software to calculate numerical results.
In order to check the effectiveness of the proposed method, the first three dimensionless frequencies of a cantilever beam carrying a tip mass beam are shown in Tab. 1.Without considering the moment of inertia of the attached mass, it is clear from Tab. 1 that the obtained values are in good agreement with those obtained by Rao [1] and Gürgöze [16].
Table 1 The effect of the variation of β M and β J on the first three dimensionless frequencies λ of cantilever beam carrying a tip mass is presented in Fig.
Moreover, the first three transverse mode shapes of the cantilever beam carrying a point mass with moment of inertia are illustrated in Fig. 3 for different values of β M and β J .As seen in this Fig. 3, β M and β J effects on fundamental mode shapes are significantly observed .Note that β M have great effects on higher mode shapes.
CONCLUSION
This paper presents the free vibration analysis of a cantilever beam with a rigid body exciting flexural vibration using SEM.The spectral stiffness matrix of the problem was derived and the first three eigenvalues are determined.For special cases results compared with existing results in literature and very good agreement was achieved.The proposed approach yields high accuracy and rapid convergence.Also, the effect of non-dimensional mass parameter and non-dimensional mass moment of inertia on the dimensionless frequency parameter and mode shapes of the system was investigated.The results show that the values of non-dimensional mass parameter and non-dimensional rotary mass moment of inertia had significant effects on the on the dimensionless frequency parameter and mode shapes of the cantilever beam with attached mass at the free end.
Figure 1
Figure 1 Schematic of a cantilever beam with an additional mass at free end | 1,708 | 2022-09-26T00:00:00.000 | [
"Engineering"
] |
590 nm LED Irradiation Improved Erythema through Inhibiting Angiogenesis of Human Microvascular Endothelial Cells and Ameliorated Pigmentation in Melasma
Melasma is a common refractory acquired pigmentary skin disease that mainly affects middle-aged women. The pathogenesis of melasma is still uncertain, while abnormal vascular endothelial cells may play a role. We previously demonstrated the yellow light of light-emitting diodes (LED) could inhibit melanogenesis through the photobiomodulation (PBM) of melanocytes and keratinocytes. In the current study, we investigated the effect of 590 nm LED on the function of human microvascular endothelial cells (HMEC-1). We revealed 0–40 J/cm2 590 nm LED had no toxic effect on HMEC-1 in vitro. 590 nm LED irradiation significantly reduced cell migration, tube formation, as well as the expression of vascular endothelial growth factor (VEGF) and stem cell factor (SCF), a pro-melanogenic factor. Moreover, we illustrated that 590 nm LED inhibited the phosphorylation of the AKT/PI3K/mTOR signaling pathway, and the inhibitory effect on HMEC-1 could be partially reversed by insulin-like growth factor 1 (IGF-1), an AKT/PI3K/mTOR pathway agonist. Besides, we conducted a pilot clinical study and observed a marked improvement on facial erythema and pigmentation in melasma patients after amber LED phototherapy. Taken together, 590 nm LED inhibited HMEC-1 migration, tube formation and the secretion of VEGF and SCF, predominantly through the inhibition of the AKT/PI3K/mTOR pathway, which may serve as a novel therapeutic option for melasma.
Introduction
Melasma is a common acquired hyperpigmentation skin disease with the clinical manifestation of symmetrical and irregular brown pigmentary macules or patches on the face. The pathogenesis of melasma remains unknown. Previous studies have shown that vascularization might be involved in the development of melasma [1].
Immunohistochemistry evaluation has demonstrated that, compared with perilesional normal skin, the melasma lesion has increased numbers of enlarged blood vessels and higher vascular endothelial growth factor (VEGF) expression, with a positive correlation between the number of vessels and pigmentation [2]. In a total of 100 benign vascular skin lesions, high-magnification digital dermatoscopy revealed a mild to marked hyperpigmentation in 89% cases and marked hyperpigmentation in 22% cases within and surrounding the vascular lesions [3]. At the cellular level, the proliferation of endothelial cells (ECs), which are found in every vascular bed and produce autocrine and paracrine molecules to regulate cell adhesion, as well as vessel permeability, also participate in the modulation of melanogenesis [4]. Regazzetti [3] showed that endothelin 1 (ET-1) released by microvascular endothelial cells increased melanogenesis signaling through the activation of endothelin receptor B and the mitogen-activated protein kinase (MAPK) pathway via
590 nm LED Irradiation and Signaling Pathway Agonist Pretreatment
HMEC-1 cells were seeded in 6-well or 96-well plates (Corning), depending on subsequent experiments, for 24 h to ensure cell adhesion. 50 ng/mL insulin-like growth factor 1 (IGF-1) (Peprotech, Rocky Hill, NJ, USA) was added 2 h before 590 nm LED irradiation, if necessary. After washing cells once with Phosphate-buffered solution (PBS) (Biosharp, Shanghai, China), the endothelial cell medium was replaced by Dulbecco's modified eagle medium (DMEM) without phenol red (Solarbio Science&Technology, Beijing, China). The LED device (590 ± 10 nm, continuous emission mode, 35 mW/cm 2 ) used in this study was provided by Xuzhou Kernel Medical Equipment Co., Ltd., Xuzhou, Jiangsu, China. The formula W = P × t was used to compute the irradiation time.
Cell Viability Assay
Cells at a density of 1 × 10 4 were plated into 96-well plates with three duplicates at each irradiation fluence. 10 µL CCK-8 solution (Biodragon immunotechnologies, Beijing, China) was added 12 h, 24 h and 48 h after 590 nm LED irradiation, and the absorption at 450 nm was measured with a spectrophotometer (Thermo, Waltham, MA, USA). Cell viability was calculated, and replicate experiments were performed using cells of diverse passages.
Flow Cytometry Analysis
HMEC-1 cells were grown in 6-well plates at a density of 5 × 10 5 and irradiated by different dosages of 590 nm LED. After 24 h, cells were isolated with 0.25% trypsin without EDTA (Gibco, Grand Island, NY, USA), centrifuged, resuspended with 4 • C PBS. Subsequently, irradiated cells were washed, stained with Annexin-V FITC & PI (BD Biosciences; San Jose, CA, USA), measured with a C6 flow cytometer (BD) and analyzed using FlowJo (BD). For reactive oxygen species (ROS) measurement, gathered cells were resuspended in serum-free medium containing DCFH-DA (1:1000, Biodragon immunotechnologies), kept at 37 • C for 20 min, washed and detected by flow cytometry.
Wound Healing Assay
The scratch wound assay has been the most common method to measure cell migratory capacity in vitro. Cells at a density of 5 × 10 5 in the logarithmic growth phase were seeded in 6-well plates with three equidistant horizontal lines on the bottom and incubated to 100% confluence. Three equispaced vertical lines were scratched perpendicular to the marked lines at the bottom with 200 µL pipette tips (Axygen, Tewksbury, MA, USA), then exfoliated cells were rinsed with PBS. After 590 nm LED irradiation, cells were cultured in serum-free medium and were photographed at the same position using an inverted microscope (Nikon, Tokyo, Japan) at 0 h, 24 h, and 48 h. The scratch area and cell migration rate were calculated using Image J (NIH, Bethesda, MD, USA).
Tube Formation Assay
A pre-chilled 96-well plate was coated with Matrigel matrix (Corning) and incubated at 37 • C for 30 min to allow the Matrigel solution to solidify. After LED irradiation, the cells were collected and plated into the pre-coated 96-well plate at a density of 5 × 10 4 . Eight hours later, brightfield photos were taken under a 200× inverted microscope, and the number of meshes were measured by Image J. Three independent experiments were performed for each fluence.
Real-Time Quantitative Polymerase Chain Reaction (RT-qPCR)
For total RNA isolation, Trizol (Invitrogen, Carlsbad, CA, USA), chloroform (China sinopharm, Shanghai, China) and isopropanol (Sangon biotech, Shanghai, China) were added into irradiated cells, subsequently followed by 75% ethanol (China sinopharm) rinsing. The reverse transcription reaction system was performed according to the manufacturer's protocol of the PrimeScript RT Master Mix kit (Takara, Tokyo, Japan). The synthesized cDNA samples were amplified and detected in the RT-qPCR system under the instruction of TB Green Premix Ex Taq II kit (Takara) in QuantStudio 6 (Thermo) (Tables S1-S5, RT-qPCR protocol).
Enzyme-Linked Immunosorbent Assay (ELISA)
According to the manufacturer's instructions of the human VEGF and SCF ELISA kit from Multisciences Biotech, Hangzhou, Zhejiang, China, standard vials were dissolved and doubly diluted for the standard curve. The obtained supernatant of irradiated cells was centrifuged, added into plates, and incubated with antigens, horseradish peroxidase (HRP)-avidin and TMB substrate. The absorption at wavelengths of 450 nm and 630 nm was measured, and the concentration of the samples was calculated according to the standard curve and dilution multiple.
Comet Assay
The condition of deoxyribonucleic acid (DNA) damage after irradiation was detected using the comet assay kit (Nanjing Jiancheng Bioengineering Institute, Nanjing, Jiangsu, China). HMEC-1 in 6-well plates was irradiated, isolated, centrifugated, and resuspended in PBS. Agarose slides were prepared by the first layer of 100 uL 0.5% normal-melting agarose (NMA), the second layer of 75 uL 0.7% low-melting agarose (LMA) mixing with 10 µL cell suspension and the third layer of 75 uL LMA. After cells lysis, DNA was unwound in alkaline buffer and determined by electrophoresis, neutralization and PI staining. Fluorescence photographs taken were analyzed by Image J. DNA damage was classified into five grades based on tailDNA percent according to manufacturer's instruction.
590 nm LED Phototherapy
The clinical research was approved by the Ethics Committee of Huashan Hospital, Fudan University (protocol code: KY2019-515), and informed consent was obtained from all participants. A total of ten patients with mild to severe melasma were treated with the amber light LED device (product code: KN-7000D, wavelength: 585 ± 10 nm, power density: 20 mW/cm 2 , irradiation area: 850 cm 2 ± 10%, donated by Xuzhou Kernel Medical Equipment Co.). Each patient was irradiated with 20 J/cm 2 LED, approximately 1000 s, once a week for eight consecutive sessions. Follow-up was performed every four weeks during the course, one month and three months after the end of treatment. Images were taken using the VISIA Complexion Analysis System (Canfield Scientific Co., Parsippany, NJ, USA); the melanin index (MI) and erythema index (EI) were recorded using the Mexameter dermaspectrophotometer (Cortex Technology, Hadsaund, Denmark) as well. The melasma area severity index (MASI) [14] was conducted by two dermatologists independently, according to the formula. All reported adverse effects were recorded.
Statistical Analysis
GraphPad Prism 6 (GraphPad Software, La Jolla, CA, USA) or SPSS Statistics 26.0 (IBM, Armonk, NY, USA) were used to perform statistical analysis on collected data. One-way ANOVA or paired t-tests were used for the statistical analysis in appropriate quantitative data. Otherwise, the Wilcoxon test was conducted for the nonparametric test. p < 0.05 was considered statistically significant.
Effects of 590 nm LED on Cell Viability of HMEC-1
To explore the influence of 590 nm LED on the cell viability of HMEC-1, a CCK-8 assay was performed 12 h, 24 h and 48 h after 0-50 J/cm 2 LED irradiation. The results show that cell viability did not change significantly after 0-50 J/cm 2 LED irradiation (p > 0.05), as shown in Figure 1A. In terms of cell apoptosis, flow cytometry with Annexin-V FITC & PI staining was conducted 24 h after LED irradiation and revealed no statistical difference among fluences of 0 to 40 J/cm 2 , whereas 50 J/cm 2 LED irradiation increased the cell apoptosis rate by 53.9 % (p = 0.035), as shown in Figure 1B. Therefore, we determined to evaluate cell function with the irradiation fluences of 0-40 J/cm 2 in subsequent experiments.
590 nm LED Inhibited Migration of HMEC-1
The process of angiogenesis depends on the proliferation and migration of ECs. To learn more about the influence of 590 nm LED on the cell migration of HMEC-1, we applied wound healing assay to detect cell mobility 48 h after 0-40 J/cm 2 LED irradiation (Figure 2A-E). The migration rate of cells which were irradiated by 20 J/cm 2 LED decreased from 21.3 % ± 2.041 to 10.3 % ± 2.039 (p = 0.005). Moreover, the cell migration rate reduced to 15.0 % ± 1.045 (p = 0.044) after 40 J/cm 2 LED exposure, as shown in Figure 2F.
590 nm LED Inhibited Migration of HMEC-1
The process of angiogenesis depends on the proliferation and migra learn more about the influence of 590 nm LED on the cell migration of H plied wound healing assay to detect cell mobility 48 h after 0-40 J/cm 2 L (Figure 2A to 2E). The migration rate of cells which were irradiated by 20 creased from 21.3 % ± 2.041 to 10.3 % ± 2.039 (p = 0.005). Moreover, the cel reduced to 15.0 % ± 1.045 (p = 0.044) after 40 J/cm 2 LED exposure, as show
590 nm LED Suppressed Tube Formation of HMEC-1
An EC tube formation assay could be used to measure angiogenesis in vitro in a fast, reproducible and quantifiable manner [15]. To observe the tube-forming ability of HMEC-1 irradiated by 590 nm LED, we performed a tube formation experiment to simulate capillary angiogenesis. Our results show that the number of meshes declined markedly after irradiation (0.621 ± 0.112-fold of control, p = 0.028 at 10 J/cm 2 ; 0.314 ± 0.164-fold of control, p = 0.019 at 20 J/cm 2 ; 0.308 ± 0.188-fold of control, p = 0.024 at 30 J/cm 2 ; 0.422 ± 0.075-fold of control, p = 0.006 at 40 J/cm 2 ), indicating PBM inhibited the tube formation of ECs in vitro, especially at the fluences of 20-40 J/cm 2 ( Figure 3).
590 nm LED Reduced Release of VEGF and SCF
Altered angiogenesis and melanogenesis are frequently found in melasma patients. We thus explored the expression of angiogenesis-related and melanogenesis-related factors after 590 nm LED treatment. Indeed, LED irradiation at a 590 nm wavelength reduced the levels of VEGF and SCF in HMEC-1. As shown in Figure 4B and 4D, the inhibitory impact was not completely dose-dependent but was the most obvious at the dose of 20 J/cm 2 (VEGF 0.708 ± 0.081-fold of control, p = 0.025; SCF 0.673 ± 0.182-fold of control, p = 0.016). By contrast, the mRNA and protein expression of ET-1, as well as TGF-β1, remained unchanged after LED irradiation (p > 0.05) ( Figure S1).
590 nm LED Reduced Release of VEGF and SCF
Altered angiogenesis and melanogenesis are frequently found in melasma patients. We thus explored the expression of angiogenesis-related and melanogenesis-related factors after 590 nm LED treatment. Indeed, LED irradiation at a 590 nm wavelength reduced the levels of VEGF and SCF in HMEC-1. As shown in Figure 4B,D, the inhibitory impact was not completely dose-dependent but was the most obvious at the dose of 20 J/cm 2 (VEGF 0.708 ± 0.081-fold of control, p = 0.025; SCF 0.673 ± 0.182-fold of control, p = 0.016). By contrast, the mRNA and protein expression of ET-1, as well as TGF-β1, remained unchanged after LED irradiation (p > 0.05) ( Figure S1).
590 nm LED Reduced Release of VEGF and SCF
Altered angiogenesis and melanogenesis are frequently found in melasma patients. We thus explored the expression of angiogenesis-related and melanogenesis-related factors after 590 nm LED treatment. Indeed, LED irradiation at a 590 nm wavelength reduced the levels of VEGF and SCF in HMEC-1. As shown in Figure 4B and 4D, the inhibitory impact was not completely dose-dependent but was the most obvious at the dose of 20 J/cm 2 (VEGF 0.708 ± 0.081-fold of control, p = 0.025; SCF 0.673 ± 0.182-fold of control, p = 0.016). By contrast, the mRNA and protein expression of ET-1, as well as TGF-β1, remained unchanged after LED irradiation (p > 0.05) ( Figure S1).
590 nm LED Inhibited Angiogenesis Predominantly via AKT/PI3K/mTOR Pathway
To illustrate the underlying mechanism of 590 nm LED on the biological function of HMEC-1, the phosphorylation level of the AKT/PI3K/mTOR pathway was measured after irradiation. The results show that 590 nm LED significantly inhibited the AKT/PI3K/mTOR pathway, which could be reversed by a 50 ng/mL AKT pathway agonist IGF-1 pretreatment without an effect on cell activity ( Figure 5A-G). Furthermore, IGF-1 could attenuate the inhibitory effect of 590 nm LED on the cell migration and tube formation of HMEC-1 ( Figure 5H,I). The suppression of 20 J/cm 2 LED on the release of VEGF from HMEC-1 cells was also reversed by IGF-1 pretreatment. Conversely, IGF-1 addition diminished the expression of SCF secretion, suggesting that the inhibition effect of 590 nm LED was unrelated to the downregulation of the AKT/PI3K/mTOR pathway ( Figure 5J). Taken together, 590 nm LED inhibited the angiogenesis of HMEC-1 predominantly through the AKT/PI3K/mTOR pathway.
590 nm LED Ameliorated Pigmentation and Facial Erythema in Melasma
In order to explore the potential therapeutic effect of 590 nm LED on melasma, we further conducted a single-center pilot clinical observation. A total of ten patients Studies revealed that AKT could be destroyed by the ubiquitin-mediated protein degradation pathway, and cellular ROS could increase Mitochondrial E3 ubiquitin protein ligase 1 (MUL1) expression, a negative regulator of AKT ubiquitination [16]. Therefore, we detected the ROS level in irradiated cells to explore the potential mechanism of AKT pathway downregulation, and the results show no statistical difference between the control group and illuminated groups, as shown in Figure S2A,B.
To monitor the safety of LED treatment, DNA damage in HMEC-1 was evaluated by comet assay. No obvious comet phenomenon was observed, and the tailDNA percent remained unchanged after LED exposure ( Figure S2C,D).
590 nm LED Ameliorated Pigmentation and Facial Erythema in Melasma
In order to explore the potential therapeutic effect of 590 nm LED on melasma, we further conducted a single-center pilot clinical observation. A total of ten patients diagnosed with mild to severe melasma were enrolled and treated with 590 nm LED phototherapy with a 20 J/cm 2 dosage, once a week, for eight weeks consecutively. The subject characteristics are shown in Table S6. Clinical images indicated a visible improvement in both facial erythema and hyperpigmentation ( Figure 6A,B). When it comes to objective assessment, the mean MASI score significantly decreased from 17.020 ± 8.140 to 13.050 ± 6.963 in week eight (p < 0.001), with a 23.3 % improvement, as shown in Figure 6C. Meanwhile, the EI and MI of these patients were significantly decreased compared with the baseline in week eight (EI 419.500 ± 57.770 to 367.700 ± 60.470, p = 0.003; MI 300.500 ± 76.400 to 258.900 ± 58.720, p = 0.035; Figure 6D,E). To be noted, no participants reported worsened symptoms or a severe adverse reaction during the whole treatment. Collectively, these results tentatively verify the efficacy and safety of 590 nm LED phototherapy to ameliorate the hyperpigmentation and facial erythema in melasma patients. Table S6. Clinical images indicated a visible improvement in both facial erythema and hyperpigmentation ( Figure 6A and 6B). When it comes to objective assessment, the mean MASI score significantly decreased from 17.020 ± 8.140 to 13.050 ± 6.963 in week eight (p < 0.001), with a 23.3 % improvement, as shown in Figure 6C. Meanwhile, the EI and MI of these patients were significantly decreased compared with the baseline in week eight (EI 419.500 ± 57.770 to 367.700 ± 60.470, p = 0.003; MI 300.500 ± 76.400 to 258.900 ± 58.720, p = 0.035; Fig 6D and 6E). To be noted, no participants reported worsened symptoms or a severe adverse reaction during the whole treatment. Collectively, these results tentatively verify the efficacy and safety of 590 nm LED phototherapy to ameliorate the hyperpigmentation and facial erythema in melasma patients.
Discussion
Light-emitting diode treatment is an emerging non-thermal light therapy modality. We previously uncovered that yellow-light LED decreased melanin synthesis through the direct regulation of melanocytes, as well as the indirect effect on keratinocytes [10,11]. Although it was clinically observed that LED phototherapy might improve the erythema
Discussion
Light-emitting diode treatment is an emerging non-thermal light therapy modality. We previously uncovered that yellow-light LED decreased melanin synthesis through the direct regulation of melanocytes, as well as the indirect effect on keratinocytes [10,11]. Although it was clinically observed that LED phototherapy might improve the erythema and pigmentation of melasma, clinical trials and underlying mechanism research are still missing. To this end, we initiated this study and revealed that 590 nm LED inhibited cell migration, tube formation, as well as the synthesis and secretion of VEGF and SCF in HMEC-1, partially via downregulating the AKT/PI3K/mTOR signaling pathway. Therefore, we concluded that, besides the effects of PBM on melanocytes and keratinocytes, 590 nm LED inhibited angiogenesis through the suppression of microvascular endothelial cells via the AKT/PI3K/mTOR pathway and reduced the release of SCF, which might serve as a new strategy for treating melasma from three aspects (Figure 7). Therefore, we concluded that, besides the effects of PBM on melanocytes and keratino cytes, 590 nm LED inhibited angiogenesis through the suppression of microvascular en dothelial cells via the AKT/PI3K/mTOR pathway and reduced the release of SCF, whic might serve as a new strategy for treating melasma from three aspects (Figure 7). The primary chromophore of PBM is the electron transport chain located in the m tochondrial membrane; in particular, the enzyme cytochrome c oxidase (CCO), opsin flavins, flavoproteins and porphyrins also play a role [17−19]. The number of mitochon dria in cells and tissues varies widely to correlate with the metabolic requirement, an cells with higher numbers of mitochondria respond better to PBM than cells with lowe numbers of mitochondria [20]. Studies on various wavelengths and different therapeut dosages of PBM's effects on fibroblasts and skin tissue, possessing fewer mitochondri have been reported, whereas the effect of 590 nm LED on vascular endothelial cells r The primary chromophore of PBM is the electron transport chain located in the mitochondrial membrane; in particular, the enzyme cytochrome c oxidase (CCO), opsin 3, flavins, flavoproteins and porphyrins also play a role [17][18][19]. The number of mitochondria in cells and tissues varies widely to correlate with the metabolic requirement, and cells with higher numbers of mitochondria respond better to PBM than cells with lower numbers of mitochondria [20]. Studies on various wavelengths and different therapeutic dosages of PBM's effects on fibroblasts and skin tissue, possessing fewer mitochondria, have been reported, whereas the effect of 590 nm LED on vascular endothelial cells remains unclear.
Generally, a longer wavelength penetrates the dermis to a greater extent than shorter wavelengths [21]. The Roscoe-Bunsen law of reciprocity expounds that the most important parameter of PBM, the power density (irradiance) measured in mW/cm 2 and the energy density (fluence) measured in J/cm 2 , is the total quantity of photons absorbed by the target cells, which is a fundamental concept of LLLT [20,22]. In this study, we used a 590 nm LED irradiation equipment with 35 mW/cm 2 irradiance for in vitro experiment and a yellow LED device with a power density of 20 mW/cm 2 for clinical observation. In regard to the energy density used in the clinical trial, we chose the dose of 20 J/cm 2 according to the non-toxic irradiation dose in a prior keratinocyte experiment [11]. The effect of mode of light delivery in PBM remains controversial [23], but the continuous wave mode was used in our study due to the function of the experimental irradiator, and we will explore further the differences between continuous and pulsed emission modes.
When it comes to the LED modulation of HMEC-1, the Arndt-Schultz law, proposed near the end of the 19th century, states in its original form that "For every substance, small doses stimulate, moderate doses inhibit, and large doses kill", which has been used as another convenient concept to explain the cellular and tissue interactions with light [20]. Indeed, cell viability detected by the CCK-8 assay was not altered significantly after 0-50 J/cm 2 LED irradiation, which is consistent with the safe and mild efficacy of 590 nm LED phototherapy observed in clinical practice. However, flow cytometry revealed the cell apoptosis rate increased under the fluence of 50 J/cm 2 , which might indicate that HMEC-1 merely underwent early apoptosis with an undamaged cell membrane. Perhaps it could be due to the different sensitivities of detection techniques. Additionally, the magnitude of PBM depends on the physiological state of the cell at the moment of irradiation, and there exists undetectable effects, as well as the variability of the results reported in the literature [24], which might explain why the inhibitory effect of 590 nm LED on cell phenotype and function, such as cell migration, tube formation and secretion, was not absolutely dose-dependent. Therefore, our findings actually accord with the basic mechanism and characteristics of PBM.
Furthermore, we found that the autocrine potent angiogenic molecule VEGF was reduced notably by 590 nm LED. It has been revealed that VEGF stimulates EC prostacyclin production, which is the direct precursor of prostaglandin E2, an activator of melanocyte derived from keratinocyte [25,26]. In addition, normal human melanocytes constitutively express functional VEGF receptor (VEGFR)-1, VEGFR-2, and neuropilin-1, among which VEGFR-2 expression is induced by ultraviolet irradiation [27]. Therefore, VEGF might potentially participate in the melanogenesis regulation of melanocytes. Moreover, 590 nm LED decreased the secretion of SCF, a paracrine factor from keratinocytes and fibroblasts which induces specific internal signaling pathways of melanogenesis in melanocytes, including the cAMP/protein kinase A (PKA), MAPK, Wnt/β-catenin, AKT/PI3K and SCF/c-Kit signaling pathways [28]. Here, we demonstrated that ECs were another source of SCF in the dermis, which is in line with previous research [5].
Angiogenesis, the process of new blood vessel formation from existing ones, depends on the proliferation and migration of vascular endothelial cells under the regulation of multiple factors. The activation of the AKT/PI3K/mTOR pathway in tumor cells has been found to increase VEGF secretion and plays an essential role in angiogenesis regulation by modulating endothelial cell migration, the formation of structurally abnormal blood vessels, as well as the expression of nitric oxide and angiopoietins in normal tissues and in cancers [29]. Previous studies found that PBM on vascular endothelial cells was related to the regulation of the AKT/PI3K signaling pathway [12]. The classic AKT agonist, IGF-1, binds to the IGF-1 receptor and induces AKT/PI3K pathway phosphorylation [30]. In the current study, we proved 590 nm LED downregulated the phosphorylated level of the AKT/PI3K/mTOR pathway in HMEC-1. Moreover, the inhibitory effect of 590 nm LED on HMEC-1 could be reversed by IGF-1, indicating that such an inhibitory effect was achieved by suppressing the AKT/PI3K/mTOR pathway.
LLLT has been widely used in clinical practice. It has been reported that PBM could alleviate skin pigmentation and erythema. During the treatment of facial acne with LED devices, alternating blue (415 nm) and red (633 nm) light, Lee [31] found the melanin level decreased significantly after the red light irradiation in contrast with blue light, whereas both wavelengths of light produced an overall statistically significant decrease in the melanin level. In the process of skin rejuvenation with 590 nm LED PBM in over 300 patients, Weiss [32] observed a softening of the skin texture and a reduction in roughness and fine lines in 90% of patients, as well as a global improvement of facial texture, fine lines, background erythema and pigmentation noted in physician treatment records in 60% of patients. In our study, we observed a significant improvement of erythema, pigmentation and skin texture in melasma patients after 590 nm LED treatment.
Our study had several limitations. Firstly, only a single-cell cytological model of HMEC-1 was performed, which was incapable of imitating adequately vascular and pigmentary regulation in human skin. A UV-induced 3D co-culture model or an artificial skin model may be required to further investigate the interaction of ECs and melanocytes in melasma. Secondly, we could not determine the potential mechanism of LLLT on SCF suppression, which could be an interesting research direction. Lastly, the sample size of our pilot clinical observation was small so that it could not allow us to perform a sub-group analysis. More prospective, randomized controlled clinic trials with larger sample sizes are needed to further evaluate the efficacy and safety of 590 nm LED light therapy in treating melasma.
The pathogenesis of melasma is complicated and the main drawback of current therapy strategy is the indeterminable efficacy and prolonged course with a high recurrence rate. Despite the forementioned limitations, considering its safe, continuable and portable character, 590nm LED phototherapy may be ideal for the treatment and maintenance control of melasma, especially for those with erythema and telangiectasis.
Conclusions
In conclusion, LED with a wavelength of 590 nm alleviated angiogenesis through inhibiting HMEC-1 migration, tube formation, as well as the synthesis and secretion of VEGF through the AKT/PI3K/mTOR pathway and might suppress melanogenesis via decreasing the release of SCF, which could be a novel therapeutic modality for melasma. | 6,265 | 2022-12-01T00:00:00.000 | [
"Biology",
"Medicine"
] |
Design of a 3-DOF Parallel Hand-Controller
Hand-controllers, as human-machine-interface (HMI) devices, can transfer the position information of the operator’s hands into the virtual environment to control the target objects or a real robot directly. At the same time, the haptic information from the virtual environment or the sensors on the real robot can be displayed to the operator. It helps human perceive haptic information more truly with feedback force. A parallel hand-controller is designed in this paper. It is simplified from the traditional delta haptic device. The swing arms in conventional delta devices are replaced with the slider rail modules. The base consists of two hexagons and several links. For the use of the linear slidingmodules instead of swing arms, the arcmovement is replaced by linearmovement. So that, the calculating amount of the position positive solution and the force inverse solution is reduced for the simplification of themotion.The kinematics, static mechanics, and dynamicmechanics are analyzed in this paper.What is more, two demonstration applications are developed to verify the performance of the designed hand-controller.
Introduction
At present, human exploration activities have reached every corner of the world.Those exploration tasks may be hazardous, such as space telerobotic maintenance, deepsea exploration, decontamination, and decommissioning of chemical and nuclear facilities.To ensure the safety of the operators, all these tasks need teleoperated robotic systems, which contain human-machine-interface (HMI) devices.Due to the combination of human decision-making capacity and the operational capability of robots, these complex tasks can be done better [1,2].What is more, a series of computer aided tasks, such as computer aided design models, telerobotic surgery, flight simulators, and feeling and telling different material [3,4], also need high accuracy haptic interface devices.All these tasks can allow the user to practice in a safe, structured environment, perhaps providing haptic feedback or enhancing the user's ability to understand and control the stored digital model [5].The tasks' execution performance is effected by the human-machine interface device [6,7].Hand-controller is the most widely used humanmachine interface device.It can be treated as a kind of sensor which tracks the operator's hand's position and outputs feedback force.
As the medium between the operators and the target environment, hand-controllers can display the haptic information to the operators and can send the position information of the operators' hand to the actuators in the target environment [8].
A number of haptic devices have been developed in the past decade.The PHANTOM Haptic Device from SensAble Technologies designed by Massie et al. [9,10] is a convenient desktop device with 3-DOF (Degrees of Freedom).Due to its cost-effectiveness, it has been widely used in a multitude of applications.It is a series mode device.Series device has the advantages of simple structures, low production cost, and concise algorithm.However, the rigidity of series device is low.The normal range of the series device's stress deformation is 1∼5 N/mm.Most of the SensAble Technologies' series devices' stress deformation is in the range of 1∼3.5 N/mm.However, a true representation of haptic information needs 1 N/mm stress deformation at least, while a representation of a "rigid body," for example, wall, needs more than 24 N/mm stress deformation [11,12].
Parallel devices usually have high rigidity and high position accuracy.Hand-controllers with closed polygon structure are not easy to deform.They can keep less deformation while reflecting relatively higher force feedback.The stress deformation of them can be much bigger than 24 N/mm.In addition, the force feedback provider, motors or hydraulic components, can be placed on the base of the parallel hand-controller.It means that the hand-controller's execution mechanism is made up with several hollow alloy tubes.Its mass is reduced for much.The mass of this kind of haptic devices is usually as low as 0.05 kg, while the series haptic devices may be as high as 2∼5 kg [13].At least one motor must be paced at the mid-joint of a series hand-controller.Reducers must be used on series haptic devices to reduce the volume and mass of the force feedback source, while keeping enough force feedback output.The reduction ration usually as high as 40 to reduces the volume and mass of the force feedback source motors.The dumping of the joint will be increased.So, a parallel haptic device can be used in the environment with low inertia and low damping [14,15].The Novint Falcon is a parallel mode haptic device made by Novint for the gaming industry [16].It has features of low inertia, high stiffness, high operating rate, and better position repeatability for the designer adopted a parallel mechanism, the delta mechanism [17], and lightweight material.So, a parallel haptic device has many advantages that a serial haptic device does not have, such as compact structure, not being easy to deform, bigger force feedback, and higher response frequency.However, most of the traditional delta haptic devices have too complex position solution algorithm and the force decomposition algorithm.Those advantages and disadvantages exist on most of the parallel haptic devices such as the OMEGA Haptic Devices from Force Dimension, designed by Arata et al. [18,19], and the delta haptic device from Force Dimension [20].Complex algorithms need more time and steps of calculation.The precision and response frequency may be reduced.
Therefore, an improved type of hand-controller with parallel structure is proposed in this paper.This type of parallel hand-controller can simplify the position solution algorithm and the force decomposition algorithm than the traditional parallel devices.This kind of hand-controller has all the delta hand-controller's characteristics such as low inertia, low friction, high stiffness, back-drivability, zero backlash, and gravitational counterbalancing.Besides, it has a simpler mechanism structure than the traditional delta structure.The simplified structure can reduce the calculation amount in kinematics and mechanics.Less calculation amount in kinematics can improve the position-sampling rate and accuracy.Less calculation amount in mechanics can enhance the feedback force's frequency response and precision.
Function and Structure
2.1.Function.Most of the hand-controllers, as humanmachine integration devices, can send the operator's hand's position information to the virtual environment, which is built in a computer.What is more, hand-controllers can display feedback force to the operators to reflect the situations in the virtual environment, such as contact, collision, extrusion, and friction.So, the position measurement and the feedback force display are the two key functions of a hand-controller.
Figure 1 shows how the hand-controller plays its row in the common application.In the control unit, the counters count the number of the pulses generated by the photo encoders.The DSP calculates the displacement of the sliders according to the counted number and then calculates the position of the hand-controller's end moving platform.In addition, the control unit also drives the motors to output specific torques so that the end moving platform of the handcontroller can output the required feedback force.Of course, the control unit also has the function to implement the data exchange between the hand-controller and the virtual environment.However, the performance of the control unit is limited by the cost, the DSP's calculation speed, and other factors.The performance of the hand-controller is limited in precision, frequency response capability, and so on.Simplifying the structure of the hand-controller helps to reduce the burden on the control unit, thereby improving the performance of the hand-controller.
Structure.
Figure 2 shows the porotype of the handcontroller proposed in this paper.It is one type of parallel device, which is simplified from the traditional delta handcontroller.Two hexagons and several links are used to compose the base of the hand-controller.Three guide rails connect the two hexagons on three of the sides.Sliders are assembled on the rails.They can move on the rails with tiny friction.Universal cardan joints are assembled on each of the sliders as shown in Figure 3. Same cardan joints are mounted on the end moving plane too.Connecting one pair of cardan joints with two hollow aluminum tubes forms a set of parallelogram mechanism as shown in Figure 4.The advantage of this structure is that it has strong antideformation capability
Guide rail Slider
Limiters Universal cardan joint but can move freely.What is more, it has a lighter weight.It is important to reduce inertia and enhance response frequency of a hand-controller.It is also used in traditional delta handcontrollers and some of the serial hand-controllers too, such as the OMEGA Haptic Devices and the PHANTOM Haptic Device mentioned in the Introduction.
However, the swing arms in conventional delta devices, as shown in Figure 5, are replaced with the slider rail modules here.The linear slider modules and the parallelogram mechanisms form a variant delta mechanism, an orthogonal delta mechanism.The orthogonal delta mechanism is usually used as an execution unit.To achieve higher position controlling accuracy and larger load capability, screws are used instead of rails.However, for a hand-controller is a bidirectional control device, the screws cannot be used here because it is one kind of self-locking structure.It makes the operator hard to push the hand-controller to input his hand's position to the system.However, a hand-controller with high performance can be moved freely when there is no need to output a force.Any extra dumping will decrease the accuracy of the outputting force.
When one of the three parallelogram mechanisms is perpendicular to the relative rail, this hand-controller cannot be pushed along the parallelogram mechanism.If the pushing force is not along the parallelogram mechanism, the handcontroller will enter into the following two statuses: the angle between the parallelogram mechanism and the rail is bigger than 90 ∘ or smaller than 90 ∘ .Both of the two statuses are the same in the position solving result.So, every point, at which the parallelogram mechanism is perpendicular to the relative rail, is the singularity of the hand-controller.Printing all those points shows that they are three cylindrical sections.To avoid this situation, the limiter is installed on the cardan joints as shown in Figure 3 so that the angles between the parallelogram mechanisms and the rails are always smaller than 90 ∘ .
Therefore, pulling the operating point, which is the end moving plane of the hand-controller, can bring the three sliders moving on the rails linearly.It is easy to calculate out the hand-controller's end coordinate through measuring the displacements of the sliders.Meanwhile, applying pulling forces on the sliders drives the hand-controller outputting a needed feedback force.
The measuring of the displacement of the sliders and the applying of the pulling forces on the sliders are accomplished by the structure shown in Figure 6.It is called transmission mechanism here.Three sets of transmission mechanism are used in the hand-controller.Each transmission mechanism includes a pulley, two pairs of bevel gears, and several couplings.The pulleys are connected to the sliders with low malleability steel wire.The rotation of the pulleys courses the sliders sliding on the rails.Meanwhile, the sliding of the sliders makes the pulleys rotating.A photo-encoder is connected to the pulley with a coupling.Photo-encoder can measure the rotation angle of the pulley, and then the slider's sliding distance can be obtained.At the same time, a DC motor is connected to the pulley with two pairs of bevel gears.The motor can output torque to the pulley.The pulley applies pulling force on the slider through the steel wire.After that, the three sliders transfer the forces to the end moving plane through the parallelogram mechanisms.Operators can feel the feedback force with the hand-controller.The direction and the value of the force can be adjusted by changing the forces applied on the sliders, which can be done through controlling the torques of each motor.The two pairs of bevel gears can help reduce the volume of the transmission mechanism and increase the outputting torque of the motor.Low malleability steel wire is used here as the transmission media.It makes the movement continuous and supple and it is not self-locking.So, the damping of the bidirectional transmission is small.
Position Positive Solutions.
Position tracking is one of a hand-controller's main functions.As for the hand-controller designed in this paper, when the operator is using it to input his hand's position information to the virtual environment, the hand-controller's end moving platform is guided by the operator's hand.It makes the three sliders moving on the rails.The displacements of the three sliders can be measured with the transmission mechanisms and the photo encoders.The kinematics analysis of a hand-controller is to derive the calculation equations of the hand-controller's end moving platform's midpoint from the sliders' displacements.
Figure 7 shows the structure diagram of the handcontroller.The parallelogram mechanisms' length is .Connecting the three guide rails' ends on the hand-controller's base brings an equilateral triangle with side length of .The side length of the end moving triangle is .Coordinate system - is established as shown in Figure 6.The origin point is set at the midpoint of the line which connects the two bottom rails' tails.Axis is alone the connecting line, pointing to the end moving plane.Axis points to the third rail's tail.Axis points to the end moving plane, along the direction of the guide rails.The end moving platform is pushed until all the three sliders get to the end of the rails and this status is treated as the beginning point of the handcontroller.Pulling or pushing the end moving plane drives the parallelogram mechanisms' cardan bases sliding on the guide rails.The photoelectric encoders and the steel wire traction mechanism can measure the distance between the plane and the cardan bases.They are ℎ , ℎ , and ℎ .The goal here is to calculate the coordinate of the end moving platform's midpoint.
Moving the three parallelogram mechanisms' equivalent midlines inward until they intersect at the midpoint of the end moving platform results in a triangular pyramid D-ABC.The length of the triangular pyramid' edge is .Foot point can be obtained by drawing plane ABC's perpendicular line through point .So that point is the circumcenter of Δ.Line AB's midpoint is point .Therefore, Vector is the unit vector of vector .It can be obtained by In (1) By now, the coordinate of point is obtained.In the entire derivation process, there are no matrix calculation, no complex coordinate transfer, and less trigonometric function (only one time).All those complex calculations bring in the errors when the control unit processes the data.Only simple basic calculation and three times of root operation are needed.The root operation and the trigonometric calculation can be done with the CORDIC (Coordinate Rotation Digital Computer) algorithm [21].Only after 5 times of iterations, the result of the calculation can achieve the required accuracy.Therefore, the simplified parallel hand-controller reduces a lot of calculation amount.It is benefit for improving the realtime capability, position-sampling accuracy, and sampling rate.
Spatial Extent Definition.
When an operator is controlling a mechanical arm with large moving range, incremental control method is usually used.For a long displacement, it can be pushed several times.Hand-controllers with large movement range reduce the times of reciprocating and improve the efficiency of position control in the long displacement control.Less times of reciprocating can also reduce the effect of mechanical hysteresis to the control accuracy.
The three guide rails' length is 330 mm.The parallelogram mechanisms' length is 250 mm.The distance between two guide rails' tail, , is 369 mm.The end moving platform triangle's side length is 38 mm.The range in the threedimensional space, which can be reached by the handcontroller's end, can be drawn based on those data and formula (5) above as shown in Figure 8.The size of this range reflects the convenience of the hand-controller in controlling large equipment.The angles between AD and DD, BD and DD, and CD and DD should be checked.To prevent the handcontroller from entering the unrecoverable status, the limiter is mounted on the universal joint mounted on the end plate.The three angles cannot reach 90 degrees.In fact, it is limited to less than 89 ∘ .In the procedure of calculating the handcontroller's moving range, the point should be abandoned at which more than one of the three angles between the parallelogram mechanisms and the rails is bigger than 89 ∘ .
The simulation result shows that the movement range of the hand-controller designed here is 110 mm * 110 mm * 330 mm.However, it is not a cube, but a similar triangular prism as shown in Figure 8(d).It has a relatively large moving range.This range meets the requirement of general mechanical arms control.Especially in -axis, the displacement is up to 330 mm.The large moving range is suitable for push-pull action when operating a large mechanical arm.
Position Tracking Accuracy.
To verify the hand-controller's position tracking performance, a verification platform is established.A programmable 3D linear displacing module, as shown in Figure 9, is used here to guide the hand-controller's end moving platform as shown in Figure 10.The coordinate of the linear displacing module's loading plane can be set by the control panel.For the accuracy of the linear displacing module is less than 0.1 mm, which is much higher than the hand-controller's common application's requirement, the set coordinate of the displacing module can be treated as the actual coordinate of the hand-controller's end moving platform's midpoint.By comparing the linear displacing module's set coordinate and the hand-controller's calculated coordinate, the hand-controller's position tracking performance can be evaluated.
Figure 11 shows the result of the position tracking verification.To achieve the max moving range in -axis and axis, the hand-controller should be guided to the middle of axis moving range first.The verification result shows that the hand-controller goes well in position tracking.Although the errors in and direction are monotonically increasing, the absolute values of the errors are small enough.The max error in direction is up to 1.55 mm.However, it is convergent.The error can be treated as a fixed offset.The offset can be used to adjust the result of the calculated displacement.So, the error can be limited within 0.2 mm.The hand-controller designed in this paper has good performance in position tracking accuracy.
Static Mechanics Inverse Algorithm.
A hand-controller with force feedback can provide accurate feedback force.This parallel hand-controller can provide feedback force with the three servomotors assembled at the tail of each guide rail.The motors can pull the slider with the steel rope through the pulleys.The pulling forces applied on the sliders can provide the resultant force, which is exactly equal to the need feedback force.The static mechanics analysis is to derive the calculation forms with which the control unit can number out how much torque the motors should provide when the hand-controller is controlled to output a feedback force to the operator certain continuously in the static status.This state is usually to display the forces applied to an object which is inside flowing liquid.
Suppose that the feedback force which to be displayed at the end of the hand-controller is ⇀ = ( , , ).At this time, the pulling forces which need to be applied on the three sliders are , , and .The vector forms of them are presented as follows: ⇀ = (0, 0, ), ⇀ = (0, 0, ), and ⇀ = (0, 0, ).Their respective components in the direction of each parallelogram mechanism are , , and .Equation ( 6) shows their solution.The parallelogram mechanisms deliver them to the end effect plane.
where ⇀ is the unit vector of ⇀ , ⇀ is the unit vector of ⇀ , and ⇀ is the unit vector of ⇀ .What is more, the relationship between the end feedback force and the three component forces is Putting ( 6) to (7) brings Presenting ( 8) in matrix form is Equation ( 9) shows the static mechanics decomposition result of the hand-controller designed here.
The DC servomotors apply the pulling forces on the sliders through the pulleys and the steel rope.The pulling force is proportional to the output torque of the motor, and the ratio is the radius of the pulley.What is more, the outputting torque of the motor has the relationship with the loop current as shown in (10). is the motor's constant, Φ is the motor's magnetic flux, and is the motor's turning radius.When a motor is in a stalled state or a low speed state and the current is under the limit of the motor's rated current, the above three parameters are constant.It means that the output torque of the motor is proportional to the current.The torque-current ratio can be obtained through calibrating the motor.Every motor's torque-current ratio is different.They should be calibrated individually.
Therefore, the outputting torque of a motor is proportional to its loop current.Thus, the pulling forces, , , and , applied on the sliders by the motors are proportional to the loop currents of the three motors' driving unit too.The ratios are , , and .All of them should be calibrated before being assembled on the device.
All the control unit needs to do is solving a linear homogeneous equations group to let the motors' driving unit output a definite current.The motors should be driven under the constant current mode.Therefore, the hand-controller can output a required feedback force.The simplified parallel hand-controller needs simple algorithm.The simple algorithm needs less calculating time and steps, which may affect the hand-controller's real-time capability, response frequency, and force feedback accuracy.In contrast, traditional delta hand-controller's mechanics inverse algorithm needs to find out its Jacobean Matrix.After that, the virtual work principle is used to calculate how much force should the three motors output.In the entire procedure, complex matrix calculations and coordinate system translations are necessary which cost more time and calculation units in DSP.
Gravity Compensation.
The hollow aluminum pipes, which constitute the parallelogram mechanism, have a certain mass.The hollow aluminum pipes' mass will affect the hand-controller's force feedback precision.As shown in Figure 12, in a set of parallelogram mechanism, the two hollow pipes' mass is equivalent of applying a force size of on the end effect plane of the hand-controller.The direction of is along the -axis's negative direction.Three sets of parallelogram mechanism bring 3 equivalent force applied on the end moving platform.In addition, the end moving platform has a weight of itself.Its direction is the same as the equivalent force mentioned above.Therefore, the total gravity compensation amount is 3 + .If we want the hand-controller to output a feedback force size of ⇀ = ( , , ), we need to output more 3 + in -axis L F g m t g m t g Figure 12: The force distribution of parallelogram mechanism.
Dynamic Mechanics Analysis
In fact, most of the applications of a hand-controller are to control a virtual or real robot to do some tasks.In the procedure of those operations, both of the hand-controller and the robot are moving.And the robot will contact other objects, which means that the hand-controller needs to output feedback force in motion.So, the dynamic mechanics analysis is to derive the calculation forms with witch the control unit can number out how much torque the motors should provide when the hand-controller wants to output a certain feedback force to the operator when it is in motion.In Section 3.1, we have obtained the position of the end moving platform according to the sliders' displacements moving on the rails.The coordinate of the end moving platform's center is defined as = ( , , ).The sliders' displacements are ℎ , ℎ , and ℎ .For the convenience of expression, they are redefined as ℎ 1 , ℎ 2 , and ℎ 3 .Although the end moving platform's coordinate can be obtained by ℎ 1 , ℎ 2 , and ℎ 3 , we still should build a generalized coordinate system containing ℎ 1 , ℎ 2 , ℎ 3 , and .This avoids the expression being too complicated.The first type of Lagrangian equation [22] In (13), is the Lagrangian equation.It can be obtained with = − . represents the total kinetic energy of the mechanics, and represents the total potential energy of the mechanics.D represents the constraint equation. represents the Lagrangian operators. is the generalized coordinate system. is the generalized forced in the generalized coordinate system .When = ( , , ), represents the forces applied on the end moving platform which is , , and .When = (ℎ 1 , ℎ 2 , ℎ 3 ), represents the forces applied on the sliders which is 1 , 2 , and 3 .
For the extra generalized coordinates ℎ 1 , ℎ 2 , and ℎ 3 , we need extra three constraint equations.According to the principle of the parallelogram mechanism's side length which is constant, we establish the constraint equations as bellow.
The total kinetic energy of the mechanics is means the end moving platform's kinetic energy. is the hollow aluminum tubes' kinetic energy. is the sliders' kinetic energy.For the sake of simplicity of expression, the weight of the universal cardan joints is ignored here.
The total potential energy of the mechanics is is the potential energy of the end moving platform. is the hollow aluminum tubes' potential energy. is the gravitational acceleration.So, the Lagrangian equation is gotten.
Adjusting (19) into matrix form can make it simple to calculate the Lagrangian operators 1 , 2 , and 3 . [ , , and are the forces applied on the end moving platform.They are known.Putting = (ℎ 1 , ℎ 2 , ℎ 3 ) into / , / q , and Γ / , associated with the Lagrangian operators 1 , 2 , and 3 gotten above, brings the forces 1 , 2 , and 3 applied on the sliders according to (13). [ Equation ( 21) shows that the forces should be applied on the sliders if the feedback force displayed by the end moving platform is ( , , ) in dynamic situation.There are no trigonometric calculations and less calculation steps than the traditional delta hand-controllers.It means that the parallel hand-controller designed in this paper has higher response frequency and precision in the case of same size, material, and manufacturing accuracy relative to the traditional delta hand-controllers.
Application Demonstration
In order to verify the performance of the hand-controller designed in this paper, two applications were developed.Operators can control the target objects in the virtual environment with this hand-controller.The target object in first application is a MOTOR MAN robot model as shown in Figure 13.The end of the robot translates in the virtual 3D space along with the hand-controller's end platform in the real 3D space.Three pointer controls dedicate the photo encoders' turning angles.Meanwhile, edit boxes display the coordinate values of the hand-controller's end platform.This application shows that the hand-controller's position acquisition accuracy and stability are in line with the needs of a good human-machine-interface (HMI) input device.
Figure 14 shows that the target object in the second application is a ball in a wooden box.Suppose that the ball is a rigid body.The deformation of it is zero when it is contacting with the wooden box, while the wall of the box has deformation.Suppose that the deformation is elastic deformation and the contact between the ball and the wall is frontal collision as shown in Figure 15.The contact force between the ball and the wall is proportional to the deformation of the wall.It is = ⋅ .When the elasticity coefficient, , is big, the collision between the ball and the wall can be treated as "rigid contact."Usually, is bigger than 24 N/mm as mentioned in the Introduction.In this condition, there is no obvious deformation on the handcontroller.It means that the hand-controller designed in this paper can output proper feedback force and display "rigid contact" truly.Therefore, it can be treated as a qualified HMI output device.In both of the two applications, the delay can be ignored.It is easy to use and the operator has a good sense of immersion.
Conclusion
A kind of hand-controller with parallel structure is designed in this paper.It is simplified from the traditional delta handcontroller.The swim arms on the traditional delta handcontroller are changed into combination of linear guides and sliders.This helps to simplify kinematics, statics, and dynamics mechanics solving procedure.There is almost no triangular calculation and coordinate system translation which cost lots of calculation resources.Less calculations means that low cost and higher precision in the condition of same level of manufacturing accuracy for every step of calculation may bring in errors.And less calculations also means higher sample rate and output rate.It helps the handcontroller improve its response frequency.Besides, for the power input part, direct driving in the traditional delta handcontrollers is changed into gear driving with two sets of bevel gears.It helps to reduce the motors' size and can adjust the installation direction of the motors.This makes the hand-controller's structure compact.Due to the part size error generated during machining and the nonlinearity of the motor torque output, the hand-controller needs to be systematically calibrated before being put into use.Therefore, in the subsequent work, an efficient, simple, highly automated calibration method needs to be designed.
Figure 1 :
Figure 1: Application scenario of the hand-controller.
Figure 2 :
Figure 2: The improved parallel hand-controller designed in this paper.
Figure 8 :
Figure 8: Spatial extension of the proposed hand-controller.
| is the circumradius of Δ.According to law of sines, it can be obtained by formula (4). | 6,671 | 2017-10-16T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
Methodology for Thermal Behaviour Assessment of Homogeneous Façades in Heritage Buildings
It is fundamental to study the thermal behaviour in all architectural constructions throughout their useful life, in order to detect early deterioration ensuring durability, in addition to achieving and maintaining the interior comfort with the minimum energy consumption possible.This research has developed amethodology to assess the thermal behaviour of façades in heritage buildings. This paper presentsmethodology validation and verification (V&V) through a laboratory experiment. Guidelines and conclusions are extracted with the employment of three techniques in this experiment (thermal sensors, thermal imaging camera, and 3D thermal simulation in finite element software). A small portion of a homogeneous façade has been reproduced with indoor and outdoor thermal conditions. A closed chamber was constructed with wood panels and thermal insulation, leaving only one face exposed to the outside conditions, with a heat source inside the chamber that induces a temperature gradient in the wall. With this methodology, it is possible to better understand the thermal behaviour of the façade and to detect possible damage with the calibration and comparison of the results obtained by the experimental and theoretical techniques. This methodology can be extrapolated to the analysis of the thermal behaviour of façades in heritage buildings, usually made up of homogeneous material.
Introduction
In order to optimize the available energy resources, it is necessary to analyse the buildings energy consumption, since the building industry has a significant weight in the consumption of resources (energy and raw materials).Thermal response of the enclosures is a very important factor in this regard.On the other hand, the thermal study of a fac ¸ade can give information regarding its pathological state.This paper develops a methodology that analyses heritage building fac ¸ades in a thermal way with a low economic cost.
It is necessary to consider multiple constructive and environmental factors in thermal response of fac ¸ades and in energy losses that occur through them.Constructive design of fac ¸ades and possible pathology or alteration of the building materials are the most important factors.A correct arrangement of the fac ¸ade layers and good carpentry are highlighted among the constructive factors.Green urban infrastructures [1] that contribute to heat mitigation [2] and to reducing ambient temperature and improving thermal comfort [1,3,4] stand out among the environmental factors.The design of roofs and green walls also influences the boundary climatic conditions [5][6][7].The density of green areas affects the incidence and absorption of solar radiation, which induces a lower surface temperature [8].
Every day there is greater interest in collecting data from buildings [9] to better understand and improve knowledge of energy use [10] and thermal comfort [11].
Some failures in building envelope occur often during the construction process [12][13][14].In historic buildings, most faults occur during their service life, so it is recommendable to monitor them.
The deterioration monitoring would give an early warning of incipient problems that allow the planning of the maintenance programs, minimizing the relevant costs [15,16].In fact, an analysis of statistical data can be performed to obtain valuable information for preventive conservation [17].Preventive conservation consists of a working method and a combination of techniques that help to determine and control the deterioration process of cultural heritage in order to take the necessary actions before it occurs [18].
The use of data monitoring systems together with improved service-life prediction models leads to additional savings in life cycle costs [19,20].The development of new sensor concepts allows for a more rational approach to the assessment of repair options and scheduling of inspection and maintenance programmes [20] in traditional buildings or other types of structures.
To facilitate more cost-effective data collection for a wide variety of important building environmental and operational parameters is necessary to search tools [21] with an affordable price.They also have to be easy to build and customize according to the needs of each case, and they can store lots of data with a reasonable accuracy.This research work combines three techniques: thermal sensors, thermography, and finite elements simulation.
On the one hand, a low-cost Arduino-based microcontroller has been employed in this research, because it is a cheap, flexible, and programmable open-source system, with easy-to-use hardware and software components [21,22].This microcontroller has been used as an interface to receive information from sensors and as a data-logger.Also, it activates or deactivates the heat source of the specimen according to the temperature recorded by the sensors.An exhaustive study has never been done to know the thermal flow with lowcost sensors, although this type of microcontroller has already been used by environmentalists with sensors [23][24][25].
On the other hand, there are several modalities [26] in the use of infrared technology, but the most common ones are active thermography, which consists of artificially heating the sample, and passive thermography, where the material or enclosure is heated by the natural effect of the solar energy.The best option is passive thermography when large surfaces are studied because it fits the real situation very well [27], for example, the fac ¸ades of buildings, especially if they are located in an urban environment where the streets are narrow.Passive thermography has also been used to assess the effect of leakage points in buildings [28].
Nondestructive techniques such as temperature sensors and thermography facilitate the study of building materials without damaging the building, especially its fac ¸ades.Most historic buildings have been built with different types of stone.Usually, these types of buildings have thick fac ¸ades composed of one or two materials.In the case of stone walls, this material covered the entire thickness of the wall.Different materials can be alternated, as, for example, the case of brick with earth or rammed earth walls, if the fac ¸ade was formed by other materials.The state of deterioration of a stone monument is characterised by the type, intensity, and extent of the damage.Determining the location of the forms of deterioration has been demonstrated to be a highly appropriate research method for preventive conservation.
Thermography may propose some difficulties if a quantitative approach is intended [29], but in this work, it is combined with two other techniques, allowing in this way locating and quantifying the magnitude of damage.
The main objective of this research is to develop a specimen in the laboratory that allows obtaining real data.The specimen consists in generating a thermal flow through a homogeneous stone material.Temperature data were recorded using Arduino-based software and hardware designed by the authors.Temperatures are confronted with thermographic technology.Finally, the data obtained help to calibrate and verify a three-dimensional model of finite elements, which allows obtaining a greater amount of data and a more global estimate of the thermal behaviour.From this specimen, this work proposes a methodology to evaluate the thermal behaviour of fac ¸ades in historic buildings and to detect pathology.
Materials and Methods
This research presents a methodology applicable to any material and historical building with the objective of evaluating its envelope thermally.
The methodology presented in this paper uses three techniques.One technique gives theoretical results and the other two obtain real and experimental results.The first technique is based on the elaboration of a finite element model with simulation software.This gives the theoretical results of the experiment, that is, the temperature reached by the material at each point with current conditions if it were homogeneous and it had no damage or failures.One of the techniques that provides experimental results is the use of temperature sensors that record the temperature data along the thickness of the fac ¸ade.And the other experimental technique used is the thermal camera, which allows mapping temperatures on the exterior surfaces.The methodology basically consists of analysing the variation of temperature data obtained theoretically and experimentally.If the data are very similar, the fac ¸ade is healthy.However, if the data change significantly in any area, there is pathology.This paper shows practical examples to understand the detection of cracks, mass faults, detachments, and so on.
Design of the Specimen Tested.
A fac ¸ade specimen, a model, has been constructed to develop this research.
The model is a box of 73 × 63 × 36 cm 3 .The exterior is made of chipboard that allows rigid and stable walls.A solid light concrete block has been placed inside the box.This block is 25 × 25 × 60 cm 3 and it is wrapped by thermal insulation of rock wool 4 cm thick, except on two of its faces.The heat flows from the inside of the box to the outside through the block of lightweight concrete.The characteristics of the materials used can be seen in Table 1.Thus, a closed and isolated chamber has been built, with the heat source simulating the conditions inside the building (Figures 1 and 2).Up to 11 thermometers have been placed inside the wooden box and inside the solid light concrete block.The heat source has been a single 60 W bulb in this case.
A piece of rock wool has been placed inside the air chamber between the heat source and the concrete block.This piece is in the central third in the plan view.This is done to avoid direct radiation to the block and, in this way, only the physical phenomena of conduction and convection will appear.These two phenomena appear in the envelopes of buildings.Table 2 summarizes the positions of each thermometer.Up to 11 temperature sensors have been placed from the heated interior chamber to the outer space at ambient temperature.Thus, the temperature reached by the air, in the interior and in the outside, can be known at any moment.Also, the temperature reaches the homogeneous material in the most prominent points: near the edges and in the central part.
It is noteworthy that the indoor sensors T9, T10, and T11 have been protected against the heat source, since it also radiates infrared energy that skews the temperature reading.
The main material of the specimen is a Ytong block.It is a cellular concrete and, therefore, very light that combines resistance and thermal insulation.The main chemical composition of this block is silica sand (70%), cement (14%), blowing agent (0.05%), and also water.The distribution of cells for a block with 500 kg/m 3 of density is macrocells (50%) and microcells (30%) [30].The minimum compressive strength is 1.5 MPa according to current standards [31].
Temperature Sensors.
The board used in this research has been the Arduino MEGA based on the ATmega328P.It contains everything needed to support the microcontroller; it is simply connected to a computer with a USB cable or powered with an AC-to-DC adapter or battery to get started [32].The board kept being powered with an AC-to-DC adapter in this research.
Custom sensor expansion boards can be developed to directly plug into the standardized pin-headers of the board.They enable the microcontroller to connect to several sensors [22,33].
This ensures that power supply will be continuous during the experiment and batteries will not be depleted in several days or weeks.
A program compiled in C++ language has been made for data collection.This program is responsible for data collection, publication, and temperature control inside the test.
The application builds an array of objects, thermometers, which take the temperature, store it, and publish it on both the serial port monitor and HTML by creating a local web server, which allows real-time access to the situation of the test through a local web page.
The structure of the program is based on objects, classes.To do this, it defines a pure virtual class called Thermometer, which defines all common data and methods from acquisition to publication.This main class is inherited by classes that are defined according to different types of sensors, Dallas DS18b20 and K probes, through the MAX 31856 digitalization and amplification module.These classes receive the inheritance of the main class, Thermometer.They also define the specific methods of data acquisition according to external libraries of free license.These libraries contain the predefined classes of the specific hardware use of each sensor.There are more than fifty different types of sensor whose deployment into practical devices facilitates long-term monitoring of structural changes, reinforcement corrosion, concrete chemistry, moisture state, and temperature [20].In this work, only temperature sensors are used.
The Dallas temperature sensor DS18B20 has been used for the main sensors.It can be powered from data line.Power supply range is 3.0 V to 5.5 V.This type of sensor measures temperatures from −55 ∘ C to +125 ∘ C with ±0.5 ∘ C accuracy from −10 ∘ C to +85 ∘ C. The DS18B20 Digital Thermometer provides 9-to 12-bit (configurable) temperature readings which indicate the temperature of the device.Information is sent to/from the DS18B20 over a 1-Wire interface, so that only one wire (and ground) needs to be connected from a central microprocessor to a DS18B20.Power for reading, writing, and performing temperature conversions can be derived from the data line itself with no need for an external power source.Because each DS18B20 contains a unique silicon serial number, multiple DS18B20s can exist on the same 1-Wire bus.This allows for placing temperature sensors in many different places.Applications where this feature is useful include HVAC environmental controls, sensing temperatures inside buildings, equipment, or machinery, and process monitoring and control [34].
K-type probes have been used to test the data obtained by DS18B20 sensors.These probes can perform measurements below 0 ∘ C.
A Dual MAX31856 thermocouple breakout board has been used to connect the K-type temperature sensors to the board.It has 19-bit temperature resolution, handles all thermocouple types (K, J, N, R, S, T, E, and B), and allows readings as high as +1800 ∘ C and as low as −210 ∘ C depending on thermocouple type, and a line frequency filtering of 50 Hz and 60 Hz is included.
Using a higher resolution external analog-to-digital convertor would provide better readings; however, since the thermistor has an accuracy of ±0.05 ∘ C in optimal conditions, the level of precision from the 10-bit ADC is sufficient [19].
In this work, up to 11 temperature sensors have been used.The variations recorded by these sensors over time are known and they are used to corroborate their accuracy and to validate this research.For this reason, all temperature sensors have been calibrated.Calibration is the result of comparing the data obtained by sensors with that obtained by high quality thermometers in a test.In this way, an affordable measurement system can be used in tests, which were previously carried out with expensive thermometers.Calibration has consisted in placing all sensors in a receptacle to test the temperature at different values.The temperature values observed in all thermometers have been very similar.The temperature differences between the sensors and the reference thermometers were lower than ±0.05 ∘ C and therefore it was not necessary to correct the data obtained.
Data of all temperature sensors are saved in real time on a micro-SD card in txt format, which can easily be imported into any spreadsheet software.Thus, it is not necessary to connect the sensors to a computer for the long period that the test can last.Micro-SD memory cards that are sold today have a huge storage capacity.Sensor and time data are stored as plain text in a comma-delimited format and each data point consists of only a few bytes of data, allowing storing billions of measurements [21].
The micro-SD memory card used on the board has been able to store the data received by the 11 sensors, every 5 minutes, for days, and it has no storage problems.A web page has been created to check the temperature of each sensor in real time.However, the web page was very simple and it was not linked to a Mysql database to store these data.
Thermographic Technology.
A FLIR B335 camera has been used for this research generating thermographic images with 320 × 240 pixels of resolution.It has a temperature range between −20 and +120 ∘ C and less than 50 mK NETD sensitivity.Further processing of the thermographic images has been done with the FLIR QuickReport software.The colour palette of these pictures can be modified, as well as the temperature range and the distance to the object (usually 1 meter).Also, the maximum, minimum, and average temperature of the studied areas can be calculated.Finally, the temperature assigned to each pixel of the image is exported in Excel format.
The authors have evaluated the contributions on thermal comfort for traditional fac ¸ades of buildings [35].
Many other previous studies have already established a link between infrared thermography and the detection of defects in stone materials, although in these studies the thermographic data for different points of the walls are interpreted by means of graphs [36].Those areas where thermal discontinuities occur are usually where defects in the material are located.On the other hand, those points which display a similar temperature demonstrate thermal inertia, that is, the tendency of a particular element to resist thermal changes, and this depends on the characteristics of the material, the moisture present, and any damage [37].
The thermal pattern of a material largely depends on its characteristics (thermal diffusion, porosity, density, etc.).The possibility of being able to clearly visualise the defects of a particular material depends on the difference between the thermal characteristics of the material and the absence of homogeneity [38].
The emissivity value in this study is 0.95 as the default value, and so we believe that the results obtained from the thermographic measurements are reliable.Moreover, emissivity is very similar for nonmetallic materials [39] in building construction.For example, concrete has 0.93 of emissivity, 0.94 for chipboard, or 0.90 for rock wool with a cloth cladding.
Finite Element Simulation.
The research has been completed with a finite element model of the specimen using the commercial program ANSYS Mechanical v.15, a finite element software used in engineering and architecture able to study multiple variables simultaneously [40].
This software allows perfectly simulating the studied case and calculating the thermal flow in each point.For this purpose, a mesh size of 0.5 cm has been used.The element type is Solid 278, a simple three-dimensional parallelepiped of 8 nodes, because it is the element that best fits in the calculations and for the model geometry.The element has a 3D thermal conduction capability.The element has eight nodes with a single degree of freedom, temperature, at each node.The element is applicable to a 3D, steady-state or transient thermal analysis.However, in [41] anyone can see the use of new finite elements for more difficult applications.Figure 3 shows a vertical section 15 cm from the edge of the three-dimensional model, where the thermometers are located, and a horizontal section through the midpoint.Thus, all elements of the model are best observed.The same materials of the laboratory test (Table 1) have been used in the finite element model.The thermal behaviour of the materials used varies because their properties of density, specific heat, and conductivity are different.Energy is more difficult to propagate when the conductivity of the material is lower.In this case, the lowest conductivity corresponds to rock wool.This way, the energy will be lost more quickly in the concrete block and in the chipboard.
The temperature in all nodes of the finite element mesh (every 0.5 cm) is shown in this figure.Inside the box the heat source raises the temperature 30 ∘ C above the outside temperature.Outside, the ambient temperature at the selected time is about 15 ∘ C.This generates a temperature gradient between inside and outside.It can be seen very clearly in Figure 3.
A more adequate understanding of the temperature gradient that reflects the finite element model is achieved in this figure.Figure 3 clearly shows how the thermal gradient occurs through the insulation small thickness of 4 cm.The gradient is wider where the lightweight concrete block is located, considering that its thermal conductivity is higher than the insulation.The temperature decreases along the entire thickness of this material.Also, it is possible to understand more complex physical phenomena by considering the three dimensions, such as the nonlinearity of the thermal gradient of some areas.
The heat exchange between the air and the wall is a complex phenomenon.Each mobile molecule of air strikes the static molecules of the wall material and exchanges with them some of its vibration.Temperature is the mean of the states of vibration.
In the interface between solid and gas, very complex phenomena occur, depending on the air velocity and the horizontal or vertical position of the solid.These phenomena also depend on the temperature of the materials.The balance of these phenomena is simulated rudely by the film coefficient of convention.
The thermography of the solid helps to set the film coefficient, by comparing the temperatures of the simulation with those obtained in the thermography.The heat flow generated by the heat source produces a convection phenomenon of the air inside the box.A heat transfer occurs between the fluid and the surfaces.Here the thermal boundary layer between both elements is very important.This boundary layer is linked with temperature gradients in the fluid caused by the presence of a surface at different temperature.When forced convection occurs, the values of the film coefficient vary between 25 and 70 approximately depending on the air velocity and material, in this case, concrete [42].In this case, the values of the film coefficient (Table 3) are set to a certain value by comparing the temperature values of the thermography with those of the finite element simulation.Inside the box, the values are higher because the space is very small and the heat source produces a forced convection movement.The values in Table 3 offer a better adjustment of the simulation with the recorded temperatures.
Validation and Verification (V & V) for Applying in
Heritage.The work presented in this paper is based on a specimen carried out in the laboratory with a homogeneous stone material (Figures 1 and 2).It is a chipboard box, totally thermally insulated, except on one of its faces where the solid light concrete block is located.A heat source that generates a thermal gradient is placed in the inner space.Up to 11 temperature sensors are placed in the specimen.It is a low-cost system that allows checking temperatures and storing the data for later analysis.
Once the specimen is set up, the heat source is switched on, in this case, a bulb of 60 W. From that moment, all data generated by the thermal sensors is recorded on an SD card.The test lasted several days, generating a high number of temperature records every five minutes, day and night.Outside temperature has been fluctuating, although the values have been maintained around 15 ∘ C inside the laboratory because it was winter.The inside temperature of the housing has also been kept constant with a temperature 30 ∘ C above the outside.The T11 thermometer has controlled the bulb's on/off switching.When the temperature difference is not equal to 30 ∘ C compared to outside, with a small margin of ±0.5 ∘ C, an order is sent to turn the heat source on or off.
In addition, during the experiment, different thermographic pictures were also captured.The temperature of all faces has been recorded from different points of view.This allows comparing temperature data and verifying them more accurately.
A three-dimensional model of the experiment with finite elements was developed to simulate the specimen after obtaining sufficient laboratory data.Data from sensors and thermography has been used to calibrate this 3D theoretical model with finite elements.
The comparison of the data obtained by the three techniques allows validating and verifying (V & V) the theoretical model.Once the finite element model has been validated, it is possible to extrapolate thermal analysis to buildings fac ¸ades in heritage.An exhaustive check of the temperatures that are reached in different points of a fac ¸ade can be realized.Extrapolations or modifications in the boundary conditions can be made to know how the material would behave in those suppositions.
After getting the data using the three techniques for the healthy block, three types of damage usual in heritage are applied to the block and the experimental data with sensors and thermal camera are taken again.The variation of these results with respect to the theoretical ones allows detecting the damage.Three types of usual damage on historic buildings fac ¸ades have been induced in the solid light concrete block.
Damage 1 represents a continuous crack with 0.5 cm of thickness and 5 cm of height and its depth covers the entire thickness of the block (25 cm).Damage 2 involves a mass loss of the material 5 cm in diameter and 10 cm deep from the inner face.Outside of the solid light concrete block nothing is seen with the naked eye.Damage 3 represents a flake, that is, a piece of the block with dimensions of 7.5 × 15 cm 2 which has been detached.Figure 4 shows the solid light concrete block, with its relative position in the box and with the location of the three damage types.
Data Obtained by Temperature Sensors.
As explained in the previous section, the micro-SD memory card recorded from the beginning the temperature and the following information: its sensor number, its serial number, the date, time, and whether the heat source is on or off.Table 4 only shows one example, because a large number of data have been stored for days.In the example in Table 4 the T11 thermometer is off.
In Figure 5, the data recorded by the temperature probes in Table 4 are shown.
Results of Infrared Thermography.
In Figure 6, three different points of view have been represented to show the temperatures reached on all the specimen faces.The inside temperature is kept constant at 30 ∘ C above the outside temperature.
Figure 7 shows a picture of the specimen and its corresponding thermographic one.The temperature of the central point of the homogeneous material is also shown in this figure.The colour scale allows knowing in a visual way what the temperature degradation of different points of the specimen is.
The methodology carried out in this research is intended to be used in historic buildings.Infrared thermography has been widely used in historic buildings (Figure 8); in this case, it shows the Seminary-School of Corpus Christi of Valencia (Spain), which was built between 1580 and 1610.The fac ¸ades of this building are composed of a limestone base.
The corners are also reinforced with this type of stone.The main part of the wall is composed of a rammed earth wall.The top of the corner is built with brick.It corresponds with the bell tower.This nondestructive technique is very useful in this type of buildings in heritage.It allows knowing the temperature of inaccessible points with a conventional thermometer and acquiring data from multiple points and detecting injuries and/or humidity.
Theoretical Results
Using the Finite Element Model.The model is calculated when the specimen geometry is entered into the calculation software, the corresponding finite elements are generated, and the relevant boundary conditions are applied.In Figures 3, 9, and 10, we observe the results of the calculation.Before drawing conclusions from the results obtained with the finite element software, the validation work is necessary.Table 5 shows the temperature variation in percentage.The lower value obtained validated these results.Once the model is validated, a large amount of information can be extracted, and extrapolations can be made, modifying some of the parameters involved.
Figure 9 shows the external face of the solid light concrete block.This is a front view.The finite element software allows knowing the temperature in any node of the mesh.The figure shows, as examples, some of the most relevant points: the midpoint, the upper right corner, and two intermediate points.The temperature of the corner (P4) is lower than the midpoint (P1) because it is further away from the heat source.
Table 5 compares the temperatures of the exterior surface of the block obtained by the finite element model and thermography.This table does not show the temperature of the only sensor on this surface, which is 17.938 ∘ C. In Figure 10, a cross-section of the solid light concrete block is shown.On the left, the outside temperature is 16.875 ∘ C. On the right, the inside temperature is 45.688 ∘ C that is almost 30 ∘ C higher than the outside temperature.The transfer of energy between each face of the solid light concrete block and air through the film coefficient is carried out with about 2 ∘ C.
In Figure 10, the five points corresponding to the actual position of the sensors placed in the specimen have been identified.From left to right, they correspond to sensors T04, T05, T06, T07, and T08.
Table 6 compares the temperatures of this section of the block obtained by the sensors and the finite element model.This table does not show the only available temperature data of the thermography, that is, 17.9 ∘ C.There is a good correspondence between the results obtained by these two techniques.
Heritage Pathology Detection.
Once the block has been damaged, the data storage is carried out again.This is in a later time, when the outside temperature is different.Due to this, it is necessary to simulate the theoretical model again with the new boundary conditions and to make new thermographic captures.
Sensors give temperatures in the depth of the block while the thermography takes its superficial data.Both aspects should be studied by comparing them with the theoretical data.Table 7 shows the results of the sensors and in Table 8 the results of the thermography are shown.
When the solid light concrete block is damaged, the inner temperature goes outwards more easily creating a thermal bridge.This is the main conclusion drawn from Table 7.The thermometers at the edge of the block (T4 and T8) reach a small temperature variation at shallow depth.However, the thermometers in the middle of the block (T5, T6, and T7) recorded a very significant temperature increase, about 17%.When the actual data are significantly different from the theoretical ones it is demonstrated that the areas with pathology are identified.
Figure 11 shows the thermographic pictures with the three damaged zones (a, b, and c) in solid light concrete block.It indicates the temperature in each zone where they are located.
Table 8 compares the temperatures of the theoretical healthy case (finite elements) with the thermography ones for the case of the solid light concrete block with damage.The temperatures obtained at these damaged points are significantly higher.A 19.5% of variation is observed in the case of a crack that crosses the entire thickness of the fac ¸ade (type 1).However, the mass loss in the middle part of the block (type 2) or a detachment (type 3) increases the temperature less than 10%.This shows that pathologies are detected using this methodology and defects that cross the entire thickness of the wall are more significant in terms of their thermal behaviour.
Conclusions
Thermal behaviour of building fac ¸ades and heat losses through them must be known.The study of the influence of these energy flows, along with other environmental and climatological factors in the deterioration of the fac ¸ades, is important.This is crucial in heritage, where buildings have suffered for centuries the inclement weather and their fac ¸ades have lasted as long as possible.Most of these historic buildings are composed of fac ¸ades of a homogeneous material, usually stone, but they can also be made of rammed earth or brick.
With the aim of applying this methodology in fac ¸ades of historic buildings, the following conclusions can be highlighted: (a) Thanks to this methodology, it is possible to understand more complex physical phenomena by considering the three dimensions, such as the nonlinearity of the thermal gradient of some areas.When performing the 3D study instead of the 2D one, the real boundary conditions are analysed and all aspects involved in the thermal behaviour at each point are considered.(b) This methodology allows detecting damage in buildings.This damage is localized when a considerable variation appears between the theoretical results (finite elements) and the experimental ones (thermal sensor and thermal camera) in some area of the fac ¸ade.Damage is located generally with a thermal bridge, that is, an area with higher temperatures than expected, because when there is some damage the section is depleted and the heat goes out to the outside more easily by this zone.(c) Accuracy of film coefficient values is essential for obtaining results in line with reality in thermal simulation programs.Infrared thermography is a very useful tool to calibrate the different film coefficient values in a building, and from these, the simulation can be done and results and conclusions of all its points can be extracted.
(d) This research has shown that it is possible and very useful to design the Arduino-based software and hardware necessary to place 11 or even more temperature probes on the same board.In addition, it is possible to store this information during the days or weeks for which the specimen has lasted.This is a very powerful and economical tool for preventive conservation.
(e) Thermal insulation produces a more pronounced thermal gradient due to its thermal conductivity.
Meanwhile, the gradient widens in the thickness of the solid light concrete block.(f) The software allows showing the temperature flows through the different materials.In this way, to find out in which areas the largest flows have originated is possible and, therefore, the greatest energy losses are known.This is vitally important for the objective pursued in this research.Specifically, the greatest energy losses have occurred at the corners of the interior space where the heat source is located.
bottom, protected from the source).It controls the heat source's on/off switching.
Figure 1 :
Figure 1: Specimen to perform the specimen without the top cover.
Figure 2 :
Figure 2: Section of the specimen with the location and sensors nomenclature.
Figure 3 :
Figure 3: Temperature in the vertical and horizontal section of the finite element model.
Figure 4 :
Figure 4: Types of deterioration in the solid light concrete block.
Figure 5 :Figure 6 :
Figure 5: Temperature through the solid light concrete block.
Figure 7 :
Figure 7: Standard picture and thermography one of the specimen.
Figure 9 :
Figure 9: Temperatures comparison on the exterior surface of the solid light concrete block, by finite elements (a) and thermography (b).
Figure 10 :
Figure 10: Temperature in the section of the solid light concrete block.
Table 1 :
Properties of the used materials.
Table 3 :
Film coefficients used in the calculations.
Table 4 :
Example of data recorded by temperature sensors.
Table 5 :
Analytical comparison of temperatures obtained on the exterior face of the solid light concrete block, by finite elements and thermography.
Table 6 :
Comparison between theoretical and sensors results.
∘ C Figure 8: Infrared thermography applied to a historic building.
Table 7 :
Comparison between theoretical and sensors results in damaged block.
Table 8 :
Comparison of the theoretical temperatures and thermographies. | 8,019.2 | 2017-01-01T00:00:00.000 | [
"Engineering",
"Environmental Science"
] |
ON STAR POLYNOMIALS , GRAPHICAL PARTITIONS AND RECONSTRUCTION
It is shown that the partition of a graph can be determined from its star polynomial and an algorithm is given for doing so. It is subsequently shown (as it is well known) that the partition of a graph is reconstructible from the set of node-deleted subgraphs.
edges.We define an m-S to be a tree consisting of a node of valency m m (called the centre of S joined to m other nodes.A 0-6 is a node and a m I-6Y is an edge.
Let G be a graph.A 6oY-COVe (or simply, a COVe) of G is a spanning sub- graph whose components are all stars.Let us associate with each m-star in G, an in- determinate or wig Wm+l; and wth each star cover C consisting of S where the summation is taken over all the star covers in G and (Wl, w 2 is a general weight vector.The basic results on star polynomials are given in the intro- ductory paper by Farrell [I]. We will show that HG the partition of a graph G can be obtained from E(G;).
This will then be used to show that R G is node-reconstructible, a result that can be established by more elementary means (see Tutte [2]).
For brevity, we will ite E(G) for E(G;w), since the same weight vector w will be used throughout the paper.Also, in partitions, we will use r k to denote the occur- of k r's.Finally, we will assume that () 0, for all r n. ence 2. STAR POLYNOMIALS AND GRAPHICAL PARTITIONS.
First of all, we state a lemma which can be easily proved.
LEMMA I. Let v be a node of valency d in G Then G contains () m-stars with centre v DEFINITION Let G be a graph with p nodes.A S%mpl m-covEr of G is a cover consisting of an m-star and p-m-1 isolated nodes.
It is clear that a simple m-cover in G will have weight w Wm+ in E(G).
A mon6mial of this form in E(G) will be referred to as a 6%mp Am, and its co- efficient, which will be denoted by c a 6dp e0e%eewt, c will be the number m m of simple m-covers in G.Note that the term w will also be a simple term.PROOF.This is straightforward.
The following lemma can be easily proved.
LEMMA 3. Let n be the largest valency of a node in G Then E(G) contains p-r-I all the terms w Wr+ (0 _< r _< n) with non-zero coefficient, i.e Cr # 0 for for (0 ! r in) Suppose that we put n in the above Lemma.Then G will consist of a set of disjoint edges and possibly isolated nodes.Clearly then the partition of G will be given by c p-2c H G (i 0 ). (2.1) Hence HG can be found from E(G).
If n I, then from Lemma 2, we get n r n r)br bk + E (k)br, for k > I. Ck rk (k For n I, HG is given by Equation (2.1).For n 0, the result is trivial.
Theorem yields an algorithm for obtaining G from E(G).This algorithm is illustrated in the following example: EXAMPLE I. Let G be a graph such that E(G) First of all, we oserve from the term w6, that G has 6 nodes i.e. p 6.The sim- 7ww and w2w Therefore c 6 c =7 and c I. Hence HG (312II)" It would be nice to be able to obtain G itself from E(G).From Theorem I, HG can be obtained.However there can be several graphs with the same partition.Since only the simple terms in E(G) are used to obtain G' it is not surprising that G itself is not clearly defined.Should G itself be clearly defined by the simple terms, then it would mean that the remaining terms of E(G) are useless as far as the characterization of G is concerned.It would be interesting to investigate the nature of these 'useless terms'.
Suppose that HG is unigraphic (i.e.there is only one graph with partition HG ), then G could be uniquely constructed from HG" Hence we have the following theorem.THEOREM 2. Let G be unigraphic.Then G can be constructed from E(G).
THEOREM 3. Let G and H be two graphs with p nodes.Then NG H if and only if E(G) and E(H) have the same simple coefficients.
PROOF.Suppose that the simple coefficients in E(G) and E(H) are equal.Then from Theorem I, G and H must have the same partition.Conversely, suppose that (r I) in E(G) and E(H) must NG H H Then from Lemma 2, the coefficients c r be equal.Finally, c i, for all graphs.Hence E(G) and E(H) have the same simple coefficients.The result therefore follows.
3o STAR POLYNOMIALS AND RECONSTRUCTION.
The following theorem is analogous to the result for circuit polynomials given in Lemma 3 of Farrell and Grell [3], with i i.We suspect that the general result holds for all F-polynomials (see Farrell [4]).Here G-x denotes the graph obtained from G by removing node x.V(G) is the node set of G.
nl, j n2, j n It is clear that the monomial w w 2 ...w p'j is the weight of a cover with P one isolated node less than the corresponding cover in G.It is therefore the weight of a cover in G-x, for some node x in G. Hence it is a monomial of the polynomial Z E(G-x;).Conversely, every cover of G-x can be extended to a cover of G by adding an isolated node.Therefore every monomial m in Z E(G-x;) yields a corr- esponding monomial wlm in G.The derivative of wlm with respect to w yields E(G) a term with monomial m.It follows that w and Z E(G-x;w) have the same mono- mials.nl, j n2 n Since A. is the coefficient of w w 2 ,J...w p'j G has A covers con- 3 P j sisting of nl, j isolated nodes n2, j edges,..., n (p-l) stars.Suppose that P,j node x is removed from G. Then G-x will have a similar cover but with nl,j-I isolated nodes.Since node x could be any of the nl, j isolated nodes in the cover, it follows that each such cover in G gives rise to nl, covers with one less nl, j -I n 2 n isolated node.Hence the coefficient of w w 2 'j...w p'j in Z E(G-x;w) is p nl,jAj.From Equation (3.1) it follows that the monomials occur in Z E(G-x;) and E(G) with equal coefficients.Hence the result follows.
w Throughout the rest of this section, we will assume that the graph has at least three nodes.Also 'reconstructible' would mean node-reconstructible.By the deck D G a graph G we would mean the set {G-x: xeV(G)}.
It is well known (see Harary [5], Kelly [6], and Chatrand and Kronk [7]) that disconnected graphs are reconstructible.It follows that H G is reconstructible if G is disconnected, and therefore the number of isolated nodes in G is reconstruc- tible.We can however, prove the latter independently.The following lemma gives a connection between the number of isolated nodes and DG.
LEMMA 4. Let G be a graph with p nodes.Then G has r (>0) isolated nodes if and only if D G has exactly r graphs with r-I isolated nodes and p-r graphs with r or more isolated nodes.
PROOF.Suppose that G has r isolated nodes.Then D G must be of the form described.Conversely, suppose that D G is as described in the theorem.Let k be the number of isolated nodes in G. Since every element of D G has at least r-I isolated nodes, G cannot have less than r-l isolated nodes or it would mean that the removal of each node from G yields at least one new isolated node, and this is impossible unless G is a matching (in which case the result holds).Therefore k _> r Since D G contains no elements with less that r-I isolated nodes, k#r-l.
Hence k > r-l.But exactly r elements of D G has r-I isolated nodes and only one node can be removed at a time from G to form an element of D G. Therefore G has exactly r nodes each of whose removal reduces k to r-l.These nodes must be themselves isolated nodes.
k _> r.Clearly k r.Therefore k r and the result follows.
From the above lemma, we see that b 0 (of Theorem I) can be obtained from D G- is given, then we can find HG provided that all the re- maining br'S (0 < r < n) can be determined.The following result is well known (see Tutte [2]).We will give different derivation using star polynomials.THEOREM 5. H G is reconstructible.
PROOF.Let G be a graph with p nodes.From Theorem 4, we have, by inte- grating both sides with respect to w l, E(G) f(ZE(G-x;w)) + C(w 2,w Wp), where C(w2,w ,Wp) is a polynomial in the weights w2,w w p Suppose that D G is given.Then Z E(G-x;w) can be found.Hence / Z E(G-x;_ can be found.But this polynomial contains all the simple terms except w There-P fore all the simple coefficients of E(G), except c can be immediately found p-I We will consider two cases (i) Cp_2 0 and (ii) Cp_2 # 0.
If Cp_2 0, then from Lemma 3, Cp_ 0 Therefore all the simple coeffi- cients will be defined.It follows from Theorem I, that H G can be found.If Cp_2 # 0 then c will be unknown.However b will be known from D G (Lemma 4) p-i Therefore the system of equations in Theorem will have p-I equations and p-! un- knowns.It can be solved to find b I, b 2, bp_ I. Hence NG can be found.
In the proof of Theorem 5, we did not give any useful practical method for find- ing H G, when c 0. We shall do so now.p-2 The equations of Theorem can be written as follows: w + 8ww2 + 19ww + 10WlW + C(w2,w3,w,w5).
[ poZyom%o of G (relative to the given weight assignment) is E(G;) Zw(C), is the number of edges in G. Therefore the sum of the valencies of the N n nodes of G is 2c kZ=l kb k b + kZ=2 kb k n =2c kE__2 kb k.
Let G be a graph with p nodes and let II G ple terms in E(G) are 6w w 2 Since the largest k for which w koccurs in E(G) is 4, it follows that n kb k 12 -2b 3b 12-8-3 I.
)bp_l + (p_2)bp_2 By adding and subtracting alternate equations, we get p-2c + c us denote the L.H.S. of this equation by S. Then S b + (-l)Pb p-l" bp_ (-I) p (S-D0)(3.3)SinceS can be found from the simple coefficients c (r p-2) and p, and b 0 r can be found (from Lemma 5), b can be found from Equation(3.3).Hence all the p-2 b's can be found by using the algorithm suggested by Theorem I.The following example illustrates the technique.
EXAMPLE 2 .
Figure I.It can be easily confirmed that2 2 By integrating with respect to w I, we get E(G) | 2,608.2 | 1988-01-01T00:00:00.000 | [
"Mathematics",
"Computer Science"
] |
Axiological Worldview of the Tajik Young People: Modern Values
. The axiological worldview of modern society may be described through a language. It is the language being a ‘tool’ of human consciousness and thinking that provides access to deep structures of consciousness. The axiological category of consciousness is also one of the key components of linguistic personality. Taking into account the relevance of the study devoted to axiological worldview of the Tajik society and values typical for modern young population, the study is based on a free association experiment conducted to reveal axiological dominants in language consciousness of Tajik young population. Students of the Russian-Tajik Slavonic University (RTSU) aged from 16 to 25 participated in the experiment. The choice of this age group to study axiological dominants made it possible to identify and analyze universal and modern values of the younger generation. The paper describes the results of the study covering modern values within the association consciousness of young people in Tajikistan.
Introduction
In linguistics the analysis of axiological preferences opens possibilities to study the national linguistic consciousness and to create the model of linguistic identity. The language fixes and reflects the system of values, attitudes, opinions of a certain society. All these combined may be called the axiological worldview.
The axiological worldview being one of the aspects of the human mindset is defined as the characteristic of the system of ideals guiding a person towards his preferences, objectives, motives and acts. The dominating values define what is the most important and significant in life of every individual. At the level of a social group there are certain accepted values shared by other people and unaccepted values which do not need any approval to follow them. However, the axiological dominants change over time in culture and in the human mindset. What was considered valuable in the last century may be irrelevant these days. This is explained by the fact that social, economic and political changes within a society may directly change the initial hierarchy of values in axiological system or introduce new values meeting the demands of a modern individual.
The axiological worldview includes the most critical meanings and valuable dominants, the combination of which forms a certain type of culture supported and maintained within a language. Besides, within one language culture this concept represents a non-uniform formation since different social groups may have diverse values. At the same time, the axiological worldview is present both in collective and individual consciousness.
Importance of the Problem
The language being the most amazing and at the same time the most sophisticated manifestation of a human, provides a person with linguistic means to produce diverse assessment of objects and phenomena of the reality. It is the language that creates, maintains and transfers values thus forming a unique axiological sphere within linguoculture of a certain nation. It is important to study axiological fundamentals of national linguistic consciousness, to create the model of a valuable system, to reveal national features within the axiological sphere of linguistic consciousness of Tajik young population.
The linguistic axiological study of value-based dominants of young people at the age between 16-25 years will make possible to reveal aspirations, interests, desires and objectives of modern young generation. The younger population constitutes that part of society, from which the society expects the most initiatives, development, improvements and changes.
Purpose of the Study
The purpose of this study is to analyze the values of young population of Tajikistan. The study in the field of various aspects of association consciousness is triggered in Tajikistan by the research group from the Russian-Tajik Slavonic University led by one of the authors of this paper within the project 'Cognitive and ethnopsycholinguistic study of the problems of tolerance and interethnic communications' (2015-2016). The study covered the issues related to ethnic stereotypes, sources of intolerance in the society, national identity [1]. This study was continued and resulted in the understanding that these aspects are closely linked to problems of linguistic discrimination [2]. However, it turned out that the problems related to the above aspects are also associated with axiological worldview. The study caused the need to identify the values of young population of Tajikistan forming the basis of their mindset.
The main methods of this study included the free association experiment, a descriptive method, a method of analysis and synthesis.
The free association experiment is an efficient method used to identify verbal associations, which give information on deep structures of linguistic consciousness. The free association experiment is based on the following principle: to the stimulus word (S) the respondents answer with words-reactions (R) coming to their mind first, at the same time the experimenter does not limit the respondents to neither formal nor semantic features of words-reactions.
The empirical data obtained during the experiment were classified and divided into the following groups: paradigmatic responses, syntagmatic responses, phrases, sentences, clichés (set phrases, sentences) and responses reflecting a proverb or a saying. In case of syntagmatic associations their grammatical class does not coincide with a stimulus word, such associations are always found in predicative relations. For example, S education -R higher, S career -R important. The associations, where words-reactions represent the same grammatical class as stimulus words, are called paradigmatic. For example, S education -R mind, S career -R money.
The next stage to study axiological dominants included the analysis of reactions to detect special characteristics of universal and modern values of young people. There was also an attempt to identify reactions to a stimulus word having the (positive or negative) assessment nature if those were present in answers of respondents. The value analysis resulted in the general calculation of the number of reactions to a stimulus word and identification of the ratio of single and non-single responses.
During the association experiment, the respondents were in total offered 16 values, of which 8 were universal (basic) values, such as family, health, friends, love, belief (religion), honesty, respect for adults and kindness. The other 8 values represented the values of modern society: career, money, wealth, visual appeal, education, tolerance, independence and success.
During the association experiment, the respondents were given a task to write the first associations coming to their mind regarding the stimulus values. The respondents had 10 minutes to complete the task alongside with an opportunity to give several associations to one stimulus.
The paper considers only a few associations with modern values of the young population.
Value Education
In recent years the value and understanding of education by modern young people has changed considerably compared to education of the Soviet period. Education became an integral part of the development of a 'stable' person in the period of unstable tenor of life within the modern society and the entire world. The public need in qualified specialists poses a demand to modern people in certain knowledge, skills and abilities necessary for professional or production activity. It is much quicker and easier for an educated person in present unstable society to adapt to social or political changes of public life. Besides, the quality of human life directly depends on education. It is no wonder that realizing this phenomenon the younger generation strives for education in order to ensure stability and confidence in the future.
The study of the value of education revealed that young people emphasize the high importance and need to get education through reactions: important 4, the most important 2, needed, the most necessary 2, everyone shall have it 3, compulsory 2, highly-demanded and responsibility. First of all, a person seeks to get education to develop himself and become intelligent (to develop as an individual, to develop erudition, sense, mind, to foster brain development). According to definitions given by respondents, education is characterized as high 19, average, normal, good and excellent. It is no wonder that students numerous times wrote high to the stimulus education since at this stage of their life they want to get higher education. There were reactions caused by the educational process: study 4, knowledge 2, RTSU 2, university 2, associate professor, school and reading. Young people associate education with future success and a diploma (to have a diploma), as well as with pride and reputation of a person. One respondent expressed the concern with low level of education in the city. The total number of reactions to education made 177, single answers -23 (13%), non-single answers -154 (87%).
Value Wealth
A person is actively involved in creation, accumulation and storage of wealth. People believe that wealth is very important and valuable. However, the definition of wealth is ambiguous since each person defines wealth and its place within the axiological worldview in a certain manner. Despite the individual nature of defining wealth, a person lives in a society, which automatically influences all members of this society thus 'forcing' them to adhere to a certain uniformity of views thereby ensuring the integration of society. Hence, the interaction of people within one environment leads to a relatively common idea of value and importance of wealth in human livelihood. Having defined and revealed the meaning of wealth in people linguoculture, what is its importance and how this wealth is reached, it is possible to draw a major conclusion on the human values for future development.
The analysis of students' reactions to a stimulus word wealth deminstrated that young people associate wealth with material and non-material benefits. Such universal values as family 13, happiness 8, health 7, relatives 2 (when the family is close), parents, love, respect, friends, family, mother and child are considered non-material benefits. Material benefits include money 12, resources, property, necessary things, luxury and house, which can be deserved and earned through work (several years of work, earn). It is better to have a moderate wealth, which brings peace. According to respondents, the wealth is achievement, authority and career of a person, as well as a source of security, success and power. The respondents believe that one cannot always be rich (
reactions-sentences: when you have a good girl; when your family is close; it is not always possible to be rich; it is a pity that wealth is the main thing for people.
According to the degree of frequence, the association field of a stimulus word wealth is presented by frequency reactions: family 13, money 12, happiness 8, health 7, (work 1, several years 1) of work 3, (earn) it is possible to earn 2, book 2 when you have a good girl 2, (when your family is close) relatives 2, parents 2, love 2, security, respect 2, 2 (not so important) not important; and single reactions: I will be rich, to have everything, necessary things, does not depend on money, it is not always possible to be rich, resources, friends, moderate, oh, yes!, success, need, it is a pity that wealth is the main thing for people, enemies, family, it is necessary, mother, property, nothing, house, luxury, I made it in life, power, peace, achievement, child, career, evil, passes, authority.
Value Career
In modern society, besides personal relations with members of a society, a person has social and production relations with representatives of this society. It means that the person is actively involved in professional activity, which gives an opportunity to use exceptional talents, skills and knowledge in practice. Work does not only provide professional environment for application and development of professional strengths of a person but stimulates and motivates a person for the upward move in the so-called 'career ladder'. In the 21st century the career became an absolutely new and relevant value. Young, educated and ambitious people spend more time, energy and efforts to achieve social heights. Successful career typifies one of the images of this social height.
A linguistic consciousness of a person can answer the question whether a career is important for modern Tajik young population. Lexemes used by people in linguistic consciousness can characterize, assess or give an idea with regard to surrounding reality. Thus, the free association experiment revealed that the participants of the study representing students of RTSU of various specialties understand the career as means of achieving the material and non-material benefits. They consider money 11, personal business 4, company, wealth and material security as material benefits. Career brings nonmaterial benefits in the form of success 4, respect 3, achievement, experience, development, self-realization, self-development and status. Career, as realized by young people, shall be successful and tremendous 2, but such career is reached only though human labor 4, diligence and hard work. The career takes place and exists in professional activity of a person (favourite profession, lawyer 2, management, manager, bank director). For some respondents a career is the objective of their life (to pursue an ambition, something we strive for), which they connect with hopes for the future (in the future 2, Insha'Allah 2, no, but it will come later). To make and achieve a career means growth over the years for young people, to be the best and to achieve the best. Besides, a person building a career has an opportunity to use the gained knowledge in career and to help people.
The opinions of respondents regarding the importance of a career in life were ambiguous. The high importance of a career is given in such reactions as it is necessary, needed, the most important, number one, while the low importance is found in such answers as a little bit important 2, nonsense, not the main thing in life.
Thus, the answers of respondents revealed the following paradigmatic reactions: money, business, purpose, diligence, work, success, successfulness, respect, lawyer, achievement, work, experience, management, manager, development, girl, selfrealization, independence, nonsense, dream, company, status, wealth, benefit; syntagmatic reactions: in the future, it is necessary, needed, tremendous, successful, do, I think; reactions-phrases: personal business, Insha'Allah, a little bit important, to be the best, the most important, bank director, self-development, growth over the years, favourite profession, material security, help, not the main thing in life, to achieve the best, to pursue the ambition, number one; reactions-sentences: no, but it will come later; all efforts and work of a person; to use the gained knowledge in career; what we strive for.
According to the degree of frequence, the association field of a stimulus word career is presented by frequency reactions: money 11, (personal 1) business 4, purpose 4, (diligence 1) work 4, (successfulness 1) success 4, respect 3, Insha'Allah 2, it is a little bit important 2, in the future 2, it (is necessary) needed 2, lawyer 2, achievement 2, tremendous 2, work 2 and single reactions: successful, experience, to be the best, management, manager, no, but it will come later, do, development, all efforts and work of a person, to use the gained knowledge in career, girl, self-realization, the most important, I think, independence, bank director, nonsense, self-development, dream, growth over the years, favourite profession, company, status, wealth, material security, help, benefit, not the main thing in life, to achieve the best, to pursue the ambition, number one, what we strive for.
Value Success
Success is another value of modern people. Success is quite often treated ambiguously. This ambiguity is caused by the fact that various people have different understanding of success, including certain, separate, and small achievements in various spheres of human life. It depends on the hierarchy of human values and on what priorities does the person set in life. For example, if an individual wants to get a well-paid job, then he/she will study hard and will seek to obtain a prestigious diploma in a reputable educational institution, which will further demonstrate his/her interest in sound academic background. Or, if a person wants to have a close-knit family, to raise children of education and culture, he/she will direct time, resources, efforts and thoughts towards family harmony. In such cases a person with a good job or happy family would be right to consider himself a successful person. The given examples indicate subjective human perception of success. Nevertheless, the modern society defined the common set of criteria illustrating human success. This set of success criteria was observed in reactions of respondents during the free association experiment.
Thus, modern young people of Tajikistan associate success with success in career 6, societal impact 2, money 2, position, social status, wealth, business, work and profession (to be a good professional). These associations may constitute the social success. However, such reactions as family 2, happiness, mother and home illustrate the fact that success is also achieved in private life. The majority of respondents were in one mind regarding the fact that a person becomes successful as a result of certain efforts (to achieve success, to study and work a lot, set targets and try to achieve them), endeavors (to try 2, aspiration, result of diligence), work (work 2, diligence, years of work), self-development (experience, good mind, clever brain, since childhood) and personal features (confidence 2, ability, activity, mind). At times the success is achieved as a result of good luck and fortune. Young people emphasize the importance of being successful in life in the following reactions: it is necessary 2, compulsory, yes, the best in life and of course. Generally, it may be concluded that the attitude of modern young people to the value of success is characterized as the purpose bringing material and 'spiritual' benefit and which shall be achieved in the future.
Thus, the answers of respondents revealed the following paradigmatic reactions: career, in career, diligence, work, confidence, family, money, influence, desire, aspiration, position, in life, in business, mother, wealth, happiness, since childhood, ability, strategy, chance, luck, mind, experience, home, work, benefit, purpose, activity; syntagmatic reactions: no, it is necessary, to try, it will be, in everything, surely yes, of course, average, personal; reactions-phrases: selfconfidence, family success, influence in society, years of work, to study and work a lot, a result of diligence, the best in life, status in society, to achieve success, set targets and try to achieve them, good mind, clever brain; reactions-sentences: it is not always possible to be successful; to be a good professional; I have no progress yet.
According to the degree of frequence, the association field of a stimulus word success is presented by frequency answers: (in career 1) career 6, (diligence 1) work 3, no 2, it is necessary 2, (in itself 1) confidence 2, to try 2, (family success) family 2, (in society) influence 2, money 2; and single answers: years of work, desire, aspiration, will be, position, to study and work a lot, in life, in everything, of course, yes, a result of diligence, it is not always possible to be successful, the best in life, in business, naturally, mother, wealth, happiness, to be a good professional, I have no progress yet, average, status in society, since childhood, ability, strategy, to achieve success, good luck, set targets and try to achieve them, luck, mind, experience, personal, good mind, home, work, benefit, purpose, activity, clever brain.
Conclusion
The analysis of modern values within axiological system of young people reveals the majority of reactions to education 177, wealth 91 and career 80. The bigger number of reactions ensures high ratio of non-single answers, which illustrates high uniformity of ideas among young people regarding such values as education, wealth and career.
Modern young people set a high value on education in life and seek to get it. The importance of getting higher education, which develops mental abilities of a person, is a key to successful career and material wealth. Young people more and more reject the previously common idea to get higher education for the sake of a diploma. They wish to gain solid and good knowledge. The current tendency of the labor market is focused on highly-qualified and competent workers, which is a necessary element towards competitiveness in any business domain.
Within the linguistic consciousness of respondents the value of wealth is associated, first of all, with such universal values as family, health, parents, happiness, love, respect, which demonstrates high standards of young people and their desire to acquire supreme values of human life, which do not depend on money.
In their pursuit for education the contemporary young people want to reach and build their future successful career. According to them, a career serves as means of achieving the social status (respect, influence, status, image, material wealth, etc.), which are presented by material and non-material benefits. At the same time the young generation realizes that in the modern world the successful career is only achieved through hard work, knowledge and diligence of a person. The young people associate success with achievements in career, money, social influence and status. The person achieves success through selfdevelopment, abilities, mind and activity, which implies work and efforts towards the achievement of success in any sphere of human life.
Thus, the analysis of modern values of Tajik young population made it possible to conclude that young people are socially active, well-focused in their aspirations, wish to achieve success, influence and status in the society through education, material wealth and career.
The obtained results will provide for better understanding of values shared by young generation and will allow taking measures to control and solve potential spiritual and moral problems since it is critical for the wellbeing of the society and for the future of the country in general. | 4,954.6 | 2018-01-01T00:00:00.000 | [
"Linguistics",
"Sociology"
] |
Auto-identification of unphysical source reconstructions in strong gravitational lens modelling
With the advent of next-generation surveys and the expectation of discovering huge numbers of strong gravitational lens systems, much effort is being invested into developing automated procedures for handling the data. The several orders of magnitude increase in the number of strong galaxy-galaxy lens systems is an insurmountable challenge for traditional modelling techniques. Whilst machine learning techniques have dramatically improved the efficiency of lens modelling, parametric modelling of the lens mass profile remains an important tool for dealing with complex lensing systems. In particular, source reconstruction methods are necessary to cope with the irregular structure of high-redshift sources. In this paper, we consider a Convolutional Neural Network (CNN) that analyses the outputs of semi-analytic methods which parametrically model the lens mass and linearly reconstruct the source surface brightness distribution. We show the unphysical source reconstructions that arise as a result of incorrectly initialised lens models can be effectively caught by our CNN. Furthermore, the CNN predictions can be used to automatically re-initialise the parametric lens model, avoiding unphysical source reconstructions. The CNN accurately classifies source reconstructions with a precision $P>0.99$ and recall $R>0.99$. Using the CNN predictions to re-initialise the lens modelling procedure, we achieve a 69 per cent decrease in the occurrence of unphysical source reconstructions. This combined CNN and parametric modelling approach can greatly improve the automation of lens modelling.
INTRODUCTION
Galaxy-galaxy strong gravitational lensing is a unique tool for investigating a wide variety of interesting astrophysical questions. Strong lensing has been used to investigate the nature of dark matter, such as placing lower bounds on neutrino masses in sterile neutrino dark matter models (Vegetti et al. 2018). Strong lensing has been effective in studying the mass profiles of elliptical galaxies both in the local universe and at cosmological scales (Koopmans & Treu 2003;Lagattuta et al. 2010). The lensing of extended sources allows for detailed analysis of galaxy density profiles which can provide insights into the dark matter substructure of galaxies (Vegetti & Koopmans 2009a,b). Combining strong lensing measurements with other probes, such as spectroscopy has lead to an increased understanding of the evolution of the mass profile in elliptical galaxies over cosmic time (Sonnenfeld et al. 2013). Time delay cosmography, where a variable background source such as a quasar is multiply imaged by a lensing galaxy allows for the inference of key cosmological parameters, such as the Hubble constant (Suyu et al. 2017); Wong et al. (2020).
In addition to learning about massive elliptical galaxies, strong lensing allows us to probe populations of high redshift source galaxies (Richard et al. 2011;Dye et al. 2018). Spatially resolved observations of strongly lensed star-forming galaxies enable the study of kinemat-★ E-mail<EMAIL_ADDRESS>ics on sub-kpc scales (Jones et al. 2010;Swinbank et al. 2009). High-resolution interferometers such as the Atacama Large Millimetre Array (ALMA) have made it possible to study these sources in exquisite detail (Dye et al. 2015).
There have been several surveys with a focus on lensing, such as the Sloan Lens ACS (SLACS) survey , the CFHTLS Strong Lensing Legacy Survey (SL2S; Cabanac, R. A. et al. (2007) and the BOSS Emission Line Lens Survey (BELLS; Brownstein et al. (2011). To date, the number of strong lensing systems we know of is still relatively small, measuring in the hundreds. This is set to change in the coming years, with two significant surveys coming online. Euclid (Laureijs et al. 2011), the European Space Agency's telescope scheduled to launch in 2022 will cover 15,000 deg 2 over 6 years and study the accelerated expansion of the universe out to a redshift of = 2. Additionally, the Vera Rubin Legacy Survey of Space and Time (LSST; Ivezic et al. 2008), also focused on the study of dark energy and dark matter, will commence science operations in 2023. LSST will cover 18,000 deg 2 over ten years in six different filters ( , , , , , ). It is expected that these surveys will discover many tens of thousands of lensing systems; 120,000 and 170,000 lenses for LSST and Euclid respectively (Collett 2015). For this reason, the development of fast, automated, and accurate pipelines for finding and modelling strong lenses is of great importance.
Typical methods for finding strong gravitational lenses are based upon visual inspection of candidate images that have been selected using properties such as morphology, colour and luminosity (Pawase et al. 2014;Sygnet, J. F. et al. 2010). Searches for high-redshift spectral lines present in lower redshift galaxies have been used to find strong gravitational lenses, such as in the SLACS survey. Techniques designed to identify arc-like structures and rings in images have been developed and applied to surveys with some success (Seidel & Bartelmann 2007;Gavazzi et al. 2014). Approaches based on the quality of fit to the data achieved by lens modelling have been developed (Marshall et al. 2009;Sonnenfeld et al. 2017), although the speed and flexibility of such approaches is a challenge for dealing with large amounts of data. Another approach to this problem utilises supervised machine learning algorithms, such as artificial neural networks and Gaussian mixture models (Bom, C. R. et al. 2017;Ostrovski et al. 2017). Recently, there has been interest in developing unsupervised machine learning algorithms to tackle the challenge of lens finding (Cheng et al. 2020).
Finding strong gravitational lenses is only one aspect of the challenge; they must also be modelled. When dealing with the lensing of an extended source, we wish to reconstruct both the source's intrinsic brightness distribution as well as model the mass distribution of the lens galaxy. One such method is that of semi-linear inversion (Warren & Dye 2003), a technique that reconstructs the pixelised source in a linear step for a given lens model. This technique has been placed within a Bayesian framework for optimising the model evidence (Suyu et al. 2006) and more recent implementations reconstruct the source on an irregular grid of pixels that can adapt to the lens magnification or the source surface-brightness (Nightingale & Dye 2015;Nightingale et al. 2018). Another method for reconstructing the intrinsic source makes use of the family of polynomials known as shapelets (Refregier 2003). An analytical reconstruction of the source can be formed using a small subset of these polynomials, leading to a reduced number of source parameters (Tagore & Jackson 2016). Convolutional Neural Networks (CNNs) have been used to reliably and automatically recover the mass-model parameters of galaxy-galaxy strong lenses in orders of magnitude less time than traditional parametric techniques Pearson et al. 2019). Furthermore, advancements have been made in the application of neural networks for reconstructing the background source of a strongly lensed system (Morningstar et al. 2019).
Techniques that model the lens mass with a parametric density profile remain a necessary and indispensable tool. There are significant difficulties involved in creating unbiased and sufficiently varied training sets for CNNs to learn from. This is a particular problem in the case of lensed high-redshift sources, where the source light is likely to be highly irregular. In addition, contamination of a lens data-set by objects such as galaxy mergers and ring galaxies poses a problem for CNN based methods. In these circumstances, a CNN will produce a set of lens model parameters without any indication of failure, whilst parametric modelling techniques will fail to fit the data since they operate within the context physically-motivated density profiles and are bound by the multiple imaging constraints of a real lens. Typically, it has been necessary to rely upon parametric techniques to obtain a robust measure of uncertainties on the lens parameters. Recently, however, a method for obtaining the uncertainties on CNN predicted parameters has been developed .
A particular issue for methods based on the pixelised source reconstruction is the existence of unphysical solutions (see Section 2 for details). Such solutions are perfectly valid, providing excellent fits to the data and can be challenging for sampling algorithms to avoid. An unsupervised modelling run can spend large amounts of time exploring the parameter space around these solutions and never converge towards the true parameter values. These solutions can be avoided with careful tuning of the model parameters, but this represents a significant investment of time for each system being modelled. For this reason, we have developed a CNN based approach to recognise these unwanted solutions and a simple prescription for updating the priors in our model to aid convergence towards the true solution. In this manner, we can iteratively improve our lens model by identifying and avoiding reconstructions that correspond to under and over-magnified solutions.
The paper is organised as follows: Section 2 describes the occurrence of unphysical solutions in the modelling process and their properties. Section 3 discusses the methodology for simulating the required images of strongly lensed galaxies, and the processes involved to create source reconstructions from these images. Additionally, an overview of the CNN architecture is provided with details on how the network was trained and the manner in which the CNN was used in conjunction with our modelling process. The results of applying this technique to our testing set of data are presented in Section 4. Finally, the results in this work are discussed along with our conclusions in Section 5. Throughout this paper we assume a flat ΛCDM cosmology using the 2015 Planck results (Planck Collaboration et al. 2016), with Hubble parameter ℎ = 0.677 and matter density parameter Ω = 0.307.
ERRONEOUS SOLUTIONS AND THEIR INVERSIONS
One of the key motivations for using the Semi-linear inversion method is the reduced computational complexity of the lens modelling process. Using analytic profiles to model the complex source light of a lensed galaxy can require exploring a highly multidimensional parameter space. Not only does this increase the likelihood of inferring a solution corresponding to a local maximum in evidence, but can also lead to biasing of the lens model due to constraints on the light profiles. Semi-linear inversion allows us to reconstruct the source light distribution in a linear step and since this distribution is pixelised, it is not constrained by an analytic profile. It does however introduce a new set of problems for the modelling process, namely under and over-magnified solutions.
These so-called under-magnified and over-magnified solutions can be understood in terms of the inferred amount of mass in the model lens galaxy. Here, we use the Einstein radius as a proxy for the mass in a galaxy. Ideally, the modelling process will converge upon the true value of the Einstein radius, along with the other model parameters, and the reconstructed source will reproduce the unlensed features of the source galaxy. If however, the modelling process converges upon a solution with too small an Einstein radius, the resultant deflection angles will also be under-estimated. This leads to the formation of an under-magnified image of the observation itself. Similarly, a model with too large an Einstein radius will over-estimate the deflection due to the lens. This will lead to an over-magnified, but this time, parity inverted image of the source. Fig. 1 illustrates this point with stylised ray diagrams for each class of source reconstruction we are considering.
Whilst these erroneous source reconstructions are obviously not the physical solution we are looking for, they exist nevertheless and can provide excellent fits to the data, thus posing a challenge for sampling algorithms to avoid them. Fig. 2 shows an example of another set of source reconstructions for a simulated observation. Here, we also show the residual and chi-squared maps for each reconstruction, showing the quality of the fit to the data. The Bayesian evidence is comparable for the under-magnified solution and the correct solution,
Observation
Ray whilst it is significantly lower for the over-magnified case. Generally speaking, we find that the under-magnified solution is much more probable to occur than the over-magnified one. This is likely due to the regularisation employed in the semi-linear inversion process. Regularisation serves to penalise overly complex solutions, which is certainly a characteristic of the over-magnified solution. In addition to regularisation reducing the likelihood of this solution, it can often be excluded by sufficiently accurate masking of the lens system. Provided the mask used when modelling the system does not extend considerably farther than the image separation, it can be used to set the upper-bound on the Einstein radius prior.
It is usually clear to the experienced modeller when something has gone wrong and an erroneous source reconstruction has been produced. It is not however so easy to discriminate between these solutions programmatically. Multiple techniques can be employed to avoid these solutions; careful tuning of the prior distributions on the lens model parameters is effective but time-consuming. For this reason, it is not a suitable method for dealing with the large numbers of lensed galaxies we expect to encounter in the coming years. Another possibility, which has the benefit of being automatic, is to create a pipeline of models that first fits an analytic light profile to the source galaxy and then uses the results of this fit to initialise the priors in the inversion process. By requiring a compact source in the initial phase of modelling, the aim is to infer a lens model sufficiently accurately to effectively rule out regions of parameter space that would correspond to under or over-magnified solutions. This lens model, along with new priors on its parameters is then used in the inversion process to refine the lens model and more accurately fit the source galaxy's light. The complex morphology of high-redshift sources poses a challenge for fitting the data with an analytic light profile, which can lead to a poorly constrained or entirely wrong lens model. If the inferred lens parameters used to initialise the model in the inversion process is of poor quality, then the modelling can once again fail at this step. Our approach to this challenge is to use a CNN that can accurately classify source reconstructions as successful or under/over-magnified. In this way, we completely remove the need to assume an analytic light profile for the source since we can throw away unwanted solutions in the inversion process that do not correspond to a compact reconstructed source. Furthermore, we have developed a simple method for updating the model to move away from these unwanted solutions towards the correct parameters. This technique requires no human intervention and the CNN classification step is extremely fast (<1s).
METHODOLOGY
The CNN described in this work requires training data consisting of labelled source reconstructions and residual images. To produce this data, it was first necessary to create a large number of simulated strong gravitational lens images. We used the lens modelling software PyAutoLens 1 (Nightingale & Hayes 2020;Nightingale & Dye 2015;Nightingale et al. 2018) to produce our simulated images and to perform the source reconstruction. Multinest (Feroz et al. 2009) was used for the exploration of parameter space where a full analysis of the data was carried out. The modelling process produces the residual images between the simulated observations and the reconstructed model image that we need for training the CNN. In Section 3.1 we describe our procedures for generating the simulated strongly lensed images. Section 3.2 details our method for generating the source reconstructions and residual images required for training our neural network. We then describe the CNN architecture used in this work in Section 3.4. The process used to update the prior distributions on the model, based on the CNN predictions is then detailed in Section 3.5.
Lensing Simulations
In this work, we have assumed that all of the foreground deflectors are early-type galaxies, and so we have adopted the Singular Isothermal Ellipsoid (SIE) mass profile (Keeton 2001). For the light profile of the background lensed galaxies, we have opted to use the Sérsic profile since it can represent a wide variety of galaxy morphologies.
The data sets generated for this work were simulated to have distributions of parameters similar to those observed in the Sloan Lens ACS (SLACS) survey ). The Einstein radius and axis ratio of our lensing galaxies were drawn from distributions fitted to the measurements of 131 strongly lensed galaxies observed in the SLACS survey (Bolton et al. 2008), whilst the orientation was allowed to vary uniformly over the full range. The Einstein radii of our lenses were drawn from a normal distribution with mean Figure 3. A selection of simulated images produced for this work, used for creating pixelised source reconstructions to train a CNN. All images have a pixel scale of 0.1 arcsec pixel −1 = 1.16 and a standard deviation = 0.42. The axis ratios of our SIE profiles were randomly sampled from a normal distribution with mean = 0.80 and standard deviation = 0.16, in close agreement with empirical studies . In all cases, the centroid of the lens was placed in the centre of the image. In this work, we did not include light from the lens galaxies in the simulations.
As with the lenses, the parameters describing our source galaxy sérsic profiles were randomly sampled from fitted distributions. In this case, we used the inferred Sérsic parameters from the parametric source reconstructions of a subset of the SLACS lenses (Newton et al. 2011). The Sérsic indices , of our sources, were randomly drawn from an exponentially modified Gaussian distribution with scale parameter = 0.723, mean = 0.71 and standard deviation = 0.97. The effective radii eff of our sources were randomly sampled from an exponential distribution with scale parameter = 6.64. We allowed the axis ratio of the sources to vary uniformly over the range [0.3, 1]. The overall intensity normalisation of the sources was drawn from a uniform distribution ∼ [10, 20] electrons s −1 , allowing for a wide variety of signal to noise ratios in our training data. The centroid of each source was uniformly distributed in the source plane, with the requirement that it lay inside the Einstein radius of the lens (i.e that there are multiple images).
In the production of our simulated images, we opted to use the pixel scale of the VIS instrument for Euclid (0.1 arcsec pixel −1 ) and the characteristic exposure time of 565 seconds (Cropper et al. 2016). The lensed image was then convolved with a Gaussian point spread function with a full-width at half-maximum of 0.17 arcseconds. A background sky of 1 electron −1 and Poisson noise due to the background sky and source light photon counts were added to the images, thus completing the simulation procedure. Some examples of our simulated images are shown in Fig. 3.
Training Data
The CNN was not trained directly on the simulated images, but rather the pixelised source reconstructions and residual images obtained from the modelling process. Before the modelling began, each simulated image needed to be masked to ensure that only the area of interest was reconstructed in the source plane and to reduce the computational load. Due to the large number of simulated images, an automated masking scheme was used. Firstly, the images were thresholded using the minimum cross-entropy approach (Li & Lee 1993). Then, the centroid of this thresholded image was found through calculating its moments. A circular annular mask, centred on the centroid of the image was then fitted to the thresholded pixels. For the inner radius of the annulus, the largest radius circle that did not contain any unmasked pixels was found, and 90 per cent of this value was used. Similarly, for the outer radius, the smallest circle containing all of the unmasked pixels was computed, and 110 per cent of this value was used. These adjusted values for the inner and outer radii of the mask were used to minimise the chances of masking out faint emission from the source.
These masked images were then modelled using PyAutoLens to produce the pixelised source reconstructions and residual images that we need for training our CNN. In all cases, we adopted the SIE mass profile to model the lens galaxy. We reconstructed the background source on a pixelised grid that adapts to the magnification of the system. For each simulated lensed image, we created three source reconstructions and three residual images, corresponding to the under-magnified, over-magnified, and correct solutions. This resulted in approximately 300,000 images to be used as training data for our network. To deal with such a large computational task, it was necessary to employ some approximate methods in the source reconstruction/lens modelling process.
For 250 of our simulated images, we performed a full analysis of the data, optimising the lens model and source parameters in the inversion process. In each case, the analysis had to be repeated three times, to produce the under-magnified, correct and over-magnified source reconstructions. When modelling each of these systems we allowed the mass-model parameters to vary uniformly over the full range of parameter space with the exception of the Einstein radius. To produce an under-magnified source reconstruction, we set a uniform prior distribution on the Einstein radius with an upper limit of 0.9 times the true value for the system, thus forcing PyAutoLens to find the under-magnified solution. To produce source reconstructions corresponding to the correct model, we allowed the Einstein radius to vary over a small range centred on its true value, guaranteeing that a sensible source reconstruction is produced. Finally, to produce overmagnified source reconstructions, we allowed the Einstein radius to vary over a range of 1.1 times the true value up to 3 times this value, again forcing PyAutoLens to find the over-magnified solution. In this manner, we built up an understanding of the properties of each class of source reconstruction.
In these tests, we observed that the mean fractional error in Einstein radius when producing an under-magnified source reconstruction iŝ ≈ −0.5. As expected, we observed no significant bias in the Einstein radius, or any of the other parameters, when using a model with priors accurately centred on the true parameter values. The mean fractional error in Einstein radius when producing over-magnified reconstructions wasˆ≈ 2. A scatter plot of the true value of Einstein radius versus the inferred value for each class of source reconstruction is shown in Fig. 4 along with the coefficients of a linear fit to the data. These fitted parameters allowed us to define an approximate transformation of the Einstein radius taking us from one class of source reconstruction to another. We found that the Einstein radius was the key parameter in controlling which class of source reconstruction was obtained. Fig. 5 shows that in both cases of erroneous source reconstructions, the axis ratio of the lens is most often under-estimated, but it does not follow an easily predictable pattern in the same way as the Einstein radius. Fig. 6 shows that there is no apparent relationship between the inferred orientation of the mass profile and its true value when either the under-magnified or over-magnified solution is found.
The relationship between the unphysical reconstructions and the correct solution allowed us to rapidly generate source reconstructions without the need for a full optimisation of the lens model. Fig. 4 shows how the predicted value of the Einstein radius relates to the true value in each of the three classes of source reconstruction we are considering here. The coefficients of a linear fit to the data allow us to construct an approximate transformation of the predicted Einstein radius to the true value for a given system. As expected, in the case of successful source reconstructions, the inferred value for the Einstein radius very closely matches the true value. The under-magnified solutions have inferred Einstein radii,ˆthat can be approximated aŝ U ≈ 0.46 E − 0.08, where is the true value for the system. Similarly, in the case of over-magnified solutions, the inferred Einstein radiiˆcan be approximated asˆ0 ≈ 2.11 E + 0.16. Using these approximate transformations, along with the true parameters describ-ing the lens, we identified the regions of parameter space where we expect each class of source reconstruction to occur. Keeping the position, axis ratio and orientation of the lens fixed to the truth, we varied the Einstein radius around its expected value and computed the linear inversion for each sample. The inversion achieving the highest evidence is considered to be the solution and we record the source reconstruction and residual image for our catalogue of training data.
Testing Data
A portion of the training data, produced as described in Section 3.2, was set aside for evaluating the CNN's performance after training. These simple source reconstructions allowed us to test the network on a set of images with similar properties to the training data. In addition, to explore whether our CNN trained on reconstructions of simple parametric sources would be capable of classifying the reconstructions of more complex lensed sources, we produced SIElensed images of high redshift galaxies extracted from the Hubble Ultra Deep Field (HUDF; Beckwith et al. 2006). For this, we used the Pipeline for Images of Cosmological Strong lensing (PICS; Li et al. 2016), simulating images to have the expected properties of Euclid VIS data (Cropper et al. 2016;Niemi 2015). A sample of these simulated images is displayed in Fig. 8. For each of these simulated images, we produced a source reconstruction corresponding to the under-magnified, over-magnified and accurate solution, following the same full analysis procedure described in Section 3.2. These source reconstructions, along with the residual images of the models that produced them, were used to test the CNN's classification ability on significantly more complex images than it was trained on. A sample of the accurate HUDF source reconstructions is shown in Fig. 9.
CNN Architecture
Deep Neural Networks are a class of Artificial Neural Networks, consisting of multiple interconnected layers of nodes. The output of a node depends upon the weights of the connections made by the previous layer, as well as the bias of the current node. This information is fed into a non-linear activation function, controlling the strength of the output. CNNs are a further subset of neural networks built around multi-dimensional data. Convolutional filters, also known as kernels, are applied to the input to extract features from the data.
The network we built to classify our source reconstructions has a forked design, with two input paths. Each path consists of three convolutional layers and three max-pooling layers. The outputs of both paths are concatenated, before being flattened and fed into two fully connected layers. Dropout is employed between each layer to improve the network's resistance to over-fitting and the Leaky Rectified Linear Unit activation (Leaky ReLU; Nair & Hinton 2010) function is used everywhere except for the final layer which employs the Sigmoid activation function. The Leaky ReLU activation function allows a small positive gradient for negative input values.
The tuneable hyper-parameters for our network, such as the number of convolutional layers, the size of the kernels and the dropout rates were set by a process of hyper-parameter optimisation. We opted to use Talos (Autonomio 2019) to automate the evaluation of model performance. In order to explore the very large parameter space, it was necessary to down-sample and look at a small fraction of combinations of parameter values. Once a rough estimate of hyperparameters had been obtained, a more thorough search was carried out in a smaller region of parameter space.
The network aims to predict the category of source reconstruction (1) where is the target value andˆthe predicted value. The network optimisation used the Nadam optimiser, which is a combination of stochastic gradient descent and Nesterov momentum (Dozat 2015).
The CNN was trained and tested on a GPU machine, vastly improving the time taken to process large numbers of images. The training took place over 50 epochs, using 120,000 pairs of images.
The weights and biases of the network are summarised as follows: • Convolutional layer: For an input image of height 1 and width 2 , the input is an ( 1 , 2 , 1) matrix. The output of a convolutional layer is an ( 1 , 2 , ) matrix, where N is the number of output filters applied in the convolution. Training adjusts the biases and weights for each filter, but their values remain fixed during each iteration. Each kernel of dimension ( 1 , 2 ) has an associated bias, giving a total of 1 × 2 × weights and N biases for each convolutional layer. The exact dimensions of each kernel are given in Fig. 10.
• Concatenate: After the three convolutional layers in each input path of the network, the outputs are concatenated to form a tensor with dimensions (13, 13, 256).
• First fully connected layer: The input is a flattened 43,264-node array, whilst the output is a 512-node array. Accordingly, there are 43, 264 × 512 weights and 512 biases.
• Final layer: The input is an array with 512 nodes, whilst the output is a 3-node array (one node for each class of source reconstruction), hence there are 512 × 3 weights and 3 biases.
• There are a total of 5,820,323 trainable parameters.
Combining CNN and Lens Modelling
The trained CNN is capable of taking a source reconstruction and a residual image, both of which are outputted in the lens modelling process, and returning an accurate prediction of whether the correct lens model has been found, or whether an under/over magnified solution has been identified. This prediction, along with the knowledge of how the inferred Einstein radius relates to each class of solution allows us to automatically correct the modelling process when erroneous solutions are found. Using the approximate transformations given in Table 1 we can update the model's prior distribution on Figure 9. A selection of accurate source reconstructions of SIE-lensed HUDF galaxies. These reconstructions were used to test CNN performance on more complicated sources than the simple parametric sources used to create its training sample. Figure 10. Structure of the CNN used in this work, showing the two input images and their respective paths in the network. There are six convolutional layers, each with max-pooling and dropout. A concatenation and flatten layer is included to join the outputs of the dual convolution pathways and connect this tensor with a 1D dense layer. LeakyReLU is used throughout the network, except for the activation of the final layer, which uses the Sigmoid activation function. The types of layers in the network at each step are given, along with the size of the kernel in pixels. The output dimensions are indicated above each block. A more detailed description can be found at the end of Section 3.4. for subsequent modelling. In this way, we aim to improve the robustness of our modelling process against unwanted solutions and reduce the amount of human intervention required to produce accurate lens-models and source reconstructions. When considering the predictions of our CNN, we will use the abbreviation UM to refer to a predicted under-magnified solution, OM for a predicted overmagnified solution and C for when the network predicts a correct reconstruction.
To test this hybrid approach to lens modelling, we simulated a new set of 100 lensed images, following the approach detailed in Section 3.1. We used PyAutoLens to model each system, conducting a full analysis, allowing all the SIE mass-model parameters to vary and reconstructing the background source on a magnification based Voronoi grid. For all of the mass-model parameters, as well as the source plane pixelisation parameters, we opted to use uniform distributions covering a suitable range of parameter space. We chose a uniform prior distribution for the position of the lens centroid, centred on the true value with a width of 0.6 arcseconds. In the case of the orientation of the lens, we allowed the full range of values ∼ [0, ] radians. The axis ratio of the lens, was able to vary over the full range of values included in the simulations ∼ [0.25, 0.999]. Again, the prior distribution of the Einstein radius followed a uniform distribution constrained only by the dimensions of the annular mask (computed according to the criteria detailed in 3.2, . Such an approach to modelling the data was taken to show the extremes of how things can go wrong without some tuning of the priors before modelling begins. Furthermore, this serves to illustrate the problems experienced by sampling algorithms when exploring large and complex parameter spaces.
Once this initial round of modelling was completed, the source reconstruction and residual images were fed into our CNN to obtain a prediction on whether the modelling had been successful or not. The next step in the process depends on the prediction of the CNN as follows: • UM prediction: The modelling process is repeated with an updated prior distribution on the Einstein radius. This new prior is defined in Table 1. The prior distributions on the other free parameters were left unchanged.
• C prediction: In this instance, we choose to repeat the modelling process with a decreased evidence tolerance and a narrowed uniform prior distribution centred on the inferred values from the previous modelling run. The goal of this repeated run is to more thoroughly explore the parameter space around the accepted solution and improve the accuracy of the model.
• OM prediction: The modelling process is repeated with an updated prior distribution on the Einstein radius, whilst leaving everything else unchanged. This new prior is defined in Table 1.
After this additional stage of modelling, the updated source reconstructions and residual images were fed into the CNN once more, providing a new prediction for each system. With this information, we proceeded similarly to before, but now we take into account the history of results for each system.
• UM prediction: -If the previous prediction was also UM, then the system is flagged for manual intervention at a later time. This indicates that the process for updating the priors was unable to move the model away from this solution, or that the CNN has misclassified a reconstruction.
-If the previous prediction was OM, this indicates that the prior update has 'overshot' the C solution and so a uniform prior on the Einstein radius is chosen to lie between the two previous values. The width of the prior was set such that it excludes the regions of parameter space that corresponded to the previous under and over-magnified solutions.
• C prediction: -If the previous prediction was UM, as before, we chose to repeat the modelling process with a decreased evidence tolerance and use narrowed uniform prior distributions centred on the inferred values from the previous modelling run.
-if the previous prediction was C, no further action required.
-If the previous prediction was OM, again, we choose to repeat the modelling process with a decreased evidence tolerance and use narrowed uniform prior distributions centred on the inferred values from the previous modelling run.
• OM prediction: -If the previous prediction was also OM, then the system is flagged for manual intervention at a later time. This indicates that the process for updating the priors was unable to move the model away from this solution, or that the CNN has misclassified a reconstruction.
-If the previous prediction was UM, this indicates that the prior update 'overshot' the correct solution and so a uniform prior on the Einstein radius is chosen lying between the two previous values. The width of the prior is set such that it excludes the regions of parameter space that corresponded to the previous UM and OM solutions.
This process can be repeated many times until an acceptable fraction of the CNN's predictions are that the correct model has been found. In practice, due to the crude nature of the prior-updating routine, there are diminishing returns on repeated cycles. The systems that become manually flagged during this process will need human intervention to guide the modelling to a suitable solution, but the overall load on the modeller is greatly reduced.
RESULTS
In this section, we present the results of testing our CNN on the reserved data-set, evaluating its performance on a per-class basis. We show that the CNN performs exceptionally well at the task of classifying source reconstructions. Additionally, we show the result of modelling 100 simulated observations using the procedure outlined in Section 3.5. This set of images were simulated according to the procedures outlined in subsection 3.1. Here, we opted to apply our iterative approach three times, observing good progress towards a complete sample of successfully modelled lenses with each step.
CNN performance
The CNN was trained on 130,000 pairs of source reconstructions and residual images, for 50 epochs. 10,000 pairs of source reconstructions and residual images were used as validation data throughout the training process. To further increase the variety in the training data, augmentation techniques were employed. Each pair of images was randomly reflected horizontally, vertically or rotated through an angle. The remaining 6,928 pairs of images were reserved as a testing set to evaluate the performance of the network on never before seen images once training had completed. Fig. 11 shows the confusion matrix for the CNN evaluated on the Figure 11. Confusion matrix for the CNN when tested on 6,928 never seen before pairs of source reconstructions and residual images for a simple Sersic source. The confusion matrix has been normalised over its rows.
testing data set. The elements of this matrix are defined such that , contains the number of true objects of class predicted to be in class . Thus the diagonal elements of represent the correctly labelled instances and the off-diagonals where the network has incorrectly labelled an observation. The values displayed in are normalised over the rows. The CNN's recall or ability to find all samples of a particular class is above 99.9 per cent in all cases and performed perfectly on our test set for both under and over-magnified source reconstructions. Similarly, our CNN's precision, or ability to not label a sample of as is greater than 99.9 per cent in all cases, with a perfect score in the case of successful source reconstructions. i.e, only successful source reconstructions were labelled as such. These results are summarised in Table 2.
As a further test of the CNN's ability to accurately classify source reconstructions, we applied it to the more complex HUDF source reconstructions described in Section 3.3. Here, the CNN gave predictions on 100 each of under-magnified, over-magnified and accurately reconstructed sources. We found that our CNN correctly classified 87 per cent of the under-magnified reconstructions, whilst misclassifying them as correctly reconstructed 8 per cent of the time, and incorrectly classifying 5 per cent of them as over-magnified. The CNN gave accurate predictions for 87 per cent of the correctly reconstructed sources, whilst incorrectly labelling 10 per cent as under-magnified and 3 per cent as over-magnified. Finally, the CNN correctly labelled 93 per cent of the over-magnified reconstructions, with just 3 per cent incorrectly labelled as under-magnified and 4 per cent mislabelled as accurate reconstructions. These results are summarised in Fig. 12. The performance of the CNN on this complex dataset is remarkably good, given the simplicity of the reconstructed sources in the training data.
Combing CNN with PyAutoLens
Here, we describe the results of applying our CNN to blindly modelled data. For this, we have used our simulated images of Sersic sources. We describe the process of using our CNN predictions to automatically adjust the prior distributions on the Einstein radius in three subsequent rounds of modelling.
The results of this are presented in Fig. 13. The initial modelling of this set of 100 lenses was carried out with no prior information on the lens model parameters and as such, under-magnified solutions have dominated the output. The bottom-right histogram in Fig. 13 shows how the proportion of different source reconstructions changes with each iteration of modelling according to our CNN predictions. Initially, our CNN identifies 88 models as UM, 11 as OM, and just 1 is identified as C. This is reflected in the error distributions for the key SIE mass model parameters. The top-left distribution in Fig. 13 shows the fractional error in Einstein radius for all 100 systems. There is a very significant peak in the initial data at = −0.45, representing the large number of under-magnified solutions, and thus under-estimated Einstein radii. We also see in the top-right distribution of Fig. 13 the significant bias towards under-estimating the axis ratio of the lens. The bottom-left distribution, showing the absolute error on the inferred orientation of the lens, reflects the seemingly random relationship between the erroneous models and the true lens orientation. Labelled as rerun 1, rerun 2, and rerun 3, we show that the application of our CNN and prior updating routine to these results leads to a huge improvement in recovering the true lens parameters for the sample. After rerun 1 has been completed, much of the bias in the Einstein radii fractional error distributions is removed, though there is still significant density in regions indicating under and overestimation of its value. Similarly, in the case of the axis ratio, a clear peak around = 0 has been formed, removing much of the probability mass in the under-estimate region of before. The inference of the orientation of the lens has also been greatly improved, as we would expect by increasing the number of successfully modelled systems. These results are reflected in the bottom right histogram of Fig. 13, showing that the proportion of successful source reconstructions has increased from 1 to 52, according to our CNN predictions. The number of under-magnified reconstructions has been decreased by 68, down to just 20. The frequency of over-magnified solutions has increased, however, suggesting that our scheme for updating the Einstein radius prior has 'overshot' the correct solution in some cases. Rerun 2 increases the number of successful reconstructions by a small margin, but mostly results in moving solutions from the overmagnified category into the under-magnified category. Significant improvements are made in the final round of modelling, rerun 3, by considering the history of models for each case. For a system that has models that have previously been classified as under-magnified and over-magnified, we can search parameter space between the inferred Einstein radii values and hopefully converge upon the correct solution. In all of the error distributions for the mass-model parameters, we see improvements, i.e taller, narrower peaks centred on zero. After the final round of modelling, we achieved a decrease of 69 per cent in the occurrence overall of unphysical source reconstructions. The final count of successful source reconstructions stands at 70, with 17 under-magnified and 13 over-magnified solutions. In principle, we could continue with this process until we no longer see any improvement in the number of successful source reconstructions being identified by the CNN, or all systems that have not been labelled as C become flagged for manual inspection.
CONCLUSIONS
Strong gravitational lensing allows us to probe the mass distributions of the lensing galaxy as well as the properties of the background sources. Upcoming surveys such as LSST and Euclid are expected to observe in excess of one hundred thousand strong gravitational lenses. To deal with this huge amount of data, it is necessary to develop fast, robust and automatic lens modelling pipelines that do not require significant time investment from humans for each system. For this reason, we constructed a CNN to detect when the modelling process has gone awry and developed a simple scheme for automatically adjusting the prior distribution on the Einstein radius to guide the sampler to the correct solution. Simulated images with the resolution and expected seeing characteristics of the Euclid VIS instrument were created, to be used as inputs for the production of source reconstructions. We chose to simulate all of our lenses as SIEs and used Sérsic profiles for our sources. In both cases, we used realistic distributions of parameters that matched those observed in the SLACS survey. From these simulated images, we produced three source reconstructions for each observation corresponding to the under/over magnified solution and the correct solution. These source reconstructions, along with the residual images for the model were used to train a CNN to classify source reconstructions. We then blindly modelled 100 strong lenses, reconstructing the background sources on a Voronoi grid. The CNN was used to detect the kind of source reconstruction that had been produced, and this information coupled with a simple scheme for updating the prior distribution on the Einstein radius was used to improve upon the fraction of successfully modelled systems.
We find that our CNN is capable of extremely accurate identification of under-magnified, successful and over-magnified reconstructed sources. The network achieves a precision and recall over 99.9 per cent, as well as an 1 -score, or harmonic mean of the precision and recall, greater than 0.99 across all classes of source reconstruction. In addition to identifying the class of solution that has been found, we have shown that a simple procedure for updating the model based on its predicted class can lead to significant improvements in the outcomes of blind modelling without the need for human intervention throughout the process.
The success of our CNN in this task suggests that our procedure for generating the source reconstructions, omitting the full exploration of parameter space, has not negatively impacted its ability to perform the task. The axis ratio of the SIE mass-model corresponding to an erroneous solution tends to be under-estimated. Our network is trained on source reconstructions produced by fixing the axis ratio to its true value. This leads to the network being trained on images produced by less elliptical lens models than it might encounter when being tested upon a freely varied model.
It is possible that incorporating the information regarding erroneous source reconstructions tendency to have an under-estimated lens axis ratio could lead to improvements in our procedure for updating the model priors. An approach that uses a Gaussian prior to bias towards higher values of , but with a standard deviation large enough to easily allow the exploration of the lower end of parameter space is something that could be investigated.
We have also tested our CNN, trained on reconstructions simple Sersic sources, on reconstructions of images generated using real sources extracted from the HUDF. The CNN continued to perform well, showing that it can generalise to a more complex dataset without any retraining. There is however an obvious detriment to the performance of the network, and so the construction of a more complex training set would likely be beneficial. Before this technique can be applied to real data, further investigations into how our simplifications affect the network's performance are needed. One such simplification that we made was to omit lens light from our simulated images. Even in the best possible scenario of lens light removal, its presence will affect the noise characteristics of the image, which can impact the source reconstruction. Realistic features in our simulated images such as cosmic rays and hot pixels were not considered. Increased complexity of the sources in our training data would be required to deal with the variety of real images that might be observed and to minimise the performance decrease due to an overly simplified training set. The question of how well this method of applying CNN predictions to parametric models generalises to real data requires further investigation. | 11,006.8 | 2020-12-08T00:00:00.000 | [
"Physics",
"Computer Science"
] |
WP-UNet: Weight Pruning U-Net with Depth-wise Separable Convolutions for Semantic Segmentation of Kidney Tumours
Background Accurate semantic segmentation of kidney tumours in computed tomography (CT) images is di�cult because tumours feature varied forms and, occasionally, look alike. The KiTs19 challenge sets the groundwork for future advances in kidney tumour segmentation. Methods We present WP-UNet, a deep network model that is lightweight with a small scale; it involves few parameters with a quick assumption time and a low oating-point computational complexity. Results We trained and evaluated the model with CT images from 300 patients. The�ndings implied the dominance of our method on the training Dice score (0.98) for the kidney tumour region. The proposed model only uses 1,297,441 parameters and 7.2e FLOPS, three times lower than those for other network models. Conclusions The results con�rm that the proposed architecture is smaller than that of U-Net, involves less computational complexity, and yields good accuracy, indicating its potential applicability in kidney tumour imaging.
Introduction
American Cancer Society has reported on the prevalence of kidney cancer in both men and women.Overall, the lifetime risk to develop kidney cancer is approximately1/48 and 1/83 for men and women, respectively.The types of kidney cancer in this study were of an advanced stage.Kidney cancers are generally this advanced because the kidneys are situated deep inside the body and are not physically perceived on a physical inspection.Several imaging methods are currently in use to track the growth of kidney tumours.This method has become increasingly popular because it can selectively extract diseased tissues and retain additional stable tissue.This approach was successful in treating small kidney masses.After the precise evaluation of the kidney tumour, details such as the kidney, tumour structure, and others can be collected.In a recent study (Hesamianet al.,2019), it was impossible to derive the essential details from computed tomography (CT) or magnetic resonance imaging scans.Kidney tumours vary in colour, form, and scale, and have a similar appearance to their parenchyma and other nearby tissues.Given the segmentation of the kidney (Kanishka Sharma, 2017) tumour area, segmenting kidney tumours is extremely di cult.
Currently, there is an increased need to deploy deep learning solutions on mobile handheld devices (Hooman Vaseli, 2019), embedded systems (Karakanis al., 2020), or machines with minimal resources.An important reason why convolutional neural networks (CNNs) are challenging to train is because they are over-parameterised (Denil, 2013), and they typically require greater computational power and storage space for training and inference.Deep learning researchers have claimed many 'pruning' strategies or quantising learned parameters on broad image datasets (LeCun et al., 1990;Alvarez and Salzmann, 2017;Han et al., 2016).Others have concentrated on teaching compact models (Howardet al., 2017;Zhanget al., 2017;Qinet al., 2018) from scratch by factorising regular convolution layers into depth-wise separable convolution layers for cheaper computations.
Although CNNs have achieved the best results in functional implementations, robustness and accuracy remain challenging.Ronneberger et al. (2015) proposed a tool called U-Net for automated medical image segmentation to solve these issues.The U-Net synthesises vital information by reducing the cost function in the rst half of the network and generates an image in the second half.Inspired by the U-Net model, we approached the current challenge of kidney tumour segmentation by proposing a WP-U-Net model.We implemented weight pruning of the U-Net with a depth-wise separable convolution architecture, and thus it re nes even tiny regions in the output tumour picture.The system precisely separates the tumour regions of the kidney and offers established quanti cation and qualitative validity.
Related Works
Several computer-aided diagnosis models and arti cial neural networks have been developed to classify and segment renal tumours using CT scans.Lingararu et al. (2011) published a computer-aided method which was used to examine a collection of brain CT scans of 43patients.In this system, tumours were robustly segmented with approximately 80% overlap.The methodology studied morphological variations between various types of lesions.Lee et al. (2017) developed a computer program capable of detecting and identifying small renal masses in CT images.Their tests yielded a speci c signal-to-noise ratio of 99.63%.Shah et al. (2017) presented a segmentation approach using machine learning.Yang et al. (2014) created a system to automatically segment CT images of the kidney based on multi-atlas registration.
First, they recorded a low-resolution image with a series of higher-resolution images to create a patientregistered image.Next, the kidney tissues were segmented and aligned to achieve the nal segmented production.
Various researchers have also experimented with the segmentation of renal tumours using deep learning.Thong et al.(2016) used an online patch-wise convolutional kernel to classify the central voxel in 2D patches.Then, the ConvNet analysed the CT scan data of each kidney tumour slice.Skalski et al. (2016) demonstrated an e cient hybrid level-set approach with elliptical-form restrictions for kidney segmentation.The RUSBoost algorithm and decision trees were used to differentiate between kidney and tumour structures, serving as a solution to class imbalance and the need for de ning additional voxels.Their model achieved an average precision of 92.1%.Wang et al. (2018) de ned a CNN-based model for kidney segmentation.They proposed a CNN-based segmentation scheme that integrates the bounding box information.They also improved the CNN model by ne-tuning the model for each picture.
Network prototypes.Deep neural networks are superior in their capacity and ability to be generalised.
Deep models that learn entirely from data produce excellent results for many tasks when compared with humans.They enhance the plot depth.Researchers have achieved further advances in neural networks.The use of skip links in deep neural networks makes them more trainable to perform tasks such as deep learning.U-Net was initially planned to resolve image segmentation, but others such as VGGNet and ResNet were designed for deep classi cation (Linguraru et al., 2011) supervision to further enhance segmentation.Network pruning has been widely studied to compress the CNN models (Heet et al., 2017(Heet et al., , 2018)).In early work, network pruning proved to be a valid way to reduce network complexity and over tting (LeCun et al., 1989;Hanson and Pratt, 1989;Hassibi et al., 1993;Strom, 1997).Recently, Han et al. (2015) pruned state-of-the-art CNN models with no accuracy loss.
Proposed Method
In this section, we propose the WP-UNet model and describe the modi ed objective function.
Image Pre-processing
All CT images were resized to 256 × 256 pixels in the training set and separated by 255 pixels to normalise the pixel values from 0 to 1.
Dataset
The KiTS challenge dataset for kidney tumour disease segmentation was used to assess the performance of WP-UNet.The KiTS dataset (Helleret al., 2019) consists of 210 high-contrast CT scans collected in the preoperative arterial process.They were chosen from a cohort of subjects who underwent partial or radical nephrectomy (Kutikov et al., 2009) for one or more kidney tumours at the University of Minnesota Medical Center and were eligible for inclusion between 2010 and 2018.The volumes included are characterised by different plane resolutions ranging from 0.437 to 1.04 mm, with slice thicknesses ranging from 0.5 mm to 5.0 mm in each case.
The dataset also provides the ground-truth mask of healthy kidney tissue and healthy tumours (Figure 1) for each case.Under the guidance of experienced radiologists, a group of medical students manually generated sample labels with only CT scan image axial projections.A detailed description of the segmentation strategy for the ground truth is described in Helleret al. (2019).The KiTs challenge dataset is provided with shape (number of slices, height, width) in the standard NIFTI format.
WP-UNet Model
Figure 2 shows the detailed architecture of the proposed WP-UNet model.The network has the properties of the encoder and decoder structure of the vanilla U-Net (Shenet al., 2015).As suggested byLiuet al. ( 2018), rst, the input image is passed into the standard convolution layer; subsequently, it is passed tothe encoder part of the WP-UNet block.Here, to improve the model's generalisation capacity, a depth-wise separable convolutional layer is used, which helps the network select the features related to translation invariance with fewer parameters (Karakanis 2020 )than the standard convolution layer.
WP-UNet encoding is composed of the following four blocks: Block1: A standard convolution layer, lters, a ReLu activation function, and a batch normalisation layer.
Up-sampling is performed in the decoder section, which is used to combine depth-wise separable convolutions and WP-UNet blocks as shown in Figure 2.It also consists of ve blocks: Block1: A depth-wise separable convolution layer with its features concatenated with the dropout layer from Block4 of the encoding path.
Blocks 2, 3, and 4: WP-UNet block and depth-wise separable layer concatenated with corresponding blocks from the encoding path.
Block 5: Two WP-UNet blocks and two depth-wise separable layers, with the last one as the nal prediction layer (Figure 2).
To improve the model performance and reduce the number of oating-point operations, we added network pruning (Liuet al., 2019) to the proposed architecture, as shown in Figure 4.The output of the network pruning (Han, 2016) WP-UNet model includes the kidney region, tumour region, and background, as shown in Figure 5.
Loss Function
In this study, the Adamoptimiser (Kingmaand Ba,2014)is applied, which correctly updates the network weights by iteration in the training data.Adam makes an average in the rst and second moments of gradients to adapt the learning rate parameter.Sabarinathan et al. (2019) proposed that the loss function be the sum of the categorical cross-entropy Dice loss channel one(C0) and Dice loss channel two (C1), as de ned in Eq. ( 1).
where L is the cross-entropy loss.In Eq. ( 2),y i and p i are the ground truth and predicted segmented images, respectively.Moreover, to ensure the loss function stability, the coe cient ϵ is used.
3.5.Performance Metrics
The key performance metrics used to measure the WP-UNet performance on the CT scan dataset are explained in this subsection.
Accuracy (AC):
Accuracy measures the percentage of correct predictions, and is given as, where TP = correctly predicted positive, TN = correctly predicted negative, FP = incorrectly predicted positive, FN = incorrectly predicted negative.
Mean Intersection over Union (Mean IOU):
The mean IOU (Hassibi and Stork, 1993)is a popular evaluation method for semantically segmented images that rst determines the IOU for each semantic class and then determines the average over classes.The mean IOU is expressed as follows: FLOPs: FLOPs essentially calculates the number of multiplications and additions of oating-point numbers to be performed by the computation device's processor.A neural network in progress requires oating-point operation calculations to estimate the complexity of the proposed model.
Training
The proposed network was trained with two outputs, namely the kidney and kidney tumour regions.The weight updates were performed using the Adam optimiser with a learning rate of 0.001.The batch size was set to 16, and the total number of epochs was set to a hundred.The training was based on Keras with a TensorFlow backend as a Google Colab deep learning framework enabled with an NVIDIA GPU such as T4(12 GB memory) with a high-memory virtual machine.
Results
The standard Dice score is considered an evaluation metric for the performance of the proposed WP-UNet model.We employed 35,865 and 10,158 images as training and validation images, respectively, in our experiments.Table 1 shows the segmentation results of the proposed WP-UNet model for the training and validation images.From the table, we observe that during training, the proposed method achieves a training accuracy of 0.98 for the tumour region.Similarly, the computational resource usage of our network is listed in Table 2. Based on the experimental results, we perceive the power of network pruning in the proposed network.Because network pruning is added to the proposed architecture, the total number of ops and parameters is three times smaller than the typical UNet architecture.In Figure 6, the qualitative effects of the KiTs19 dataset on the proposed WP-UNet model are shown.We used the provided input images and ground-truth reality images to perform the experiments.The segmented performance image isdepicted in Figure 5.The red-coloured area is the kidney region in the output picture, and the green-coloured part is the kidney tumour.Numerous structures outside the tumour and kidney areas were neglected for simplicity.The nal segmented output closely matches the groundtruth image from the quantitative results, which demonstrates the usefulness of the proposed WP-UNet.
Conclusion
Medical image segmentation is an important preliminary step in the identi cation of kidney organ structure and tumour tissues in CT image scans to aid in illness diagnosis, treatment, and general analysis.Early diagnosis is necessary to help in preventing complications that may arise due to late detections.However, with the increasing availability of large biomedical data, the workload on nephrologists, radiologists, and other experts in the eld has also increased.To help provide easier, accurate, and timely detections, several deep learning methods have been proposed, most of which have proven to be successful.The U-Net architecture is one such model that is widely accepted among researchers for biomedical image segmentation tasks.
In this study, weight pruning UNet (WP-UNet) was proposed for the segmentation of kidney tumour data with limited computational resources.The WP-UNet architecture makes use of depth-wise separable convolutions (Figure 2) and pruning to reduce the parameters and oating-point operations.Moreover, the WP-UNet deep learning method exhibits a faster inference speed than that of the UNet method.
Our ndings indicatedthat the proposed WP-UNet architecture yielded a satisfactory accuracy.Our system obtained a Dice score of 0.9799 and 0.9599 for the preparation and validation sets, respectively.The proposed WP-UNet model achieved the best segmentation outcomes in terms of the Dicescore and usage of computational resources.Additionally, WP-UNet is shown to have a faster inference speed on test data and is bene cial for situations whereinrapid and accurate segmentation results are required.
Figures Figure 1
Figures
Table 1 :
Comparison of results between WP-UNet and other models | 3,138.8 | 2021-05-18T00:00:00.000 | [
"Computer Science",
"Medicine"
] |
Authentication, Scale-Relativity, and Relational Kindhood
This paper proposes a new natural kinds framework according to which kindhood is relational, dynamic, and scale-relative . Reflecting on the ontogenesis of a scientific classification, I argue that there are two distinct conceptual stages to a scientific classification: a first stage in which enough entities and relations must be authenticated for kindhood to emerge and a second in which the nature of authenticated entities and relations is investigated. The new framework is scale-relative and explains both the changing nature of the entities and relations themselves as well as the changing nature of the classifications in which they are organised.
1 Entities, as explained below are a variety of authenticated phenomena. Entities and relata are used interchangeably throughout, albeit in a way that does not make any deep metaphysical assumptions about their nature.
2 Hacking (1983) makes a similar remark in relation to experiment: "A completely mindless tampering with nature with no understanding or ability to interpret the result, would teach almost nothing" (p. 153). theoretical knowledge that a researcher or group of researchers can be said to hold at any given time. 3 This conceptual distinction will ultimately serve to show what kind of ontology can be justified within a complex theoretical framework, once the complex layers of the theoretical framework are understood and justified.
It will be argued that entities and their relations are usually authenticated prior to the development of perspectives on their nature. 4 It will ultimately be established that a research tradition affords the authentication of empirically genuine entities and relations, whilst perspectives are developed to study their precise nature in terms of their origin, constitution, or evolution. To the extent to which the distinction between research traditions and perspectives is accepted, it will be argued that entities and their relations are perspective-independent empirical phenomena. As authenticated phenomena, independent of perspectives, the commitment to entities and their relations will be shown to constitute a legitimate ontological commitment for a natural kinds account.
The second thesis concerns the evolution of a scientific classification. It will be argued that by understanding kindhood as relational, dynamic, and scale-relative we can account for both the changing nature of the phenomena themselves as well as the changing nature of the classifications in which they are organised. To establish the second thesis, the methodology of authentication will be further grounded in the history and philosophy of science through Whewell's (1837a;1837b;1837c) history and Whewell's (1840a;1840b) philosophy of classificatory sciences, which constitutes the first extended modern survey of the methodology and ontology of inductive sciences. In particular, Whewellian considerations will serve to illustrate the interplay between the authentication of phenomena and the application of classificatory principles for their hierarchical organisation and evolution.
Ontogenetic considerations and Whewellian historical lessons will be ultimately used to show that classifications emerge with empirically driven authenticated relations and entities and evolve with the development of perspectives which are continuously informed and reinforced through 'unintermitting' observations of scale-relative empirical phenomena.
There are two novel aspects of this paper. First, it constitutes an in-depth exploration of scale-relativity and especially of previously underappreciated scales such as numerosity and of the interaction between different scales. Second, the paper introduces ontogenetic considerations to separate two distinct conceptual stages of scientific classifications which play very different roles, i.e., authentication and perspectival development.
The present account is first and foremost informed by views on scale-relativity proposed by Ladyman and Ross (2007) and Bursten (2016). 5 A pivotal role is also played by Laudan's (1977) account of progress in science, Hacking's (1983) and other New Experimentalists 6 views on experiment and observation in science, and most importantly, the many ideas on the nature of scientific classifications present in Whewell's (1837a;1837b;1837c;1840a;1840b) extended survey of the ontology and methodology of scientific classifications. These accounts have been invaluable in shaping the original framework proposed in this paper. The present account has also been influenced by Ladyman and Ross's (2007) real patterns based account of natural kinds as well as by Boyd's (1991;1999b;1999a) homeostatic property cluster kinds and cognate naturalistic accounts such as Magnus's (2012), Massimi's (2014), and Slater's (2015). The resulting account can be situated within the so-called 'practice and history oriented shift', most recently exemplified in the various proposals found in Kendig (2016b), and stemming from earlier work in a range of fields begun in mid-70's (see Soler et al. (2014)).
The paper is structured as follows: Section 2 explains how scientific classifications emerge by establishing a principled conceptual distinction between the authentication stage and the perspectival development stage. Section 3 describes the evolution of scientific classifications by showing how the interplay between the authentication of entities and relations and the application of classificatory principles gives rise to dynamic, scale-5 The views of Dennett (1991), Ross (1995), and Wallace (2010) on real patterns have also been invaluable in shaping the present account.
6 A systematic philosophy of experiment, i.e. the New Experimentalism, begun to emerge in the 80's with the works of Hacking (1983), Cartwright (1983), Ackermann (1985), Franklin (1986), Galison (1997), and others. These, as well as more recent works, played a substantial role in shaping the author's views. relative, relational kindhood. Conclusions follow in section 4.
In their Standford Encyclopaedia article on natural kinds, Bird and Tobin (2017) offer the Standard Model classification of fundamental particles as one of the paradigmatic examples of natural kinds. They claim that "[t]he standard model in quantum physics reveals many kinds of fundamental particles (electron, tau neutrino, charm quark), plus broader categories such as kinds of kind (lepton, quark) and higher kinds (fermion, boson)". The Chemical Yet a closer look at how these classifications were designed and how they evolved, and continue to evolve, reveals both a marked neglect of scale-relativity in these discussions, as well as associated problems therewith.
For example, The Periodic Table of Elements can be said to be vulnerable to a 'scaling problem', caused by some superheavy elements (Z=119 onwards). Such elements may turn out to threaten the periodicity of elements which constitutes the periodic table's organising principle (Ball 2019). This is because the lifetime of superheavy elements with atomic number higher than 119 is too short for them to acquire outer electrons which make them have chemical properties and thus count as chemical elements (see Kragh 2017 for details). Similarly, discoveries relating to neutrino mass may be said to point to a 'scaling problem' for The Standard Model too, since "the mechanism for neutrinomass generation and its energy scale" (Rayner 2020) is not yet known, but may point to "physics at a very high energy scale such as the Grand Unification of elementary particle interactions" (Kajita 2015, p. 21).
The main point to emphasise in connection to these examples is not that these classifications aren't outstandingly empirically successful, but rather that they are evolving classifications, with no rigid structure or final form. Another related point to emphasise here is that valuable lessons about the methodology and ontology of scientific classifica-tions can be lost by neglecting scale-relativity and the ontogenesis of scientific classifications. Though such lessons have not been lost on philosophers of biology or biologists who focus on scientific classifications 7 , on philosophers of chemistry with a historicist bent (e.g. Scerri (1998;, Chang (2016)), or historians of science (e.g. Kragh 2013; 2018; 2019), they have not yet become the mainstay of natural kinds debates. 8 In what follows the role and implications of scale-relativity for scientific classifications will be investigated. Scale-relativity will be shown to have both an ontological and a corresponding methodological dimension and to play different roles at different stages of classificatory development. In particular, two conceptually distinct stages will be delineated: authentication and perspectival development. The first stage, as we shall see, concerns the validation of a phenomenon as empirically genuine and plays a distinct role for the ontology of scientific classifications, whilst the second stage will be shown to be crucial for understanding the precise nature of any phenomena.
Authentication
Authentication refers to the stabilisation and validation of phenomena and is necessary in order to eliminate, insofar as it is possible, potential errors due to experimentation, measurements, or "freak results" (p. 18) and in order to resolve disagreements. 9 Authentication consists of both a theoretical and empirical component but it is ultimately about phenomena. Authentication is required in connection to any new phenomena, at any stage within the development of a classification. The theoretical side of authentication does not presuppose full elucidation of the nature of the phenomena in question. The phenomena must nonetheless be embedded within a scientific theory which has, at least in principle, physical significance and some degree of relational coherence with cognate theories. The theoretical and empirical components are important for the following reasons: 7 The relation between evolution and scientific classifications has been the focus of heated debates in biology and philosophy of biology during the '70 and '80, see Kearney (2007) and Richards (2016) for helpful overviews and Sober (2000) for a standard reference.
8 Some natural kinds debates continue to centre on outmoded Kripkean and Putnamiam ideas about kinds, see for example the recent Synthese Special Issue on Natural Kinds: Language, Science, and Metaphysics, Moreno (2019). 9 See Creţu (2020) for the authentication of the positron and attending disagreements.
i. because a phenomenon can be theoretically validated or embedded within a scientific theory but not be experimentally validated (e.g. strings or super superheavy elements past Z=119, the Higgs Boson prior to 2012); ii. because a phenomenon can be empirically validated, but not theoretically validated (e.g. the positron between 1931-1933, plausibly dark matter); iii. because a phenomenon can be partially authenticated (e.g. the authentication of the Quaking Aspen as an individual tree rather than as a clonal colony); iv. because a phenomenon can be mis-authenticated. For example, the infamous OPERA superluminal neutrinos, although initially experimentally validated were subsequently shown to have been mis-authenticated due to measurement errors (see Reich (2011), Brumfiel (2012)). 10 Authentication then can be neither purely theoretical nor purely empirical. Authentication plays a foundational role in the incipient stage of a scientific classification but it continues to play a significant role throughout its development too. 11 Authentication determines that a phenomenon is; perspectival development determines what it is.
Authentication can only be achieved within a research tradition, against a certain background. A research tradition, following Laudan (1977) can be understood as a set of assumptions about what basic entities might there be in the world, how such entities might interact, and how they might be studied. A research tradition is not static and over time can become very specialised and complex. Thus, depending on the phenomenon at hand, the research tradition which studies it and its stage of development, authentication may involve minimal assumptions about the nature of the world or a more complex network of assumptions. For example, the most common assumptions in connection to scientific classifications are that the world is structured, that it is stable enough to be amenable to study and observation, that some entities can be grouped together so as 10 For more examples of allegedly incontrovertible empirical facts which turned out not to be authentic phenomena, see Bondi (1955).
11 Authentication implies, though is not reducible to, the empirical confirmation of a phenomena.
to enable significant generalisations, that entities can be organised in hierarchies etc. 12 In the case of more advanced research traditions, such as The Standard Model, complex assumptions enter the authentication process and perspectives can become involved in the process too. Note, however, that even in such cases a distinct conceptual role is played by those perspectives that enter into the authentication process and those which concern the development of theories regarding the nature of the authenticated phenomena.
That is to say that the origin, evolution, and constitution of any phenomena can be properly investigated only once the phenomena are validated and made amenable to further investigation. 13 For example, chemical elements past Z=119 cannot as yet, if at all, be stabilised for the time required to acquire outer electrons which would enable further investigation into their nature; such elements then are not as yet authenticated.
It is further worth emphasizing that authentication can be a lengthy and complex process. The Standard Model contains more than one example of lengthy and complex authentication. The authentication of the neutrino constitutes one such example. The neutrino was predicted in 1930 as an essentially massless particle to resolve particular anomalies in β − decay, it was first detected in 1956, decades later was found to have mass, and its status is still not fully resolved (see Brown (1978), Kajita (2015), Hernandez (2016), and Rayner (2020) for details). 14 Another example concerns the classification of the positron which involved a drawn out process of authentication prior to further investigations into its nature (Creţu 2020, Roqué 1997, Darrigol 1988, Hanson 19611962).
The case of the positron is significant for making another observation in connection to authentication, namely that any new phenomenon is authenticated in relation to other phenomena. For example, the positron was authenticated as a new particle only in relation to and by comparison with other existing particles, i.e., the electron, the proton, and the neutron. This is not to say that the authentication of the positron was an entirely theoretical matter. Nor is it to say that perspectives on the nature of the positron were not 12 This point about assumptions is extensively made by Kant (1781), see especially the Appendix pp. 590 -604, and also by Whewell (1840a), see especially pp. 18 -41. 13 Feest (2011) offers similar suggestions. 14 Hoefer and Martì (2020) also discuss the lengthy process of establishing the reference of the neutrino whilst also suggesting that The Standard Model physics should be placed in a 'quarantine' zone -a zone which does not yet give rise to scientific 'lore' or a core of scientific truths. developed prior to its authentication. Rather, the claim is that we can only profess to have understood the nature of a phenomenon if the phenomenon is genuine, that is, if it has been authenticated as a genuine phenomenon. Only then can its nature be precisely determined.
The distinction between authentication and perspectival development is precisely aimed to capture these two distinct conceptual stages in the classification and study of phenomena.
Two more examples will further serve to highlight the importance of authentication as a distinct conceptual stage in the development of a scientific classification as well as its drawn out character. A first case in point concerns the emergence of the first modern astrophysical classifications which, similarly to the positron case, was also marked by a relatively drawn out authentication. Fat, thin, and fluted patterns on the spectroscopic photographs were authenticated without prior knowledge of the information contained within them (see Cannon and Pickering 1901, Russell 1919, Hoffleit 1991. These authenticated patterns, revealed in the spectra of stars constituted the basis of the first three instalments of the The Henry Draper Catalogue, the third instalment being internationally adopted in 1910. With some modifications, the third instalment of The Henry Draper Catalogue is still in use today. Investigations into the nature of stars emerged only after the authentication and classification of stars based on their spectral characteristics. A second case in point comes once more from The Standard Model and concerns its most recent addition, the Higgs Boson. Though popular accounts are wont to offer definite pronouncements in relation to the 'discovery' of the Higgs Boson as a singular event, a closer look reveals in fact a relatively complex authentication process. To be precise, the historical details show that the July 2012 discovery was a discovery of a "Higgs-like particle" and neither the CMS nor the ATLAS discovery papers claimed to have definitely discovered the Higgs Boson, but only to have discovered a new boson (see Franklin (2017)). 15 In an analysis of the discovery, Dawid (2015) pointed out the ongoing authentication of the Higgs Boson 16 and recently Mättig and Stöltzner (2019) 15 "Both groups promised a more rigorous test of their conclusions and a further search for physics beyond the SM. Both the conclusion and the title of the papers claimed the discovery of a new boson, but neither definitely claimed that it was the Higgs boson" (Franklin (2017), pp. 272-273. 16 Dawid (2015) cautioned that "[i]t remains to be seen whether the discovered particle has the properties predicted by the standard model of particles physics or must be understood in terms of an extension of the standard model such as supersymmetry", p. 76.
showed that "[w]ith the growing evidence that the newly discovered particle has properties consistent with the SM expectations, most physicists accepted it to be a Higgs, and at least tentatively, a SM Higgs" (p. 93). Besides its relatively complex authentication, what the case of the Higgs Boson illustrates is that discovery does not equal authentication.
For a phenomenon to count as fully authenticated it must be both experimentally and theoretically validated. Note, however, that theoretical validation does not imply a full elucidation of the precise nature of the phenomena. To begin with, historical practices of classification, as described in Whewell's History and Philosophy of the Inductive Sciences, suggest that the authentication of entities traditionally preceded the authentication of relations. In particular, as Whewell (1840a) notes in The Philosophy of the Inductive Sciences, "... before we can attend to several entities as like or unlike, we must be able to apprehend each of these by itself as one thing" (p. 449). To use Whewell's example, the basic idea here is that to be able to talk about a tree, in a forest of trees, we must apprehend the tree as one unit, with its own trunk, branches, leaves and so on. Only once we have thus singled out or authenticated each tree, we can attend to what is alike and what is different amongst the trees.
Yet, the converse is equally true of scientific practice. For instance, the aforementioned example concerning astrophysical classifications, shows that the spectral characteristics of stars, which denote relations amongst stars, were authenticated prior to the authentication of individual stars per se. To be precise, classifications were designed on the basis of their spectral lines, initially based on the strength of the lines and later width, flutedness, and haziness also became relevant. The strength of the spectral lines signifies the temperature of a star; the width can be correlated with the luminosity of a star, whilst the shape of the line can offer information about the atmosphere of a star (see Green and Jones (2015) for more details).
What the examples above indicate is that depending on the scientific practice at hand, it will be a contingent matter whether we attend to the authentication of the relations or of the entities first. Note that on the present account, further specifications of what entities are and to what extent, if at all, they can be further decomposed can only be done on a case by case basis, once perspectives onto their nature have been developed. 17 Entities, here, are those items which classificatory systems, in different sciences, seek to group into kinds and higher hierarchies. Such entities may on occasion be both new items whose status is provisionally debated, items whose reality is not outright contested, or items that are judged by common sense to be real entities.
Recognising the importance of both entities and relations as the basis of any classification has the added advantage of removing unnecessary limitations to the domain of applicability of scientific classifications. For example, Ladyman and Ross (2007) take natural kinds to be inapplicable to quantum contexts where all entities such as electrons possess the same properties, i.e., rest mass, charge, spin, and are thus intrinsically indistinguishable from one another. 18 Since natural kinds classifications require that entities differ in their detailed characteristics whilst sharing other characteristics, natural kinds frameworks seem inappropriate in situations such as the quantum context, where all entities share all the same intrinsic characteristics. 19 However, if it is possible to distinguish a class of identical entities from another class of identical entities, the basis of a classification becomes once again discernible. Thus, whilst all electrons are defined by particular quantum numbers, the electron's quantum numbers differ from the quantum numbers of other quantum particles. That is to say, the electron is a distinct kind from the positron say, precisely because the two differ in some of their characteristics and have been authenticated as different entities. It seems then that the individuality issue in quantum mechanics concerns the nature of phenomena and not the classification of quantum phenomena as 17 A similar point, albeit within a different framework is also made by Reydon (2016). 18 Ladyman (2007) and Ladyman (2015) defend a form of weak discernibility compatible with a relational approach to quantum particles, an approach that is congenial to the present account.
19 Thanks to Richard Dawid for discussion on this point.
such. 20
This brings us to another point worth highlighting, namely that authentication is (2019); for further discussions see Ross (2007), ch.3, Muller andSaunders (2008) and Caulton (2013). 21 The present account is nonetheless compatible with forms of 'practical individuation' and 'epistemic individuation', for details see Bueno et al. (2018). 22 For details on the individuation of plants, see Clarke (2010;. For details on the natural history of the Quaking Aspen see Mitton and Grant (1996). 23 For a related discussion about the purposes of classifications, and a relational approach to kindhood, see the excellent paper of Okasha (2002).
subsist. To be precise, within a specified scientific domain, on large enough timescales there are no entities and on small enough timescales there are no relations, and hence no kinds. Moreover, depending on how extended the timescale is, the same entity may be regarded as either an object, an event, or a process. For example, on timescales small enough, certain supernovae can be regarded as stellar explosion events. On timescales that track the evolution of a star from progenitor to explosion, the supernovae can be regarded as one object that naturally evolves towards its explosion, just as humans naturally evolve to then eventually die. Furthermore, on an even lengthier timescale, supernovae can be regarded as particular types of astrophysical processes. 24 For these reasons, the present account is committed to the fact that both relations and relata are necessary for purposes of classification 25 and neither can be eliminated in a truly practice and scale-relative framework.
We have thus far shown that no classification can proceed without authentication.
But authenticated phenomena change or evolve (ontological evolution) and the classifications that track the phenomena must change accordingly (methodological and conceptual evolution), though not necessarily, or even usually, simultaneously. To understand how this happens we'll need to analyse the perspectival development stage of classifications before we move on to a more detailed analysis of scale-relativity in section 3.
Perspectival Development
This section aims to establish that no classification can grow and evolve without understanding the nature of authenticated phenomena. Such understanding, as we shall see, requires the constant development of 'perspectives' on the nature of the phenomena. It is perspectives, and not research traditions, that particularise the ontology of nature. Before we look at some examples, let us first say more about perspectives.
Perspectives are sophisticated theoretical frameworks that encompass the set of 24 For details on the evolution of supernovae see Zeilik and Gregory (1998) and Green and Jones (2015). 25 The present view is thus compatible with three distinct views concerning the relative priority of relations and relata: a) a view on which relations are primary and entities are secondary, see Stachel's (2006); b) a view on which entities are primary and relations are secondary, see Russell (1911); and c) a view on which neither entities nor relations are primary, see Esfeld and Lam (2008), Pooley (2006). theoretical interests and background theoretical knowledge that a researcher or group of researchers can be said to hold at any given time. They have a narrower scope than research traditions and are thus more specialised and fine grained. But, since they are sponsored by research traditions, they also inherit a large proportion of the assumptions of the research tradition.
The role of perspectives is to determine, to the extent to which it is possible, the precise nature of the authenticated phenomena. The establishment of perspectives thus relates to the interpretation of the phenomena. Since phenomena, even authenticated phenomena, can generally underdetermine their interpretation, to determine the precise nature of the phenomena, post-authentication perspectival development is necessary. Perspectives must be compatible with and applicable to the empirical phenomena, explanatory, and at least in principle testable. It may be the case that, at the level of perspectives, the interplay between authenticated empirical phenomena and theoretical principles of classification is overall less independent from anthropocentric concerns. For this reason it is important to emphasise that authentication within a research tradition is largely independent of perspectives (a point we will return to towards the end of the next section). 26 To illustrate, consider once again the case of the Higgs Boson. One might think that the existence and theoretical role of the SM Higgs Boson, as well as its nature (properties, interactions, etc.) were clear to physicists long before the Higgs Boson was eventually discovered in July 2012 and that physicists knew well what they were looking for before they actually found it.
However, a closer look at the history of the Higgs Boson reveals a similar structure to the one described above, namely that perspectival development on the nature of the Higgs Boson followed authentication. More importantly, the details of the Higgs also highlight two other important lessons: that the theoretical nature of an entity may or may not correspond to the empirical nature of the entity and that discovery does not equal authentication (a point already emphasised). The history of the Higgs search and discovery shows that the determination of the energy range within which the mass mechanism of the Higgs could be found involved a host of complex arguments, strategies, and indirect evidence (see Dawid (2015) and Franklin (2017)). What this means is that physicists knew only roughly what/where to look for. It would thus be inaccurate to claim that having a prediction and knowing roughly what the energy range where a Higgs like particle could be found amounts to knowledge of the nature (properties, interactions, etc.) of the SM Higgs Boson. It is not the case that the precise properties of the SM Higgs Boson were known before its authentication or the perspectival development stage. Rather, as Mättig and Stöltzner (2019) point out, in 2011, "physicists were rather undecided whether the SM Higgs Boson would eventually be found" (p. 74) and expected that "finding a particle consistent with the SM Higgs would only be the first step in further investigating the properties of the new particle" (p. 80). Even after the discovery of a 'Higgs-like' particle was announced in 2012, physicists would not even claim that it was definitely the SM Higgs Boson, much less that they knew the nature of the discovered particle.
Various alternative perspectives to the SM Higgs Boson were still advocated for as late as 2012. For example, perspectives in which the Higgs was seen as a composite particle were still supported by a remarkable number of theorists even post discovery (see Mättig and Stöltzner (2019)). What can be suggested is that the discovery precipitated increasing perspectival development on the nature of the discovered Higgs-like particle which led to "growing evidence that the newly discovered particle has properties consistent with the SM expectations" (Mättig and Stöltzner (2019) the former was eventually abandoned.
As regards the classification of stars, it is plausible to suggest that the authentication of the spectra was largely ongoing during at least the first two versions of the Henry Draper Catalogue. This is because the first catalogue focussed primarily on the strength and width of the spectral lines, whilst Antonia Maury noticed further peculiarities in the shapes of the lines such as flutedness and haziness. A number of different perspectives were developed after the authentication of stellar spectra. Some astronomers argued that the spectra reveal different evolutionary stages of a star (e.g. Antonia Maury and Ejnar Hertzsprung), whilst others took the spectra as offering clear information about the constitution of stars. 28 What these examples show is that the two conceptual stages, authentication and perspectival development, play very different roles in the development and evolution of a scientific classification. Authentication is necessary for the theoretical and empirical validation of the phenomena, that is, for establishing that the phenomena is; whilst perspectival development is necessary for establishing the precise nature of the phenomena, understanding what it is. In the next section we'll take a closer look at the impact of scale-relativity on scientific classifications.
Relational Kindhood and Scale-Relativity
The aim of this section is to explain how the interplay between the authentication of phenomena and the development of perspectives on their nature gives rise to relational kindhood. Further, it will be shown how scale-relativity complicates relational kindhood.
In particular, it will be shown that the principle of scale-relativity has both a methodological and an ontological component, both of which play crucial roles in the shaping and evolution of scientific classifications. Historical and contemporary philosophical lessons, from Whewell (1840a; and Ladyman and Ross (2007) respectively, will be brought to 28 Even amongst those who took spectra to reveal different evolutionary stages of a star, there was some disagreement with regard to which evolutionary stages do the different spectra reflect. Henri Norris Russell, as opposed to Antonia Maury, believed that red signifies the beginning of a star's life, that the star then warms up and becomes yellow or white, and ultimately cools down to its original red light. light to establish the claim that kindhood is relational, scale-relative, and dynamic.
Scale Matters
In their survey of physics and the special sciences, Ladyman and Ross (2007) note that we are now in a position to study events on previously unimaginable spatiotemporal and energetic scales. Physics, for example, studies phenomena that last from anywhere around a tiny fraction of a second to years and decades and can also focus on spatial scales infinitely smaller than the "spatial scales of a millimetre to a few thousand miles" which "are all that have concerned us until recently" (p. 11); astrophysics studies phenomena that similarly can last from a fraction of a second to millions of years; whilst geology "require[s] us to adopt time scales that make all of human history seem like a vanishingly brief event" (p. 11). What these examples point to is the scale-relativity of ontology, where, [s]cale relativity of ontology is the more daring hypothesis that claims about what (really, mind-independently) exists should be relativized to (real, mindindependent) scales at which nature is measurable (p. 200).
For example, as Ladyman and Ross note "at the quantum scale there are no cats; at scales appropriate for astrophysics there are no mountains" (p. 199). A variation of scale, either temporal, spatial or energetic, may reveal more or less or different kinds of phenomena. A case in point here comes from biology, where "in histories of lineages at small enough temporal scales there is no natural selection, because natural selection requires a substantial minimum number of reproductive events" (p. 203). Whilst Ladyman and Ross (2007) were the first to introduce and explicate the principle of scale-relativity in contemporary literature, they didn't go nearly far enough. 29 This is on the one hand, due to their restricted focus on spatiotemporal scales and length scales, and on the other hand, due to their explicit focus on the ontological dimension of scale-relativity and contemporary sciences.
However, by combining lessons from modern and contemporary scientific practices with the wisdom of historical lessons more aspects of scale-relativity become salient. For example, by reflecting on Whewell's example of the trees, we come to understand not only that individual trees must be authenticated, but also that enough of them must be authenticated in order to identify relations amongst them, and hence put the basis of a scientific classification. The basic idea behind this example is that the number or the numerosity scale of entities studied matters more than previously appreciated. 30 What numerosity entails is that "more is different" (Anderson 1972), and that sometimes mere numerosity can make a dramatic difference (see Ladyman and Wiesner 2020). That is, some phenomena become visible only with an increase in quantity, whilst other phenomena can only occur given enough entities or iterations of relations. Let's explicate this in more detail.
Numerosity concerns the number of entities needed to erect a classification and the classificatory changes that occur with changes in quantities. It thus plays both a foundational role and a developmental role. It was already shown that any classification must begin with the authentication of phenomena. It must now be emphasised that enough entities must be authenticated to put the basis of a classification. This is because in a context where there is only one entity, there are no kinds. Even when two completely different entities have been authenticated, we might still be reluctant to talk about kinds. This is because we may have no reason to suppose that there are other entities similar to the two different entities we have authenticated. However, once we have authenticated three entities, if the third entity turns out to be sufficiently similar to at least one of the existing entities, we can begin to talk about kinds. Once we have thus sorted the three entities into kinds, the next entity we authenticate will be assessed in reference to our already existing entities and kinds. What these considerations suggest is that erecting a classification requires a minimum number of entities. To put it differently kinds themselves only become visible with an increase in the number of authenticated phenomena.
The number of entities authenticated matters not only for separating entities into kinds, but also in their evolution. Depending on how many entities are compared with one another, only certain relations will obtain or become salient. For example, before the discovery of the positron, both charge and mass constituted salient differences between the known existing particles, the electron and the proton. After the discovery of the positron it became clear that particles can have the same mass but opposite charge. The main point to emphasise here is that, an increase or decrease in the original sample of entities authenticated and compared, temporally or spatially, or even energetically, may make more or other relations salient. What this means is that classificatory schemes can change more or less dramatically with an increase or decrease in the numerical scale. It is thus unsurprising that scientific classifications are numerosity relative. As Whewell remarks, singling out entities, comparing them, grading observed likeness and differences is a laborious process that involves on the one hand assumptions and on the other hand unintermitting observations of empirical regularities. Both are nec-essary, for without assumptions or without any empirical regularities, we would not be able to distinguish phenomena from one another and arrange them in hierarchies or be able to study their nature. As Bondi (1955) points out, the privileging of some form of theory-neutral observation "seems to be the result of a deep human prejudice, that if only one continues to look at an object for long enough its nature will become apparent. In science this is, of course, nonsensical. One could stare at a piece of wood for years if not generations without discovering its atomic nature, or being able to infer its properties in any way from appearances" (p. 160). What this points to is the back and forth between empirical observations and assumptions and organising principles involved in any process of classification. This is because the more entities and relations are observed the more laborious the process of organising likenesses and differences in a way that is exact, precise, and empirically adequate becomes. The more laborious the organisation, the more contrived it seems. However, the process is always the same, involving assumptions and entities and relations equally. As more observations become available, the same process is carried out at increasingly larger scales. Just as Whewell notes, the process repeats itself as follows: "[a]s individuals by their resemblances form kinds, so kinds of entities, though different, may resemble each other so as to be again associated in a higher class; and there may be several successive steps of such a classification" (p. 457).
Perspective Independence
It is true that both of these acts "of singling out one entity and of finding relations amongst many" are "operations of the mind", which makes it seem that any result of these operations would itself be an operation of the mind. To the extent to which one accepts perspective-independence, one would, however, not draw such a parochial conclusion.
Instead, one would see that neither operation is purely an operation of the mind. Both operations are grounded in repeated observations of empirical regularities. On the one hand, repeated observations of trees in forests, and in isolation, warrant the belief that "assertions concerning the object shall be possible"(p. 452). On the other hand, repeated observations of trees would eventually lead one to notice that likeness in the shape of leaves is far more common than likeness in the shape of the branches. Thus, on the basis of such observations, the belief that "general assertions shall be possible" (p. 454) is also warranted. What these assumptions signify is that entities and relations are robust beyond their authentication, that is, that they are projectible on a given scale, though may not be projectible on another scale. For example, even the 'authentication' of a single tree in an aspen grove cannot be discarded as outright erroneous on all scales. After all, it is plausible to suggest that its authentication proceeded on a scale on which the Aspen is a robust (tree-like) phenomena, but once further investigation into its nature was undertaken and its root system was studied further, it became clear that the Aspen is not in fact a tree but a grove, and perhaps should be properly investigated on a different scale. It is important to note that the above assumptions are not infallible and that they are warranted to the same degree as induction is warranted. Finally, it is worth emphasising that the two It is not solely the contribution of background assumptions and principles of classification that limit the scope of a classification; the scale-relativity of classifications and the methodological complexity of navigating the interaction of scales, dictate the limited and changing character of a scientific classification. For example, classifications can change with an increase or decrease of entities on particular scales. Thus, as Bursten (2016) similarly notes, "it is a scale-dependence in the systems themselves that provide opportunities and support for scale-dependent changes in the landscape of kinds in a lab" (p. 3). The more general conclusion to draw here is that to understand how classifications work and evolve it is not sufficient to acknowledge the mutual contribution of nature on the one hand and of background assumptions and principles of classification on the other hand. It is equally important to acknowledge the specific, fine-grained 'contributions' of the world itself and the specific limitations dictated by different scales and by different domains of inquiry.
It will be instructive at this point to clarify the ontology entailed by the present account. To do this, a few distinctions are in order. It is standardly assumed that natural kinds must be mind-independent and objective. These notions are not, however equivalent, though often objectivity and mind-independence are conflated. It is not surprising that the two notions are conflated, since objectivity is necessary, but not sufficient for mindindependence. At the same time, mind-independence is not necessary for objectivity. To get a clear grasp on objectivity and mind-independence, further distinctions are called for. 31 A classification can be said to be objective when it is unambiguous and intersubjectively well-founded. 32 Objectivity is a methodological notion, pertaining to the practice of science and not to the nature of the world. 33 A classification can be objective without being mind-independent, for example the classification of flags. Flags, and what they represent in different circumstances, are human constructs whose ongoing existence and function is dependent upon humans maintaining such constructs and their ongoing performance (Thomasson 2014). In contrast, when a classification is assumed to be mind-independent, it must be independent of human thought. 34 However, since no inquiry can proceed without at least some theoretical assump-31 See also Khalidi (2016)'s paper for a four-tier distinction between types of mind-dependence, as well as Franklin-Hall (2015)'s paper, who distinguishes between 'fully objective' and 'fully mind-independent kinds'. 32 Giere (2006) similarly defines objectivity as "reliable intersubjective agreement", p. 34. 33 Feminist critiques of science have significantly shaped the way we view objectivity in relation to scientific research. Of particular note are the works of Longino (1990), Harding (1991), and Douglas (2009). Daston and Galison (2007) have also offered a historicised conception of objectivity, which significantly influenced the present account.
tions about the nature of the world -e.g., that the world is structured, that it is stable enough, that there are hierarchies of entities etc. 35 -complete independence from human thought is impossible to attain. What can be attained, as per ontogenetic considerations and Whewellian historical lessons, are scientific classifications which emerge with empirically driven authenticated relations and entities and evolve with the development of perspectives on the nature of authenticated entities and relations which are continuously informed and reinforced through unintermitting observations of scale-relative empirical phenomena. Thus, insofar as authentication is empirically driven and perspective-less, a tenable, albeit situated, ontological commitment to scale-relative entities and relations becomes available.
The present account, with its commitment to dynamic and scale-relative relational kindhood can be placed squarely alongside Ladyman and Ross's (2007) real patterns based account of natural kinds but it can also be placed within the company of some version of Boyd's (1991;1999b;1999a) homeostatic property cluster kinds stripped of its essentialist connotations 36 as well as cognate naturalistic accounts such as Magnus's (2012), Massimi's (2014), and Slater's (2015). The present account can also be situated within the 'practice and history oriented shift', most recently exemplified in the various proposals found in Kendig (2016b), and stemming from earlier work in a range of fields begun in mid-70's (see Soler et al. (2014)). Importantly, the methodology offered here with its fine-grained two stage distinction and its discussion of scale-relativity, particularly numerosity, may lead to fruitful elaborations and improvements for any natural kinds account that has yet to recognise the significance of scale-relativity and ontogenetic considerations.
To sum up, scientific classifications are designed and sustained through the continuous back and forth between empirical observations of entities and relations and the refinement of principles of classification to maintain and increase the success of predictions retrodictions, or explanations that the relevant classification sustains. Such classifications are inherently situated due to authentication, as well as the interactions between differ-35 See fn. 12. See also Massimi (2014), Haslanger (2016), Kendig (2016a). 36 Whilst many authors read Boyd's homeostatic property cluster kinds in broadly realist nonessentialist terms, a few authors have identified hidden essentialist assumptions in Boyd's account. See for example, Griffiths (1999), Massimi (2014), and Slater (2015). ent scales, both ontologically and methodologically. The commitment to authenticated entities and relations, without which scientific classifications neither emerge nor evolve, constitutes a bone fide, achievable ontological commitment. 37
Conclusion
Scientific classifications are invaluable for understanding what entities there are and have been in the world and how they relate to one another. They are equally invaluable for facilitating all forms of epistemic endeavours such as explaining the nature of various phenomena, or making a variety of predictions and retrodictions. Scientific classifications are thus as much about a world of phenomena independent of us as they are about our relation to those phenomena. It was shown that a scale-relative, relational, and dynamic approach to kindhood, informed by both science and the history of science, can help us acquire a better methodology and retain a bone fide ontology. Without examining the science and the history we might fail to notice the dynamic and scale-relative dimensions of our classifications. We might fail to take into account the effects of time, space, energy, numerosity, and perhaps other scales, on our interaction with and understanding of the world around us. The approach developed in this paper motivates a renewed focus on the science and the history of scientific classifications with a particular focus on the stages of their development and their scale-relativity. | 10,418.8 | 2022-02-01T00:00:00.000 | [
"Philosophy"
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The Essential Oils and Eucalyptol From Artemisia vulgaris L. Prevent Acetaminophen-Induced Liver Injury by Activating Nrf2–Keap1 and Enhancing APAP Clearance Through Non-Toxic Metabolic Pathway
Artemisia has long been used in traditional medicine and as a food source for different functions in eastern Asia. Artemisia vulgaris L. (AV) is a species of the genus Artemisia. Essential oils (EOs) were extracted from AV by subcritical butane extraction. EO contents were detected by electronic nose and headspace solid-phase microextraction coupled with gas chromatography (HS-SPME-GC-MS). To investigate the hepatoprotective effects, mice subjected to liver injury were treated intragastrically with EOs or eucalyptol for 3 days. Acetaminophen (APAP) alone caused severe liver injury characterized by significantly increased serum AST and ALT levels, ROS and hepatic malondialdehyde (MDA), as well as liver superoxide dismutase (SOD) and catalase (CAT) depletions. EOs significantly attenuated APAP-induced liver damages. Further study confirmed that eucalyptol is an inhibitor of Keap1, the affinity K D of eucalyptol and Keap1 was 1.42 × 10−5, which increased the Nrf2 translocation from the cytoplasm into the mitochondria. The activated Nrf2 increased the mRNA expression of uridine diphosphate glucuronosyltransferases (UGTs) and sulfotransferases (SULTs), also inhibiting CYP2E1 activities. Thus, the activated Nrf2 suppressed toxic intermediate formation, promoting APAP hepatic non-toxicity, whereby APAP was metabolized into APAP-gluc and APAP-sulf. Collectively, APAP non-toxic metabolism was accelerated by eucalyptol in protecting the liver against APAP-induced injury, indicating eucalyptol or EOs from AV potentials as a natural source of hepatoprotective agent.
INTRODUCTION
Artemisia is a class of fragrant annual herb species of the composite family, distributed widely in Asia, Europe, and North America. It has a long history of traditional and popular use as both medicine and food with medicinal literature documentation since the Eastern Han Dynasty in 1st-century China (Song et al., 2016). Artemisia leaves have been considered to have a broad range of functions including anti-diarrhea, anti-inflammation, cough relief, antioxidant, and hepatoprotection (Giangaspero et al., 2009;Ferreira and Luthria, 2010;Obolskiy et al., 2011;Meng et al., 2018). The search for active compounds from Artemisia has led to the discovery and isolation of many phytochemicals and essential oils (EOs) with interesting activity. Artemisinin, a sesquiterpene lactone with antimalarial properties, is a prominent example (Gaur et al., 2014). EOs from other plants have been used in the treatment of inflammation, against free radicals, and for their hepatoprotective effect (Yoon et al., 2010;Younsi et al., 2017). Artemisia vulgaris L. (AV) is a major and common Artemisia plant that was first recorded by Ben-Cao-Gang-Mu (Ming Dynasty, 16th century by Shizhen Li), who stated that the leaves should be collected and dried in summer for medical uses, including improving Yang-qi and decreasing skeleton raw.
Eucalyptol (1,8-cineole) is one of the major essential oils in AV. Eucalyptol has been used as a percutaneous penetration enhancer (Levison et al., 1994), an antibacterial and expectorant (Giamakis et al., 2001), and as an anti-inflammatory (Juergens et al., 1998) or antihypertensive agent (Lahlou et al., 2002). Eucalyptol acted as a strong inhibitor of proinflammatory cytokines such as tumor necrosis factor (TNF)-α and interleukin (IL)-1β and showed an GRAPHICAL ABSTRACT analgesic effect in an inflammatory model. Even though there is a report about eucalyptol acting against fatty liver in mammals and zebrafish (Cho, 2012;Murata et al., 2015), the effect and mechanism of eucalyptol against drug-induced liver injury remain unclear.
Drug-induced liver injury has become a major public health concern (Asrani et al., 2018;Real et al., 2019). Acetaminophen (APAP) overdose is the leading cause of drug-induced acute liver failure. Oxidative stress is considered to be the primary cellular event in APAP-induced liver injury (Nikravesh et al., 2018;Zhao et al., 2018). Under overdose conditions, most APAP is metabolized by phase II conjugating enzymes, mainly sulfotransferase (SULT) and UDP-glucuronosyltransferase (UGT), converting it to nontoxic compounds, which are then excreted with the urine. The remaining APAP, approximately 5-9%, is metabolized by the cytochrome P450 enzymes (CYPs), mainly CYP2E1, into the highly reactive intermediate metabolite N-acetyl-p-benzoquinone imine (NAPQI). NAPQI is usually rapidly detoxified by conjugating it with glutathione (GSH). However, when phase II metabolizing enzymes are saturated after APAP overdose, excessive NAPQ1 can deplete GSH, leading to covalent binding of sulfhydryl groups in cellular proteins and resulting in liver oxidative stress (Lancaster et al., 2015;Du et al., 2016). Nuclear factor erythroid 2-related factor 2 (Nrf2) is likely activated by redox status changes induced by NAPQI. Nrf2 dissociates from Keap1 and translocates into the nucleus to stimulate transcription of target genes with the help of small Maf proteins. These preceding processes led to the transcriptional activation of antioxidant enzymes, such as NAD(P)H, quinone oxidoreductase 1 (NQO1), heme oxygense-1 (HO-1), glutamate cysteine ligase (GCL), and glutathione S-transferase A (GSTA), increasing the expression of SOD and CAT (Loboda et al., 2016). In this study, the common reagent APAP that induced drug liver injury was chosen to explain the mechanism of AV and eucalyptol hepatoprotection.
PCR amplification started with the denaturing step at 94°C for 3 min, followed by 36 cycles of denaturation at 98°C for 20 s, annealing at 58-60°C for 20 s, extension at 68°C for 50 s, and a final extension at 68°C for 6-8 min before cooling to 10°C.
The original sequences were assembled using CodonCode Aligner V3.0 (CodonCode Co., Centerville, MA, USA). The ITS2 sequences were subjected to Hidden Markov Model (HMM) (Keller et al., 2009) model analysis to remove the conserved 5.8S and 28S DNA sequences (Koetschan et al., 2012). The ITS2 sequences were aligned using Clustal W (Thompson et al., 2002), and the genetic distances were computed using MEGA 6.0 according to the Kimura 2-Parameter (K2P) model (Tamura et al., 2011). Subsequently, MEGA6.0 software 20 was employed to construct an unrooted phylogenetic tree based on alignments using the neighbor-joining (NJ) method with the following parameters: JTT model, pairwise gap deletion, and 1,000 bootstraps. Furthermore, maximum likelihood, minimal evolution, and PhyML methods were also applied in the tree construction to validate the results from the NJ method. Annotated ITS2 sequences of Sample 1, Sample 2, Artemisia vulgaris, Artemisia lavandulifolia, Artemisia argyi, and Artemisia annua were folded by energy minimization using the ITS2 database web server (http://its2.bioapps.biozentrum. uni-wuerzburg.de/) for secondary structure analysis.
Subcritical Butane Extraction of AV-EOs and Purification
The EOs were obtained by subcritical butane extraction apparatus (Henan Subcritical Biological Technology Co., Ltd., Anyang, China). The liquid/solid ratio was 30:1, the temperature was 45°C, extraction time was 34 min, and the particle size was 0.26 mm. The extract was subjected to hydrodistillation in Clevenger-type apparatus for 2 h. The oil/water emulsion produced was collected and stored at 4°C overnight to separate the essential oil from the residual water. The essential oil was then removed and stored in an amber glass bottle at room temperature until further use.
Electronic Nose Analysis
The constituent of EOs from AV was captured by measuring the headspace PEN3 (Airsense Analytics system GmbH, Schwerin, Germany). The e-nose system consisted of a fully automated Headspace-Sampler, an array of ten sensors (Alpha MOS company, France), and an electronic unit for data acquisition. The MOS sensors consisted of W1C (aromatic), W5S (broadrange), W3C (aromatic), W6S (hydrogen), W5C (aromaliph), W1S (broad-methane), W1W (sulphur-organic), W2S (broad-alcohol), W2W (sulph-chlor), and W3S (methane-aliph). Volatile organic compounds (VOCs) were injected into the Portable Electronic Nose PEN3 system using an auto-sampler at a low rate of 60 ml/min from 10 ml sealed glass vials containing 1 ml of oil sample. The VOCs were carried by pure gas (carrier gas) at 5 psi and exposed to the sensor chambers. The relative change in the resistance (G0/G) value determines the response of sensors for oil samples. TheΔR/R value was monitored precisely for 130 s. The data were analyzed using Loading (Lo) and principal component analysis (PCA). The PCA values were determined using Eq 1 Determination of Essential Oil Ingredients by Headspace Solid-Phase Microextraction Coupled to Gas Chromatography (HS-SPME-GC-MS) The EOs were analyzed on an HS-SPME-GC-MS system consisting of commercial manual sampling SPME devices (Supelco, Inc. Bellefonte, PA, USA). SPME fibers with 100 μm polydimethylsiloxane (PDMS), 65 μm PDMS/divinylbenzene (PDMS/DVB), 85 μm polyacrylate (PA), 85 μm carboxen/ PDMS (CAR/PDMS), and 70 μm carbowax/DVB (CW/DVB) were used. The analysis was carried out on a GC system (GC-2010, Shimadazu Tokyo, Japan) coupled with a flame ionization detector (FID). All the fibers were conditioned before use in the GC injector, according to the instructions provided by the manufacturer. Separation was performed using a DB-5 capillary column (30 m × 0.25 mm I.D. and 0.25 μm, J&W Scientific, CA, USA).
The instrument parameters for the analysis were as follows: N2 flow: 1.47 ml/min; column temperature program: held at 40°C for 3 min, then increased from 40 to 70°C at 15°C/min and maintained for 1 min, and then increased to 250°C at 30°C/min and held for 1 min. The detector temperature was held at 280°C. In optimized conditions, the temperature of the injector was set at 250°C, and the desorption process was performed in the splitless mode for 2 min.
For the HS-SPME experiments, EOs (3 ml) were placed in a 10 ml glass vial. The vial was closed with Teflon-lined septa (Supelco, Pennsylvania, USA). The standard solutions and EOs samples were stored at room temperature. Afterwards, a fiber was introduced into the headspace of the vial for 10 min at the same extraction temperature. After extraction, the fiber was removed from the vial, inserted into the inlet of the GC, and desorbed at 250°C for 2 min.
Compounds, Targets, and Pathway Analysis
AV compounds (85) were used to analyze the ADME properties using SwissADME (swissadme.ch/index.php). Based on the Lipinski rule, a total of 31 compounds were finalized for target fishing and pathway analysis. All selected compounds from SN structural data were retrieved from Pubchem (https://pubchem.ncbi.nlm. nih.gov/). Active components were identified and compared with Similarity Ensemble Approach (SEA) (http://sea.bkslab. org/) (Keiser et al., 2007) and Drug Repositioning and Adverse Reaction via Chemical-Protein Interactome (DRAR-CPI) (http:// cpi.bio-x.cn/drar/) (Luo et al., 2011). Furthermore, Comparative Toxicogenomics Database (CTD) (http://ctdbase.org/) was applied for the target mining process. The target genes of AV were applied for pathway analysis using The Database for Annotation, Visualization and Integrated Discovery 6.8 server (DAVID) (http:// david.abcc.ncifcrf.gov): analytical tools used to identify the gene or proteins systematically. KEGG pathway information was retrieved (Supplementary Table 1) (Dennis et al., 2003).
Experimental Animals
The experimental protocol was reviewed and approved by the Ethics Committee of the Institute of Modern Biotechnology for the Use of Laboratory Animals. A total of 42 (15 male and 15 female) inbred Kunming mice (18-20 g) aged 4 weeks and 12 inbred SD rats (200-220 g) were obtained from the animal center of Zhengzhou University (Zhengzhou, China). The animals were kept under controlled conditions at temperature 22 ± 2°C, humidity 70% ± 4% with 12 h light-dark cycling.
Experiment 2: Rats were randomly divided into two groups of five each. APAP group: 300 mg/kg; eucalyptol-APAP group: 5 ml/ kg eucalyptol with oral administration after APAP (300 mg/kg) treatment for 1 h. After eucalyptol treatment for 0.2, 0.5, 0.75, 1, 1.5, 2, 4, and 6 h, the plasma was collected for high performance liquid chromatography (HPLC) or high performance liquid chromatography-tandem mass spectrometry (HPLC-MS/MS) analysis. The plasma samples were mixed with acetonitrile and centrifuged at 13,000 g for 15 min at 4°C.
Determination of Serum ALT and AST Levels
Enzymatic activities of aspartate aminotransferase (AST) and alanine aminotransferase (ALT) in serum were evaluated by spectrophotometer using commercial diagnostic kits (Nanjing Jiancheng Institute of Biotechnology, Nanjing, China).
Determination of Histology
Liver tissues were fixed in 10% formalin and embedded in paraffin for histological assessment. Samples were sectioned 5 µm and stained with hematoxylin and eosin. The slides were examined under a light microscope with photo-micrographic attachment.
Determination of Hepatic ROS, SOD, CAT, and MDA Levels
Frozen liver tissues were homogenized in ice-cold PBS. The supernatants were collected after the homogenate was centrifuged at 3000 g, 4°C for 10 min. Superoxide dismutase (SOD), catalase (CAT), and malondialdehyde (MDA) levels were measured with a spectrophotometer using the commercially available assay kits as per the manufacturer's instructions (Nanjing Jiancheng Bioengineering Institute, Nanjing, China). The reactive oxygen species (ROS) levels were assayed with a fluorescence detector using commercial kits (Jiancheng Bioengineering Institute, Nanjing, China). The protein concentrations in tissue homogenates were measured with Bradford protein assay using bovine serum albumin as the standard (Jiancheng Bioengineering Institute, Nanjing, China).
Determination of Drug Metabolism-Related Gene Expressions
Total mRNA was isolated from frozen liver tissues using a Total RNA kit (Tiangen, Beijing, China). Quantitative real-time PCR (qPCR) was carried out for the amplification of cDNA using 2×SYBR Green I PCR Master Mix (Vazyme, Nanjing, China). The PCR procedure consisted of 95°C for 30 s followed by 35 cycles of 95°C for 15 s, 58°C for 30 s, and 72°C for 30 s. The PCR primers were used as shown in Table 1. The melting curve and dissociation curve were extrapolated to confirm primer specificity and product purity. The relative abundance of each mRNA was calculated with the formula 2 −(ΔΔCt) , where ΔΔCt = (Ct Target -Ct GAPDH ) treatment − (Ct Target − Ct GAPDH ) control.
Determination of CYP2E1 and Nrf2 Protein Expression
For Nrf2 expression analysis, the extraction and isolation of cytoplasmic and nuclear proteins were performed using a Cytoplasmic and Nuclear Protein Extraction Kit (Beyotime, Nanjing, China), according to the manufacturer's instructions. For CYP2E1 expression analysis, the extraction and isolation of microsomal proteins were carried out as described previously (Jiang et al., 2016;Chen et al., 2019). The protein concentration was determined by BCA assay kit (Beyotime, Nanjing, China). Equal amounts of protein extracts were subjected to SDS-polyacrylamide gel electrophoresis under reducing conditions in concentrate protein gel 5% (pH = 6.8) and separating protein gel 12% (pH = 8.8). The separated proteins were transferred to PVDF membranes using tank transfer for 2 h at 200 mA in Tris-glycine buffer with 15% methanol. Membranes were blocked with 5% skimmed milk for 3 h and incubated for 12 h with anti-CYP2E1 (1:1500, Boster, Wuhan, China), anti-Nrf-2 (1:500, Bioss, Beijing, China), anti-GAPDH (1:1000, Boster, Wuhan, China), and anti-Lamin B (1:500, Bioss, Beijing, China) for 2 h at 37°C. The secondary antibodies (IgG/ HRP) were incubated for 2 h at 37°C. The images of the blots were visualized by ECL (Genshare, Xi'an, China).
Molecular Docking
Molecular docking was employed to study the interactions between the eucalyptol and the Keap1 using Autodock vina version 1.1.2 package. The three-dimensional (3D) structure of the Keap1 (PDB ID: 3WN7) was retrieved from the RCSB Protein Data Bank (http://www.rcsb.org). The 2D structure of the eucalyptol was drawn by ChemBioDraw Ultra 14.0 and converted to the 3D structure by ChemBio3D Ultra 14.0 package. The AutoDockTools version 1.5.6 was used to obtain the docking input files. The binding site of the Keap1 was identified as center_x: 3.766, center_y: 1.122, and center_z: 19.296 with dimensions size_x: 15, size_y: 15, and size_z: 15. To increase the accuracy of the calculation, the value of exhaustiveness was set to 20. In addition, the default parameters were used, if it was not mentioned. The best docking pose as judged by the Vina score was chosen and further analyzed using PyMoL 1.7.6 software (http://www.pymol.org/).
SPR Interaction and Affinity Analysis
To understand the interactions between eucalyptol and the Keap1 protein, we performed an affinity measurement using surface plasmon resonance (SPR) technology. The SPR validation experiment was performed with the bScreen LB 991 Label-free Microarray System (Berthold Technologies, Germany). To validate detection of the eucalyptol-Keap1 interactions, the photo-crosslinker sensor chip was used. Rapamycin and DMSO were selected as system positive control and negative control, respectively. We arranged kinetic constant tests with FKBP12 immediately after the sample tests. During the SPR test, the Keap1 protein (MyBioSource, Vancouver, Canada) was diluted separately with running buffer to 200, 400, 800, 1600, and 3200 nM and injected for 600 s at a flow rate of 0.5 µl s −1 at associating stage, followed by running buffer for 360 s at a flow rate of 0.5 µl s −1 at each dissociating stage. At the end of each associating-dissociating cycle, the surface was regenerated to remove any remaining bound material with a pulse of 10 mM glycine-HCl (pH 2.0) at 20 µl min −1 for 30 s. Nrf2 GCTGATGGAGTACCCTGAGGCTAT ATGTCCGCAATGGAGGAGAAGTCT HO-1 TGCCAGTGCCACCAAGTTCAAG TGTTGAGCAGGAACGCAGTCTTG NQO1 GGAGACAGCCTCTTACTTGCCAAG CCAGCCGTCAGCTATTGTGGATAC GCLC TGAGATTTAAGC CCCCTCCT TTGGGATCAGTCCAGGAAAC GSTA2 TCAGTAACCTGCCCACAGTGAAG GCATGTTCTTGACCTCTATGGCTGG UGT1A1 CACGCTGGGAGGCTGTTAGT CACAGTGGGCACAGTCAGGTA UGT1A6 CACGTGCTACCTAGAGGCACAG GACCACCAGCAGCTTGTCAC UGT1A9 GAAGAACATGCATTTTGCTCCT CTGGGCTAAAGAGGTCTGTCATAGTC SULT1A1 CCCGTCTATGCCCGGATAC GGGCTGGTGTCTCTTTCAGAGT SULT2A1 TAGGGAAAAATTTAGGGCCAGAT TTGTTTTCTTTCATGGCTTGGA CYP2E1 CACCGTTGCCTTGCTTGTCTG CTCATGAGCTCCAGACACTTC GAPDH ACATGGCCTCCAAGGAGTAAGA GATCGAGT TGGGGCTGTGACT The raw sensorgrams and measurements of the binding process of ligands and proteins were recorded in real time. The response unit (RU) of surface resonance was compared to determine the different binding affinities between each sample dot. The response unit data collected on the SPR biosensor was further processed to eliminate any artifacts such as non-specific binding and differences in buffer composition. The process and analysis of association and dissociation rate constants (K a /K on and K d /K off respectively) and the equilibrium dissociation constant (K D , K d /K a ) were performed using the data analysis software of the bScreen LB 991 unlabeled microarray system according to a single-site binding model (1:1 Langmuir binding) with mass transfer limitations for binding kinetics determination.
LC-MS/MS Analysis of APAP and its Metabolites
Plasma samples were obtained 0.2, 0.5, 0.75, 1, 1.5, 2, 4, and 6 h after different treatments. The concentrations of APAP and its conjugated metabolites were analyzed using modified LC-MS/MS. Briefly, plasma samples were centrifuged at 13,000g for 15 min at 4°C. The supernatants were diluted with ultrapure water. Reversed phase chromatography of APAP, APAP-glucuronide (APAP-gluc), and APAP-sulfate (APAPsulf) was carried out using an ACE AQ C18 column (Advanced Chromatography Technologies, UK; 2.1×100 mm, 3 μm) at 50°C at a flow rate 0.3 ml/min. Mobile phase A was 0.2% formic acid in acetonitrile, while mobile phase B was 0.1% formic acid in methanol. The condition of chromatographic separation was 2% B from 0 to 0.5 min, held at 95% B for 0.8 min and then to 2% B at 3.31 min, followed by 5 min of column equilibration using 2% B.
The mass spectrometer was operated in ESI+Agilent Jet Stream mode with multiple reaction monitoring (MRM). The target compounds were detected by monitoring the m/z transition: m/z 150.0→107.0 for APAP, m/z 326.0→150.0 for APAP-gluc, and m/z 230.0→150.0 for APAP-sulf, with a dwell time of 100 ms for each mass transition. TIS temperature was 500°C, and TIS voltage was 3.5 kV. Curtain gas, nebulizing gas, TIS gas, and collision gas was 25, 90, 80, and 10 units, respectively. Collision energy and collision cell exit potential are 14 and 80 V for APAP, 5 V and 100 V for APAP-gluc, and 30 and 110 V for APAP-sulf, respectively. The mass spectrometer was operated at unit mass resolution for both Q1 and Q3 quadruples.
Statistical Analysis
The results were presented by means of, at least, five measurements, duplicated for each set, having a coefficient of variation less than 5%. One-way ANOVA followed by Duncan's multiple range test (p < 0.05) with SPSS 20.0 (SPSS Inc., Chicago, IL, USA) was applied for the mean values compared.
Phylogenetic Relationships
DNA barcode analysis with ITS2 sequence was used to investigate the evolutionary history and phylogenetic relationships of sample 1. A phylogenetic tree based on NJ cluster algorithm was constructed in Figure 1A. NJ sequence similarity analysis discovered that sample 1 was close to its close species from Artemisia (Artemisia vulgaris, Artemisia lavandulifolia and Artemisia annua). The branches indicate the bootstrap values for 1000 replicates. Furthermore, inter-species variations were also calculated and the results showed that Sample 1 and Artemisia argyi showed the highest similarity (0.005), while Sample 2 and Artemisia vulgaris showed the highest similarity (0.003) as presented in S. Table 2. The secondary structure of ITS2 of Sample 1 is similar to Artemisia argyi, while Sample 2 is similar to Artemisia vulgaris ( Figure 1B). Compared with multiple analysis FIGURE 1 | Species identification of sample 2 by phylogenetic tree and ITS2 secondary structure. (A) Phylogenetic tree of the four Artemisia species constructed with the ITS2 sequences using the neighbor-joining (NJ) method; (B) ITS2 secondary structure. methods, the results show that Sample 1 was Artemisia argyi L, and Sample 2 was Artemisia vulgaris L.
E-Nose Analysis
To analyze the volatile organic compounds from AV, the e-nose was used. The polar plot display of sensor values of EOs from AV at 57s was given by the cursor in the measurement window. The sensor of W2W, W1W, and W1S was highly sensitive to the EOs of AV (Figure 2A), indicating that the collected EOs contained sulph-chlor, sulphur-organic and broad-methane. The flying data were examined with PCA to visualize the response patterns in the feature space of principal components (PC). Two PCs, namely, PC1 and PC2, which explained 80.4% and 16.4%, respectively, of the data variance, were chosen based on the Eigen values (p > 0.5). Using PCA, the three main odors of AV were sulph-chlor, sulphur-organic, and broadrange ( Figure 2B). The Lo analysis revealed that W5S and W1W have higher response to the compounds of AV, indicating that the broad range and sulphur-organic were present in EOs of AV. W6S, W5C, W2S, and W3S were not sensitive to the EOs of AV ( Figure 2C).
Effect of EOs and Eucalyptol on APAP-Induced Hepatotoxicity
APAP-treated mice exhibited hepatocellular injury ( Figure 3B) compared with control group (Figure 1A). More than half of the centrilobular hepatocytes were swollen with marked cytoplasmic vacuolation and condensed nuclei. The white spots were on the liver, while the EO and eucalyptol group did not show hepatotoxic effects (Figures 3C-G). ALT and AST levels were significantly increased by 2.67-fold and 2.06-fold in the APAP group, respectively, as compared to the control group ( Figure 3F). APAP-EO and APAP-EU decreased the ALT and AST activities compared with APAP-treated liver. The liver indexes were 4. 43, 4.98, 4.48, 4.46, 4.42, 4.41, and 4.42 in the control-, APAP-, APAP-EO-, APAP-EU-, APAP-NAC-, EO, and EU group, respectively.
Hepatic Antioxidant Effects of AV-EOs and EU on Oxidative Stress Biomarkers
To investigate the antioxidant effect of AV-EOs and EU, the levels of oxidative stress biomarkers were examined in mice (Figure 4). APAP treatment significantly increased the content of MDA and ROS by 2.38-and 1.92-fold, respectively. APAP administration resulted in a significant decrease in the activities of SOD and CAT to 0.72-and 0.44-fold.
APAP-EO or EU co-administration reversed the decrease in OD and CAT and reduced the levels of ROS and MDA. Meanwhile, EOs and eucalyptol could eliminate ROS (p < 0.05).
Effect of AV-EU on Oxidative Stress-Related Gene Expression
qPCR analysis indicated that APAP-EU co-treatment alleviated APAP-induced reduction of GCLC and GSTA. EU treatment significantly increased the levels of HO-1, NQO1, GCLC, and GSTA2, suggesting EU's activities in antioxidant mediation ( Figure 5).
Effect of AV-EU on APAP Metabolism
APAP and its major conjugates in plasma were analyzed using HPLC-MS/MS. The AUC of APAP in the APAP group was significantly higher (1.65 fold) than in APAP-EU treatment group, and APAP-EU significantly increased the levels of AUC of APAP-gulc and APAP-sulf in plasma ( Figure 6A).
The hepatic mRNA expressions of UGT1A1, UGT1A6, and UGT1A9 in the eucalyptol-treated group were 2.3-, 1.95-, and 2.07-fold higher than the control group ( Figure 6B), respectively. Compared with the control group, the mRNA expression of UGT1A6 significantly decreased 0.45-fold after APAP treatment. AV-EU post-treatment increased the mRNA levels of UGT1A6. Likewise, eucalyptol increased SULT1A1 and SULT2A1 mRNA levels by 2.5-and 2.0-fold, respectively ( Figure 6C). The expression of CYP2E1 was significantly increased (2.8-fold) after APAP treatment; the mRNA levels of CYP2E1 significantly increased after eucalyptol treatment ( Figure 6D).
Effect of AV-EU on Nrf2 Expression
The theoretical binding mode of the eucalyptol in the Nrf2 binding site of the Keap1 was illustrated in Figure 7A. Detailed analysis showed that the compound eucalyptol was positioned at the hydrophobic pocket, surrounded by the residues Tyr-525, Ala-556, Tyr-572, and Phe-577, forming a stable hydrophobic binding. Importantly, the "O" atom of eucalyptol formed the key hydrogenbond interaction with the residue Arg-415, with a bond length of 2.9 Å. The hydrogen bond was the main interaction between eucalyptol and Keap1. According to the affinity measurement, eucalyptol showed a strong affinity (K D = 1.42 × 10 −5 ) for Keap1 protein. The association rate constants k on and k off were 1.75 × 10 3 and 2.49 × 10 −2 , respectively. Their binding curves during the test are shown in Figure 7B. These interactions helped to anchor eucalyptol in the Nrf2 binding site of Keap1. In addition, the estimated binding energy of eucalyptol is −5.5 kcal•mol −1 , suggesting that eucalyptol is an inhibitor of the Keap1.
qPCR and WB analysis show that eucalyptol treatment increased Nrf2 mRNA (Figures 7B, C) and stimulated the nuclear translocation of Nrf-2 transcription factor. The ratio of protein FIGURE 6 | Effects of eucalyptol on the APAP metabolic disposition. APAP: APAP treatment group; APAP+EU: EU was intragastrically administrated after APAP treatment group; APAP+NAC: NAC was oral administration after APAP treatment group. EU: EU was intragastrically administrated. a, b, c different letters indicate statistically different groups (p < 0.05). expression of nuclear Nrf-2 and cytoplasmic Nrf-2 in eucalyptol was 5.8-fold higher than that of the control group ( Figure 7C).
DISCUSSION
AV is one of the famous Artemisia species compared to others such as A. absinthium, A. nilagirica, and A. deserti, (Kazemi et al., 2013;Pelkonen et al., 2013;Sati et al., 2013). AV-EOs have a high content of eucalyptol and Cis-β-Terpineol, which shown antiinflammatory and antioxidant effects against various diseases, including respiratory disease, pancreatitis, colon damage, and non-alcoholic steatohepatitis (Murata et al., 2015;Seol and Kim, 2016). In our present study, treatment with AV-EOs and eucalyptol significantly attenuated APAP overdose (300 mg/kg) and induced the increase of serum aminotransferase and hepatic histopathological lesions (Figure 3), suggesting that AV-EOs possess the ability to prevent APAP-induced hepatotoxicity.
Many studies on Artemisia did not result in any significant adverse effects in food/water consumption, body weight, mortality, hematology, serum biochemistry, organ weight, and histopathology (Wan et al., 2017;Yun et al., 2017); high-dose (752 mg/kg) usage of Artemisia may pose health based on mutagenesis and hepatotoxicity, suggesting that high-dose application of the extract in the treatment of serious disease is not recommended (Kalantari et al., 2013). Artemisia abstinthium may have neurotoxic; because of the major activity of thujone, it can inhibit the gammaaminobutyric acid A (GABAA) receptor causing excitation and convulsions in a dosedependent manner (Pelkonen et al., 2013). In our study, AV-EOs do not contain thujone (Table 2), and the dose of essential oil from Artemisia vulgaris was lower than the toxic dose. Our data show that dose of essential oil from Artemisia vulgaris (5%, 100 ml/kg) did not induce the liver injury. The liver index in the APAP group was significantly higher than that of the control group, while no significant difference was observed among APAP-EO (AV) , EO, and control group. Compared with compounds of EOs and the liver function indicators after EO treatment, we speculate that low dose of AV is safe.
APAP has non-toxic and toxic metabolic pathways in the liver. In the non-toxic pathway, APAP was glucuronidated and sulfated into APAP-gluc and APAP-sulf and excreted into blood and bile with the involvement of UGT and SULT family (Cao et al., 2017). In this study, the levels of UGT1A1, UGT1A6, UGT1A9, SULT1A1, and SULT2A1 were significantly increased after eucalyptol treatments, suggesting eucalyptol-enhanced APAP metabolism by the non-toxic pathway. The Nrf2 gene, with the consensus of TGAG/CNNNGC (N represents any base), is essential for inducing an increase in UGT and SULT family's expression (Hayes and Dinkova-Kostova, 2014). Eucalyptol significantly increased the mRNA expression of Nrf2 ( Figure 7B). Eucalyptol can directly combine with Keap1 at site Arg-415, which was Nrf2-Keap1 binding site. Eucalyptol showed a strong affinity for Keap1 protein. The activated Nrf2 was transferred from cytoplasmic into nuclear. The expression of Nrf2 mRNA was also increased, resulting in an increase in nuclear/ cytosolic relative expression under EO treatment ( Figure 7C). In addition, Nrf2 is a transcription factor that modulates endogenous antioxidant enzymes (Hou et al., 2018;Liu et al., 2018;Mahmoud et al., 2018). EOs stimulate Nrf2 activation. The activated Nrf2 binds to the antioxidant response element and further activates the transcription of gene encoding for antioxidants and detoxifications including heme oxygenase-1 (HO-1), NAD(P)H: quinone oxidoreductase-1 (NQO-1), and glutathione-synthesizing enzymes [glutamate-cysteine ligase catalytic subunit (GCLC)] (Hu et al., 2018). Our results suggest that EOs increased Nrf2 transfer from the cytoplasm to the nucleus, thereby leading to the transcriptional activation of antioxidant enzymes (HO-1, SOD, and CAT; Figs. 4 and 5) and phase II metabolic enzymes (UGT and SULT, Figure 6). The second metabolism pathway of APAP was a toxic reaction. Overdosed APAP was transferred into NAPQI by CYP2E1 (Ganetsky et al., 2018), which undergoes chemical and enzymatic conjugation to GSH. The toxic pathway could lead to lipid peroxidation; antioxidant enzyme activities were reduced, and the levels of ROS were increased. Here, APAP increased MDA and ROS levels and decreased the activities of SOD and CAT, suggesting that APAP-induced hepatic dysfunction is caused by oxidative stress. The expression of CYP2E1 was significantly increased by APAP and decreased by eucalyptol treatment (Figure 6). CYP2E1-deficient mice were resistant to the liver injury-induced APAP, while the transgenic mouse expressing human CYP2E1 was susceptible to the conversion of APAP to NAPQI. Our results show that eucalyptol inhibits CYP2E1 expression and attenuates liver injury. The pathway analysis study also reported the following active compounds: 2-Butanone,3methyl-, 1-Octene, Benzaldehyde, Phenol,4-methyl-, Octanal, 1-Nonene, and Hexanal. These compounds represent the effective targets such as Aldo-keto reductase family 1 member C1, Alcohol dehydrogenase 1B, Cytochrome P450 2A6, and Cytochrome P450 1A2, which are involved in the metabolism of xenobiotics by cytochrome P450 and drug metabolism-cytochrome P450 pathway, respectively, which is related to CYP2E1 expression.
Collectively, AV-EOs can prevent APAP-induced liver injury through two pathways: down-regulation of CYP2E1 expression, which decreases plasma concentration of APAP into NAPQI, and the up-regulation of the expression of the detoxification pathway. The up-regulation pathway includes inhibitory binding with Keap1, which stimulates Nrf2 translocation from cytoplasm into mitochondria, activates Nrf2, and thus increases the activity of antioxidant enzymes (SOD, GSH, CAT, and GPx) and phase II enzymes (SULTs and UGTs) (Figure 8), thereby decreasing APAP plasma concentration and accelerating APAP harmless metabolism.
DATA AVAILABILITY
All datasets generated for this study are included in the manuscript and the supplementary files.
ETHICS STATEMENT
The mice were obtained from the animal center of Zhengzhou University (Zhengzhou, China). The experimental protocol was reviewed and approved by the Ethics Committee of the Institute of Modern Biotechnology for the Use of Laboratory Animals. | 7,137.2 | 2019-07-25T00:00:00.000 | [
"Biology",
"Medicine"
] |
Flexible Self-Organizing Maps in kohonen 3.0
Self-organizing maps (SOMs) are popular tools for grouping and visualizing data in many areas of science. This paper describes recent changes in package kohonen , implementing several different forms of SOMs. These changes are primarily focused on making the package more useable for large data sets. Memory consumption has decreased dramatically, amongst others, by replacing the old interface to the underlying compiled code by a new one relying on Rcpp . The batch SOM algorithm for training has been added in both sequential and parallel forms. A final important extension of the package’s repertoire is the possibility to define and use data-dependent distance functions, extremely useful in cases where standard distances like the Euclidean distance are not appropriate. Several examples of possible applications are presented.
Introduction
The kohonen package (Wehrens and Kruisselbrink 2018) for R (R Core Team 2018), available from the Comprehensive R Archive Network (CRAN) at https://CRAN.R-project.org/ package=kohonen, was published ten years ago as a tool for self-organizing maps (Kohonen 1995), providing simple yet effective visualization methods. A particular characteristic of the package was the possibility to provide several data layers that would contribute to the overall distances on which the mapping would be based. Since then, the package has been applied in different fields like environmental sciences (Vaclavik, Lautenbach, Kuemmerle, and Seppelt 2013), transcriptomics (Chitwood, Maloof, and Sinha 2013), and biomedical sciences (Wiwie, Baumbach, and Rottger 2015), to mention but a few.
Self-organizing maps (SOMs) aim to project objects onto a two-dimensional plane in such a way that similar objects are close together and dissimilar objects are far away from each other. Obviously, such a visualization is extremely useful for data sets with large numbers of objects, but also in cases where the number of variables is large -everything is brought back to similarities between objects. What distinguishes SOMs from approaches like principal component analysis (PCA) or principal coordinate analysis (PCoA) is the discrete nature of the mapping: Objects are mapped to specific positions in the 2D plane, called units. Each unit is associated with an object called a codebook vector, usually corresponding to the average of all objects mapped to that unit. The codebook vector can be seen as a "typical" object for that area of the map. Mapping data to a trained SOM is nothing more than calculating the distance of the new data points to the codebook vectors, and assigning each object to the unit with the most similar codebook vector (the best matching, or "winning", unit).
For training SOMs several different algorithms are used: The standard ones are the online and the batch algorithms (Kohonen 1995). In both cases, training objects are compared to the current set of codebook vectors. The codebook vector of the winning unit, as well as units within a certain radius of the winning unit, are changed to become more similar to the new object mapping to it. During training, the radius slowly decreases; in the end of the training only the winning unit is updated. The difference between the online and batch SOM algorithms is that the update of the winning unit(s) in the online algorithm is done after each individual object, whereas the batch algorithm does not change the codebook vectors until the whole data set has been presented. Then, the cumulative change based on all objects in the training set is applied in one go.
Several R packages implement more or less elaborate versions of the SOM: class (Venables and Ripley 2002), the basis of the original kohonen package, implements both the online and batch algorithms, using the .C interface to compiled code. The som package (Yan 2016) provides the basic online version of the SOM, with training done in C++ using the .Call interface. Package SOMbrero (Olteanu and Villa-Vialaneix 2015) provides methods for handling numerical data, contingency tables, and dissimilarity matrices. Different scaling methods for data of particular types are included. All functions are pure R -no compiled code is used, which leads to a relatively slow training phase. The package supports a shiny (Chang, Cheng, Allaire, Xie, and McPherson 2018) interface for dynamic visualization of results. The RSNNS package (Bergmeir and Benítez 2012) is an R wrapper to the SNNS toolbox written in C++, including SOMs as one of many types of neural networks. Finally, a very recent publication introduced the somoclu package (Wittek, Gao, Lim, and Zhao 2017), providing a general toolbox for training SOMs with support for cluster and GPU computations, and interfaces to Python (Van Rossum et al. 2011), MATLAB (The MathWorks Inc. 2017) and R.
The kohonen package provides extensive visualization possibilities 1 as well as fast training and mapping using compiled code. However, several limitations were becoming apparent (see, e.g., Boyle, Araya et al. 2014). Memory management was not very efficient, unnecessarily declaring potentially large memory chunks; the lack of parallelization support meant that even in simple desktop and laptop computers computing power was not fully used; and finally, fixed distance functions were implemented and no others could be added by the user without explicitly recompiling the package. In a major overhaul, these issues have been addressed, leading to version 3.0. Finally, the package has been extended with the batch algorithm, including support for parallel computing.
In the next section, we will discuss these and other changes in more detail. This is followed by three application examples, highlighting the capacity of the package to handle large data sets and the use of data-specific distance functions. Benchmarks are given, comparing the efficiency of the new version with the previous version of the package. The paper ends with an outlook to future developments and some conclusions.
Changes in the kohonen package, version 3.0
Since the publication of the kohonen package in 2007 a number of small improvements had been made prior to version 3.0, mostly affecting the plotting functions, and often in response to user requests or bug reports. At some point it became apparent, however, that in order to stay relevant the package needed a more fundamental overhaul, making it faster and, especially, more memory-efficient, in order to be able to tackle larger data sets. The changes in version 3.0 of the kohonen package are discussed below. They correspond to using a different interface for calling the underlying compiled code, the possibility to define and use problem-specific distance functions on the fly, the inclusion of the batch algorithm for training SOM maps, and smaller miscellaneous improvements.
Switching from .C to Rcpp
The most important change in the package is not visible to the user and consists of the replacement of the .C interface, inherited from the class package, by a more efficient Rcpp solution. The advantages of using the Rcpp interface to the underlying compiled code rather than the original .C interface are clear and well documented (Eddelbuettel and François 2011). Here, it is particularly important that Rcpp works directly on the R objects, passed as function arguments, instead of making local copies of these objects. This is much more memory-efficient and especially for large data sets can make a huge difference in performance.
In addition, several functions were redesigned and rewritten at the compiled-code level. The som and xyf functions now are wrappers for the supersom function, applicable in situations with one and two data layers, respectively. In versions before 3.0, each of these functions had its own C implementation, which made the code hard to maintain. As a beneficial side effect, som and xyf can now be used when there are NAs in the data, something that in earlier versions was only possible with the supersom function. If the argument maxNA.fraction is set to zero (the default) no checks for NAs are performed, which leads to a further speed increase. Function bdk has been deprecated, since it offered no added benefits over xyf and was roughly twice as slow. The main functions of the package, supersom and the S3 methods predict and map for 'kohonen' objects have been rewritten completely. Especially the latter has become much more memory-efficient: For data sets with many records mapping could take as long as the training phase. Although we have tried to keep the results obtained as close as possible to the original code, there is no complete backwards compatibility -when applying the same settings, the new kohonen version will give results that are slightly different from the old version.
Flexible definition of distance measures
In the previous version of the kohonen package basically two distance measures were available: the Euclidean distance for numeric variables, and Tanimoto distance for factors. The latter could only be used in xyf networks. Version 3.0 not only provides more predefined distance measures (the Euclidean distance, the sum-of-squares distance, the Manhattan dis-tance, and the Tanimoto distance), they now can be used in all SOM types, and can be defined for each layer separately 2 . By default, the Tanimoto distance is used for factors or class membership matrices, and the sum-of-squares distance in all other cases. Note that also the so-called U-matrix visualization, showing the average distance of each SOM unit to its neighbors and available through the type = "dist.neighbours" argument of the plot method for 'kohonen' objects, now is taking into account the specific distances used in training the map, as well as their corresponding weights. The same holds for methods used for grouping codebook vectors -up to now clustering (e.g., in the examples of the plot method for 'kohonen' objects) was performed on Euclidean distances in one layer only, and did not take into account either different distance metrics nor weights. A new function has been included, object.distances, to allow the user to calculate distances between data points (and also between codebook vectors), according to the weighted combination of distances employed in the SOM.
Specific distance functions appropriate for the data at hand can be defined by the user in C++, again for every data layer separately 3 . In ecological applications, for example, several specific different distance functions are routinely used, such as the Bray-Curtis and Jaccard dissimilarities (Goslee and Urban 2007). A user-provided function implementing such a distance should take two vectors of real numbers, corresponding to the data and the codebook vectors, the number of variables, and the number of NA values, and should return one number. An example will be given below.
The batch SOM algorithm
The batch SOM algorithm has been available for a long time in the class package. Amazingly, the central loop of the algorithm contains only four lines of pure R code. The main difference with the original SOM algorithm is that the map update is performed less frequently: only after the complete data set has been presented are the codebook vectors updated -in that sense, the algorithm is very similar to the k-means algorithm. The learning rate α therefore is no longer needed.
Already on the wish list in Wehrens and Buydens (2007), this algorithm has been now included in the kohonen package. It is written in C++ for maximum performance, and is available through the mode = "batch" argument of the som functions. Whereas it is hard to define a useful parallel version of the online algorithm, the batch SOM algorithm does lend itself for parallelization: The task of finding the best matching units for all records in the data set is split up over different cores (Lawrence, Almasi, and Rushmeier 1999). This data partitioning parallel version is available using mode = "pbatch". By default, all cores are used. This can be changed by the user through the cores argument of the supersom function.
Miscellaneous changes
Several smaller changes have been made to the package as well. These are outlined in brief below.
Changes in plotting functions. Several extensions of the plotting functions have been implemented: On the request of several users now hexagon-and square-shaped units can be used in the plot functions. This is particularly useful for larger SOMs, where the white space between circular units would be a distraction. If SOM units are grouped in clusters, the cluster boundaries between units can be visualized. The validity of the clusters can be assessed by showing the average distance to neighboring codebook vectors as unit background color, available as type = "dist.neighbours" in the plot method for 'kohonen' objects. Examples of these new features can be seen on the corresponding manual page.
Weighing different data layers. The default system of weighing different data layers has been changed. Since distances are crucially dependent on the units in which the data have been recorded, a set of internal distance.weights is calculated first, corresponding to the inverses of the median distances in the individual data layer. The application of these weights ensures an (approximately, at least) equal contribution of all layers to the final distance measure -the user-defined weights are then used to influence this further. A user who wants to bypass this behavior is able to do so by setting normalizeDataLayers to FALSE.
Changes in SOM grid specification. An additional argument, neighbourhood.fct has been added to allow for a Gaussian neighborhood, that by definition always includes all units in the map in the update step. The "bubble" neighborhood is still retained as the default, since it is much faster. Related to this, the default for the radius parameter has changed: For both the "bubble" and "gaussian" neighborhoods the default is to decrease linearly to a value of zero, starting from a radius that includes two-thirds of the distances in the map. Note that in the "bubble" case only winning units will be updated when the radius is smaller than 1. Finally, the toroidal argument has been moved to a more appropriate location, the somgrid function (which is now no longer imported from the class package).
Growing larger SOMs. In some cases it may be cost-effective to train a small SOM first, to get the global structure of the data, and to extend the map with additional units in a later stage. Function expandMap, doing exactly this, has been introduced in this version of kohonen (taken from the soon to-be-phased out package wccsom, Wehrens 2015, see below). This is one of two ways of obtaining a SOM with many units, potentially more than there are records (known as an emergent SOM); the other way (already available since the first version of the package) is to explicitly provide the initialization state through the init argument.
Applications
Some of the new features in kohonen will now be highlighted. First, we use an application in image segmentation, an example of SOMs in a Big Data context, to present some relevant benchmarks. Then, we show a couple of examples of the use of user-defined distance functions. Code to reproduce the examples in this paper is included as demos in the kohonen package: R> demo("JSSdemo1", package = "kohonen") This will run the first example from the paper on image segmentation -the other two demos are available as "JSSdemo2" and "JSSdemo3", respectively. Note that especially the first example will take some time to complete (on an average PC from 2018 not more than a minute, though).
Image segmentation
SOMs are particularly useful for grouping large numbers of objects. An area where this is relevant is pixel-based image segmentation: Even a relatively small image already can contain thousands of pixels, and databases of thousands and thousands of images are becoming increasingly common. The aim then is to obtain an accurate description of the original images using a limited set of "colors", where colors may be either true colors (RGB values, as in this paper), or artificial colors obtained from spectroscopic measurements (Franceschi and Wehrens 2014). In many applications, specific colors will be associated with objects in the image. Here, we use one image from a set of artificial images from pepper plants, where the objective is to separate the peppers from the plants and the background (Barth, IJsselmuiden, Hemming, and Van Henten 2018). 4 In principle, segmentation of an image using self-organizing maps is easy enough -one can present the color values of the individual pixels to the SOM and observe where they will end up in the map. The image that we will use as an example, a synthetic (but very realistic) image of a pepper plant is shown in the left plot of Figure 1. Image segmentation can help in getting a simple and quick idea of the number and the size of the peppers on a large number of plants, a process known as high-throughput phenotyping.
The segmented image is shown in the right panel of Figure 1. It consists of a total of 32 different colors, each corresponding to one SOM unit. The cartoon-like representation still shows the most important features. In this case we have performed the analysis using two layers of information, the RGB values of the individual pixels in the first SOM layer, and the pixel positions in the image in the second. The idea is that pixels mapping to the same unit in the SOM will not only have the same color, but will also be close together in the image. The tessellation-like pattern in the segmented image that is the result from this is clearly visible. To achieve this, we give quite a high weight to the pixel coordinate layer: R> somsegm1 <-supersom(imdata, whatmap = c("rgb", "coords"), + user.weights = c(1, 9), grid = mygrid) The RGB codebook vectors are shown in the left plot of Figure 2. The background colors are associated with the dominant pixel classes mapping to the individual units (where only the two most important classes are shown explicitly and the other six are merged as "other" -note that since this is a synthetic image, the true pixel classes are known). One can see that the brightest colors (the largest R, G and B segments) correspond to peppers (the pastel purple background color), as one might expect. Note that there are two separate units where pepper pixels tend to be projected, because of the second information layer, the X-Y coordinates of the pixels (middle panel in Figure 2). Each circle depicts the position of the unit in the original image; the fill color corresponds to the RGB color of the units. The numbers correspond to the SOM units; these are covering the image in a regular fashion. The numbers of the pepper units are indicated in red. Unit 23 corresponds to the left pepper in the image, and unit 11 to the right pepper. Finally, the right plot in Figure 2 shows the location of the pixels mapping to the the pepper units in the original image. Although these units contain some non-pepper pixels the overall result is quite satisfying.
It can be a definite advantage that the two peppers in the image are projected in different areas of the map, illustrating that image segmentation on the pixel level can sometimes profit from additional information -in this case pixel coordinates. Other types of information that can be useful include information of neighboring pixels, and depth information. While these could conceptually also be included as extra columns in the original data, leading to one SOM layer only, keeping this information in additional layers provides more flexibility: One can use different weights for different layers (as was done here), or even use different distance functions, appropriate for particular layers.
One of the main reasons for redesigning the kohonen package was the difficulty of analyzing larger data sets, in particular those with many records. Especially memory usage was not optimized. The improvement in the new package version is illustrated here by some simple benchmarks. These benchmarking experiments consist of image segmentation of parts of the pepper plant image, RGB information only (5.5 Mb), on hexagonal grids of eight by four units, the same as used in the example. Five different pixel subsets were used, ranging in size from 5,000 pixels to 200,000 pixels. The assessment of memory usage 5 was performed using the profmem function from the package with the same name (Bengtsson 2018), keeping track of memory allocation during execution of the training or mapping phases. Speed benchmarking was performed using the microbenchmark package (Mersmann 2018), and was done on a HPC cluster node with an Intel Xeon CPU E5-2660 processor having eight physical cores and two logical cores per physical core. One hundred repetitions are used for speed benchmarking (the default microbenchmark).
Memory allocation during training with several forms of the supersom function as well as during mapping the data to the trained SOM is shown in Figure 3. The old version of the package is always shown as the bottom line in the plots. Training in the new version is more efficient than in the old version, with small differences between batch and online algorithms. Parallel batch algorithms show the same memory allocation as the batch algorithm, independent of the number of nodes used in the parallel version. In the mapping phase, where data are projected to a fully trained SOM, a huge improvement in memory usage is visible. Memory profiling results are obtained on two computers, one running Linux and one running Windows, and are virtually identical.
The improvement in speed is shown in Figure 4, showing the time needed for training the SOM, and for mapping data, respectively. Training is considerably faster in the new version, here showing an almost two-fold speed improvement. In the new version, differences between the online and batch training are small; also the parallel batch algorithm using one core only gives comparable timings (as expected). Using the parallel batch algorithm using more than one core provides further considerable speed improvements. Also mapping is much faster in the new version. Finally, the new version presents the opportunity to avoid checks for NA values by providing maxNA.fraction = 0L (obviously for data without NAs), which would lead to another speed-up.
User-defined distance functions
In some cases, the usual Euclidean or related distance functions are simply not optimal, and one would rather use specific measures appropriate for the data at hand. From version 3.0 onwards, such functions can be written and compiled in C++, and a pointer to the function can be provided to the SOM functions in kohonen. We give two examples, one from ecology, comparing sites according to the number of different plant species found in each site, and a crystallographic one comparing spectra where peaks are shifted in different samples.
Ecological applications.
Package vegan (Oksanen et al. 2018) contains a pair of data sets containing information on 24 sites, one set concentrating on cover values of 44 plant species at the sites, the other on soil characteristics (Väre, Ohtonen, and Oksanen 1995). Even though the data set is too small for a realistic application of SOMs, it does provide a good illustration of the possibilities of using several data layers associated with specific distance functions. First, the data are loaded and converted to matrices: R> data("varespec", package = "vegan") R> data("varechem", package = "vegan") R> varechem <-as.matrix(varechem) R> varespec <-as.matrix(varespec) We train the SOM using the majority of the data, the training set, and assess its value using the rest, the test set, here consisting of the last five records: R> n <-nrow(varechem) R> tr.idx <-1:(n -5) R> tst.idx <-(n - The aim is to group sites in such a way that sites in the same SOM unit have both a similar species profile and similar soil characteristics. For comparing species counts over different sites, often a Bray-Curtis dissimilarity is used, defined by This is implemented in C++ as follows: In this piece of code, the Bray-Curtis dissimilarity is the function brayCurtisDissim. A valid dissimilarity function in this context has four arguments: The first two are the vectors that will be compared, the third is the length of the vectors (they should be equally long), and the final argument is the number of NA values in the first of the two vectors. It is assumed that the second vector (which corresponds to the codebook vectors) never contains NA values. Note that in this example we do not allow NAs at all: Any input NA value will immediately lead to an NA value for the distance. The last two lines define the function createBrayCurtisDistPtr that creates a pointer to the distance function. The name of this pointer-generating function is to be passed as argument to the SOM training and mapping functions. The C++ code can be compiled using the Rcpp package:
R>
R> library("Rcpp") R> sourceCpp(code = BCcode) Training the map now is easy. We simply provide the names of the appropriate distance functions corresponding to the data matrices: R> set.seed(101) R> varesom <-supersom(list(species = specmat.tr, soil = chemmat.tr), + somgrid(4, 3, "hexagonal"), dist.fcts = c("BrayCurtis", "sumofsquares")) Note that saving such a map will save the name of the distance functions employed. Loading it again in a new session will work as expected provided that the corresponding functions are available in the workspace, which can require recompiling the corresponding C++ code.
The trained map now can be used for making predictions as well: If a new object is mapped to a particular unit (using the same distance functions as when training the map), then it can be assumed that it is very close to the other objects mapping to that unit. In this way, predictions can be made, e.g., for data layers that are absent. Without the newdata argument, the predict method for 'kohonen' objects returns for each record the averages of the training objects mapping to the same winning unit. The predict function allows one to provide the unit.predictions values explicitly: An alternative would be to use codebook vectors rather than averages of objects. In most cases, this would lead to very similar predictions.
R> trainingPred <-predict(varesom) R> names(trainingPred)
[1] "predictions" "unit.classif" "unit.predictions" "whatmap" The result is a list, where the unit.predictions element contains the average values for individual map units, the unit.classif element contains the winning units for data records, and predictions is the combination of the two. Both unit.predictions and predictions are lists with, in this case, two elements: soil and species. We can visualize the expected values for soil parameters using a color scale, as is shown in Figure 5. The code to generate the first panel is shown here: R> plot(varesom, type = "property", main = "Nitrogen ( Predictions for test data can be made using the newdata argument. The new data should contain at least some data layers that are also present in the training data (the agreement is checked comparing the names and dimensions of the data layers; if no names are given, it is assumed that the data layers are presented in the same order). Layers may be selected or weighted by using the whatmap and user.weights arguments, providing a simple way to test different scenarios. If these arguments are not provided, the values used in training the map are taken, usually also the most meaningful option. As an example, predictions for the test set based on the mapping according to the soil data only are obtained as follows: R> soilBasedPred <-predict(varesom, newdata = list(soil = chemmat.tst)) R> lapply ( 550 -0.340 -0.6510 -0.942 21 -0.809 -0.192 -0.3604 -0.107 Again we see the effect of a unit to which no training data are mapped, leading to NA values in the predictions. In some cases, it could be useful to impute these by interpolation from neighboring units. Classification of powder patterns. In Wehrens, Melssen, Buydens, and De Gelder (2005) and Willighagen, Wehrens, Melssen, De Gelder, and Buydens (2007), a SOM package using a specialized distance function for comparing X-ray powder diffractograms was presented, called wccsom. These powder patterns provide information on the crystal cell structure (De Gelder, Wehrens, and Hageman 2001) which is important in 3D structure elucidation. Structures represented by similar unit cell parameters give rise to very similar patterns; however, patterns may be stretched or compressed, based on the unit cell size. In many cases, one is not interested in the unit cell size, and would like to group patterns on the basis of the peaks in the powder pattern, irrespective of the stretching of compression that has taken place. To do this, a distance (WCCd) based on the weighted cross-correlation (WCC) was used in package wccsom, given by Here, f and g are vectors of observations (in this case along measurement angles, but in other applications this could be a time axis, for example). W is a banded matrix with ones on the diagonal and values progressively smaller further away from the diagonal. After a certain number of rows (or columns), only zeros are present; this number, the width of the band, is indicated with a parameter θ. If θ = 0 (and W becomes a diagonal matrix) the second term on the right hand side in the equation reduces to the Pearson correlation coefficient. The WCC has also been used in other applications, such as aligning chromatographic profiles (Wehrens, Carvalho, and Fraser 2015b) using the ptw package (Bloemberg et al. 2010;Wehrens, Bloemberg, and Eilers 2015a).
The purpose of this example is to show how to emulate the wccsom package with kohonenthe wccsom package itself will soon be phased out. More information on the background and the interpretation of the results can be found in the original wccsom publications (Wehrens et al. 2005;Willighagen et al. 2007).
The code for the WCCd dissimilarity is saved in a file called wcc.cpp (in the inst/Distances sub-directory of the package), structured in much the same way as previously the Bray-Curtis distance (which is available in the same directory). Parameter θ is hard-coded in this distance function (here it is set to a value of 20); if one wants to try different values of θ it is easy to define several distance functions. The data consist of 131 structures, a subset of a set of 205 used earlier in Wehrens et al. (2005) and Willighagen et al. (2007).
R> data("degelder", package = "kohonen") R> mydata <-list(patterns = degelder$patterns, + CellVol = log(degelder$properties[, "cell.vol"])) Figure 6 shows the powder patterns of four of the structures from two different space groups. Studying the variability in such a data set may show interesting groupings and may help in the structure elucidation of unknown compounds (Wehrens et al. 2005).
When mapping the patterns to a SOM, the X-ray powder patterns are used as the first layer, and the cell volume as the second layer. This will bring crystal structures together that have similar diffraction patterns as well as similar cell volumes. Since the cell volume has a very large range, logarithms are used. The distance function for the cell volume is the standard sum-of-squares distance, and the WCCd distance is defined in wcc.cpp: R> sourceCpp(file.path(path.package("kohonen"), "Distances", "wcc.cpp")) R> set.seed (7) R> powsom <-supersom(data = mydata, grid = somgrid(6, 4, "hexagonal"), + dist.fcts = c("WCCd", "sumofsquares"), keep.data = TRUE) The codebook vectors of the trained map are shown in Figure 7. The crystal structures with the largest cell volumes are located in the left part of the map. We could use such a map to estimate the cell volume for new diffraction patterns, simply by projecting the powder patterns into the map on the basis of the WCCd dissimilarity. Then, the cell volume associated with the winning unit will be used as the prediction: R> cellPreds <-predict(powsom, newdata = mydata, whatmap = "patterns") R> names(cellPreds) [1] "predictions" "unit.classif" "unit.predictions" "whatmap" R> cellPreds$predictions$CellVol[1:5, ] asageg asuyes axerie axerok azuyoj 8.091085 6.852079 8.093932 7.121513 7.290206 Again, the predict function makes it possible to combine data in a number of different ways. Here we present the complete data including all layers, and use the whatmap argument to determine which layer is to be used for mapping the objects to the map. In many cases this is easier than subsetting the data or creating specific new data objects, and allows for an easy investigation of different scenarios and the relation between the individual data layers.
Conclusions and outlook
In this Big Data era there is more and more need for methods that group large numbers of records, and fuse different data layers associated with these records. SOMs, and in particular the supersom variant implemented in the kohonen package, are very useful tools in this respect. They can be used to assess groupings in the data, but also to see structure within groups. The package enables users to investigate their data in a quick and easy way, and allows for what-if scenarios by switching data layers in or out, or by changing weights for individual layers. This paper concentrates on several improvements of the package. In particular the possibility of including data-specific distance or dissimilarity functions is an important feature that should increase the applicability of SOM methodology in a number of fields. It should be noted that the update of the codebook vectors during training still is done through (weighted) averaging; conceivably, for some types of data and distance functions this is not the optimal route. In the same way as user-defined distance functions, user-defined update functions are a real possibility. Significant performance improvements have been obtained, also by the inclusion of the batch algorithm and, in particular, its parallel version.
As it is now, the package is a reasonably rounded and complete set of functions. One obvious extension is to make the plotting functions more interactive, so that it would be more easy to switch between different visualizations. Another major improvement in the context of Big Data would be if objects could be sampled from external databases without explicitly having to import them in the form of one self-contained data set, or to allow streaming data to come in for permanent updates of the codebook vectors. The latter aspect would almost automatically also require aspects of the interactive graphics mentioned earlier. For these and other improvements, user contributions are warmly welcomed. We hope in the mean time that the package will continue to find use in many diverse fields of science. | 7,908.6 | 2018-11-12T00:00:00.000 | [
"Computer Science"
] |
Epistemic Feelings are Affective Experiences
This paper develops the claim that epistemic feelings are affective experiences. To establish some diagnostic criteria, characteristic features of affective experiences are outlined: valence and arousal. Then, in order to pave the way for showing that epistemic feelings have said features, an initial challenge coming from introspection is addressed. Next, the paper turns to empirical findings showing that we can observe physiological and behavioural proxies for valence and arousal in epistemic tasks that typically rely on epistemic feelings. Finally, it is argued that the affective properties do not only correlate with epistemic feelings but that we, in fact, capitalise on these affective properties to perform the epistemic tasks. In other words: the affective properties in question constitute epistemic feelings.
Introduction
Increasingly, epistemic feelings are shown to underpin our capacity for metacognition and our pursuit of epistemic and intellectual goods: they are responsible for our immediate sense of knowing, familiarity, understanding, coherence and rightness (e.g. Ackerman & Thompson, 2017;de Sousa, 2008;Michaelian & Arango-Muñoz, 2014;Proust, 2013). Various descriptions of epistemic feelings have been proposed such as "feelings concerning the subject's own mental capacities and mental processes" (Michaelian & Arango-Muñoz, 2014, p. 97) or "feelings that enter into the epistemic processes of inquiry, knowledge and metacognition" (de Sousa, 2008, p. 189). 1 I will understand epistemic feelings as feelings that signal epistemic properties broadly construed. 2 Now, how do epistemic feelings feature into our ontology of mind, i.e. what kind of psychological state are they? Here I provide a case for Affectivism about epistemic feelings, the claim that epistemic feelings are affective experiences. 3 I am not the first to assimilate epistemic feelings with affective experiences. The grounds for this association have not been bulletproof, however. Some just assume that epistemic feelings are affective (Arango-Muñoz, 2014;Dokic, 2012;Dub, 2015). Others employ an "affective by association" strategy by grouping epistemic feelings together with more established affective experiences such as surprise (Carruthers, 2017a;de Sousa, 2008;Prinz, 2007Prinz, , 2011). Yet others rely on a handful of empirical findings and considerations that taken by themselves appear inconclusive (Proust, 2015). So while the idea behind Affectivism is not new, it lacks solid footing. Here, I aim to provide such a footing. For that I bring the accumulating but scattered evidence together and reinforce the case for Affectivism.
Having a strong case for Affectivism matters. The idea that epistemic feelings are affective experiences is not unanimously accepted. In fact, some assume it to be false (Clore, 1992;Clore & Huntsinger, 2007;Stepper & Strack, 1993) while others refer to epistemic feelings as introspective evidence for the existence of distinctive cognitive phenomenology (e.g. Dodd, 2014;Smithies, 2013; but see Arango-Muñoz, 2019). The idea of distinctive cognitive phenomenology is controversial. Needing to invoke distinctive cognitive phenomenology to shed light on the nature of epistemic feelings would make for a difficult point of departure. Affectivism, on the other hand, lets us start rather strong: it would allow us to apply the wealth of theoretical and empirical resources available for affective experiences to understand better epistemic feelings.
Although this issue might appear theoretical at first, it harbours practical implications for the ways we approach many psychopathologies. Conditions such as bipolar disorder, schizophrenia, obsessive-compulsive disorder or Capgras syndrome are marked by unusual patterns in what subjects consider right, known or familiar. It seems plausible that (alterations in) epistemic feelings have a role to play in properly conceptualising these states (e.g. Dub, 2015;McLaughlin, 2010). Against this background, understanding epistemic feelings as affective experiences might shed new light on the nature of such psychopathologies and allow us to make targeted adjustments to the ways we approach them.
Here is how I will build my case for Affectivism about epistemic feelings: In section 2 I will provide the reader with a better grasp of epistemic feelings. In section 3 I will establish some diagnostic criteria by outlining what is characteristic about affective experiences: valence and arousal. Based on that I will argue that epistemic feelings display these marks of affective experiences. For that, I will address a challenge coming from introspection in section 4: introspectively, it does not seem obvious that epistemic feelings are affective. I will try to undercut the force of this observation by appealing to the mild nature of epistemic feelings and by providing some phenomenal exhibits that are introspective evidence for the idea that epistemic feelings are affective. Appeals to introspection have their limits, however. For the remainder of the paper, I will thus rely on empirical findings to make a case for Affectivism that goes beyond introspection. In section 5, I will show that we can observe physiological and behavioural proxies for valence and arousal in epistemic tasks that typically rely on epistemic feelings. In section 6, I will show that this occurrence is not merely correlational but that we, in fact, capitalise on the affective properties to perform said epistemic tasks. In other words: the affective properties in question constitute the epistemic feelings. In this context it will also come to the fore that the valence in question is conscious. Finally, I will conclude my case for Affectivism in section 7.
Grasping Epistemic Feelings
A good way to get a grasp of epistemic feelings is to consider some typical situations in which one would experience these familiar phenomena. Remember for instance the last time you encountered a person seemingly for the first time but had the impression that you had seen her before. Such FEELINGS OF FAMILIARITY (FOF) (Whittlesea & Williams, 1998) happen to everyone from time to time and can be directed at all kinds of things (e.g. people, songs, places, odours). Consequently, we take FOFs to mean that we have encountered a certain content before. A closely related feeling is the puzzling DÉJÀ-VU EXPERIENCE (Brown, 2003) where, against your better knowledge, it seems to you as if you have already been in the situation you find yourself in now.
For another epistemic feeling, think back to your time in school. In situations when a teacher was probing the knowledge of one of your classmates, asking her questions such as "When did the French Revolution start?" or "What is the capital of Australia?" it might have occurred to you that you knew the answer. Importantly, this feeling struck you before you had the chance to retrieve the relevant information from memory. Suppose now, that, encouraged by this FEELING OF KNOWING (FOK) (Koriat, 2000), you tried to go on and retrieve the relevant information. Although a FOK might be a relatively reliable predictor of retrieval success, it does not guarantee it. And so, in some cases you might run into what is commonly known as the TIP-OF-THE-TONGUE EXPERIENCE (TOT) (Schwartz & Metcalfe, 2014), the unpleasant feeling that the relevant information is (stuck) on the tip of your tongue. That is, you are in possession of the relevant information but are currently unable to produce it.
Here are some other examples of epistemic feelings:
Characterising Affective Experiences
In this section, I will briefly outline features that are characteristic to affective experiences. In the sections that follow, I will then use these features as diagnostic criteria and argue that epistemic feelings have these features and are thus affective experiences. First off, affective experiences are phenomenally conscious, there is something "it is like" to have an affective experience. 4 Feeling pain in one's wrist and feeling sad about it are phenomenally conscious states-but so are seeing blue and feeling one's heartbeat. However, only the former two are affective experiences. So what distinguishes non-affective from affective experiences? That is, apart from being conscious, what are the marks of affective experiences?
Arguably, the central feature of affective experiences is phenomenal valence, i.e. the felt positivity or negativity of certain experiences (e.g. Barrett, 2006;Charland, 2005). This basic positivity or negativity is often made sense of in hedonic terms as pleasantness or unpleasantness or in value terms as seeming value or disvalue (Carruthers, 2017b;Teroni, 2018). Affective experiences are valenced experiences. Neither the visual experience of something blue nor the bodily sensation of one's heartbeat are felt as positive or negative by themselves. However, exteroceptive experiences and non-affective bodily sensations naturally prompt or co-occur with affective experiences such as pain, sadness, enjoyment or fear which do feel positive or negative.
It is important to emphasise that when I talk of valence I mean valence as a phenomenal property of affective experiences. Such phenomenal valence needs to be distinguished from associated but ultimately non-phenomenal properties such as emotion-or object valence (Colombetti, 2005). Importantly, phenomenal valence also needs to be distinguished from its unconscious functional counterpart: unconscious valence. Unconscious valence has a functional profile reminiscent of phenomenal valence in motivating aversive (avoidance, cessation) or appetitive (approach, continuation) behaviours (e.g. Berridge & Kringelbach, 2015;Winkielman et al., 2005).
Another characteristic phenomenal aspect of affective experiences is felt arousal: During an affective experience the subject feels a more or less localised increase or decrease (i.e. change) in level of activation, energy or excitement. Such felt arousal co-varies with but is distinct from actual physiological arousal states (Colombetti & Harrison, 2018;Satpute et al., 2019).
Note that both properties of affective experiences, valence and arousal, are gradable: affective experiences can be more or less positive or negative and (de)activating. Now if epistemic feelings can be shown to have these features, then this can be taken as solid evidence for them being affective experiences.
I say that valence and arousal are characteristic to affective experiences. What does that mean? Is it to say that they are essential and/or unique to affective experiences? I do think that this is true of phenomenal valence: if something has valence, then it is an affective experience and not otherwise. Valence is arguably the best candidate for "the mark of the affective", picking out the family of affective experiences as a natural psychological kind (Fernandez Velasco & Loev, 2021). With arousal matters are more complicated. This is partly because the relationship between valence and arousal is a matter of debate (Kuppens et al., 2013, for a review). Some take valence and arousal to be two sides of the same coin, one standing for the "polarity" (i.e. positive or negative) and the other for the "volume" (i.e. intensity) of an affective experience (e.g. Barrett & Bliss-Moreau, 2009;Russell, 2003). Others take valence and arousal to be closely associated but dissociable dimensions (e.g. Anderson et al., 2003;Kuhbandner & Zehetleitner, 2011). The lesson that we can draw either way, I think, is this: even if, in contrast to valence, arousal might not be essential or unique to affective experiences, it is often considered in the same breath with valence when it comes to characterising affective experience. So even though I will focus on valence as the central indicator of affective experiences, occasional mention of arousal in epistemic feelings will support the present agenda.
The Challenge from Introspection
Why think that epistemic feelings are affective experiences? As proponents of cognitive phenomenology are right to point out: when one introspects, it does not seem obvious that they are. 5 In comparison to affective experiences such as migraines, fears or orgasms, epistemic feelings are not obviously experienced as positive, negative or arousing. This datum threatens to undermine the case that epistemic feelings are affective experiences at the outset and thus needs to be addressed first.
The force of this observation is weakened by acknowledging that, usually, epistemic feelings have only a subtle positivity or negativity and degree of arousal. In other words, epistemic feelings typically come in the form of mild affective experiences. This is not unlike, say, affective aesthetic experiences.
There is a lesson here. Part of the problem for acknowledging mild affective experiences lies in the approach traditionally taken towards affective experiences. When we think of affective experiences, the focus tends to lie on a few paradigm cases of affective experiences such as pain and fear. But in what sense are pains and fears paradigms of affective experiences? Without doubt, they exhibit the features characteristic of affective experiences-valence and arousal-to an extraordinarily high degree. But in being "very loud" as affective experiences, they are actually quite special, rare occurrences. A much larger part of our affective life is plausibly constituted by the little, subtle movements of our affective sensibilities. These affective experiences are not only all too often neglected in the face of their few "violent" conspecifics but also easy to neglect because of their calm nature. Now, we might be able to triangulate this mild part of our affective life that is often lost to introspection by considering this: Phenomenally obvious paradigmatic affective experiences are relatively rare occurrences in comparison to, say, perceptual experiences and thoughts which are with us literally all the time. However, we know something about affective experiences that appears somewhat at odds with this apparent scarcity. Importantly, we can see the feature in question instantiated in paradigmatic affective cases: Affective experiences are typically caused by perceptual experiences and thoughts and they interact with these states in significant ways. 6 Now, we have perceptual experiences and thoughts all the time. If these are involved with affective experiences, does it mean that they get only involved with them under exceptional circumstances? Does it mean that outside of these exceptional circumstances we go about our business as some kind of "Kantian Angels" driven purely by thought and perceptual experiences-only to be sometimes thrown off our enlightened path by affective seizures?
A more natural construal is that our ever-present perceptual experiences and thoughts lead to affective experiences that are just as ever-present. Most of them, however, are not present as phenomenal ruptures but as gentle guides of thought and action. The reason why we tend to think about affective experiences in the former "violent" way might be because we tend to study the tip of the affective iceberg that happens to be more phenomenally salient.
From an evolutionary standpoint it appears plausible that we have affective experiences that are concerned with epistemic properties. Epistemic properties are of relatively high survival value to our species, a species that strongly relies on social coordination and the exchange of information. Furthermore, the importance of epistemic propertiesin contrast to e.g. specific colours-is relatively invariant across contexts. It seems thus plausible that we have evolved a suite of affective states that swiftly detect these properties in our external and internal milieus (Sperber et al., 2010).
This perspective also brings to the fore that the function of affective experiences is not to be violent but to make things salient and prepare us to adaptively respond to them (Brady, 2009;Kozuch, 2020). Consequently, they typically direct our attention towards something else than themselves, towards something that matters. It is thus not surprising that we are only able to get a good look at them in exceptional circumstances-such as when they are violent or when there is, consciously, not much else to look at. Now, add to this our documented unreliability to introspect the nature of our experiences, especially affective experiences (Haybron, 2008;Schwitzgebel, 2008), and you get a sense for why becoming aware of mild affect-while beneficial for theoretical and personal reasons-is not at all an easy task.
So if epistemic feelings are affective experiences and, furthermore, mild affective experiences, then it is rather unsurprising that their affective nature tends to elude us. That's why we need to go beyond introspection and look at empirical work, something I will do in the next sections.
For the remainder of this section let me note that so far, I have been fighting a defensive battle concerning the power of introspection to shed light on the affective nature of epistemic feelings. Yes, epistemic feelings are usually mild affective experiences-typically the positive or negative valence integral to them does not come "in a very large quantity (or a high intensity), explosively" (Bramble, 2013, p. 212). This is, however, not to say that epistemic feelings cannot be reasonably intense, giving us some introspective evidence for their affective nature. To demonstrate this, I ask you to read the following passage and try to understand what it is about: A newspaper is better than a magazine. A seashore is a better place than the street. At first it is better to run than to walk. You may have to try several times. It takes some skill but it is easy to learn. Even young children can enjoy it. Once successful, complications are minimal. Birds seldom get too close. Rain, however, soaks in very fast. Too many people doing the same thing can also cause problems. One needs lots of room. If here are no complications it can be very peaceful. A rock will serve as an anchor. If things break loose from it, however, you will not get a second chance. (Bransford & Johnson, 1972, p. 722) How do you feel? Probably confused, unable to understand-this FEELING OF NOT UNDERSTANDING is a negative epistemic feeling (e.g. Silvia, 2010). Now try to attend to what phenomenally happens when I give you the following hint: kite. You likely feel much better now; suddenly everything seems to fall into place. What you just experienced is a reasonably intense FEELING OF UNDERSTANDING (e.g. Dodd, 2014).
My favourite illustration of a FEELING OF WRONGNESS (FOW) is, alas, not well compatible with the present format. It consists in making you look at upward flowing water. 7 Looking at it, you supposedly experience a clearly unpleasant FOW about what you see. Presumably, many of us experience similar (but less intense and continuous) FOWs on seeing (or imagining) things such as a crooked picture or cars driving on the left/ right side of the street.
Consider now FEELINGS OF RIGHTNESS (FORs). Think about, for instance, the last time you were arranging furniture until it "looked" or felt right. The internet has recently spawned a genre of video clips that capitalises on the FORs of the audience. These clips show events and actions that typically involve the meticulous manipulation of physical objects such as peeling wood. In fact, "Oddly Satisfying" videos have become prominent enough to be featured in WIRED and The New York Times (Faramarzi, 2018;Matchar, 2019). Their appeal is admittedly better demonstrated than described. I recommend the same-named subreddit and YouTube channel. 8 In fact, descriptions of highly intense instances of FORs occurring during ecstatic seizures (Picard, 2013) or intoxication (James, 1882, pp. 206-208) allow for an instructive peak into the affective nature of epistemic feelings. The extremely magnified feelings in these reports are the result of exceptional mental conditions. It stands to reason, however, that they are just extraordinary representatives of feelings that, in much lower dosages, are ordinary and regular ingredients of our phenomenal life. What makes these testimonies so remarkable is that we encounter FORs with their phenomenal volume turned up very high and a positive valence that comes "in a very large quantity (or a high intensity), explosively".
These examples demonstrate that epistemic feelings can in fact be reasonably intense and clearly positive, negative and arousing.
In this section I addressed the worry that the affective nature of epistemic feelings is not introspectively obvious. In its course I strived to illustrate and explain that epistemic feelings are usually (but not always) only mildly valenced and arousing. These reflections serve to give at least initial plausibility to the idea that epistemic feelings are affective experiences. Luckily, however, there is harder evidence available. I now turn to empirical findings.
The Correlation of Affective Properties and Epistemic Feelings
In the following two sections I will make a case for epistemic feelings being affective experiences by reviewing empirical findings. In this section, I will establish the case for a covariation between affective measures and epistemic feelings. Then I will present studies that suggest that the relationship is not merely correlational but that the affect constitutes epistemic feelings.
As discussed in section 3, it is distinctive of affective experiences to possess a phenomenal valence. Thus, if it can be shown that epistemic feelings have phenomenal valence, then this can be taken as evidence that they are affective experiences.
As in general with phenomenal qualities, valence cannot be measured directly. One thus has to rely on indirect evidence by measuring observable variables assumed to be associated with valence. Luckily, several valence-associated variables have been identified in the form of psychophysiological and behavioural responses (Mauss & Robinson, 2009).
It is generally assumed that valence is bodily realised (e.g. Craig, 2009;Damasio & Carvalho, 2013). Now, epistemic feelings co-vary with bodily changes in the form of specific interoceptive alterations and facial muscle activity (Fiacconi et al., 2016(Fiacconi et al., , 2017Forster et al., 2016;Topolinski et al., 2009; for a review Winkielman et al., 2003). 9 Topolinski et al. (2009), for instance, presented subjects with word triads that either did or did not share a common remote associate (e.g. coherent triad SALT, DEEP, FOAM implying SEA vs. incoherent triad DREAM, BALL, BOOK). They found that relatively to presenting incoherent triads, presenting coherent triads activated the smiling muscle, zygomaticus major, and inhibited the frowning muscle, corrugator supercilii. Such patterns of facial muscle activity are regarded as symptomatic for positive affect (Larsen et al., 2003).
Epistemic feelings have also been shown to lead to increased liking, a behavioural measure of positive valence (e.g. Forster et al., 2013;Trippas et al., 2016, experiment 1;Topolinski & Strack, 2009b, experiment 1, 2009cWinkielman et al., 2003). Trippas and colleagues, for instance, presented subjects with simple arguments that were either logically valid or invalid. 10 They did not ask subjects to reason about the arguments but simply to rate how much they spontaneously liked them. They found that relatively to invalid arguments, valid arguments were liked more.
Another indicator of valence in epistemic feelings is the finding that they lead to affective priming effects (Topolinski & Strack, 2009c, experiment 2). In affective priming, subjects evaluate a target stimulus with an affective connotation, say, the word "poison" as positive or negative after being presented with an affectively-laden prime stimulus, say, the word "cake". If target and prime have the same/ opposite affective connotation then the evaluation of the former is facilitated/hampered. Such priming effects can e.g. be read out from a subject's response time in making target evaluations. Assuming that the previously mentioned coherent word triads trigger positive epistemic feelings, Topolinski and Strack used word triads as affective primes and negative and positive words as targets. They found that while incoherent word triads did not lead to changes in response time, coherent triads slowed subjects down when they had to subsequently evaluate a negative word. 11 Another established physiological proxy of affective experiences is the skin conductance response (SCR) which is associated with the second characteristic of affective states: felt arousal. Ordinarily, the occurrence of FOFs co-varies with a discriminatory SCR for familiar and unfamiliar stimuli (e.g. faces or words) (Ellis et al., 1999;Morris et al., 2008). Capgras patients display a similar SCR to familiar and unfamiliar faces indicating, among other things, the absence of a FOF on whose basis they could discriminate between familiar and unfamiliar individuals (Ellis et al., 1997). The patients recognise the familiar person (or sometimes pet or object) visually but the usual affective response ordinarily elicited by the sight of the individual in question (inter alia a FOF) is missing (Pacherie, 2010). 12 I think these findings show that epistemic feelings co-vary with affective properties such as valence and arousal. This, in turn, strengthens the case for the thesis that epistemic feelings are affective.
Affective Properties Constitute Epistemic Feelings
What we have seen so far is that affect arises during epistemic tasks. However, this does not establish that the affective properties play any genuine epistemic role. In fact, it might be mere correlation. The observed changes in affective markers might not be part of epistemic feelings but rather consequences of other things that happen during the epistemic task. Perhaps the subjects in the experiments are simply happy or frustrated as a result of detecting or failing to detect an epistemic property? Or they are excited or anxious about the task? I think these are legitimate considerations-it is plausible that there might be episodes of happiness and frustration as well as excitement and anxiety during the experiments. That is, there might be affective experiences that occur during the experimental tasks that are not epistemic feelings. However, I think that this is well compatible with the idea that the epistemic feelings on which the epistemic tasks themselves capitalise are affective as well. This is, (some of) the observed affective properties indeed constitute epistemic feelings. In this section I will make the case that the covariation between epistemic feelings and affective properties is not just a correlation but a constitution relationship.
Particularly instructive evidence comes from two kinds of misattribution studies: The first kind of studies observes false positives of epistemic properties based on incidentally induced affect. That is, inducing nondiagnostic affect leads subjects to incorrectly judge that an epistemic property is present. The first part of this section will be concerned with these studies. The second part of this section will be dedicated to the second kind of misattribution studies. These go the other way around: the researchers make the subject believe that the affect they experience during an epistemic task is not diagnostic for the presence of an epistemic property. This turns out to strip the subject of her ability to accurately detect the epistemic property, indicating that epistemic properties are detected based on affect, and, since the affect can be misattributed, that the affect in question is conscious.
The first kind of studies generates a misattribution of seemingly non-affective properties such as familiarity, coherence and grammaticality based on induced positive or negative affect. 13 In the familiarity studies, novel stimuli are rated as more familiar (or unfamiliar) as a result of the affect manipulation. This holds true for various affect manipulations: i) making participants contract the smiling muscle, zygomaticus major, or the frowning muscle, corrugator supercilii (Phaf & Rotteveel, 2005, experiment 2); ii) using faces that are either attractive (Monin, 2003) or display emotions (by e.g. smiling or frowning) (Baudouin et al., 2000;Garcia-Marques et al., 2004, experiment 1;Lander & Metcalfe, 2007); iii) using subliminal primes in the form of happy versus neutral faces (Duke et al., 2014;Garcia-Marques et al., 2004, experiment 2) or happy versus sad words (Phaf & Rotteveel, 2005, experiment 1). In the coherence and grammaticality studies (Topolinski & Strack, 2009a), affect is either induced via the contraction of the mentioned facial muscles or the subliminal presentation of happy and sad faces. As a consequence of the affect manipulation, items are more (less) often judged as coherent and grammatical.
Crucially, Duke and colleagues and Topolinski and Strack explicitly demonstrate that the effect of induced affect closely mirrors the effects of processing fluency (as well as actual familiarity, coherence and grammaticality) on familiarity, coherence and grammaticality judgments (Duke et al., 2014;Topolinski & Strack, 2009a). This needs a little unpacking. To understand the importance of this finding, we need to familiarise ourselves with the construct of processing (dis)fluency (Alter & Oppenheimer, 2009). Processing fluency is a process property that refers to the "ease", understood as relative speed, with which a given cognitive process is executed. 14 There are a couple of things that we know about processing fluency. For instance, it is a prominent proximal cause of epistemic feelings, leading to judgments of epistemic properties such as familiarity or coherence (e.g. Unkelbach & Greifeneder, 2013). Now, there is something else that we know about processing fluency: it has been found to trigger positive affect (Winkielman et al., 2003). We can now connect the dots between these two observations.
When the researchers induce fluency-independent affect, they find that it mirrors the effects of fluency on judgments of epistemic properties. This parallel effect suggests two things: First, the induced affect seems to be used for epistemic judgments. This indicates that the typical results of fluency in the form of epistemic feelings, on the one hand, and affect, on the other, are two sides of the same coin. Second, we observe characteristic effects on epistemic judgments without fluency being involved. This indicates that what matters for the epistemic judgments is not processing fluency per se but its seemingly multiply realisable product: positive affect. This implies that it does not matter whether it is processing fluency or something else that causes this positive affect. Rather it appears that given a specific context, say, a task relying on the detection of an epistemic property such as familiarity or coherence, epistemic feelings can be triggered by whatever triggers affect. This affect, in turn, is correctly or incorrectly taken to signal the presence of the epistemic property. Fluency emerges thus as only one of many possible antecedents of epistemic feelings.
Against this background, it appears likely that epistemic feelings in general (i.e. also those not caused by fluency) are constituted by transient, context-specific positive or negative affect. This point is reinforced by the second kind of misattribution studies, to which I now turn. While in the first kind of studies the subjects misattribute seemingly non-affective epistemic properties based on affect, in this kind of studies the misattribution goes the other way around: Informative affective reactions are discounted by being misattributed to an irrelevant source (Topolinski & Strack, 2009b, 2009c. In these studies, the experimenters ask subjects to make semantic coherence judgments by discriminating between word triads that either share a common remote associate (e.g. SALT, DEEP, FOAM implying SEA; coherent triad) or not (e.g. DREAM, BALL, BOOK; incoherent triad).
In the fluency reattribution condition, the subjects are told that the "easiness of reading and the fluency with which the meaning of words is recognized" (Topolinski & Strack, 2009b, p. 614) is due to a task-irrelevant source: background music. In the affect-reattribution condition, the subjects are told that the positive affect that might arise in the course of the task is due to the background music. The authors show that while misattributing fluency has no effect on performance, misattributing affect essentially strips subjects of the ability to detect the property of semantic coherence (above chance level).
Importantly, the aim of the researchers was to find out what is felt in the task: the processing fluency triggered by processing semantically coherent items or the positive affect that is triggered by the processing fluency. The authors conclude that their "finding strongly suggests that it is not the fluency that is used as internal cue in intuitive judgments of semantic coherence, but rather the fluencytriggered positive affect" (p. 615). This is a crucial finding in two respects.
First, this strengthens the initial case made on the basis of the findings by Duke and colleagues and Topolinski and Strack by suggesting that epistemic feelings consist in context-specific, transient positive or negative affect. Fluency is not a cue available in experience to use for judgment. What is available is the result of fluency: positive affect. The researchers additionally back this conclusion with the finding that coherent triads are liked more than incoherent triads but are not rated as more fluent in processing (Topolinski & Strack, 2009b, experiment 1).
Reinforcing and extending this point, Balas and colleagues find that altering the semantic coherence task to include word triads that themselves are neutral but have an affect-laden common remote associate has a characteristic impact on judgments of semantic coherence: 15 there is an increase in accuracy and speed for triads with positive associates relative to those with neutral and negative ones. On this basis, the authors argue that "fluency-based positive affect can be strengthened or weakened by affective responses induced through partial activation of an affectively valenced memory content (i.e., solutions to triads)." (Balas et al., 2012, p. 318) This, in turn, brings the point home (in line with Duke et al., 2014 andStrack, 2009a) that "fluency of processing is not the only source of affective response that can influence intuitive judgements" (Balas et al., 2012, p. 312).
Together these findings imply that seemingly nonaffective epistemic properties such as coherence are (sometimes) detected based on affective epistemic feelings. 16 This is shown by the fact that in specific contexts (e.g. cognitive tasks) positive or negative affect correctly or incorrectly signals the presence or absence of the task-relevant property.
Second and perhaps even more important: The valence in epistemic feelings needs to be conscious in order to make them affective experiences. However, I discussed in section 3 that behaviour can also be biased by unconscious valence. That is, the epistemic behaviours observed in the experiments might not be the result of conscious epistemic feelings but of some unconscious action-biasing valenced states that are functionally analogous to epistemic feelings, "epistemic nudges" (see footnote 4). That such epistemic nudges occur is, I think, plausible.
However, we cannot explain the present experimental findings simply by relying on them. On the contrary, the mentioned studies demonstrate that the affect integral to epistemic feelings is conscious. This is because the subjects can misattribute the conscious affective signals that they would usually use to make conscious judgments. This contrasts with e.g. their inability to misattribute and use the unconscious processing fluency directly. Subjects cannot misattribute something that is unconscious since there is nothing to (correctly or incorrectly) attribute in the first place. The present finding, thus, rules out something that might seem like a possible explanation when one considers unconscious valence. Instead, what we observe in the experiments appears to be the result of affective experiences-epistemic feelings.
Conclusion
Here, I have provided a case for the idea that epistemic feelings are affective experiences. I first outlined the characteristic features of affective experiences: phenomenal valence and felt arousal. Using these as diagnostic criteria I proceeded to make the case that epistemic feelings possess said features. To give this idea initial plausibility, I explained why the affective nature of epistemic feelings might not appear introspectively salient: epistemic feelings are usually only mildly valenced and arousing. I also provided some phenomenal examples where the affective nature of epistemic feelings is introspectively salient.
I then turned to empirical findings to show that epistemic feelings covary with affective markers. Specifically, epistemic feelings covary with interoceptive changes, variations in SCR and facial muscle activity, proxies for the affective properties of valence and arousal. Furthermore, positive epistemic feelings lead to increased liking and can serve as positive affective primes-behavioural proxies for the presence of valence.
I went on to make the case for the covariation between epistemic feelings and affective properties being not just a correlation but a constitution relationship. For that, I presented studies that observe false positives of epistemic properties based on incidentally induced affect. That is, inducing nondiagnostic affect leads subjects to incorrectly judge that an epistemic property is present. This speaks in favour of an affective constitution of epistemic feelings.
Secondly, I made the case that the constitutive affect in question is conscious. It thus not only causally biases epistemic behaviour but phenomenally constitutes epistemic feelings that provide conscious guidance for the subject's epistemic behaviour. To build the case for this idea, I recounted studies where the following happens: the experimenters make the subject believe that the affect they experience in an epistemic task is not diagnostic for the presence of an epistemic property. As a consequence, the subject loses her ability to accurately detect the epistemic property. This does not only indicate that epistemic properties are detected on the basis of affect but also that the affect in question is conscious. Based on the reviewed findings I conclude that epistemic feelings are affective experiences. Thus, Affectivism is true.
This conclusion is not without consequence. I mentioned at the outset that epistemic feelings are plausibly involved in psychopathologies such as bipolar disorder, schizophrenia, obsessive-compulsive disorder or Capgras syndrome. Specific aspects of these conditions can be cast in a new light by applying what we know about affective experiences to epistemic feelings. If e.g. the delusions characteristic to manic episodes are not put in place by faulty reasoning but by abnormal affective experiences, say aberrant feelings of rightness or wrongness, then quite different considerations apply when making an assessment. Arguably, we have significantly less intentional control over the ways we feel than over the ways we reason. Additionally, affective experiences are typically imbued with motivational force and are thus particularly hard to override (Brady, 2009;McLaughlin, 2010). This perspective has thus implications for the agency and responsibility we ascribe to somebody in a manic episode. Similar considerations apply to the ways we go about treatment. As e.g. demonstrated by exposure therapy, maladaptive affective experiences can be changed but they are sensitive to very different kinds of evidence than is reasoning.
All this shows is that identifying epistemic feelings as affective experiences is good news because it allows us to apply the wealth of theoretical and empirical resources that we have for the latter to understand the former. At the same time, we realise how the affective realm expands into domains traditionally considered the province of "cold" cognition. It turns out that affect is an integral part of our intellectual and epistemic lives.
Declaration of Conflicting Interests
The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the H2020 Marie Skłodowska-Curie Actions under grant number 675415 and the Agence Nationale de la Recherche under grant agreement ANR-10-IDEX-0001-02 and ANR-17-EURE-0017.
ORCID iD
Slawa Loev https://orcid.org/0000-0001-7205-4778 Notes 1 Epistemic feelings are also sometimes called cognitive, metacognitive or noetic feelings (e.g. Clore, 1992;Koriat, 2000;Dokic, 2012). 2 In a jargon familiar to emotion scholars: epistemic feelings are those phenomenal states that have epistemic properties as their formal objects (Kenny, 1963) or core relational themes (Lazarus, 1991). Alternatively, it suffices for the present purpose to zero in on epistemic feelings extensionally: epistemic feelings are simply those feelings that I describe and discuss in the remainder of this article. 3 Two clarificatory notes: First, calling epistemic feelings "feelings" is a conventional practice and does not presuppose that they are affective experiences. I will argue that epistemic feelings are affective experiences. Second, I want to remain neutral on whether epistemic feelings constitute a natural (psychological) kind. However, if Affectivism is true then epistemic feelings are part of a larger family of states that plausibly qualifies as a natural (psychological) kind: affective experiences. 4 That affective experiences are conscious is a conceptual truth (Clore, 1994;Lacewing, 2007). This is not to say that there can be no (analogous) unconscious affective states. It is only to say that there can be no unconscious affective experiences. The same goes for epistemic feelings. Whatever one's use of the term, "feelings" are usually understood as experiences and are thus necessarily conscious. Thus epistemic feelings are necessarily conscious (Koriat & Levy-Sadot, 2000). This is not to say, however, that there can be no analogous unconscious states, say, some kind of "epistemic nudges". 5 In fact, proponents of cognitive phenomenology go a step further by suggesting that the phenomenology of epistemic feelings is cognitive (rather than affective) in nature (e.g. Dorsch, 2016). 6 For instance, perceptual and cognitive states provide affective experiences with their specific intentional object. When you are afraid of a bear, it is your fear that represents the bear as fearsome, but it is your multisensory perceptual experience that represents the bear that your fear is about (Deonna & Teroni, 2012;Bain, 2013). In other words: affective experiences engage with perceptual and cognitive states in representational division of labour. 7 Here is a video of upward flowing water: https://youtu.be/NiOAfQZ wn0g. 8 For FOWs: there is an "Oddly Unsatisfying" analogue to Oddly Satisfying videos on the web. 9 The interoceptive changes in question are variations in cardiac cycle and heart muscle activity. Note that these changes can also be understood as relating to arousal rather than valence. On the other hand, the facial muscle activity is a sure sign for valence (see further below in the main text).
10 An example of a valid argument used is: [P1: All wines are mips; P2: No mips are tools; C: No wines are tools] An example of an invalid argument used is: [P1: All wines are mips; P2: No mips are drinks; C: Some wines are drinks]. 11 The authors provide a convincing explanation for why coherent triads did not facilitate positive evaluations: First, they note the possibility of a flooring effect in that no further acceleration of the evaluative judgment might have been possible. Second, they review findings showing that the relative contribution of facilitation in affective priming is generally smaller than that of inhibition and even tends to disappear in cases of weak affective primes such as the word triads used by the authors. Third, they point out that inhibition effects are typically observed when the time interval between the presentation of prime and target is short while facilitation effects are typically observed when they are relatively longer. They convincingly argue that the intervals in their experiment tended to be short (Topolinski & Strack, 2009c, pp. 1480-1481. 12 Additionally, there might be a pronounced alienating feeling of unfamiliarity (Bayne and Pacherie, 2005). It is also important to note that more recent work suggests that the relationship between dampened SCRs towards familiar individuals (indicating a lack of arousal), deficient FOFs and the Capgras delusion is more complex than previously assumed (see Coltheart and Davis, 2022, for a review). It might thus turn out that Capgras syndrome is not a clear-cut case of evidence for a link between arousal and FOFs. Nevertheless, FOFs remain important for understanding Capgras syndrome. 13 There are also analogous findings on the relationship between confidence and affect (e.g. Lufityanto et al., 2016;Sidi et al., 2017). I omit discussing them because of space constraints. 14 Naturally, given that there are many kinds of cognitive processes, there are many kinds of fluencies: perceptual fluency, retrieval fluency, encoding fluency, answer fluency, conceptual fluency, to name a few. 15 An example for a positive/negative coherent triad is: COMPETITION, FINISH, ROUND implying MEDAL; CANDLES, NOVEMBER, STONE implying GRAVE. 16 Of course, nothing precludes that the mentioned non-affective epistemic properties are also sometimes assessed via judgments that are based on something else than epistemic feelings. | 9,835 | 2022-05-30T00:00:00.000 | [
"Philosophy",
"Psychology"
] |
Amazon at MRP 2019: Parsing Meaning Representations with Lexical and Phrasal Anchoring
This paper describes the system submission of our team Amazon to the shared task on Cross Framework Meaning Representation Parsing (MRP) at the 2019 Conference for Computational Language Learning (CoNLL). Via extensive analysis of implicit alignments in AMR, we recategorize five meaning representations (MRs) into two classes: Lexical- Anchoring and Phrasal-Anchoring. Then we propose a unified graph-based parsing framework for the lexical-anchoring MRs, and a phrase-structure parsing for one of the phrasal- anchoring MRs, UCCA. Our system submission ranked 1st in the AMR subtask, and later improvements show promising results on other frameworks as well.
Introduction
The design and implementation of broad-coverage and linguistically motivated meaning representation frameworks for natural language is attracting growing attention in recent years. With the advent of deep neural network-based machine learning techniques, we have made significant progress to automatically parse sentences intro structured meaning representation (Oepen et al., , 2015May, 2016;. Moreover, the differences between various representation frameworks has a significant impact on the design and performance of the parsing systems. Due to the abstract nature of semantics, there is a diverse set of meaning representation frameworks in the literature (Abend and Rappoport, 2017). In some application scenario, tasks-specific formal representations such as database queries and arithmetic formula have also been proposed. However, primarily the study in computational semantics focuses on frameworks that are theoretically grounded on formal semantic theories, and * * Work done when Jie Cao was an intern at AWS AI sometimes also with assumptions on underlying syntactic structures.
Anchoring is crucial in graph-based meaning representation parsing. Training a statistical parser typically starts with a conjectured alignment between tokens/spans and the semantic graph nodes to help to factorize the supervision of graph structure into nodes and edges. In our paper, with evidence from previous research on AMR alignments (Pourdamghani et al., 2014;Flanigan et al., 2014;Wang and Xue, 2017;Chen and Palmer, 2017;Szubert et al., 2018;Lyu and Titov, 2018), we propose a uniform handling of three meaning representations from Flavor-0 (DM, PSD) and Flavor-2 (AMR) into a new group referred to as the lexical-anchoring MRs. It supports both explicit and implicit anchoring of semantic concepts to tokens. The other two meaning representations from Flavor-1 (EDS, UCCA) is referred to the group of phrasal-anchoring MRs where the semantic concepts are anchored to phrases as well.
To support the simplified taxonomy, we named our parser as LAPA (Lexical-Anchoring and Phrasal-Anchoring) 1 . We proposed a graph-based parsing framework with a latent-alignment mechanism to support both explicit and implicit lexicon anchoring. According to official evaluation results, our submission for this group ranked 1st in the AMR subtask, 6th on PSD, and 7th on DM respectively, among 16 participating teams. For phrasal-anchoring, we proposed a CKY-based constituent tree parsing algorithm to resolve the anchor in UCCA, and our post-evaluation submission ranked 5th on UCCA subtask.
Anchoring in Meaning Representation
The 2019 Conference on Computational Language Learning (CoNLL) hosted a shared task on Cross-Framework Meaning Representation Parsing (MRP 2019, which encourage participants in building a parser for five different meaning representations in three distinct flavors. Flavor-0 includes the DELPH-IN MRS Bi-lexical Dependencies (DM, Ivanova et al., 2012) and Prague Semantic Dependencies (PSD, Hajic et al., 2012;. Both frameworks under this representation have a syntactic backbone that is (either natively or byproxy) based on bi-lexical dependency structures. As a result, the semantic concepts in these meaning representations can be anchored to the individual lexical units of the sentence. Flavor-1 includes Elementary Dependency Structures (EDS, Oepen and Lønning, 2006) and Universal Conceptual Cognitive Annotation framework (UCCA, Abend and Rappoport, 2013), which shows an explicit, many-to-many anchoring of semantic concepts onto sub-strings of the underlying sentence. Finally, Flavor-2 includes Abstract Meaning Representation (AMR, Banarescu et al., 2013), which is designed to abstract the meaning representation away from its surface token. But it leaves open the question of how these are derived. Previous studies have shown that the nodes in AMR graphs are predominantly aligned with the surface lexical units, although explicit anchoring is absent from the AMR representation. In this section, we review the related work supporting the claim of the implicit anchoring in AMR is actually lexical-anchoring, which can be merged into Flavor-0 when we consider the parsing methods on it.
Implicit Anchoring in AMR
AMR tries to abstract the meaning representation away from the surface token. The absense of explicit anchoring can present difficulties for parsing. In this section, by extensive analysis on previous work AMR alignments, we show that AMR nodes can be implicitly aligned to the leixical tokens in a sentence.
AMR-to-String Alignments A straightforward solution to find the missing anchoring in an AMR Graph is to align it with a sentence; We denote it as AMR-to-String alignment.
ISI alignments (Pourdamghani et al., 2014) first linearizes the AMR graph into a sequence, and then use IBM word alignment model (Brown et al., 1993) to align the lin-earized sequence of concepts and relations with tokens in the sentence. According to the AMR annotation guidelines and error analysis of ISI aligner, some of the nodes or relations are evoked by subwords, e.g., the whole graph fragment (p/possible-01 :polarity -) is evoked by word "impossible", where the subword "im-" actually evoked the relation polarity and concept "-"; On the other side, sometimes concepts are evoked by multiple words, e.g., named entities, (c/city :name (n/name :op1 "New":op2 "York")), which also happens in explict anchoring of DM and PSD. Hence, aligning and parsing with recategorized graph fragments are a natural solution in aligners and parsers. JAMR aligner (Flanigan et al., 2014) uses a set of rules to greedily align single tokens, special entities and a set of multiple word expression to AMR graph fragments, which is widely used in previous AMR parsers (e.g. Flanigan et al., 2014;Wang et al., 2015;Artzi et al., 2015;Pust et al., 2015;Peng et al., 2015;Konstas et al., 2017;Wang and Xue, 2017).
Other AMR-to-String Alignments exists, such as the extended HMM-based aligner. To consider more structure info in the linearized AMR concepts, Wang and Xue (2017) proposed a Hidden Markov Model (HMM)-based alignment method with a novel graph distance. All of them report over 90% F-score on their own hand-aligned datasets, which shows that AMR-to-String alignments are almost token-level anchoring.
AMR-to-Dependency Alignments Chen and Palmer (2017) first tries to align an AMR graph with a syntactic dependency tree. Szubert et al. (2018) conducted further analysis on dependency tree and AMR interface. It showed 97% of AMR edges can be evoked by words or the syntactic dependency edges between words. Those nodes in the dependency graph are anchored to each lexical token in the original sentence. Hence, this observation indirectly shows that AMR nodes can be aligned to the lexical tokens in the sentence.
Both AMR-to-String and AMR-to-dependency alignments shows that AMR nodes, including recategorized AMR graph fragements, do have implicit lexical anchoring. Based on this, Lyu and Titov (2018) propose to treat token-node alignments as discrete and exclusive alignment matrix and learn the latent alignment jointly with parsing. Recently, attention-based seq2graph model also achieved the state-of-the-art accuracy on AMR parsing . However, whether the attention weights can be explained as AMR alignments needs more investigation in future.
Taxonomy of Anchroing
Given the above analysis on implicit alignments in AMR, in this section, we further discuss the taxonomy of anchoring of the five meaning representations in this shared task.
Lexical-Anchoring According to the bi-lexical dependency structures of DM and PSD, and implicit lexical token anchoring on AMR, the nodes/categorized graph fragments of DM, PSD, and AMR are anchored to surface lexical units in an explicit or implict way. Especially, those lexical units do not overlap with each other, and most of them are just single tokens, multiple word expression, or named entities. In other words, when parsing a sentence into DM, PSD, AMR graphs, tokens in the original sentence can be merged by looking up a lexicon dict when preprocessing and then may be considered as a single token for aligning or parsing.
Phrasal-Anchoring However, different from the lexical anchoring without overlapping, nodes in EDS and UCCA may align to larger overlapped word spans which involves syntactic or semantic pharsal structure. Nodes in UCCA do not have node labels or node properties, but all the nodes are anchored to the spans of the underlying sentence. Furthermore, the nodes in UCCA are linked into a hierarchical structure, with edges going between parent and child nodes. With certain exceptions (e.g. remote edges), the majority of the UCCA graphs are tree-like structures. According to the position as well as the anchoring style, nodes in UCCA can be classified into the following two types: 1. Terminal nodes are the leaf semantic concepts anchored to individual lexical units in the sentence 2. Non-terminal nodes are usually anchored to a span with more than one lexical units, thus usually overlapped with the anchoring of terminal nodes.
The similar classification of anchoring nodes also applies to the nodes in EDS, although they do not regularly form a recursive tree like UCCA. As the running example in Figure 1, most of the nodes belongs to terminal nodes, which can be explicitly anchored to a single token in the original sentence. However, those bold non-teriminal nodes are an-chored to a large span of words. For example, the node "undef q" with span <53:100> is aligned to the whole substring starting from "other crops" to the end; The abstract node with label imp conj are corresponding to the whole coordinate structure between soybeans and rice In summary, by treating AMR as an implicitly lexically anchored MR, we propose a simplified taxonomy for parsing the five meaning representation in this shared task.
Model
For the two groups of meaning representations defined in Section 2, in this section, we propose two parsing framework: a graph-based parsing framework with latent alignment for lexically anchored MRs, and a minimal span-based CKY parser for one of the phrasally anchored MRs, UCCA. 2
Graph-based Parsing Framework with Latent Alignment
Before formulating the graph-based model into a probabilistic model as Equation 1, we denote some notations: C, R are sets of concepts (nodes) and relations (edges) in the graph, and w is a sequence of tokens. a ∈ Z m as the alignment matrix, each a i is the index of aligned token where ith node aligned to. When modeling the negative log likelihood loss (NLL), with independence assumption between each node and edge, we decompose it into node-and edge-identification pipelines.
2 After the CKY parser gets the related phrasal spans, graph-based parser can also be used to predict the relations between nodes.
In DM, PSD, and AMR, every token will only be aligned once. Hence, we train a joint model to maximize the above probability for both node identification P (c i | h a i ) and edge identification P (r ij | h a i ,c i ,ha j ,c j ), and we need to marginalize out the discrete alignment variable a.
Alignment Model
The above model can support both explicit alignments for DM, PSD, and implicit alignments for AMR.
Explicit Alignments For DM, PSD, with explicit alignments a * , we can use P (a * ) = 1.0 and other alignments P (a|a = a * ) = 0.0 Implicit Alignments For AMR, without gold alignments, one requires to compute all the valid alignments and then condition the node-and edgeidentification methods on the alignments.
However, it is computationally intractable to enumerate all alignments. We estimate posterior alignments model Q as Equation 3, please refer to Lyu and Titov (2018) for more details.
• Applying variational inference to reduce it into Evidence Lower Bound (ELBO, Kingma and Welling, 2013) • The denominator Z Ψ in Q can be estimated by Perturb-and-Max(MAP) (Papandreou and Yuille, 2011) score each alignment link between node i and the corresponding words, g i is node encoding, and h a i is encoding for the aligned token.
Node Identification
Node Identification predicts a concept c given a word. A concept can be either NULL (when there is no semantic node anchoring to that word, e.g., the word is dropped), or a node label (e.g., lemma, sense, POS, name value in AMR, frame value in PSD), or other node properties. One challenge in node identification is the data sparsity issue. Many of the labels are from open sets derived from the input token, e.g., its lemma. Moreover, some labels are constrained by a deterministic label set given the word. Hence, we designed a copy mechanism (Luong et al., 2014) in our neural network architecture to decide whether to copying deterministic label given a word or estimate a classification probability from a fixed label set.
Edge Identification
By assuming the independence of each edge, we model the edges probabilites independently. Given two nodes and their underlying tokens, we predict the edge label as the semantic relation between the two concepts with a bi-affine classifier (Dozat and Manning, 2016).
Inference
In our two-stage graph-based parsing, after nodes are identified, edge identification only output a probility distribution over all the relations between identified nodes. However, we need to an inference algorithm to search for the maximum spanning connected graph from all the relations. We use Flanigan et al. (MSCG, 2014) to greedily select the most valuable edges from the identified nodes and their relations connecting them. As shown in Figure 2, an input sentence goes through preprocessing, node identification, edge identification, root identification, and MCSG to generate a final connected graph as structured output.
Minimal Span-based CKY Parsing Framework
Let us now see our phrasal-anchoring parser for UCCA. We introduce the transformation we used to reduce UCCA parsing into a consituent parsing task, and finally introduce the detailed CKY model for the constituent parsing.
Graph-to-CT Transformation
We propose to transform a graph into a constituent tree structure for parsing, which is also used in recent work (Jiang et al., 2019). Figure 3 shows an example of transforming a UCCA graph into a constituent tree. The primary transformation assigns the original label of an edge to its child node. Then to make it compatible with parsers for standard PennTree Bank format, we add some auxiliary nodes such as special non-terminal nodes, TOP, HEAD, and special terminal nodes TOKEN and MWE. We remove all the "remote" annotation in UCCA since the constituent tree structure does not support reentrance. A fully compatible transformation should support both graph-to-tree and tree-to-graph transformation. In our case, due to time constraints, we remove those remote edges and reentrance edges during training. Besides that, we also noticed that for multi-word expressions, the children of a parent node might not be in a continuous span (i.e., discontinuous constituent), which is also not supported by our constituent tree parser. Hence, when training the tree parser, by reattaching the dis-continuous tokens to its nearest continuous parent nodes, we force every sub span are continuous in the transformed trees. We leave the postprocessing to recover those discontinuous as future work.
For inference, given an input sentence, we first use the trained constituent tree parsing model to parse it into a tree, and then we transform a tree back into a directed graph by assigning the edge label as its child's node label, and deleting those auxiliary labels, adding anchors to every remaining node.
CKY Parsing and Span Encoding
After transforming the UCCA graph into a constituent tree, we reduce the UCCA parsing into a constituent tree parsing problem. Similar to the previous work on UCCA constituent tree parsing (Jiang et al., 2019), we use a minimal spanbased CKY parser for constituent tree parsing. The intuition is to use dynamic programming to recursively split the span of a sentence recursively, as shown in Figure 3. The entire sentence can be splitted from top to bottom until each span is a single unsplittable tokens. For each node, we also need to assign a label. Two simplified assumptions are made when predicting the hole tree given a sentence. However, different with previous work, we use 8-layers with 8 heads transformer encoder, which shows better performance than LSTM in Kitaev and Klein (2018).
Tree Factorization In the graph-to-tree transformation, we move the edge label to its child node. By assuming the labels for each node are independent, we factorize the tree structure prediction as independent span-label prediction as Equation 4. However, this assumption does not hold for UCCA. Please see more error analysis in §4.4 CKY Parsing By assuming the label prediction is independent of the splitting point, we can further factorize the whole tree as the following dynamic programming in Equation 5.
Span Encoding For each span (i, j), we represent the span encoding vector v (i,j) = [ y j − y i ] ⊕ [ y j+1 − y i+1 ]. ⊕ denotes vector concatenation. Assuming a bidirectional sentence encoder, we use the forward and backward encodings y i and y i of i th word. Following the previous work, and we also use the loss augmented inference training. More details about the network architecture are in the Section 4.2
Summary of Implementation
We summarize our implementation for five meaning representations as Table 1. As we mentioned in the previous sections, we use latentalignment graph-based parsing for lexical anchoring MRs (DM, PSD, AMR), and use CKYbased constituent parsing phrasal anchoring in MRs (UCCA, EDS). This section gives information about various decision for our models.
Top The first row "Top" shows the numbers of root nodes in the graph. We can see that for PSD, 11.56% of graphs with more than 1 top nodes. In our system, we only predict one top node with a N (N is size of identified nodes) way classifier, and Table 1: Detailed classifiers in our model, round bracket means the number of ouput classes of our classify, * means copy mechanism is used in our classifier. At the end of shared task, EDS are not fully supported to get an official results, we leave it as our future work.
then fix this with a post-processing strategy. When our model predicts one node as the top node, and if we find additional coordination nodes with it, we add the coordination node also as the top node.
Node Except for UCCA, all other four MRs have labeled nodes, the row "Node Label" shows the templates of a node label. For DM and PSD, the node label is usually the lemma of its underlying token. But the lemma is neither the same as one in the given companion data nor the predicted by Stanford Lemma Annotators. One common challenge for predicting the node labels is the open label set problem. Usually, the lemma is one of the morphology derivations of the original word. But the derivation rule is not easy to create manually. In our experiment, we found that handcrafted rules for lemma prediction only works worse than classification with copy mechanism, except for DM. For AMR and EDS, there are other components in the node labels beyond the lemma. Especially, the node label for AMR also contains more than 143 fine-grained named entity types; for EDS, it uses the full SEM-I entry as its node label, which requires extra classifiers for predicting the corresponding sense. In addition to the node label, the properties of the label also need to be predicted. Among them, node properties of DM are from the SEMI sense and arguments handler, while for PSD, senses are constrained the senses in the predefined the vallex lexicon.
Edge Edge predication is another challenge in our task because of its large label set (from 45 to 94) as shown in row "Edge Label", the round bracket means the number of output classes of our classifiers. For Lexical anchoring MRs, edges are usually connected between two tokens, while phrasal anchoring needs extra effort to figure out the corresponding span with that node. For example, in UCCA parsing, To predict edge labels, we first predicted the node spans, and then node labels based that span, and finally we transform back the node label into edge label.
Connectivity Beside the local label classification for nodes and edges, there are other global structure constraints for all five MRs: All the nodes and edges should eventually form a connected graph. For lexical anchoring, we use MSCG algorithm to find the maximum connected graph greedily; For phrasal anchoring, we use dynamic programming to decoding the constituent tree then deterministically transforming back to a connected UCCA Graph 3
Dataset and Evaluation
For DM, PSD, EDS, we split the training set by taking WSJ section (00-19) as training, and section 20 as dev set. For other datasets, when developing and parameter tuning, we use splits with a ratio of 25:1:1. In our submitted model, we did not use multitask learning for training. Following the unified MRP metrics in the shared tasks, we train our model based on the development set and finally evaluate on the private test set. For more details of the metrics, please refer to the summarization of the MRP 2019 task ,
Model Setup
For lexical-anchoring model setup, our network mainly consists of node and edge prediction model. For AMR, DM, and PSD, they all use one layer Bi-directional LSTM for input sentence encoder, and two layers Bi-directional LSTM for head or dependent node encoder in the bi-affine classifier. For every sentence encoder, it takes a sequence of word embedding as input (We use 300 dimension Glove here), and then their output will pass a softmax layer to predicting output distribution. For the latent AMR model, to model the posterior alignment, we use another Bi-LSTM for node sequence encoding. For phrasal-anchoring model setup, we follow the original model set up in Kitaev and Klein (2018), and we use 8-layers 8headers transformer with position encoding to encode the input sentence.
For all sentence encoders, we also use the character-level CNN model as character-level embedding without any pre-trained deep contextualized embedding model. Equipping our model with Bert or multi-task learning is promising to get further improvement. We leave this as our future work.
Our models are trained with Adam (Kingma and Ba, 2014), using a batch size 64 for a graph-based model, and 250 for CKY-based model. Hyperparameters were tuned on the development set, based on labeled F1 between two graphs. We exploit early-stopping to avoid over-fitting.
Results
At the time of official evaluation, we submitted three lexical anchoring parser, and then we submitted another phrasal-anchoring model for UCCA parsing during post-evaluation stage, and we leave EDS parsing as future work. The following sections are the official results and error breakdowns for lexical-anchoring and phrasalanchoring respectively. Table 2 shows the official results for our lexical-anchoring models on AMR, DM, PSD. By using our latent alignment based AMR parser, our system ranked top 1 in the AMR subtask, and outperformed the top 5 models in large margin. Our parser on PSD ranked 6, but only 0.02% worse then the top 5 model. However, official results on DM and PSD shows that there is still around 2.5 points performance gap between our model and the top 1 model. Table 3 shows that our span-based CKY model for UCCA
Error Analysis on Lexical-Anchoring
As shown in Table 4, our AMR parser is good at predicting node properties and consistently perform better than other models in all subcomponent, except for top prediction. Node properties in AMR are usually named entities, negation, and some other quantity entities. In our system, we recategorize the graph fragements into a single node, which helps for both alignments and structured inference for those special graph fragments. We see that all our 3 models perform almost as good as the top 1 model of each subtask on node label prediction, but they perform worse on top and edge prediction. It indicates that our bi-affine relation classifier are main bottleneck to improve. Moreover, we found the performance gap between node labels and node anchors are almost consistent, it indicates that improving our model on predicting NULL nodes may further improve node label prediction as well. Moreover, we believe that multitask learning and pre-trained deep models such as BERT (Devlin et al., 2018) may also boost the performance of our paser in future.
Error Analysis on Phrasal-Anchoring
According to Table 7, our model with ELMo works slightly better than the top 1 model on anchors prediction. It means our model is good at predicting the nodes in UCCA and we belive that it is also helpful for prediction phrasal anchoring nodes in EDS. However, when predicting the edge and edge attributes, our model performs 7-8 points worse than the top 1 model. In UCCA, an edge label means the relation between a parent nodes and its children. In our UCCA transformation, we assign edge label as the node label of its child and then predict with only child span encoding. Thus it actually misses important information from the parent node. Hence, in future, more improvement can be done to use both child and parent span encoding for label prediction, or even using another span-based bi-affine classifier for edge prediction, or remote edge recovering.
Conclusion
In summary, by analyzing the AMR alignments, we show that implicit AMR anchoring is actually lexical-anchoring based. Thus we propose to regroup five meaning representations as two groups: lexical-anchoring and phrasal-anchoring. For lexical anchoring, we suggest to parse DM, PSD, and AMR in a unified latent-alignment based parsing framework. Our submission ranked top 1 in AMR sub-task, ranked 6th and 7th in PSD and DM tasks. For phrasal anchoring, by reducing UCCA graph into a constituent tree-like structure, and then use the span-based CKY parsing to parse their tree structure, our method would rank 5th in the original official evaluation results. | 6,001.8 | 2019-01-01T00:00:00.000 | [
"Computer Science",
"Linguistics"
] |
Dissecting a heterotic gene through GradedPool-Seq mapping informs a rice-improvement strategy
Hybrid rice breeding for exploiting hybrid vigor, heterosis, has greatly increased grain yield. However, the heterosis-related genes associated with rice grain production remain largely unknown, partly because comprehensive mapping of heterosis-related traits is still labor-intensive and time-consuming. Here, we present a quantitative trait locus (QTL) mapping method, GradedPool-Seq, for rapidly mapping QTLs by whole-genome sequencing of graded-pool samples from F2 progeny via bulked-segregant analysis. We implement this method and map-based cloning to dissect the heterotic QTL GW3p6 from the female line. We then generate the near isogenic line NIL-FH676::GW3p6 by introgressing the GW3p6 allele from the female line Guangzhan63-4S into the male inbred line Fuhui676. The NIL-FH676::GW3p6 exhibits grain yield highly increased compared to Fuhui676. This study demonstrates that it may be possible to achieve a high level of grain production in inbred rice lines without the need to construct hybrids.
populations by sequencing of bulked pools sampled across the distribution of trait phenotypes. This approach was applied to lines derived from F1 crosses between hybrid line parents and enabled the identification of regions that contribute to the observed heterosis between the parents for grain/yield traits. This approach enabled fine mapping of a previously identified QTL, GW3p6, to an interval of 5.9kb. They validated that the allele in GZ63-4S at candidate gene in this interval, OsMADS1, contributes to heterosis between GZ63-4S and FH676 supported by increased grain yield in NILs containing this allele. All of these results are significant and of broad interest to the community.
However, the authors have based their alignment and mapping on the Nipponbare build 4.0 from 2009. Yet, Kawahara et al (2013) released an improved build of Nipponbare, IRGSP 1.0 (Rice, 6:4 doi: 10.1186(Rice, 6:4 doi: 10. /1939; this build of the Nipponbare genome is now the preferred build. In order for their results to be more easily accessible, coordinates presented in the results should be remapped to the updated build. Additionally, several high-quality rice genome builds for indica type genomes are available that have qualities on par with that of the temperate japonica type Nipponbare: Since both parental lines in this study are indica types, some comparison at osMADS1 locus to the most relevant indica build(s) is warranted. Since GZ63-4S has Minghui 63 in its parentage (and MH63 has IR8 in its), the most appropriate genomes for comparison are MH63 and IR8. This comparison would extend the results beyond the description of its occurrence in the resequenced genomes from the authors in their prior studies.
The manuscript needs significant editing to improve the English. I suggest that a native English speaker undertake this task or that they avail of a service provider. The edits were too numerous for me to list them all. Some examples: Line 21 change to: … contribution to solving the food crisis. Line 22 change to: …heterosis for grain yield is mainly … Line 29 change to: …sequencing of graded pool-samples … Line 34 Use "that" NOT "which" Line 40 change to: … demonstrated that heterotic genes … Line 43 change to: … without the need to construct … Reviewer #3 (Remarks to the Author): Review: Dissecting a heterotic gene through GradedPool-1 Seq mapping informs a new 2 rice-improvement strategy, by Wang et al.
This manuscript describes the development and utilization of a new quantitative trait loci (QTL) mapping approach (GradedPool-Seq;GPS) using bulked progeny (segregant) next-generation sequencing of rice F2 population. Following phenotype of a population derived from F1 hybrid, which was showing superior phenotype for growth traits over the mid-parent phenotype (heterosis), the plants are grouped to low, mid and high values. Next, DNA from representative of each group are subjected to whole genome sequencing for identification of enriched alleles in the highest pool. Using GPS methodology authors managed to obtain mapping to a resolution of app. 400Kbp for grain weight QTL. This was further fine-mapped using larger F2 population derived from a RIL down to a resolution of a known single gene of rice, i.e. GW3p6 (OsMADS1), that confer a significant increase of app. 8% for grain weight and length. These partially dominant effects were also confirmed in nearly isogenic lines for this allele originating from maternal parent, and effects were also observed in genome edited mutated plants for this gene that showed malformed seeds. Functional analysis of the identified alternative spliced variants implicate the C-termini function, which is supported by previous studies on this gene. Furthermore, allele mining of the rice gene pool, or Pan Genome, indicate that this grainweight increasing allele is found only in small portion of the rice breeding material. These results led authors to suggest GPS as a novel method for dissecting heterosis to its elusive genetic components and utilize this directly on breeding plant material with less need to construct non-predictive hybrids.
Overall, the presentation of the data is very clear and straightforward. The authors combine both empirical data and simulations on the same dataset to highlight the power of their method. Now, there are several limitations that the authors fail to mention despite their knowledge in heterosis in general, and that of grain yield particularly. Grain yield is of course the golden grail of heterosis, and the more interesting trait that different models are attempting to resolve. The GPS method, at least the way presented, is compatible for single plant traits. This is true for F2 population composed of individuals that are both genotyped and phenotypes, however traits as grain yield requires groups of plants or plots to obtain phenotypic value, and so is the need to find QxE interactions. Perhaps the authors could try is to mention this limitation and test the compatibility of the GPS for F2:F3 families, for example, in which genotype is conducted in the F2 population and the grain yield phenotype in F3. Although this dilutes the allelic effect by half or more since quarter and half of selfed heterozygous plant are homozygous and heterozygous for the allele of interest. At least this is how it used to be done in advanced backcross method by Tanksley, for example, who tried to solve the use of introgression directly to breeding. Currently, the GPS is good as any other QTL mapping approach for continuous traits, other than yield that requires plots.
Second point with regard to grain yield heterosis that is overlooked, or at least I could not find any mentioning even in supplementary data, is that the GPS is not compatible with the overdominant model for heterosis, which does appear in the introductory part of the manuscript (row 64). In case the gene contributing to hybrid vigor is overdominant, i.e. heterozygous genetic value surplus both homozygous for two alleles, then how would GPS identify such locus? If it would not, then at least this should have been discussed.
The results section begins with describing the GPS methodology. It states the selection of 100-150 individuals from each bulk. It is indeed useful and relevant to have simulations to understand better the power of the GPS to identify QTL (supplementary Fig. 5) For the sake of clarity the number of plants in bulk be better presented as percentage of the F2 population and not a number of individuals. This is true for presenting the information in the text, as well as in the figures and supplementary table 1. One naive question in that regard is what is the proportion of plants collected for DNA extraction? If one needs to phenotype all, extract DNA (from individuals) for half or more, then what is the cost-effectiveness in the whole process? These consideration needs some more explanation. In addition, it would be useful to understand in these simulations the needed QTL effect in order for it to be identified.
In the last part of the results authors present pyramiding of the OsMADS1_GW3p6 with another QTL for a grain yield component, i.e. PN3q23. I found the presentation of the results somewhat confusing. First, it is obvious that there seems to be epistatic interactions or diminishing effects between the two QTL and that the carrier of both QTL does not show a significant effect of the single QTL. In general, without having a detailed table, rather than a bar plot and pie chart that confuses the reader it is impossible to judge the added value of this pyramiding. By eyeball of bars and large STE of the double introgression it seems that having one or two QTL does not seem to make a significant difference, but I may be wrong. Again, a detailed table will clarify this.
Minor comments: Abstract: Second sentence in abstract is a bit redundant (heterosis appears twice). So are the last two sentences in review, with redundant "demonstrated", and grammatical mistake (need and not needs).
Introduction: ¬ rice hybrid varieties are not necessarily heterozygous in any locus (row 50). ¬ > rows 60 -66 are too lengthy for a single sentence Results ¬ Row 135-to compute and not computer The authors refer the reader to a link that 1) written in Chinese, and 2) cannot be displayed. This does not allow to asses the GPS software as part of this review.
To conclude, this manuscript is divided between to two parts, i.e. the QTL mapping by GBS, and the proof for the functionality of the gene on a quantitative trait. Both are impressive is breadth, but none of them is fully novel, i.e. there are previous similar QTLseq approaches that take almost similar approaches, and the functional analysis of the GW3p6 was shown previously by map based cloning efforts. The only perhaps novelty is the finding of a less used allele in the maternal gene pool that implicate this for rice breeding, and the success in pyramiding two QTL to achieve 14% increase in single plant grain yield although the implications in the field still require additional proof. In addition, it would strengthen the manuscript to add some discussion on the limitations of the GPS (see abovesingle plant traits, dominant genes,etc.) rather than paint it all positive but this could be a matter of personal preference.
Responses to referees for the manuscript of NCOMMS-19-00043A:
Reviewer #1
1, Based on the widely different plant phenotypes and their frequency distribution, F2 populations could be classified into three types: Grade 1 (i.e., the highest bulk), Grade 2 (i.e., middle bulk), and Grade 3 (i.e., the lowest bulk). It is easy to understand that the SNP variations were not related to the heterotic phenotype, it would present 50% reference reads and 50% alternate reads in all three bulks, whereas the related SNP would have great distinction of the ratio of reference reads to alternate reads between Grade 1 and Grade 3.
In Fig.1b, the related SNP in Grade 1 was associated only with higher ratio of reference reads to alternate reads, it is also possible that the related SNP in Grade 1 was associated with lower ratio of reference reads to alternate reads. Thus, the authors should include this additional analysis when they mapped the heterosis-related genes associated with three or more graded groups based on the measured phenotypic values of contrasting phenotypes.
Yes, it is a very good comment. In the previous Figure 1b, we only presented one situation that the related SNP in Grade 1 was associated with higher ratio of reference reads to alternative reads, whereas we did not show the other situation that the related SNP may have lower ratio of reference reads to alternate reads. We have corrected the Figure 1 in the revision. The newly modified Figure 1 includes the analysis of two situations when we mapped the heterotic genes associated with multiple groups based on the measured phenotypic values of contrasting phenotypes. We also added the description in the text (Line113-115).
2, in the previous studies, the authors have reported that they developed the interval mapping method and mapped several heterozygous locus which played an important role for yield-related traits, including GW3p6. Using this new method GradedPool-Seq, is it possible to dissect the new heterosis-related QTL/genes associated with grain production?
Yes, it is possible to dissect new heterosis-related genes association with grain production using the GradedPool-Seq method. In the results of Figure 2b, the new heterosis-related QTLs are also shown. On chromosome 6, there is an unknown heterosis-related QTL with high effect value, which need further verification.
In our previous studies, Composite Interval Mapping (CIM) method is still powerful and has many advantages in QTL mapping. For example, it can improve the efficiency and the accuracy of mapping by controlling background genetic effects to a large extent. However, CIM is also time-consuming in rice hybrid breeding because each line in the large population needs to be genotyped. Therefore, we developed the new GPS method to rapidly map heterozygous loci.
Compared to the CIM method, the GPS method may have higher efficiency when extremely large sample size is used. Thus, it is convenient to dissect new heterosis-related genes association with grain production using the GradedPool-Seq method.
3, the GW3p6 allele is same as the previously reported OsMADS1lgy3 allele. This alternatively spliced protein OsMADS1lgy3 has been shown to be associated with the increased grain size and grain yield. In addition, the previous studies have demonstrated that the introduction of the OsMADS1lgy3 allele into indica hybrid rice resulted in increases in both grain length and grain weight, to increase grain yield by a mean of 7.1%. Thus, the part of functional analysis and yield improvement of OsMADS1GW3p6 can be removed.
We did notice that OsMADS1 lgy3 can increase grain yield in a restorer line 9311. The mode of inheritance of the OsMADS1 lgy3 is semi-dominant, indicating an important role of lgy3 allele in hybrid rice. In our study, we directly cloned the OsMADS1 GW3p6 from the male-sterile line Guangzhan63-4S (a commonly used parent in hybrid rice breeding) by GPS, and identified the OsMADS1 GW3p6 to be a grain weight-related heterosis gene. We also introduced the GW3p6 allele from male-sterile line into the restore line Fuhui676 to demonstrate a significant yield-improvement of NIL-FH::GW3p6 over the Fuhui676. This could be a complementary result to the previous reports. In addition, we applied transient expression assay of promoter activity to prove that the change of 1000-grain weight is not related to the promoter, and the results of gene editing in the C Domain of OsMADS1 proved that the alternatively spliced protein OsMADS1 GW3p6 was associated with the increased grain size and grain yield. Table 3 currently) showed that approximately 4% hybrid rice contained the OsMADS1 GW3p6 , because most accessions of hybrid rice in our collection belonged to hybrid rice of three-line system. Generally speaking, the proportion of OsMADS1 GW3p6 is low in the hybrid rice of three-line system, and modest in the hybrid rice of two-line system. We found that OsMADS1 GW3p6 may come from japonica rice --from the pan-genome data of OsMADS1 GW3p6 , we can find that OsMADS1 GW3p6 is an allele widely existing in tropical japonica rice, but most hybrid rice varieties have indica background resulting the relatively low proportion of OsMADS1 GW3p6 in hybrid rice. Therefore, by dissecting the function of OsMADS1 GW3p6 , we can make better use of the yield-increasing effect of OsMADS1 GW3p6 .
4, according to Supplementary
Considering that OsMADS1 GW3p6 showed a significant improvement to grain weight, it will have great potential in hybrid rice breeding, and will play an important role on contributing to the rice heterosis.
The GPS method improves the efficiency of identifying heterosis genes greatly. In more hybrid rice varieties, we can focus on more heterosis traits, and find more heterosis genes by GPS.
A whole set of pipeline is provided in the article, and three major sections is also shown in Supplementary Figure 1. After that, introducing heterosis genes to restore line or male-sterile line and selection of hybrid combinations purposefully will be beneficial to hybrid rice breeding.
5, previous studies have demonstrated that the alternatively spliced allele is a semi-dominant
allele with respect to grain length, grain weight and grain yield per plant. In this manuscript, the author showed that the near isogenic line (NIL-FH::GW3p6 ) had a large increase in yield compared with FH, but was still less production slightly to F1. How to explain these different type of observations in F1?
Although we have demonstrated that the NIL-FH::GW3p6 has a significant yield-improvement over the Fuhui676 or NIL-FH::GW3p6/Fuhui676, we have to mention that the high grain-production of the hybrid rice GLY-676 (F1) is resulted from genetic effects of multiple alleles. Detailed explanations are as following: Firstly, the grain yield of F 1 generation is controlled by multiple genes. Although the near isogenic line (NIL-FH::GW3p6) had a large increase in grain production compared with FH, it is still far from enough to rely on the introduction of only one gene, even if the gene production effect of the OsMADS1 GW3p6 is powerful. That's why we continue to find new heterosis genes from male-sterile line (for example, another heterosis related gene PN3q23 underlying panicle number).
When pyramiding two or more heterosis-related genes, the gap between the grain production of F 1 and near isogenic line will be smaller.
Secondly, numerous minor genes also may play a role in heterosis. It is hard to map and character the minor QTL genes, but the effect of a largr number of minor genes is one of the reasons why the grain yield of NIL-FH:GW3p6 is less than F 1 .
Thirdly, the over-dominance effects of certain heterozygous genes and epistatic effects among different genes may also contribute to grain yield of F 1 .
We added these discussions in the revision (Line375-376).
Reviewer #2
Thank you for your recognition of our work, we want to make a big step-forward on rapidly dissecting complex traits regarding to heterosis for rice breeding. Therefore, a good and accessible result will help breeders to do hybrid rice breeding more efficiently.
The manuscript needs significant editing to improve the English. I suggest that a native
English speaker undertake this task or that they avail of a service provider. The edits were too numerous for me to list them all.
Some examples:
Line 21 change to: … contribution to solving the food crisis.
Line 22 change to: …heterosis for grain yield is mainly …
Line 29 change to: …sequencing of graded pool-samples … Line 34 Use "that" NOT "which" Line 40 change to: … demonstrated that heterotic genes … Line 43 change to: … without the need to construct … We are very honored that you have wasted a lot of energy in providing us language guidance. We have revised the manuscript word for word, and some grammatical errors and inappropriate expressions are avoided as far as possible. At the same time, we also invite service providers to further polish, hoping to make the manuscript more accessible and understandable.
QTL mapping approach for continuous traits, other than yield that requires plots.
We appreciate reviewer's recognition of our work, and we agree with the kind reviewer that our new GPS approach is as good as any other QTL mapping approach currently. However, our methods have low power in finding QxE interactions and other limitations, which were added in the discussion sections of the revision (Line 347-350). Thanks!
Second point with regard to grain yield heterosis that is overlooked, or at least I could not find any mentioning even in supplementary data, is that the GPS is not compatible with the overdominant model for heterosis, which does appear in the introductory part of the manuscript (row 64). In case the gene contributing to hybrid vigor is overdominant, i.e. heterozygous genetic value surplus both homozygous for two alleles, then how would GPS identify such locus? If it would not, then at least this should have been discussed.
Yes! The GPS may not work very well with the overdominant loci. To identify QTLs through the software GPS, the SNPs related to the agronomic traits need have a great distinction of reference reads to alternative reads. However, for the overdominant loci, there may be a great distinction of heterozygous genotypes to homozygous genotypes, but less great distinctions of reference reads to alternative reads. We added the statement in the revision (Line350-356). In addition, it would be useful to understand in these simulations the needed QTL effect in order for it to be identified.
100-150 individuals from each bulk. It is indeed useful and relevant to have simulations
We agree. We should present the number of plants in bulk as percentage, but not the number of individuals. We added a new column of percentage in Supplementary Table 1 as suggested. In the text, we also added the description in the text (Lines 109-110 and Lines 613-614).
For BSA and whole-genome sequence of bulked DNA, we added the detailed description in methods section (lines 603-610 and lines 617-628). In F 2 populations, we usually phenotype all F 2 individuals for a certain trait, and the F 2 population sizes in this work are not very large (typically, ~500 individuals), it's easy to phenotype all. According to the phenotypic values, we divided F 2 individuals into several pools. The pool size and the number of pools are based on population size and phenotypic differences. After that, the genomic DNA were extracted from the mixed equal mass leaf tissue of F 2 individuals in each pool. The equal mass fresh leaf tissue (~0.05g) of each individual was mixed in a mortar, and then the genomic DNA of them was extracted for further sequencing. The cost of extracting DNA in equal mass fresh is economical.
For the cost-effectiveness aspect in the whole process of GPS, we think it's very economical than other fine-mapping methods. Applying GPS doesn't require to genotype all individuals, which is time-saving and labor-saving (especially, we will not need to perform sequencing library construction for each line). More details in the whole process were added in the text (lines 334-346).
For QTL effect, we agree the reviewer #3's comment. We added the description on QTL effects in Supplementary Note 1 (Lines 92-93).
4.In the last part of the results authors present pyramiding of the OsMADS1_GW3p6 with
another QTL for a grain yield component, i.e. PN3q23. I found the presentation of the results somewhat confusing. First, it is obvious that there seems to be epistatic interactions or diminishing effects between the two QTL and that the carrier of both QTL does not show a significant effect of the single QTL. In general, without having a detailed table, rather than a bar plot and pie chart that confuses the reader it is impossible to judge the added value of this pyramiding. By eyeball of bars and large STE of the double introgression it seems that having one or two QTL does not seem to make a significant difference, but I may be wrong.
Again, a detailed table will clarify this.
We have provided a detailed table to show the yield-increasing effect of the plants harboring the two heterosis related genes. The detailed table were presented as Table 2 in manuscript (see below). The number of the plants containing PN3q23 and GW3p6 is small, which caused eyeball of bars and large STE of the double introgression. We only have a small number seeds of GLY-676, and we chose nearly the same number of NIL plants, although the number of NIL plants is enough.
We have used more NIL plants to calculate the yield increasing effect, and more detailed data about yield per plant is available in source data. We initially thought the bar plot and pie chart were more intuitive, but judging the added value of genes' pyramiding is impossible. From the results of Table 2, the grain yield of plants carrying GW3p6 and PN3q23 is significantly higher than that of FH, as well as NIL-FH::GW3p6. In addition, we still provide the pie chart as Figure 5b. Benefiting from the results of Table 2, it's easy to understand the pie chart. The calculation method of heterotic contribution rate is described in the methods (Line726-733). The yield-increasing effect of the plants containing GW3p6 and PN3q23 proved the genes with incomplete dominance from maternal parent played a significant role in heterosis. The pie chart of heterosis contribution could show a small number heterosis genes explained the majority of heterosis effects.
In addition, in the process we pyramiding another gene PN3q23 underlying panicle number, we found the plants carrying PN3q23 had greater number of panicles than FH and NIL-FH::GW3p6, besides the yield-increasing effect. The detailed information was provided as Supplementary Table 2.
5.Minor comments:
Abstract: Second sentence in abstract is a bit redundant (heterosis appears twice). So are the last two sentences in review, with redundant "demonstrated", and grammatical mistake (need and not needs).
Introduction:
Ø rice hybrid varieties are not necessarily heterozygous in any locus (row 50).
Ø Row 135-to compute and not computer
We are very grateful to you for pointing out the mistakes in language so carefully. We have corrected it as suggested.
6.The authors refer the reader to a link that 1) written in Chinese, and 2) cannot be displayed. This does not allow to asses the GPS software as part of this review.
We have optimized our pipeline of GPS to be smoother and simpler. We also provided a single compressed zip file containing the software with a detailed readme.txt. In addition, we have corrected the mistakes raised by reviewer 3. Thanks for the comments. The QTL-seq approaches combine BSA (bulked-segregant analysis) with genome-wide sequencing to identify QTL associated with target traits. Although the GPS approach has some similarities to QTL-seq, they have some differences in terms of algorithm and results. We also repeated the data of QTL-seq method, and the supplementary figure 4 showed that the GPS had a higher resolution. We hope the highly efficient GPS method can dramatically accelerate crop improvement in a cost-effective manner.
7.To conclude
In addition, we added some discussion on the limitation of the GPS as suggested, it's helpful for improving the level of the article. Thanks again.
REVIEWERS' COMMENTS:
Reviewer #1 (Remarks to the Author): In this revised version, the authors have added additional data and answered the questions which I addressed, now it is accepted for publication.
Reviewer #2 (Remarks to the Author): GPS provides a useful addition to the breeder's toolkit, and your analyses have contributed further to development of hybrid rice.
Thank you for considering all of my comments and addressing them. It is nice to see the comparison of mapping between different Nipponbare builds and to see results for mapping to the indica type Minghui 63. Further, I appreciate your effort improving the grammar, spelling and writing. There are a few places, especially in the added text, where there are minor problems. For example on line 32, it should be "inbred" not "inbreed".
Reviewer #3 (Remarks to the Author): The introduction of next generation sequencing (NGS) in the past few years have led to the development of quantitative trait loci (QTL) discovery by establishing and phenotyping a segregating population and selecting individuals with high and low values for the trait of interest, which are characterized for differences in allele frequencies. One most prominent pipeline, termed QTLseq, was described by Takagi Biol. ], in which G statistic is calculated for each SNP based on the observed and expected allele depths and the value is smoothed by considering relative distance of neighboring SNPs. Of course, these are not the only studies that deal with this QTL mapping approach (only recently came a new paper by Mansfeld and Grumet in Plant Genome, QTLseqr: An R Package for Bulk Segregant Analysis with Next-Generation Sequencing) but they do give a perspective on the state-of-the-art in this field. Now, this study by Wang et al. is presenting a new analysis termed GradedPool-Seq for dissecting QTL in rice for grain weight traits using F2 population, and resequencing three groups of bulked individuals, each is app. 20-30% of the whole phenotyped population. Already in the introductory part the authors fail to present, for example, the Magwene (2011) work, and in general it seems that there is too much avoidance from what has been done in this field. Instead, the comparison of the new GPS method is conducted to mapping of qualitative trait mutants, and with regard to QTL it is compared only to the QTL-seq only. The authors show that the GPS has app. 5X more resolution, i.e. from 2M bp to app. 400 Kbp. In fact, I find this difference not very significant; having a 5X resolution would both requires follow-up mapping population to achieve a single gene resolution. And Indeed, this is shown in this work with an heterozygous recombinant inbred lines used for finer mapping of the QTL after this was mapped in F2 population. To summarize, I don't find this difference between QTL-seq and GPS significant enough with regard to change in the breeding or gene cloning procedures. Moreover, considering other studies in the field, e.g. Magwene et al. 2011 andMansfeld andGrumet (2019), it seems that this study is of greater interest to those interested in rice genetics.
Reviewer #1 (Remarks to the Author):
In this revised version, the authors have added additional data and answered the questions which I addressed, now it is accepted for publication.
Thank you for your comments.
Reviewer #2 (Remarks to the Author): GPS provides a useful addition to the breeder's toolkit, and your analyses have contributed further to development of hybrid rice.
Thank you for considering all of my comments and addressing them. It is nice to see the comparison of mapping between different Nipponbare builds and to see results for mapping to the indica type Minghui 63. Further, I appreciate your effort improving the grammar, spelling and writing. There are a few places, especially in the added text, where there are minor problems. For example on line 32, it should be "inbred" not "inbreed".
Thank you for checking our manuscript carefully. And We are grateful for your positive comments. We revised the manuscript word for word to correct grammar and check spelling again.
Reviewer #3 (Remarks to the Author): The introduction of next generation sequencing (NGS) in the past few years have led to the development of quantitative trait loci (QTL) discovery by establishing and phenotyping a segregating population and selecting individuals with high and low values for the trait of interest, which are characterized for differences in allele frequencies. One most prominent pipeline, termed QTLseq, was described by Takagi et al. (2013) and since then was widely used in several crop plants for many traits. The other main computational tools to evaluate statistical significance of QTL from NGS-BSA was proposed by Magwene et al. (2011) [Magwene, P.M., J.H. Willis, and J.K. Kelly. 2011. The statistics of bulk segregant analysis using next generation sequencing. PLOS Comput.
Biol. ], in which G statistic is calculated for each SNP based on the observed and expected allele depths and the value is smoothed by considering relative distance of neighboring SNPs. Of course, these are not the only studies that deal with this QTL mapping approach (only recently came a new paper by Mansfeld and Grumet in Plant Genome, QTLseqr: An R Package for Bulk Segregant Analysis with Next-Generation Sequencing) but they do give a perspective on the state-of-the-art in this field. Now, this study by Wang et al. is presenting a new analysis termed GradedPool-Seq for dissecting QTL in rice for grain weight traits using F2 population, and resequencing three groups of bulked individuals, each is app. 20-30% of the whole phenotyped population. Already in the introductory part the authors fail to present, for example, the Magwene (2011) work, and in general it seems that there is too much avoidance from what has been done in this field. Instead, the comparison of the new GPS method is conducted to mapping of qualitative trait mutants, and with regard to QTL it is compared only to the QTL-seq only. The authors show that the GPS has app. 5X more resolution, i.e. from 2M bp to app. 400 Kbp. In fact, I find this difference not very significant; having a 5X resolution would both requires follow-up mapping population to achieve a single gene resolution. And Indeed, this is shown in this work with an heterozygous recombinant inbred lines used for finer mapping of the QTL after this was mapped in F2 population. To summarize, I don't find this difference between QTL-seq and GPS significant enough with regard to change in the breeding or gene cloning procedures. Moreover, considering other studies in the field, e.g. Magwene et al. 2011 andMansfeld andGrumet (2019), it seems that this study is of greater interest to those interested in rice genetics.
First of all, we appreciate the reviewer's comments. In our introduction section, we emphatically introduce several QTL mapping methods, but not statistical algorithms. Now we cite Mansfeld and Grumet's paper in Introduction section to enrich our manuscript. As the reviewer said, the methods we mentioned were not the only studies that deal with QTL mapping. Our GPS method with Ridit analysis will be a very good complement to the QTL mapping work and rice breeding. The reasons why we chose QTL-seq method as the comparison: (1) QTL-seq can work in F2 population (2) the similarity between QTL-seq and GPS method in experimental design (3) QTLseq can map QTLs (4) QTL-seq is a popular method in QTL mapping work currently. Therefore, the higher resolution of GPS than that of QTL-seq method will be convincing in QTL mapping.
The high resolution in QTL mapping will help to accelerate the progress of fine-scale mapping and breeding. Of course, GPS cannot achieve a single gene resolution. But applying GPS method in gene cloning and breeding will be cost-effective and time-saving. | 7,862.4 | 2019-07-05T00:00:00.000 | [
"Agricultural and Food Sciences",
"Biology"
] |
Fission stories: using PomBase to understand Schizosaccharomyces pombe biology
Abstract PomBase (www.pombase.org), the model organism database (MOD) for the fission yeast Schizosaccharomyces pombe, supports research within and beyond the S. pombe community by integrating and presenting genetic, molecular, and cell biological knowledge into intuitive displays and comprehensive data collections. With new content, novel query capabilities, and biologist-friendly data summaries and visualization, PomBase also drives innovation in the MOD community.
Introduction
Over the past decade, PomBase (www.pombase.org), the authoritative model organism database (MOD) for the fission yeast Schizosaccharomyces pombe, has supported the fission yeast research community by integrating and presenting all types of genetic, molecular, cell biological, and systems-level knowledge relevant to S. pombe. In addition to about 200 laboratories dedicated to fission yeast research, PomBase serves a growing number of users who focus on other organisms but rely on data generated in S. pombe for inferences about orthologous genes and conserved eukaryotic cell biology. As fission yeast research has grown in complexity and breadth of relevance, PomBase has kept pace, supporting emerging experimental and data-handling techniques, enabling researchers to ask novel questions, and driving innovation in the MOD community.
PomBase's primary aims remain to standardize, integrate, and display fission yeast research, to disseminate datasets and new knowledge to the wider scientific community, and to highlight the added value these efforts bring.
The core of PomBase consists of a growing body of comprehensive, reliable knowledge derived by manual curation of the fission yeast literature. Manual curation covers a wide range of data types, including molecular functions, biological processes, cellular locations, macromolecular complexes, phenotypes, alleles and genotypes, protein modifications, physical interactions, genetic interactions, DNA and protein sequence features, and orthologs in human and budding yeast (Saccharomyces cerevisiae). Annotations generated by computational methods supplement manually curated data for function, process, and location data represented using the Gene Ontology (GO; The Gene Ontology Consortium 2000Consortium , 2021. Table 1 summarizes annotation types and totals. Literature curation makes extensive use of ontologies, including GO, the Sequence Ontology (Eilbeck et al. 2005), the Protein Ontology (Natale et al. 2017), the Mondo Disease Ontology (developed by the Monarch Initiative; Mungall et al. 2017;Shefchek et al. 2020), and the protein modification ontology PSI-MOD (Montecchi-Palazzi et al. 2008). We have contributed many new classes, corrections, and other revisions to all of these ontologies. For example, since 2018 PomBase curators have raised over 500 issues in the GO Consortium (GOC)'s GitHub tracker for ontology structure and content (https://github.com/geneontology/go-ontol ogy/issues) and over 80 issues on the Mondo tracker (https:// github.com/monarch-initiative/mondo/issues). We have also pioneered annotation quality control methods that are being adopted throughout the GOC. Notably, we developed a method to use observed coannotation patterns to identify annotation outliers and to build rules that allow automated outlier detection ). Using this system, we have corrected thousands of annotations, and we collaborate with the GOC to continue rule development and to deploy a pipeline for error detection and reporting.
PomBase curators develop and maintain the Fission Yeast Phenotype Ontology (FYPO), a logically robust vocabulary that is designed for fission yeast but is also the leading candidate for further development into an ontology of cell-level phenotypes for all eukaryotes (Harris et al. 2013). FYPO currently comprises over 7500 terms, used in almost 97,000 annotations. FYPO development now uses the Ontology Development Kit (ODK; Matentzoglu 2021) for releases, which provides a release pipeline that seamlessly incorporates ontology reasoning, continuous integration checks, and generation of production files in Web Ontology Language (OWL) and Open Biomedical Ontologies (OBO) formats.
Our broad and deep ontology-based curation standardizes data from large-and small-scale publications, making a wide range of published data compatible with FAIR (Findable, Accessible, Interoperable, and Reusable; Wilkinson et al. 2016) data sharing principles. Furthermore, our field-leading community curation project actively engages researchers in building the PomBase collection of FAIR-shared biological knowledge. We have recently described the insights gained from the project, including our experience with approaches that maximize participation, and the unanticipated added value that arises from cocuration by publication authors and professional curators . To date, we have assigned over 1800 publications to authors for curation and have received over 975 submissions in response (54% response rate). Our online curation tool, Canto (Rutherford et al. 2014), has also been deployed for several other communities, including PHI-base (Urban et al. 2020), FlyBase (Larkin et al. 2021), and the new Schizosaccharomyces japonicus MOD JaponicusDB (see Rutherford et al. 2022).
Alongside its established, ongoing data stewardship activities, PomBase has introduced new features that enable biologists to integrate diverse molecular data into human-friendly summaries of biology. Below, we provide an overview of the new and updated features and describe how biologists can use new and existing data and tools to place their results into broader contexts. Taken together, PomBase activities give rise to a long-term collaboration with users to curate the knowledge gained from fission yeast research into an integrated overview of conserved cell biology to ensure that the resulting knowledge can be used to its full potential.
Querying PomBase
PomBase provides robust, intuitive search interfaces to enable biologists to easily retrieve and combine data of diverse types from multiple sources.
Simple search
A simple search, available in the header of every PomBase page, offers quick access to several commonly used PomBase pages.
The search finds gene pages matching fission yeast names, synonyms, systematic IDs, UniProtKB accessions (The UniProt Consortium 2020), or gene product descriptions. Human gene symbols (Tweedie et al. 2021) or S. cerevisiae gene names, ORF names, or IDs (Cherry et al. 2012;Engel et al. 2021) can also be used to find curated orthologs. Publication pages and ontology term pages can be retrieved using relevant IDs (PubMed or ontology IDs). Text searches generate autocomplete suggestions from matching gene product descriptions, ontology term names, and publication titles, author names, and dates.
Advanced search
Since the reimplementation of the website in 2017, PomBase has provided an advanced search facility (https://www.pombase.org/ query) that supports querying for gene sets based on a wide variety of criteria, including ontology annotations, gene product attributes (e.g., protein length, mass, domains, or modifications), genomic location, conservation, etc. Complex queries can be constructed by combining single queries in the query history. The history, with links to result sets, is stored locally in the user's web browser, and out-of-date results are highlighted and refreshed upon following result links. We have previously described links between ontology terms in query results, ontology term pages, and gene lists, which support data integration throughout the PomBase website .
Recent enhancements include improved phenotype querying, enhanced options for display and download of search results, and new tools for saving and sharing queries.
The search now provides an expanded set of query parameter options for phenotypes: experimental conditions can be used as search criteria for phenotype annotations, using the same condition descriptors as shown on PomBase web pages and in Canto. For example, a query can retrieve genes that show abnormal chromosome segregation mutant phenotypes specifically at high or low temperatures. Genes can also be selected based on the phenotypes of haploid or diploid, or single-or multilocus, genotypes. For single-locus haploids, the expression level can be specified.
The display of search results is now highly customizable. Each query in the history has a link to a page of results that shows the count, query details, and a list of matching genes. By default, systematic IDs, names, and gene product descriptions are shown. The display can be customized by choosing additional columns (including a selection of gene expression data), and the list can be sorted on any column.
Similarly, selected data can be downloaded for genes in the list, via a popup that offers three sets of options: • A "Tab delimited" option offers the same data as the results web page, for inclusion in a downloaded text file; • A "Sequence" tab retrieves amino acid or nucleotide sequences in FASTA format, with checkboxes to select which items are included in the headers. When "Nucleotide" is selected, flanking sequence options similar to those on the gene page are available; • A "GO annotation" tab downloads a file in GAF2.1 format (http://geneontology.org/docs/go-annotation-file-gaf-format-2.1/) that includes direct annotations (but not those inferred by transitivity) for the selected branch(es) of GO.
To facilitate query reuse and sharing, entries in the PomBase advanced search query history now show brief, user-editable query descriptions, and a toggle to show or hide additional details. All result pages from the advanced search now have a unique permanent URL that can be bookmarked and shared with colleagues. A set of "Commonly used queries" uses this system to provide convenient shortcuts to frequently sought data, such as all genes with disease associations (see below) or all proteincoding genes of unknown biological role.
ID mapper
On a related note, we have developed an identifier mapper that retrieves S. pombe genes for a selection of different input ID types.
Users can now find S. pombe genes using UniProtKB accessions, and retrieve manually curated orthologs for S. cerevisiae using standard gene names or ORF names, and for human using standard gene names or HUGO Gene Nomenclature Committee (HGNC; Tweedie et al. 2021) identifiers. S. pombe genes found via the ID mapper can be sent to the advanced search with a single click.
From data to biological narratives
Much of PomBase's recent work helps further our goal of enabling researchers to take data found in PomBase-from their own results combined with those of others-and build narratives that elucidate a biological topic with broad applicability.
Intuitive annotation displays
In the PomBase reimplementation, we introduced display filtering on gene, publication, and ontology term pages for phenotype annotation tables, to narrow the list by broad phenotypic category, and (in the detailed view) by evidence. We have now added filtering for more annotation types and expanded the set of filtering options. Display filtering is now available for all three branches of GO, and for qualitative or quantitative gene expression annotations. For GO and gene expression annotations, detailed views now offer filters for observations made during specific cell cycle phases, which use annotation extensions (Huntley et al. 2014) specifying the relevant phase. All of the above annotation types, as well as genetic and physical interactions, can also be filtered to distinguish between high-vs lowthroughput experiments. The display of protein features on gene pages has been updated to improve legibility and provides an interactive graphical view in which mousing over any feature shows additional details in a tooltip and highlights the full entry in the accompanying table.
For ease of use, we have improved the appearance of PomBase pages on small screens such as tablets and smartphones.
Comprehensive knowledge representation
To ensure that coverage of S. pombe research is current and complete, we organize annotation reviews by biological process. We have recently comprehensively reviewed and updated annotations in three broad areas of biology: tRNA metabolism, mitochondrial biology, and transmembrane transport. Because these topics are not intensively studied in fission yeast, the updates primarily affect GO annotations inferred from orthologs. We have also reviewed a fourth topic, chromatin silencing, to bring annotations into alignment with substantial, ongoing revisions to chromatin-mediated transcriptional regulatory functions and processes in GO.
The S. pombe GO annotation corpus also now includes a set of annotations from the GOC's Phylogenetic Annotation and INference Tool (PAINT) pipeline (Gaudet et al. 2011), which propagates GO annotation across all species based on protein family membership. Before incorporating PAINT annotations into PomBase, we reviewed the predictions made for S. pombe and reported errors to the GOC for over 500 protein families, improving the accuracy of the PAINT annotation corpus for all species. Like all GO annotations imported into PomBase from external sources, PAINT annotations are filtered for redundancy with experimentally supported annotations .
Qualitative gene expression annotations now use an expanded set of descriptors, accommodating ribosomal density data as well as more precisely defined RNA and protein level terms.
To ensure coverage of high-throughput experiments, we have continued to build the collection of data tracks, and associated well-curated metadata, in the PomBase JBrowse (Buels et al. 2016) instance; the browser now hosts 330 tracks from 28 publications. To improve browser data visibility, gene pages now display JBrowse images that have clickable features and a link to open the fully functional browser in a new tab or window. Data tracks from datasets hosted in the PomBase genome browser can also now be browsed, selected, and loaded from their respective publication pages.
PomBase is now a Partner Database with microPublication, whose remit is to publish "brief, novel findings, negative and/or reproduced results, and results which may lack a broader scientific narrative" (https://www.micropublication.org/; Raciti et al. 2018). This partnership thus enables fission yeast researchers to publish individual experimental results that have not been included in traditional publications, thereby building a collection of S. pombe data that fill gaps in available datasets.
Publication pages are now also available for reviews and methods papers as well as microPublications.
Ontology slims
Ontology subsets can provide overviews of annotation across a gene set or the whole genome. PomBase has long provided the fission yeast Biological Process (BP) GO slim, a subset of the GO BP ontology designed to cover as many annotated gene products as possible, while remaining informative about the gene product's physiological role in the cell Wood et al. 2019). To complement the BP slim, we have now created three new ontology subsets. The fission yeast Molecular Function (MF) and Cellular Component (CC) slims summarize the MF and CC branches of GO, respectively; together, all three GO slims provide a simple yet comprehensive summary of S. pombe's biological capabilities by grouping gene products using broad classifiers from the full breadth of GO.
The third new ontology subset is drawn from Mondo and gives an overview of genes with human orthologs implicated in disease. To accompany the Mondo slim, we have improved coverage for gene curation that associates disease descriptors with fission yeast orthologs of human disease-causing genes; over 1400 S. pombe genes now have curated disease associations. PomBase curators also collaborate with Mondo to improve its disease classification, especially in areas relevant to fission yeast diseasegene associations.
All of the PomBase ontology slims are integrated into annotation displays and querying. For each slim, a summary page lists the terms and IDs with links to ontology term pages and provides a genome-wide overview of annotated genes. In addition to the number of genes annotated to each slim term, the slim page identifies sets of genes that are not annotated to any term in the ontology or are annotated only to terms that do not have paths in the ontology to any slim term. On gene pages, annotation tables show slim terms applicable to a gene in the headers. On all pages where they appear, gene lists are linked to the advanced search, allowing the gene list to be combined with any other results in a new query. Slim annotations can also be retrieved for any advanced search result list.
We also maintain an up-to-date list of protein-coding S. pombe genes that are broadly conserved in eukaryotes (present in vertebrates), but have not been assigned an informative role from the GO BP slim (https://www.pombase.org/status/priority-unstudiedgenes; Wood et al. 2019).
Quick Little Tool
The Quick Little Tool (QuiLT) is a new feature that allows users to view multiple types of annotation in a single graphical display. Inspired by our analysis of conserved unstudied proteins (Wood et al. 2019), QuiLT generates a graphic for any gene list uploaded or obtained in advanced search results. QuiLT visualization is also linked to PomBase pages that list genes annotated to an ontology term, and on the "Priority unstudied genes" page (see above). QuiLT has display options for deletion viability, presence or absence of budding yeast orthologs, presence or absence of human orthologs, annotation from each branch of GO, characterization status for protein-coding genes, taxonomic distribution, and protein length. The display is interactive, allowing users to highlight subsets of the list, filter the display, toggle annotation types on and off, reorder the list to focus on features of most interest, and download the image. Figure 1 shows QuiLT visualization of genes that are conserved in vertebrates and were found to be associated with chronological lifespan in a recent study (Romila et al. 2021). The authors compared their list of long-lived mutants with all genes previously associated with the phenotype 'increased viability in stationary phase' (FYPO:0001309) to uncover novel aging-associated genes; among the latter genes, they then readily identified conserved genes using the catalog of conserved unstudied genes described above, as well as genes associated with diseases in human.
Pathways
A new gene page section, "Molecular pathway," connects genes in PomBase to depictions of biochemical and signaling pathways. At present, this section is shown for any gene that appears in a pathway entry in the Kyoto Encyclopedia of Genes and Genomes (KEGG) database (Kanehisa and Goto 2000;Kanehisa 2019;Kanehisa et al. 2021), linking to the relevant KEGG page(s) and to a PomBase page listing all genes connected to the pathway. The Molecular pathway section will figure prominently in the future development of data integration in PomBase (see below).
Future directions
We will continue all of the well-established activities described above, ensuring that PomBase presents comprehensive, qualitycontrolled, curated knowledge from large-and small-scale S. pombe experiments. In addition, a diverse set of enhancements is under development.
To improve the accuracy and coverage of sequence feature annotation, a comprehensive overhaul of 5 0 and 3 0 untranslated region lengths is in progress, and we will gradually add observed transcript isoforms to more genes. The whole-genome sequence will also be updated to fill gaps, correct errors, and incorporate new telomeric sequence data, and resubmitted to the International Nucleotide Sequence Database Collaboration (INSDC; https://www.insdc.org/) databases.
We will continue to enhance PomBase's simple and advanced search tools with new features and capabilities, such as better handling of genes with multiple transcript isoforms, improved querying for phenotype conditions, and import/export of query histories. We also plan to investigate options, such as user accounts, to enable researchers to configure PomBase page displays, browser settings, etc. and to make saved settings and query histories more portable.
Most importantly, we will focus effort on building richer, more comprehensive connections among curated data of all types. Notably, we will adapt S. pombe GO annotations to follow the "GO Causal Activity Modeling" principles established by the GOC for GO-CAMs (Thomas et al. 2019), using our large, detailed body of existing GO annotations. Manually curated S. pombe GO annotations already include a rich set of extensions that capture reaction substrates, effector-target connections, high-confidence physical interactions, complexes, and regulatory effects. Converting these extended annotations to GO-CAM models will improve PomBase's representation of how protein activities are connected into pathways and how pathways are connected to each other. Pathway diagrams generated by software using GO-CAM data will be shown in the Molecular pathway section of gene pages. Furthermore, by integrating GO-CAM-based pathways with curated information about which genes and pathways relate to human diseases, and what proteins remain unstudied across species, PomBase will enable users to develop an emergent understanding of cell biology relevant throughout the eukaryotes. Biological stories crafted from fission yeast data will thus shed light on all biological systems.
Data availability
PomBase has used open-source tools and code to develop a modular, customizable, and readily reusable system that supports daily data updates and an intuitive web-based user interface . All PomBase code is available from the PomBase GitHub organization (https://github.com/pombase), where each major aspect of the project-including curation, website, Chado database, FYPO, and Canto-has a dedicated repository.
In addition to the web page displays and query result downloads described above, PomBase data can be downloaded in bulk from the website (see https://www.pombase.org/datasets and https://www.pombase.org/data). We have recently switched all downloads to use the HTTPS protocol, superseding FTP. Available downloads include nightly dumps and monthly snapshots of the entire Chado curation database, and a range of specific curated datasets, including GO annotations, single-allele phenotypes, protein modifications, high-confidence physical interactions, and manually curated ortholog lists. | 4,660.6 | 2021-09-08T00:00:00.000 | [
"Biology",
"Computer Science"
] |
The New Compound of (2R, 4S)-N-(2, 5-difluorophenyl)-4-Hydroxy-1-(2, 2, 2-Trifluoroacetyl) Pyrrolidine-2-Carboxamide to Mediate the Expression of Some Apoptosis Genes by the HepG2 Cell Line
Objectives: Hepatocellular carcinoma is one of the most frequent cancers worldwide, for the treatment of which various therapy protocols and drugs have been introduced; however, none of them has suppressed cancer tissues completely. New research programs have been developed on cancer and the accompanied effects of novel synthesized compounds on cancer cell lines. Our latest reports on the molecular basis of cancer revealed a pattern of changes in gene expression triggered in the cancer pathway. Methods: HepG2 cell lines were cultured under similar conditions in both test and control groups. The IC50 concentration of the (2R, 4S)-N-(2, 5-difluorophenyl)-4-hydroxy-1-(2, 2, 2-trifluoroacetyl) pyrrolidine-2-carboxamide compound was used in the treatment group. After 48 hours from the culture, the expressional profiles of apoptosis pathway genes (84 genes) were studied using the PCR array method. Results: The findings demonstrated that the expression of some apoptosis-related genes pertaining to TNF, BCL2, IAP, and caspase families was regulated by (2R, 4S)-N-(2, 5-difluorophenyl)-4-Hydroxy-1-(2, 2, 2-Trifluoroacetyl) Pyrrolidine-2-Carboxamide. In the same vein, an alteration was observed in the expression of both pro-apoptotic and anti-apoptotic genes associated with the extrinsic and intrinsic apoptosis signaling pathways. Conclusions: According to the data obtained, the pyrrolidine-2-carboxamide compound was demonstrated to be able to regulate the apoptotic activities of HepG2 cells by affecting both pro-apoptotic and anti-apoptotic relevant genes.
Introduction
Cells are considered as the basic structural and functional units of human life. Normally, older cells undergo division and proliferate in order to generate newer ones; in addition, they are destroyed as a result of apoptosis in a complicated process, so equilibrium exists between live and dead cells, under normal circumstances (Hanahan and Weinberg, 2000). The malignancy of liver cancer is among the six most frequent cancer types, being considered the third cause of cancer deaths worldwide (Moy et al., 2013). Unfortunately, the incidence rate of the various types of liver cancer has increased in developing countries in recent years. There exists no efficient treatment for liver cancer to date, so the development of advanced treatments for the disease will be highly valued. Accordingly, a wide variety of synthetic pro-apoptotic
N-heterocyclic structures are the major classes of such compounds that play a major role in medicinal chemistry and in particular in drug synthesis (Ten Holte et al., 2001). Organofluorine compounds (organoFs) have been utilized by a large number of pharmaceutical, agrochemical, and drug industries in the past few decades (Hudlicky, 1979). From among them, trifluoroacetimidoyl chlorides substituted molecules have been investigated extensively, with the indication that these fluorinated structures demonstrate interesting biological activities (Polshettiwar and Varma, 2010;Romero et al., 2015).
Based on the introduction above, the authors of this article synthesized the new derivative of (2R, 4S)-N-aryl-4-hydroxy-1-(2, 2, 2-trifluoroacetyl) pyrrolidine-2-carboxamides (Darehkordi and Ramezani, 2017) (Figure 1). Apoptosis is defined as a homeostatic cellular event by which cell populations are preserved in tissues. The apoptosis phenomenon occurs normally as cells proliferate or become aged. Apoptosis is also involved actively in defensive processes, principally in the pathogenesis of a variety of human diseases including, viral infections, autoimmune diseases, and cancer (Norbury and Hickson, 2001). It is well established that some anticancer drugs act by inducing apoptosis in order to exert their cytotoxic effects (Ferreira et al., 2002).
Synthetic compounds which possess cytotoxic properties have apoptosis-inducing potentials in numerous types of human cancer cells. The study of apoptosis-inducing effects under both normal and modified conditions is of high significance (Hersey and Zhang, 2001). Thus, the present study was conducted aimed at investigating the effects of the (2R, 4S)-N-(2, 5-difluorophenyl)-4-Hydroxy-1-(2, 2, 2-Trifluoroacetyl) Pyrrolidine-2-Carboxamide derivative on cellular apoptosis in human hepatocellular carcinoma cells (HepG2 cells). For this purpose, the authors of this article used RT2 Profiler PCR Arrays to detect the profile of gene expression changes in response to the new derivative of pyrrolidine-2-carboxamide in HepG2 cells.
Chemical compound preparation
The powdered sample was provided by dissolving 5mg of the chemical compound in 1mL of DMSO (dimethyl-sulphoxide) to achieve an appropriate concentration of 5mg/mL. Next, the produced stock solution was filtered through a 0.45µM filter, before use in each assay. In the following step, 400µL of the stock solution was mixed up gently and enriched with 600µL of RPMI 1640 at appropriate concentrations (125µg), which was required for examinations by serial dilution .
The cell culture method
A sample of HepG2 cells was provided from the National Cell Bank of Iran (the Pasteur Institute of Iran, Tehran). The cells were cultured in a 25mL culture flask in the RPMI 1640 medium (Gibco, Pasteur Institute, Tehran, Iran). Next, they were supplemented with 10% fetal bovine serum (FBS) (Gibco, USA), penicillin-streptomycin (100 U/mL) and incubated at 37°C in a humidified atmosphere containing 95% O 2 and 5% CO 2 . As already mentioned in brief, cell growth inhibition (IC 50 ) was calculated to be 50% for pyrrolidine-2-carboxamide after 48 hours (62.5µg/mL) . The nonmalignant cells (L929) were also cultured under similar conditions in the RPMI 1640 medium containing 5% (v/v) of fetal bovine serum (FBS) and 100 units/mL of penicillin-streptomycin. The cultures were left overnight and then incubated at the required concentrations of the pyrrolidine derivative (62.5µg/mL) for 48 hours to be examined by the realtime Profiler PCR Array (The RT2 Profiler PCR Array, SABiosciences, USA).
RT2 Profiler PCR array
The RT2 Profiler PCR Array (SABiosciences, USA) was performed to analyze the expression of a panel of genes involved in the apoptosis pathway (Human Apoptosis PCR Array, RT2 Strand Kit, SABiosciences, USA) together with 5 housekeeping genes. This Real-Time PCR (RT-PCR) kit contained 84 apoptosis-related genes, 5 housekeeping genes, as well as 3 RNA and PCR quality controls. The cells received either a relative concentration of the new therapeutic compound of (2R, 4S)-N-(2, 5-difluorophenyl)-4-Hydroxy-1-(2, 2, 2-Trifluoroacetyl) Pyrrolidine-2-Carboxamide) or the control medium alone and were kept at 37°C. Following 48 hours from the treatment, the cells were rinsed with PBS and harvested through centrifugation for the purpose of RNA isolation. The total RNA content was extracted using the Qiagen kit (USA) in accordance with the manufacturer's recommended protocol. The purity and fidelity of the RNA were examined using the spectrophotometric method (by the calculation of the 260/280nm absorbance ratio) and running on the 1.5% agarose gel, with electrophoresis utilized to assess the purity and integrity of RNA. The first strand of cDNA was generated by the RT2 First Strand kit (Qiagen, USA) from 1.0µg of the total RNA for 96-well plates. An ABI, Step 1 plus RT2 PCR Detection System (ABI, Step 1 plus, USA), was applied for the real-time PCR analysis. For each PCR array plate, an experimental cocktail was produced using 998.4µL of the RT2 qPCR master mix, 96µL of the first strand cDNA's synthesis reaction, and 825.6µL of ddH2 O. The 20µL reaction of the experimental cocktail was aliquoted into each PCR array well. The RT2 qPCR thermal cycling program included one cycle at 95°C for 10min, 40 cycles at 95°C for 15s, 60°C for 40s, and 72°C for 30s (Mirzaei et al., 2014).
Statistical analysis
The authors of this article analyzed the data quantitatively by employing the 2 -(∆∆Ct) method, with the threshold cycle (CT) values exported and analyzed using the web-based software of RT2 Profiler PCR Array Data Analysis, version 3.5 (HTTP:// PCR data analysis. sabiosciences.com/pcr/array analysis. PHP). The fold changes of the relevant genes were calculated by the 2 -(∆∆Ct) formula. The PCR array was performed in triplicate for each sample, i.e. the extract-treated sample and the control sample.
Discussion
Despite extensive research conducted on the treatment of liver cancer to reduce its incidence rate, this type of malignancy is still considerably frequent in the world (Siegel et al., 2014). The present study examined the apoptotic effects of pyrrolidine derivatives on human hepatoma (HepG2) cells. In a similar study, the cytotoxic effects of this derivative were explored on HepG2 cells by the MTT assay, and the cells were double-stained with Annexin-V and PI for the in-vitro flow cytometric detection of apoptotic cells, with the results indicating that it induced HepG2 cell apoptosis significantly at 125µL concentrations after 48 hours . To achieve the research goals, the authors of this article extended the mentioned study making use of the PCR array technology. Apart from developing cancer treatment methods, another way of fighting cancer could be the designing of new therapeutic agents, which act though either the upregulation of pro-apoptotic molecules or the downregulation of anti-apoptotic molecules (Fesik, 2005;Call et al., 2008). In addition, to explore the underlying molecular mechanisms of apoptosis induced by the pyrrolidine derivative, the PCR array technology was used in this article. Research results indicate that pyrrolidine is able to modify apoptosis-induced gene expression . To better understand molecular mechanisms, we specified the expression of apoptosis-related genes by a quantitative real-time PCR array technology and found out that this derivative reduced cell viability and induced apoptosis. This PCR array included a wide range of gene families involved in apoptosis, such as TNF ligands and their receptors, BCL-2 members, caspase, IAP, and TRAF (Table 1). The array data showed that the expression of many genes was connected with the extrinsic and intrinsic apoptosis signaling pathways ( Table 2). The perforingranzyme-dependent killing of the cells was changed significantly together with these changes, with this being remarkably important in the case of anti-apoptotic genes and supporting the assumption that this pyrrolidine derivative was able to exert its apoptotic effects mostly by the downregulation of these genes (Table 1).
As Table 2 shows, the expression of Bcl-2, being known for its anti-apoptotic properties, decreased significantly (Reed, 2008). In the same vein, the expression of other anti-apoptotic molecules, including Bcl2L1, Bcl2L11, IGF1R, BRAF, and CD40LG decreased dramatically. Furthermore, in addition to the two main apoptotic pathways, i.e. the extrinsic and the intrinsic ones, an additional pathway has been detected that includes T-cell mediated cytotoxicity and perforin-granzyme, being dependent on the killing of the cells (Igney and Krammer, 2002). Although the Bcl-2 gene family plays a significant role in both pro-apoptotic and anti-apoptotic pathways, it could be assumed that the reduction in the expression of caspases has been probably due to the fact that these two pathways have been able to affect each other (Table 1) (Reed, 2008). Moreover, the expression of caspases 3 and 5 has increased significantly, with this implying that perforin-granzyme has been further initiated by the cleavage of caspase 3, leading to DNA fragmentation, the degradation of cytoskeletal and nuclear proteins, and the formation of apoptotic bodies (Table 1) (Martinvalet et al., 2005). In the present study, the expression of FASLG l and TNF receptor death domains increased, thereby playing a significant role in signaling pathways, in order of transferring the death signal from the cell surface to the intracellular space (Rubio-Moscardo et al., 2005). In the same vein, P53 played a pivotal role by mediating cellular death after damage, with its pro-apoptotic function having depended on transcription factors, including c-Myc (Table 1) (Marnett and Plastaras, 2001). In the present study, it was demonstrated that the expression of the p53 gene increased significantly, yet another membrane p53 family, i.e. the p73 gene, was downregulated in response to this derivative (Table 2) (Flores et al., 2002).
It is worth noting that the remarkable downregulation of Bcl-2 and IGF1R in the present study could imply that these genes have been the potential targets of cancer drug developments (Chipuk and Green, 2008;Zhou et al., 2017).
In conclusion, as far as the authors of the present article are concerned, these findings are novel and address the apoptotic potential of the new pyrrolidine-2-Carboxamide derivative for the first time. The Pyrrolidine-2-Carboxamide derivative was shown to induce apoptosis in HepG2 cells. It also affected the expression of some genes involved in apoptosis pathways. However, further experiments are required to evaluate these types of compounds to examine their pharmacological properties as the sources of pharmacologically valuable products against human cancer cells.
Funding Statement
Not applicable. | 2,791.6 | 2019-05-01T00:00:00.000 | [
"Medicine",
"Chemistry"
] |
Revealing the Intrinsic Electronic Structure of 3D Half‐Heusler Thermoelectric Materials by Angle‐Resolved Photoemission Spectroscopy
Abstract Accurate determination of the intrinsic electronic structure of thermoelectric materials is a prerequisite for utilizing an electronic band engineering strategy to improve their thermoelectric performance. Herein, with high‐resolution angle‐resolved photoemission spectroscopy (ARPES), the intrinsic electronic structure of the 3D half‐Heusler thermoelectric material ZrNiSn is revealed. An unexpectedly large intrinsic bandgap is directly observed by ARPES and is further confirmed by electrical and optical measurements and first‐principles calculations. Moreover, a large anisotropic conduction band with an anisotropic factor of 6 is identified by ARPES and attributed to be one of the most important reasons leading to the high thermoelectric performance of ZrNiSn. These successful findings rely on the grown high‐quality single crystals, which have fewer Ni interstitial defects and negligible in‐gap states on the electronic structure. This work demonstrates a realistic paradigm to investigate the electronic structure of 3D solid materials by using ARPES and provides new insights into the intrinsic electronic structure of the half‐Heusler system benefiting further optimization of thermoelectric performance.
The knowledge of electronic structure is essential for understanding the physical properties of solids, such as the electrical resistivity ρ, thermopower α, and optical absorption, which lay the foundation of modern solid-state electronic devices, such as solar cells and thermoelectric modules. It has been established since the middle of the 20th century that the best thermoelectric materials are narrowbandgap semiconductors due to their characteristic electronic structure. [1] The bandgap, E g , a foremost parameter derived from the electronic structure, plays a vital role in determining the peak value of the figure of merit zT of a thermoelectric semiconductor. [2,3] With increasing temperature, the thermally excited minority carriers cross the bandgap, rapidly deteriorate the thermopower, and cause an increase of electrical and thermal conductivities, [3] making the zT peaks at a certain temperature. Therefore, higher E g generally leads to higher peak zT for a certain thermoelectric material. The band effective mass, m b *, another important parameter derived from the electronic structure, has an opposite contribution to carrier mobility and thermopower. [4,5] A probable solution to this dilemma is to take advantage of band anisotropy. The dispersive band guarantees high carrier mobility while the flat band direction serves as the carriers' reservoir securing good thermopower. [4,6] Therefore, accurate determination of the electronic structure is significant for understanding the high thermoelectric performance of good thermoelectric materials. [3,6,7] Half-Heusler compounds have recently attracted considerable attention from the thermoelectric community. [8,9] Three representative systems, i.e., MNiSn (M = Ti, Zr, and Hf), [10,11] MCoSb, [12,13] and RFeSb (R = V, Nb, and Ta), [14,15] have been developed as good thermoelectric materials with zT values above unity. These good results make the half-Heusler system very promising for high-temperature power generation especially with their good mechanical properties and thermal stability. Different from some other good thermoelectric materials, one remarkable feature contributing to the high zT of half-Heusler compounds is their high electrical power factor (PF = α 2 /ρ). Therefore, in-depth experimental investigation of the electronic structure and accurate acquisition of the related parameters (e.g., E g , m b *, and anisotropic factor) would be significant for understanding the good thermoelectric performance of half-Heusler compounds. Particularly, under the context of that lattice thermal conductivity of thermoelectric materials has been well tamed through multiple strategies. [16] MNiSn, as the first found half-Heusler thermoelectric system, [17] serves as a ripe platform for exploring the intrinsic origin of high PF. In recent years, large density of states near Fermi energy, [18] low deformation potential, [19] and high band degeneracy, [20] have been recognized as important factors that contribute to high PF. However, there are still some unresolved problems related to the electronic structure of MNiSn, such as "the real E g of MNiSn." This problem can be dated back to the original work of Aliev et al., [16,17] who first found that the intermetallic compounds MNiSn consisting of three metallic elements show a semiconducting behavior. Using the temperature-dependent resistivity and optical transmittance and reflectance measurements, they reported an E g of approximately 0.2 eV based on polycrystalline samples synthesized by arc-melting, which was confirmed by subsequent studies. [21] All these results are summarized in Figure 1a. However, a dilemma emerged when the first-principles calculations were carried out to study the electronic structure of ZrNiSn. In 1995, Öğüt and Rabe reported a calculated E g of 0.5 eV, [22] which was later validated by following theoretical calculations. [18,23] It is easily found that the experimental E g is much smaller than the calculated one. This is highly unexpected because the first-principles calculations usually underestimate, not overestimate the bandgap of a material. [24,25] With the considerable experimental [17,21] The red region shows the E g obtained from the single crystals in this work. E g_re is obtained from the resistivity measurement: ρ ≈ exp(E g_re /2k B T). E g_op is derived from the optical measurement. E g_GS is the Goldsmid-Sharp bandgap. [34] E g _ ARPES is derived from the ARPES study. E g_FP is from the first-principles calculations. b) Crystal structure of ZrNi 1+x Sn (left panel) and ZrNiSn (right panel), respectively, drawn with VESTA. [35] The corresponding electronic structure is exhibited below the crystal structure. CB and VB denote the conduction and valence bands, respectively. c) Schematic showing the pseudo-binary phase diagram of ZrNi 1+x Sn and ZrNiSn. [33] The blue and red arrows indicate high-temperature and lowtemperature preparation techniques, respectively. results, it is found that in nominally stoichiometric polycrystalline ZrNiSn, generally synthesized by high-temperature technique (e.g., arc melting, induction melting, and levitation melting), there is always some excess Ni occupying the interstitial sites. [25][26][27][28] As a result, the actual composition becomes ZrNi 1+x Sn (x is about 5%). These interstitial Ni atoms form additional in-gap states in the forbidden gap, [29] which lead to that the observable E g is the gap between the conduction band (CB) and the in-gap states, instead of the valence band (VB), [25] as schematically shown in Figure 1b. Although this finding well explains the difference between the observable experimental E g and the calculated one, the real E g of ZrNiSn, the gap between CB and VB, remains unresolvable. Furthermore, there is still no experimental work that directly investigates the CB of ZrNiSn using angle-resolved photoemission spectroscopy (ARPES) technique, which is significant for understanding its high power factor and zT since ZrNiSn is a good n-type thermoelectric material.
These above-mentioned issues principally can be resolved by performing high-resolution ARPES studies on ZrNiSn, which enable direct observation of the intrinsic electronic structure. [30] Recently, ARPES experiments have been carried out to investigate the quasi-1D and 2D thermoelectric materials CsBi 4 Te 6 [31] and SnSe, [32] respectively, and significantly different intrinsic electronic structure was revealed. However, it is more challenging to perform ARPES study on 3D crystals in contrast to the 2D layered compounds. A big technical problem is how to cleave the crystal to secure a well-ordered surface. Furthermore, for the current study, to observe the CB of ZrNiSn, heavily doped n-type single crystals are needed because only occupied electronic states below the Fermi level can be resolved by ARPES. Additionally, the existence of Ni in-gap states in the forbidden gap might cause difficulties in distinguishing the CB and VB. In this work, we have overcome these challenges and first revealed the intrinsic electronic structure of 3D half-Heusler compound ZrNiSn by ARPES. An unexpectedly large intrinsic bandgap and anisotropic CB are directly observed by ARPES.
Previous studies have demonstrated that the existence of Ni in-gap states in ZrNi 1+x Sn makes the observable E g much smaller than the real one, [25] as shown in Figure 1b. Therefore, to observe the intrinsic E g of ZrNiSn, it is crucial to growing the crystals with reduced Ni interstitial defects. From the pseudobinary phase diagram of the ZrNi 1+x Sn and ZrNiSn system (Figure 1c), it is found that there is an obvious increase in the solubility of excess Ni in ZrNi 1+x Sn with increasing temperature. As an intermetallic compound, ZrNiSn polycrystalline ingots were usually synthesized by using arc melting, induction melting, or levitation melting. [9,10,28] The ingots are formed after rapid cooling from its liquid state (the melting point of ZrNiSn is 1465 °C), [33] as indicated by the thick blue arrow in Figure 1c. Thus, more Ni interstitial defects might be easily formed in the obtained polycrystalline samples. To obtain the crystals with less Ni interstitial defects, it is crucial to growing the crystals at lower temperatures with a slow-growing rate, as shown by the thin red arrow in Figure 1c.
Herein, undoped and Sb-doped ZrNiSn single crystals have been grown with a low-temperature preparation technique, i.e., solidification in a Sn-rich melt by slow cooling (2 °C h −1 ) from 1100 to 650 °C, details can be found in the Experimental Section. The optical image of the as-grown crystals, which have a typical length of 2 mm and shiny surfaces, is shown in Figure 2a. Powder X-ray diffraction (XRD) patterns of undoped ZrNiSn and Sb-doped ZrNiSn 0.97 Sb 0.03 crystals are shown in Figure S1 (Supporting Information) and no obvious impurity phase is observed. The crystallinity and orientation of the crystals are further checked with Laue diffraction measurement. The obtained Laue diffraction pattern can be indexed based on the 43 F m space group and superposed well with a theoretically simulated pattern ( Figure S2, Supporting Information). The optical and backscattered scanning electron microscope images of the polished ZrNiSn and ZrNiSn 0.97 Sb 0.03 single crystals in Figures S3 and S4 (Supporting Information), respectively, show the homogenous phase. The lattice parameter of ZrNiSn single crystal is calculated to be 6.1033(2) Å at 300 K (Table S1, Supporting Information), which is appreciably smaller than the value of 6.1141(1) Å for ZrNi 1.046 Sn, [26] indicating that the studied single crystals might have fewer Ni interstitial defects. The actual compositions of the undoped ZrNiSn and Sb-doped ZrNiSn 0.97 Sb 0.03 single crystals were carefully examined using energy-dispersive X-ray spectroscopy (EDX) and wavelengthdispersive X-ray spectroscopy (WDX), respectively (details are in Tables S2 and S3, Supporting Information). The results indicate a smaller amount of excess Ni (about 1-2%) in the studied single crystals, compared to that of about 5% in the polycrystalline crystals using high-temperature preparation technique. [25,26] Moreover, we found the actual composition of the as-grown single crystals still shows similar excess Ni of about 1-2% even under the condition that the initial Ni content is changed. For further validation, the inductively coupled plasmaoptical emission spectroscopy (ICP-OES) analysis was carried out on the undoped single crystals. The actual composition is identified as Zr 0.995 Ni 1.009 Sn 0.996 with a standard deviation of approximately 1% for each element (Table S4, Supporting Information), agreeing well with the WDX results. Therefore, the lattice parameter and compositional analyses demonstrate the high-quality of the as-grown single crystals with fewer Ni interstitial defects, paving a good foundation for carrying out the ARPES study.
For ARPES experiments, Sb-doped n-type ZrNiSn 0.97 Sb 0.03 single crystals are chosen so that the CB could be observed. The crystals are first oriented along the [110] direction and then cut into bar sharp. To secure a well-ordered cleavage surface of these 3D crystals, a small incision perpendicular to [110] direction is first cut using a 50 µm wire saw ( Figure S5, Supporting Information). With this pre-processing of the crystals, we have reached a high success rate to cleave this 3D crystal, as evidenced by the shiny and flat (110) cleavage surface ( Figure S5b, Supporting Information). The ARPES measurements are thus carried out on the (110) surface, which corresponds to the red plane in the bulk Brillouin zone (Figure 2b). With the photon energy ranging from 60 to 160 eV, we can capture the information of the electronic structure of ZrNiSn in a whole Brillouin zone. The photon energy-dependent Fermi surface map of ZrNiSn 0.97 Sb 0.03 in k y -k z plane is presented in Figure 2c. The data show strong dispersion along k z direction, indicating the bulk electronic band information. The CB at X point is clearly resolved, agreeing with the calculated electronic structure ( Figure 2d). The energy-dependent 3D intensity plot of the photoemission data in k x -k y plane is presented in Figure 2d, which show clear CB and VB.
For further analysis of the intrinsic electronic structure, 2D ARPES intensity plot along Γ-X direction acquired with the photon energy of 125 eV at 17 K is exhibited in Figure 2f. This experimental electronic structure enables us to check whether the Ni in-gap states exist or not. As previously reported by Zeier et al., [25] 5% excess Ni on interstitial defects are expected to produce flat in-gap states within the k x -k y plane. However, such flat bands are not observed in the forbidden gap (Figure 2f), indicating a negligible effect of Ni in-gap states in the studied single crystals. Without the obvious effect of Ni in-gap states, the experimental electronic structure offers a chance to resolve the real E g between CB minimum and VB maximum. To accurately characterize the E g , we consider the energy distribution curves at the Γ and X points ( Figure S6, Supporting Information). The energy distribution curves show a peak at −0.71 eV, corresponding to the VB maximum at Γ point. The intensity peak of the electron pocket is at −0.05 eV, pointing to the CB minimum at X point. As a result, the E g -ARPES of ZrNiSn is derived as 0.66 ± 0.1 eV. The error bar is set by the energy resolution of the ARPES experiment. This unexpectedly large E g_ARPES is approximately two to three times higher than the values previously reported on the polycrystalline samples synthesized by high-temperature technique (as shown in Figure 1a).
The experimental electronic structure from ARPES enables us to directly acquire the electronic structure-related parameters of ZrNiSn, i.e., band effective mass and anisotropic factor, which are important for understanding the origin of high PF in half-Heusler thermoelectric materials. The Fermi surface mapping of ZrNiSn 0.97 Sb 0.03 in the k x -k y plane is presented in Figure 3a. The CB at the X point shows an obvious anisotropy with an ellipsoid shape, which is much flatter along the X-Γ direction (k x axis) than that along the X-U direction (k y axis). To confirm this result, the Fermi surface was further calculated using the first-principles calculations at a carrier concentration of 5 × 10 20 cm −3 , matching the experimental n H of ZrNiSn 0.97 Sb 0.03 ( Figure S7, Supporting Information). Figure 3b shows the calculated electron pocket with the same Brillouin zone setup with Figure 3a, which also exhibits an ellipsoidal Fermi surface. To obtain the band effective mass, ARPES intensity plots along the X-U and X-Γ directions are presented in Figure 3c,d, respectively. The electron pockets are fitted with a parabola (red lines). Along X-U, we obtain E − E F = (−0.05 ± 0.01) + 5 × k y 2 , while along X-Γ, E − E F = (−0.05 ± 0.01) + 0.8 × (k x + 1.06) 2 . According to the formula m* = ћ 2 (∂ 2 E/∂k 2 ) −1 , the derived effective mass along X-U (m t *) and X-Γ (m l *) directions is 0.76 and 4.8 m e , respectively. As a result, the anisotropic factor K (K = m l */m t *) is calculated to be about 6. In comparison, the m l * and m t * from the calculated electronic structure (Figure 2d) are 0.4 and 3.3 m e , respectively, giving a K value of 8.
Combining the results from ARPES and calculations, it is
Adv. Sci. 2020, 7, 1902409 Figure 2. a) Optical image of as-grown single crystals on a 1 × 1 mm 2 grid. b) Brillouin zone with high-symmetry points. In the momentum coordinate, k x -k y is set up within the red plane, while the k y -k z plane in blue. c) Fermi surface intensity plot in the k y -k z plane at k x = 0, acquired with linear horizontal photon with photon energy ranging from 60 to 160 eV. The black lines represent the Brillouin zone in the k y -k z plane. d) Calculated electronic band structure for ZrNiSn. e) 3D intensity plot of the photoemission data, showing the Fermi surface and electronic structure of ZrNiSn, including two electron pockets at X point and a hole pocket at Γ point. f) ARPES intensity plots along Γ-X direction, taken with the photon energy of 125 eV as indicated in (c).
confirmed that the CB of ZrNiSn has a relatively large anisotropic characteristic. Large band anisotropy was also found for the other good thermoelectric materials, [3,4,6,36] such as PbTe (K = 8), SnTe (K = 9), and GeTe (K = 22). Previously, high band degeneracy N v was found contributing to the high performance of half-Heusler compounds. [20] Herein, together with the experimentally confirmed large band anisotropy K, the so-called Fermi surface complexity factor N v K [5] is expected to be high for half-Heusler compounds, which lays the electronic structure origin of their high electrical PF.
Moreover, the density of the state effective mass m d * can be calculated via the expressions: m d * = N v 2/3 m b * and m b * = (m l * × m t * 2 ) 1/3 , where N v is the band degeneracy and equals to 3 for the CB of ZrNiSn. The derived m d * from the ARPES data is 2.9 m e , which shows good consistency with the value of 2.8-3.0 m e calculated from the effective mass model [37] based on the transport data. [19] To crosscheck the bandgap, we performed optical reflectivity measurement on undoped ZrNiSn single crystal at 10 and 300 K. The derived optical conductivity is presented in Figure S8 in the Supporting Information. To extract the indirect E g-op and direct E g from the spectra, we plotted (ε 2 ω 2 ) 1/2 and (ε 2 ω 2 ) 2 versus frequency to estimate the bandgaps, respectively (Figure 4a,b), where ε 2 is the imaginary part of the complex dielectric function. The extrapolations of the linear parts of these spectra intersect the axis of abscissa providing the values of the bandgaps. [38] As a result, an indirect E g_op of 0.45 ± 0.1 eV was derived, which is in agreement with E g_FP , but smaller than that of E g_ARPES . Different experimental techniques generally have different uncertainty of energy resolution, which might explain the deviation of E g from the optical and ARPES measurements. Moreover, a direct bandgap of about 1 eV was also derived for ZrNiSn (Figure 4b), corresponding to the minimum direct bandgap of 0.9 eV at X point from the calculated electronic structure (Figure 2d).
Furthermore, the electrical resistivity ρ of undoped ZrNiSn single crystals above room temperature was measured and shown in Figure 4c. The ρ exhibits a typical semiconducting behavior. The bandgap E g_re is estimated using the high-temperature resistivity data, as shown in the inset of Figure 4c. E g_re of 0.46 eV is obtained for the studied single crystals, which is twice larger than the one obtained from polycrystalline samples by Aliev et al. [17] The derived bandgap from electrical resistivity shows a reasonable agreement with the ones from first-principles calculations, and the ARPES and optical measurements. Therefore, it can be concluded that the low-temperature growth technique used in this work guarantees high-quality ZrNiSn samples with fewer Ni interstitial defects, enabling the manifestation of the unexpectedly large intrinsic bandgap.
The large bandgap is generally desired for high peak zT at elevated temperatures, as it can effectively suppress the thermal excitation of minority carriers and bipolar effect. The comparison of peak zT values for the three famous half-Heusler thermoelectric systems MNiSn, MCoSb, and RFeSb is shown in Figure S9 in the Supporting Information. The zT of MNiSn system peaks between 800 and 1000 K, whereas the zT of MCoSb and RFeSb does not culminate even above 1100 K. The reason for this difference lies in that MNiSn system, synthesized by high-temperature technique, generally has excess Ni interstitial defects and thus shows a smaller E g (0.2-0.3 eV, [21] Figure 1a). In contrast, the E g is generally larger than 0.5 eV for MCoSb and RFeSb systems. [13,14] The above results demonstrate that MNiSn crystals with fewer Ni interstitial defects could be grown with low-temperature technique, which enables the manifestation of the unexpectedly large intrinsic E g (0.5-0.6 eV) in MNiSn. Therefore, a higher peak zT might be achieved at higher temperatures in n-type MNiSn with fewer Ni interstitial defects to match its p-type counterpart (MCoSb and RFeSb).
It is thus interesting to further check the Seebeck coefficient of the as-grown single crystals above room temperature. Due to the small size of single crystals, it is not possible to measure the Seebeck coefficient with commercial ZEM-3 and Linseis LSR-3 systems. Herein, a home-made setup with a two-probe configuration [39] was employed to measure the Seebeck coefficient of the single crystals. It is challenging to get reliable Seebeck coefficient of the undoped crystals due to the large contact resistance, but we succeed in measuring the Seebeck coefficient of heavily doped single crystals. As exhibited in Figure 4d, the absolute Seebeck coefficient of these heavily doped crystals shows a degenerate-semiconductor behavior and keeps increase up to 900 K, which is the upper limit temperature of the homemade setup. It is expected that the Seebeck coefficient should further rise with increasing temperature above 900 K.
MNiSn system with fewer Ni interstitial defects demonstrates a large intrinsic bandgap and thus suppressed bipolar effect. Moreover, higher carrier mobility and lattice thermal Adv. Sci. 2020, 7,1902409 conductivity are also expected due to the lack of point defect scattering. [40] Therefore, distinct from utilizing the Ni interstitial defects to suppress the lattice thermal conductivity, the investigation of the intrinsic electronic structure in this work demonstrates a new direction of half-Heusler thermoelectric research, namely, enhancing the electrical properties by eliminating the intrinsic defects. Some very recent experimental works on Ni-poor TiNiSn system have shown that it is indeed promising to improve the electrical power factor and zT value by reducing Ni content. [40,41] Considering that (Zr,Hf)NiSnbased compounds generally demonstrate higher zT than the TiNiSn system even with excess Ni interstitial defects, it is thus optimistically predicted that higher thermoelectric performance might be achieved in (Zr,Hf)NiSn-based compounds by eliminating the Ni interstitial defects.
In summary, based on the well understanding of processing-structure-property relationships, high-quality undoped and Sb-doped ZrNiSn single crystals with fewer Ni interstitial defects have been grown using the low-temperature technique. High-resolution ARPES experiment was successfully carried out to reveal the intrinsic electronic structure for the first time. An unexpectedly large intrinsic bandgap of 0.66 ± 0.1 eV was found by ARPES, which is approximately two to three times higher than the values reported in previous polycrystalline samples with considerable Ni interstitial defects. Moreover, the anisotropic characteristic of the conduction band of ZrNiSn was directly observed and the experimental effective mass and anisotropic factor were derived from the ARPES study. These results demonstrate a feasible paradigm to investigate the electronic structure of the 3D solid materials by using ARPES and provide new insights into the intrinsic electronic structure of the half-Heusler system which could be helpful to further enhance their thermoelectric performance.
Experimental Section
Single Crystal Growth and Characterization: The undoped ZrNiSn and Sb-doped ZrNiSn 1−y Sb y single crystals were grown using the Sn Flux method. [42] The starting powders of Zr, Ni, Sn, and Sb were mixed together in a molar ratio of 1:1+x:10:y (x = −0.1-0.15, y = 0-0.04). Next, the mixture was sealed in a dry quartz tube under high vacuum. The tube was heated up to 1100 °C in 15 h and further dwelled for 24 h. For crystal growth, the tube was slowly cooled down to 650 °C at a rate of 2 °C h −1 . After the growth process, the liquid Sn flux was removed by either decanting or centrifuging. Some additional Sn on the surface of the crystal was further cleaned by etching in dilute hydrochloric acid. The crystals were checked and oriented at room temperature by a Laue X-ray diffractometer. The phase purity of the crystals was checked using XRD on a Philips X'pert diffractometer with Cu Kα radiation (λ = 1.54184 Å). To study the microstructure and the actual composition, the crystals were first polished and examined using optical microscopy. The scanning electron microscope (SEM) backscattering images were obtained using SEM (JSM7800F, JEOL). Quantitative electron probe microanalysis of the crystals was carried out using an EDX spectroscopy analyzer (Phoenix V 5.29, EDAX) and a WDX spectrometer (Cameca SX 100) using the pure elements as standards. To further confirm the actual composition of ZrNiSn single crystals, ICP-OES was carried out. Three independent weights of approximately 5 mg (exactly weighed in) sample were digested with an acid mixture of 2.75 mL HCl, 0.5 mL HNO 3 , and 50 µL HF in the microwave system MLS-Ethos Plus at 155 °C for 15 min. After being cooled to room temperature, each solution was completely transferred into a volumetric flask (50 mL) and filled up with ultrapure water. All three solutions were analyzed using an Agilent 5100 Adv. Sci. 2020, 7,1902409 direct E g , respectively. c) Electrical resistivity versus temperature for two undoped ZrNiSn single crystals, denoted as S2 and S3, respectively. The inset shows the E g_re estimated using the formula: ρ ≈ exp(E g_re /2k B T). The polycrystalline data are taken from Aliev et al. [17] d) Temperature-dependent Seebeck coefficient for four Sb-doped single crystals denoted as S4 to S7.
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SVDV ICP-OES. The matrix-matched standards for the calibration of the spectrometer were prepared from single-element standards. The Hf content was below the limit of detection (< 100 ppm).
Longitudinal and Hall resistivities were measured by a standard four-probe method using the Physical Property Measurement System (PPMS, Quantum Design). The accuracy of the resistivity measurement was ± 3%. Hall carrier concentration n H was calculated using the equation n H = 1/(eR H ), where e is the unit charge and R H is the Hall coefficient. The carrier mobility µ H was calculated using µ H = R H /ρ. The resistivity above room temperature was measured with a homemade setup using the four-probe method.
Optical Measurement: The optical reflectivity measurements were performed on an undoped ZrNiSn single crystal with a lateral dimension of 2 × 2 mm 2 . The crystal had a polished shiny surface with an orientation along 〈111〉. The optical reflectivity R as a function of frequency ω was measured using a standard method [38] with a Bruker Hyperion microscope attached to a Bruker Vertex 80v Fourier transform spectrometer. Freshly evaporated gold mirrors served as the references. Complex optical conductivity was obtained from R(ω) using Kramers-Kronig transformations. [38] High-frequency extrapolations were made utilizing the X-ray atomic scattering functions. For the extrapolations toward zero frequency, a constant (dielectric) reflectivity was assumed.
ARPES: The ARPES experiments were conducted at the SIS endstation at Swiss Light Source, with a Scienta R4000 analyzer. The photon energy was in the UV region (20-200 eV). The samples with a typical size of about 1 × 1 × 2 mm 3 were cleaved at 15 K in high vacuum chamber, with base vacuum higher than 5 × 10 −11 Torr.
First-Principles Calculations: First-principles calculations on ZrNiSn were performed using the projector augmented wave method, as implemented in the Vienna ab initio simulation package (VASP). [43] The Perdew-Burke-Ernzerhof generalized gradient approximation [44] for the exchange-correlation potential was used for the band structure calculation. The k-mesh of the calculation for the Fermi surface, which was visualized in the XcrySDen package, [45] was 45 × 45 × 45 for the primitive cell. A plane-wave energy cutoff of 520 eV and an energy convergence criterion of 10 −4 eV for self-consistency were adopted. All the atomic positions were relaxed to equilibrium until the calculated Hellmann-Feynman force on each atom was less than 10 −2 eV Å −1 .
Supporting Information
Supporting Information is available from the Wiley Online Library or from the author. | 6,638.8 | 2019-11-06T00:00:00.000 | [
"Materials Science"
] |
Design of a Scaffold Parameter Selection System with Additive Manufacturing for a Biomedical Cell Culture
Open-source 3D printers mean objects can be quickly and efficiently produced. However, design and fabrication parameters need to be optimized to set up the correct printing procedure; a procedure in which the characteristics of the printing materials selected for use can also influence the process. This work focuses on optimizing the printing process of the open-source 3D extruder machine RepRap, which is used to manufacture poly(ε-caprolactone) (PCL) scaffolds for cell culture applications. PCL is a biocompatible polymer that is free of toxic dye and has been used to fabricate scaffolds, i.e., solid structures suitable for 3D cancer cell cultures. Scaffold cell culture has been described as enhancing cancer stem cell (CSC) populations related to tumor chemoresistance and/or their recurrence after chemotherapy. A RepRap BCN3D+ printer and 3 mm PCL wire were used to fabricate circular scaffolds. Design and fabrication parameters were first determined with SolidWorks and Slic3r software and subsequently optimized following a novel sequential flowchart. In the flowchart described here, the parameters were gradually optimized step by step, by taking several measurable variables of the resulting scaffolds into consideration to guarantee high-quality printing. Three deposition angles (45°, 60° and 90°) were fabricated and tested. MCF-7 breast carcinoma cells and NIH/3T3 murine fibroblasts were used to assess scaffold adequacy for 3D cell cultures. The 60° scaffolds were found to be suitable for the purpose. Therefore, PCL scaffolds fabricated via the flowchart optimization with a RepRap 3D printer could be used for 3D cell cultures and may boost CSCs to study new therapeutic treatments for this malignant population. Moreover, the flowchart defined here could represent a standard procedure for non-engineers (i.e., mainly physicians) when manufacturing new culture systems is required.
Introduction
Scaffolds are solid structures usually made of a polymeric material that is used for a wide range of applications. They provide a necessary support for three-dimensional (3D) cell growth, thanks to their biocompatibility and biodegradability [1], and are extremely useful in in vitro 3D cell cultures. Traditional cell culture is applied to two-dimensional (2D) models on flat surfaces, but this methodology is not representative of the cells' physiological environment and usually confers them with less malignancy. The literature has reported that 3D cell culture with scaffolds can increase the cancer stem cell (CSC) population [2][3][4]. CSCs correspond to a small population within the tumor which is resistant to chemotherapy and capable of dividing to form the tumor again after treatment small percentage within the tumor, the population expansion and enrichment described would help in their study and promote further development of therapeutic strategies.
Additive manufacturing (AM) technologies have arisen as a novel set of tools with which to fabricate scaffolds [5,7]. In particular, 3D printers based on fused filament fabrication (FFF) technology are one of the most accessible and simplest options [8]. They are open-source, low-cost machines which usually use thermoplastic materials [9,10] and can easily be modified to improve the quality of the printed 3D products [11]. A variety of biocompatible polymers can be used for scaffold production with FFF. Poly-L-lactic acid (PLA) is a biodegradable thermoplastic aliphatic polyester that has great potential in clinics thanks to its biocompatibility and restorability. Consequently, it is widely used in tissue engineering [12]. Poly(ε-caprolactone) (PCL; Figure 1) is also a biodegradable polyester proven to be biocompatible and toxic-dye-free, but it has a slower degradation rate and different mechanical and physical features. For instance, PCL has a lower melting point (60 °C), reflecting its lower hydrogen bonding and polarity which determine its chemical and molecular behavior. Moreover, PCL does not have any isomers so there are no variances in the melting temperature and biological degradation. Due to these characteristics, its use in tissue engineering, drug delivery, and cell cultures is increasing [2,3,6,13,14]. PCL can be also used as copolymers, such as PCL-collagen and PCL-gelatin, and in combination with other polymers, for example PLA or PEG [13,15]. As scaffold production with 3D printers is a new area, greater effort should be made to determine the optimal parameters for the process [1,6,9]. The processing parameters in question are closely related to the properties of the polymer chosen and the subsequent application intended for the scaffold(s). First, the design parameters determine the architecture of the scaffold and can comprise the filament diameter, the distance between filaments, and the deposition angle [16]. They can also be modified depending on the desired design and application of the scaffold. Second, fabrication parameters control the printing process. These parameters include the extruder and bed temperature, deposition velocity, and layer height, and are closely linked to the material of the polymer and the environment [9,17].
When scaffolds are produced for tissue engineering or regenerative medicine, controlling features, such as pore size, pore shape, or mechanical strength, is mandatory [9,18]. Although there are some studies into the 3D printing of scaffolds based on fused deposition modeling (FDM) [19,20] very few analyze the effects the architecture of the scaffold may have on cell proliferation, and none develop schematic procedures or methods aimed at retaining any knowledge gained. Grémare et al., [21] studied the physicochemical and biological properties of PLA scaffolds produced by 3D printing (FFF). The authors studied four different square pore sizes (0, 150, 200, and 250 um). Results showed that scaffold pore size had negligible effects on their mechanical properties. After three and seven days of human bone marrow stromal cell (HBMSC) culture being applied, the scaffolds exhibited excellent viability and homogeneous distribution regardless of the pore size. Hutmancher et al. [22] studied the mechanical and cell culture response of PCL scaffolds using 61 ± 1% porosity and two matrix architectures. Results showed that five-angle scaffolds had significantly lower stiffness under compression loading than those with a three-angle pattern. Data also revealed that in terms of cell proliferation, while a scaffold with a 0/60/120° lay-down pattern had a higher proliferation rate in the first 2 weeks, the scaffolds with a 0/72/144/36/108° lay-down overtook the three-angle matrix architecture in Weeks 3 and 4. Recently, Rabionet et al. [23] analyzed the effects of tubular scaffold architecture on cell proliferation for vascular applications. Results showed the strong influence the As scaffold production with 3D printers is a new area, greater effort should be made to determine the optimal parameters for the process [1,6,9]. The processing parameters in question are closely related to the properties of the polymer chosen and the subsequent application intended for the scaffold(s). First, the design parameters determine the architecture of the scaffold and can comprise the filament diameter, the distance between filaments, and the deposition angle [16]. They can also be modified depending on the desired design and application of the scaffold. Second, fabrication parameters control the printing process. These parameters include the extruder and bed temperature, deposition velocity, and layer height, and are closely linked to the material of the polymer and the environment [9,17].
When scaffolds are produced for tissue engineering or regenerative medicine, controlling features, such as pore size, pore shape, or mechanical strength, is mandatory [9,18]. Although there are some studies into the 3D printing of scaffolds based on fused deposition modeling (FDM) [19,20] very few analyze the effects the architecture of the scaffold may have on cell proliferation, and none develop schematic procedures or methods aimed at retaining any knowledge gained. Grémare et al., [21] studied the physicochemical and biological properties of PLA scaffolds produced by 3D printing (FFF). The authors studied four different square pore sizes (0, 150, 200, and 250 um). Results showed that scaffold pore size had negligible effects on their mechanical properties. After three and seven days of human bone marrow stromal cell (HBMSC) culture being applied, the scaffolds exhibited excellent viability and homogeneous distribution regardless of the pore size. Hutmancher et al. [22] studied the mechanical and cell culture response of PCL scaffolds using 61 ± 1% porosity and two matrix architectures. Results showed that five-angle scaffolds had significantly lower stiffness under compression loading than those with a three-angle pattern. Data also revealed that in terms of cell proliferation, while a scaffold with a 0/60/120 • lay-down pattern had a higher proliferation rate in the first 2 weeks, the scaffolds with a 0/72/144/36/108 • lay-down overtook the three-angle matrix architecture in Weeks 3 and 4. Recently, Rabionet et al. [23] analyzed the effects of tubular scaffold architecture on cell proliferation for vascular applications. Results showed the strong influence the 3D process parameters have on the scaffold architecture and, subsequently, cell proliferation. Narrow pores produced lower cell proliferation due to the lower oxygen and nutrient exchange.
As the literature has reported, cell proliferation onto a scaffold depends on the material, the architecture, and cell kinetics. Whenever physicians need to work with cells, they require the best scaffolding features to obtain ideal cell culture results. In fact, the main problem was that scaffolds did not provide the same results for different lines of cells when the cells are cultured. When working with cells, physicians have different purposes and goals. For instance, they may want to enrich or treat the cells or to determine the impact a drug is having/has had on the cells. While identical scaffold features do not provide the same results, the cell line does. In fact, each cell line works better with different scaffold features. For this reason, this work aims to optimize the design features and the selection of the manufacturing process parameters when the open-source 3D extruder machine RepRap is utilized. This methodology focuses on manufacturing PCL scaffolds suitable for 3D cancer cell cultures and CSCs expansion as a first step before expanding to other cell lines. Both design and fabrication parameters have been optimized by following a specific flowchart step by step, and checking a measurable variable. In addition, preliminary in vitro experiments were performed to study the impact the scaffold design and fabrication have on the efficiency physicians require from the 3D cell culture and the scaffolds produced. Therefore, a sample application for the mass production of PCL scaffolds using a low-cost machine could be used to improve cancer stem cell research. The flowchart developed here provides a novel methodology to adjust process parameters to print micrometric scaffolds suitable for three-dimensional cell culture because, as is demonstrated, each cell line required different scaffold features. Hence, an optimization diagram could represent a common procedure which could be used by non-engineering professionals when a 3D cell culture protocol has to be established de novo. Physicians working with 3D cell cultures usually need some kind of rules or guidelines to follow to set up the cell culture. This paper's contribution is the methodology required to set up the 3D printing technology for a new line of cell culture by first defining the design characteristics and then the parameter selection for the manufacturing process. This paper does not contribute to the knowledge about PCLs or the 3D printing machine itself, but instead provides a methodology for physicians. The contribution is the method and steps to follow when scaffolds need to be manufactured for a new cell line.
Material
A 3 mm poly(ε-caprollactone) (PCL) wire (Perstorp, Malmö, Sweden) with a density of 1145 Kg/m 3 and a molecular weight of 80,000 g/mol, was used to fabricate circular scaffolds 19 mm in diameter (Corning Life Sciences, New York, NY, USA). PCL is a biodegradable polyester with a low melting point (60 • C) and a glass transition of about −60 • C.
Three-Dimensional Printer Machine
An open-source and modular RepRap BCN 3D+ printer (CIM, Barcelona, Spain) was used to produce three-dimensional scaffolds ( Figure 2). This printer was selected because of its capacity to allow a user to optimize its parameters as they see fit. It uses fused filament fabrication (FFF). First, the filament was unwound from a roll of wire and supplied to the extruder. Then, the material was extruded through the nozzle using different temperatures depending on the value being tested. Finally, the printed filament was deposited onto a heated platform (also known as a bed).
Scaffold Design and Additive Manufacturing
SolidWorks (Waltham, Massachusetts, Estats Units) was the computer-aided design (CAD) software chosen for the scaffolds' design. The stereolithography (STL) file formats the designs that were transferred to the computer-aided manufacturing (CAM) software Slic3r to establish the fabrication parameters. This software, while maintaining the SolidWorks design, generated G-code files which can control and regulate the machine to obtain the correctly-printed scaffolds. Scaffold design features were selected based on other research work focused on tissue engineering which had similar goals to this work, i.e., cell enrichment or treatment, or drug delivery applicability. The features are described in Table 1. Previous screening experiments were carried out to adjust the range of the scaffold design features.
Process Parameter Optimization
The fabrication parameters and design feature values used for the experimental setup are shown in Table 1. A wide range of characteristics and parameter values were selected from the literature as the screening values with which to start. A wide range of processing parameters were selected based on the research work focused on tissue engineering with similar goals to ours, i.e., the enrichment or treatment of cells of the applicability for drug delivery. Thus, previous screening experiments were carried out to adjust the range of the processing parameters for the scaffolds. By following a sequential flowchart (Figure 3), the optimal tested value to be selected for each parameter was determined. Optimization was first performed using a generic geometrical form. A fixed circular
Scaffold Design and Additive Manufacturing
SolidWorks (Waltham, Massachusetts, Estats Units) was the computer-aided design (CAD) software chosen for the scaffolds' design. The stereolithography (STL) file formats the designs that were transferred to the computer-aided manufacturing (CAM) software Slic3r to establish the fabrication parameters. This software, while maintaining the SolidWorks design, generated G-code files which can control and regulate the machine to obtain the correctly-printed scaffolds. Scaffold design features were selected based on other research work focused on tissue engineering which had similar goals to this work, i.e., cell enrichment or treatment, or drug delivery applicability. The features are described in Table 1. Previous screening experiments were carried out to adjust the range of the scaffold design features.
Process Parameter Optimization
The fabrication parameters and design feature values used for the experimental setup are shown in Table 1. A wide range of characteristics and parameter values were selected from the literature as the screening values with which to start. A wide range of processing parameters were selected based on the research work focused on tissue engineering with similar goals to ours, i.e., the enrichment or treatment of cells of the applicability for drug delivery. Thus, previous screening experiments were carried out to adjust the range of the processing parameters for the scaffolds. By following a sequential flowchart (Figure 3), the optimal tested value to be selected for each parameter was determined. Optimization was first performed using a generic geometrical form. A fixed circular scaffold design was used as the control pattern: 0.4 mm in diameter and layer height extruded filament, 1 mm distance between filaments, 90 • deposition angle, 19 mm in diameter scaffold, and eight scaffold layers. As optimization progressed, design feature values were replaced by the optimal ones, resulting in a final scaffold design suitable for three-dimensional cancer cell culture. Furthermore, the cancer cell culture is now more like real physiological conditions, including an enrichment of the CSCs' subpopulation. Each step on the flowchart presented in Figure 3 included parameter testing and a physical scaffold variable measurement to assess the quality of the printing. Thus, optimal parameter values were sequentially determined and considering the final application as the optimal function to be reached. Physical variables, such as printed filament diameter, first layer height, and real distance between filaments, were measured using an inverted optical microscope (Nikon, Tokyo, Japan). Printed structures, as well as a nanometric ruler, were placed on the stage. Binomial variables (material adhesion, adhesion of contiguous filaments, printing quality such as the absence of blobs etc.) were assessed by sight. Finally, the cell efficiency of the different deposition angles was evaluated through a three-dimensional breast cancer cell culture to validate the parameters selected. Breast CSCs were used because their expansion would represent a new opportunity to develop new treatments against cancer stem features related to cancer relapse and metastasis.
Scaffold Sterilization
Scaffolds were sterilized following a previously-described methodology [2,24]. Meshes were submerged in a 70% ethanol/water solution overnight, washed with PBS (Gibco, Walthman, MA, USA), and finally exposed to UV light for 30 min. Only the top side was irradiated because PCL has a semi-transparent behavior when exposed to UV wavelengths [25]. This sterilization method was followed to avoid any changes in the stents' final properties [18].
Three-Dimensional Cell Culture in Scaffolds
Scaffolds were designed by considering their subsequent use in regular 12-well cell culture microplates. First, cells were detached from the original cell culture microplate and counted using the trypan blue dye method. As viable cells possess an intact membrane, trypan blue cannot penetrate them, but as dead cells have an altered membrane the dye can penetrate them. Therefore, trypan blue was added in a cell sample and cell viability was counted using a Neubauber Chamber (Marienfeld-Superior, Lauda-Königshofen, Germany) and an inverted optical microscope. A total of 100,000 cells (MCF-7) or 40,000 (NIH/3T3) in 250 µL cell suspension were placed onto the center of the scaffolds' surface to allow cell attachment. After 3 h of incubation, 1.5 mL of fresh medium was added to cover the scaffold and the cells were incubated for 72 h. Then, the scaffold was placed in a new well to quantify only the cells attached. It was washed with PBS and 1 mL of trypsin was added. After incubation, 2.5 mL of fresh medium was added, and the cell suspension was collected and centrifuged at 1500 rpm for 5 min. Finally, the supernatant was discarded, and the cells were re-suspended and counted.
Statistical Analysis
Results were collected from at least six independent experiments. All data are expressed as mean ± standard error (SE). Data were analyzed by Student's t test.
Results: Scaffolds Production
Following the method developed, experimental work was first carried out to find the best way to produce scaffolds which can sustain cell cultures. Sequential work was done to set scaffold design features and manufacturing process parameters.
Optimization of Process Parameters
Processing parameters were optimized to achieve high quality scaffold printing for cell culture application. Thus, different physical scaffold variables were measured to ensure the correct fit between the computer design and the printed scaffold. The processing parameters included both fabrication and design parameters as shown in the "Experimental Setup" section (Table 1). Processing parameters were chosen according to the literature and the state-of-art [9,11,16,17]. However, the process optimization methodology explained here, based on a sequential flowchart (Figure 3), is both innovative and unique.
Experiments were initially carried out with a generic scaffold design (see Section 2.4 "Methods") to set the fabrication parameters and then adjusted to the design parameters required to produce the scaffolds.
Fabrication parameters (extruder and bed temperature, deposition velocity, and layer height) were introduced with Slic3r software. These parameters are related to the characteristics of the polymeric material (mainly PCL) and the printing process. However, different values were tested for the parameters (by checking the measurable variable mentioned in Table 1) in order to meet scaffold manufacturing requirements.
Once the polymeric material and its fabrication parameters had been characterized and set, design features were subsequently established using the SolidWorks 3D software. Parameters, such as filament diameter, distance between filaments, and deposition angle, were tested. These are related to the three-dimensional design of the scaffold and the effect they have on the cancer cell culture.
First, to determine the optimal fabrication parameters, a fixed scaffold design was established as a control pattern: 90 • deposition angle, 0.4 mm in diameter filament and 1 mm distance between filaments. This enabled us to do printings with the same design, but different fabrication parameters, to find the optimal ones. Later, as the design parameters were optimized, they were replaced.
Following the flowchart defined in Figure 3, all the parameters were characterized and selected sequentially to obtain the appropriate setup for producing 3D-printed scaffolds. The optimization of each process parameter is described in the following sections.
Extruder Temperature
Poly(ε-caprolactone) was chosen as the polymer to work with because of its compatibility with cell cultures. PCL has a low melting point (60 • C). To achieve enough malleability and considering there is some heat dissipation, higher temperatures were also tested to find the optimal value (Table 1). A fixed scaffold design described in the Methods section was printed. Then, the printed filament diameter was measured as a physical variable. Low extruder temperatures (65-80 • C) could not melt the material enough, thus the amount of the extruded material was low. As a consequence, the printed filament diameter was smaller than the one designed (0.4 mm). High temperatures (90 • C) melt the polymer excessively and also increase the diameter of the filament due to flattening and some blobs being produced. Therefore, the optimal extruder temperature was established at 85 • C. The printed filament diameter was 0.39 ± 0.05 mm.
Bed Temperature
To set the optimal bed temperature, a generic geometrical scaffold design was printed, and two different measurable variables were evaluated. Material adhesion was assessed as a binomial variable (yes/no), firstly testing the lowest temperature (25 • C, Table 1). If the printed material had not adhered enough to the surface (no), another printing was performed, this time with a higher bed temperature. Once the material had adhered to the surface (yes), the first layer height was then measured. Bed temperatures ranging from 25 to 33 • C gave a non-adherent first layer scaffold. In addition, much higher temperatures (37 • C) melt the material excessively, flattening the filament and decreasing the height of the first layer (lower than the 0.4 mm designed one). A 35 • C bed temperature was considered optimal as this allowed first layer adhesion and the filaments were not flattened. Their first layer height was 0.37 ± 0.07 mm.
Deposition Velocity
The goal with this parameter was to find a high deposition velocity without forgetting the quality of the printed scaffold. The printed filament diameter was chosen as the tangible variable with which to analyze the impact this parameter has on the scaffold. The optimal deposition velocity was established as being 10 mm/s. The filament diameter was 0.42 ± 0.05 mm. When the speed was faster (20 and 30 mm/s) the material did not have enough time to deposit itself on the surface, resulting in smaller filament diameter or sometimes even discontinuous filament production.
Filament Diameter
At this point, the diameter of the printed filament deposited on the collector was analyzed. Extrusion and deposition velocity can exert a direct influence on fiber morphology. Therefore, once he manufacturing velocity had been fixed, the diameter of the extruded filament was evaluated next. Three different design filament diameters were tested: 0.175, 0.3, and 0.5 mm. To ensure the filaments remained tangent along the vertical axis, the printer's layer height was adjusted to each design filament diameter. Diameters that were too large caused the adhesion of two contiguous filaments, favored by their proximity and elevated temperature. For this reason, the first variable studied was the possible adhesion of contiguous filaments, such as a binomial variable (yes/no). Thus, only the values that did not cause the adhesion of two filaments in the same layer were selected to continue the analysis (0.175 and 0.3 mm). The second measured variable was the printed filament diameter. A design diameter of 0.175 mm caused erratic printing because the amount of material was too low to form a linear filament. The final value tested, 0.3 mm, was found to be optimal as it gave a printed filament diameter of 0.31 ± 0.02 mm. The established filament diameter value also determined the thickness of each layer. The scaffolds were manufactured with eight layers, so the final thickness of the scaffolds was 2.4 mm.
Layer Height
Layer height is defined as the distance between two connected layers along the Z axis. Since all layers are designed and printed on top of each other, this parameter was determined by the printed filament diameter. For this reason, the filament diameter, although being a design parameter, was established before finishing, optimizing the fabrication parameters ( Figure 3). In some cases, the deposited material tends to flatten out and so the printed height is lower. At that point, two different values were analyzed: 0.3 mm (the whole filament diameter) and 0.28 mm (because of a certain flattening) and the quality of the printing recorded (absence of blobs). In this case, 0.3 mm was found to be the optimal layer height for our design as flattening, due to high temperatures, did not occur. When evaluating smaller established heights, the printing process produced blobs.
The absence of filament flattening may be attributed to the relatively low extruder temperature used, (85 • C, see Section 2.1) which can be considered low compared with other biocompatible polymers used in 3D printing, such as PLA [9,12].
Distance between Filaments
This is a key parameter because it affects the pore size of the scaffold [9]. This design parameter consists of the shortest distance between the axis of two filaments located within the same layer. We were interested in achieving small pore sizes, thus, we focused on the testing small distances (0.5, 0.7, 1 mm). Nevertheless, small distances between filaments may be problematic if two contiguous filaments join. For this reason, the real distance between filaments was measured to take into account whether this value matched that of the one expected (designed).
Distances of 0.7 and 1 mm gave no filament joining, so real distances were higher than 0. Within these values, the smallest value was chosen (0.7 mm). Taking into account this parameter and the optimal filament diameter previously established, the distance between the outer parts of two contiguous filaments was, consequently, 0.4 mm (Figure 4).
Materials 2018, 10, x FOR PEER REVIEW 9 of 14 filaments join. For this reason, the real distance between filaments was measured to take into account whether this value matched that of the one expected (designed). Distances of 0.7 and 1 mm gave no filament joining, so real distances were higher than 0. Within these values, the smallest value was chosen (0.7 mm). Taking into account this parameter and the optimal filament diameter previously established, the distance between the outer parts of two contiguous filaments was, consequently, 0.4 mm (Figure 4).
Deposition Angle
Once all previous parameters were optimized, three different scaffolds with different deposition angles were designed and manufactured, thus obtaining different pore characteristics, which may influence cell attachment and growth ( Table 2). As high-quality printings for all three designs were achieved, it was agreed to test the adequacy for 3D cell culture with all three designs.
An MCF-7 breast carcinoma cell line was used to preliminarily evaluate scaffold ability in terms of three-dimensional cell culture. MCF-7 cells were seeded onto scaffolds and cultivated for 72 h. Then, attached cells were trypsinized and counted. No cells were counted on the 90° scaffolds. Under an optical microscope, no cells were observed on the filament, but rather attached at the bottom of the microplate well (Figure 5a), which is in agreement with cell counting. Scaffolds of 45° showed a subtle cell adhesion of 3.52 ± 1.16% when compared with the 2D control. We subsequently tested 60° scaffolds, which showed an increased cell adhesion of 26.50 ± 10.98%. In both cases, cells were previously observed at the well bottom and attached to the scaffold filaments, with the last ones are indicated by white arrows (Figure 5b,c, respectively).
Deposition Angle
Once all previous parameters were optimized, three different scaffolds with different deposition angles were designed and manufactured, thus obtaining different pore characteristics, which may influence cell attachment and growth ( Table 2). As high-quality printings for all three designs were achieved, it was agreed to test the adequacy for 3D cell culture with all three designs.
An MCF-7 breast carcinoma cell line was used to preliminarily evaluate scaffold ability in terms of three-dimensional cell culture. MCF-7 cells were seeded onto scaffolds and cultivated for 72 h. Then, attached cells were trypsinized and counted. No cells were counted on the 90 • scaffolds. Under an optical microscope, no cells were observed on the filament, but rather attached at the bottom of the microplate well (Figure 5a), which is in agreement with cell counting. Scaffolds of 45 • showed a subtle cell adhesion of 3.52 ± 1.16% when compared with the 2D control. We subsequently tested 60 • scaffolds, which showed an increased cell adhesion of 26.50 ± 10.98%. In both cases, cells were previously observed at the well bottom and attached to the scaffold filaments, with the last ones are indicated by white arrows (Figure 5b,c, respectively). Then, scaffolds were also evaluated through fibroblast cell cultures. Murine NIH/3T3 fibroblasts were seeded onto the three designs during 72 h and cell proliferation was assessed. In this case, fibroblasts adhered to all three scaffold models ( Figure 6), with the highest cell proliferation value being found on the 90° design (56.30 ± 5.03% compared to the 2D control). The other two architectures exhibited slightly smaller values. For instance, 60° scaffolds presented a 49.52 ± 5.62% cell growth and 45° models, 39.11 ± 8.12%, compared to the monolayer culture. Then, scaffolds were also evaluated through fibroblast cell cultures. Murine NIH/3T3 fibroblasts were seeded onto the three designs during 72 h and cell proliferation was assessed. In this case, fibroblasts adhered to all three scaffold models ( Figure 6), with the highest cell proliferation value being found on the 90° design (56.30 ± 5.03% compared to the 2D control). The other two architectures exhibited slightly smaller values. For instance, 60° scaffolds presented a 49.52 ± 5.62% cell growth and 45° models, 39.11 ± 8.12%, compared to the monolayer culture. Then, scaffolds were also evaluated through fibroblast cell cultures. Murine NIH/3T3 fibroblasts were seeded onto the three designs during 72 h and cell proliferation was assessed. In this case, fibroblasts adhered to all three scaffold models ( Figure 6), with the highest cell proliferation value being found on the 90° design (56.30 ± 5.03% compared to the 2D control). The other two architectures exhibited slightly smaller values. For instance, 60° scaffolds presented a 49.52 ± 5.62% cell growth and 45° models, 39.11 ± 8.12%, compared to the monolayer culture. Then, scaffolds were also evaluated through fibroblast cell cultures. Murine NIH/3T3 fibroblasts were seeded onto the three designs during 72 h and cell proliferation was assessed. In this case, fibroblasts adhered to all three scaffold models ( Figure 6), with the highest cell proliferation value being found on the 90° design (56.30 ± 5.03% compared to the 2D control). The other two architectures exhibited slightly smaller values. For instance, 60° scaffolds presented a 49.52 ± 5.62% cell growth and 45° models, 39.11 ± 8.12%, compared to the monolayer culture. Then, scaffolds were also evaluated through fibroblast cell cultures. Murine NIH/3T3 fibroblasts were seeded onto the three designs during 72 h and cell proliferation was assessed. In this case, fibroblasts adhered to all three scaffold models ( Figure 6), with the highest cell proliferation value being found on the 90 • design (56.30 ± 5.03% compared to the 2D control). The other two architectures exhibited slightly smaller values. For instance, 60 • scaffolds presented a 49.52 ± 5.62% cell growth and 45 • models, 39.11 ± 8.12%, compared to the monolayer culture.
Optimal Process Parameters Values
After the optimization experiments and basic cell culture tests had been completed, the optimal processing parameters for PCL scaffold printing were established (see Table 3) once the methodology had been applied to set each optimal parameter for cell cultures and for future experiments with CSCs culture enrichment using PCL scaffolds.
Discussion
In this work, a methodology to optimize the processing parameters for PCL scaffold production using a RepRap 3D printer has been developed. By using an optimization flowchart, PCL scaffolds suitable for cell culture were manufactured (Figure 3). The optimal processing parameters determined are closely related to those defined in other studies using the same technology and material. Domingos et al., (2013) set up an 80 °C printing temperature, 10 mm/s velocity, an approximately 0.3 mm filament diameter and a layer height of 0.28 mm [15]. A previous study by the same research group used an extrusion temperature of 70 °C and a speed of 8 mm/s [1]. These small variations support the idea of using a single, common methodology ( Figure 3) to optimize the processing parameters. Compared with previous work in the literature, the flowchart provided here makes it easier to adjust scaffold design features and processing parameters according to cell line characteristics. Several case studies were run to validate the flowchart depicted in Figure 3. Results
Optimal Process Parameters Values
After the optimization experiments and basic cell culture tests had been completed, the optimal processing parameters for PCL scaffold printing were established (see Table 3) once the methodology had been applied to set each optimal parameter for cell cultures and for future experiments with CSCs culture enrichment using PCL scaffolds.
Discussion
In this work, a methodology to optimize the processing parameters for PCL scaffold production using a RepRap 3D printer has been developed. By using an optimization flowchart, PCL scaffolds suitable for cell culture were manufactured (Figure 3). The optimal processing parameters determined are closely related to those defined in other studies using the same technology and material. Domingos et al., (2013) set up an 80 • C printing temperature, 10 mm/s velocity, an approximately 0.3 mm filament diameter and a layer height of 0.28 mm [15]. A previous study by the same research group used an extrusion temperature of 70 • C and a speed of 8 mm/s [1]. These small variations support the idea of using a single, common methodology ( Figure 3) to optimize the processing parameters. Compared with previous work in the literature, the flowchart provided here makes it easier to adjust scaffold design features and processing parameters according to cell line characteristics. Several case studies were run to validate the flowchart depicted in Figure 3. Results show how cell culture is improved by using scaffolds which allow cell cultures to be created in 3D conditions and optimized based on the cells' features. In addition, process parameters were also evaluated using cell culture experiments. All scaffold culture experiments presented sterility resulting from the sterilization procedure described here. Both 60 • and 45 • scaffolds showed adequate design parameters for the MCF-7 cell cultures. In particular, the 60 • scaffold design displayed the highest percentage of cell attachment, and exhibited good biocompatibility for the MCF-7 breast cancer cells. In contrast, the NIH/3T3 fibroblast cells presented a more homogeneous growth along the three scaffold designs. However, the 90 • scaffold showed the highest cell proliferation value. Therefore, different kinds of cells may prefer different scaffold architectures, further demonstrating the need of a common procedure to find the optimal values. Moreover, a tumor and a non-tumor cell line were tested, showing the flexibility of the flowchart described here.
Three-dimensional cell culture on scaffolds may also be improved by other fabricationindependent parameters such as polarity of cell culture plates, culture media and time [26], as well as different cell culture types, including a dynamic model [27]. This optimization will be the focus of further studies as we attempt to improve cell attachment percentages. Furthermore, CSC population enrichment by cell culture on scaffolds will be evaluated using different approaches.
To date, most of the work related to scaffold production focuses on optimizing design features and forgets about improving fabrication parameters [1,9,16]. In this work, a flowchart to optimize the parameters of the whole process has been proposed ( Figure 3) to help with their selection. In addition, this methodology may be further used to set up scaffold manufacturing (both the design features and the fabrication parameters) when using a RepRap 3D printer or any other AM technologies and/or materials.
Conclusions
In this work, the design features and fabrication parameters of scaffolds and the RepRap 3D printer were optimized to produce PCL scaffolds suitable for three-dimensional cell cultures. The optimization was performed following a detailed and unidirectional flowchart, thus providing some procedural guidelines with great potential for other popular manufacturing technologies and materials. The contribution of this paper is for scaffolds made with PCL materials. However, this experiment was only carried out to validate the methodology developed as a valuable method for future cell cultures. Often, physicians work with 2D cell cultures, but, as seen here, 3D cell cultures appear to be good method of improving cell culture enrichment. Furthermore, as the design features and manufacturing parameters need to be set for the different cell lines used each time, this methodology will help physicians and other operators to do just that.
Moreover, the scaffolds produced were proven to allow cell attachment and cell growth. The 60 • scaffold design mainly worked for the MCF-7 cells and the 90 • for the NIH/3T3 fibroblasts. Three-dimensional cell cultures with PCL scaffolds fabricated with a 3D printer offer both researchers and clinics a set of novel applications for the future. The flowchart developed represents a new tool with which to quickly manufacture scaffolds for a wide range of applications, including cell cultures and tissue engineering. For instance, the use of 3D cell cultures can boost CSC populations to study new therapeutic treatment. | 8,776.6 | 2018-08-01T00:00:00.000 | [
"Engineering",
"Materials Science",
"Medicine"
] |
Susceptibility of Fat Tissue to SARS-CoV-2 Infection in Female hACE2 Mouse Model
The coronavirus disease (COVID-19) is a highly contagious viral illness caused by severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2). COVID-19 has had a catastrophic effect globally causing millions of deaths worldwide and causing long-lasting health complications in COVID-19 survivors. Recent studies including ours have highlighted that adipose tissue can act as a reservoir where SARS-CoV-2 can persist and cause long-term health problems. Here, we evaluated the effect of SARS-CoV-2 infection on adipose tissue physiology and the pathogenesis of fat loss in a murine COVID-19 model using humanized angiotensin-converting enzyme 2 (hACE2) mice. Since epidemiological studies reported a higher mortality rate of COVID-19 in males than in females, we examined hACE2 mice of both sexes and performed a comparative analysis. Our study revealed for the first time that: (a) viral loads in adipose tissue and the lungs differ between males and females in hACE2 mice; (b) an inverse relationship exists between the viral loads in the lungs and adipose tissue, and it differs between males and females; and (c) CoV-2 infection alters immune signaling and cell death signaling differently in SARS-CoV-2 infected male and female mice. Overall, our data suggest that adipose tissue and loss of fat cells could play important roles in determining susceptibility to CoV-2 infection in a sex-dependent manner.
Introduction
COVID-19 is a viral respiratory illness, caused by severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) [1]. It causes debilitating disease manifestations in many infected people and increases mortality in people with comorbidities, including metabolic disorders and heart diseases [2][3][4][5][6][7][8]. The causes of death in COVID-19 patients include cardiomyopathy, stroke, cardiac arrest, sepsis, and organ failure [9][10][11][12][13][14]. At least 50% of COVID-19 survivors are known to face lingering health issues, which include a racing heartbeat, shortness of breath, achy joints, and damage to the heart, lungs, kidney, and brain [15,16]. A recent meta-analysis review that included 47,910 patients (age 17-87 years) estimated the prevalence of 55 long-term post-COVID-19 effects, where 58% of patients suffer from fatigue, 12% of which is due to significant weight loss [17]. Other clinical reports suggest that the post-COVID-19 stage is associated with acute (30%) and chronic weight loss (56%) and malnutrition [18]. Loss of body weight is linked with body fat mass and the pathophysiology of fat cells. Adipocytes, also known as fat cells, regulate inflammatory signaling and immune response [19][20][21][22][23][24]. It is well known that body fat levels and distribution patterns differ between the sexes and races [25][26][27], which may influence the susceptibility to SARS-CoV-2 infection, COVID-19-associated symptoms, and side effects. Importantly, recent studies have shown that SARS-CoV-2 infects adipose tissue [28,29]. In the present pilot study, we investigated the effect of SARS-CoV-2 infection on adipose tissue physiology and the pathogenesis of fat loss in a murine model of COVID-19 using humanized angiotensin-converting enzyme 2 (hACE2) mice. We used both male and female hACE2 mice intra-nasally infected with SARS-CoV-2. We demonstrated that CoV-2 infects adipose tissue and persists around the lipid droplets in white adipose tissue (WAT) of CoV-2-infected mice 10 days post infection (DPI). Our studies revealed that in male and female mice, CoV-2 infection differently affects adipose tissue and regulates immune signaling. Thus, the alterations in adipose tissue metabolic and immunologic functions may affect the whole-body immune and metabolic homeostasis differently in males and females during acute COVID-19 illness and the post-COVID-19 phase. These data may help explain the higher COVID-19 susceptibility in males compared to females.
Results
Earlier, we demonstrated that SARS-CoV-2 infection alters pulmonary pathology in hACE2 mice differently in males and females [30]. In particular, we showed a significantly increased viral load and infiltration of immune cells in the lungs of infected male mice compared to female mice at 10 DPI [30]. However, both male and female mice showed decreased body weight compared to control mice. Our earlier studies suggest that decreased body weight is likely caused by a loss of body fat mass [30]. Therefore, we investigated the role of adipose tissue in CoV-2 infection using white adipose tissue (WAT) of infected and uninfected control mice (10 DPI) as detailed in the Materials and Methods section. To investigate the pathological effects of SARS-CoV-2 infection in the WAT of hACE2 mice, we performed histological and biochemical analyses of WAT samples at 10 DPI. Age and sex-matched uninfected mice served as controls. We used n = 8 mice/group (4 uninfected and 4 CoV-2 infected) for both sexes. We observed no mortality during CoV-2 infection in mice up to and including 10 DPI. However, the histological analysis of WAT samples has revealed a significant difference in their pathology between the sexes. Therefore, we analyzed all data separately for males and females as presented below.
SARS-CoV-2 Infection Alters Adipose Tissue Morphology Differently in Male and Female hACE2 Mice
Histological analysis of WAT was performed using H&E ( Figure 1a) and Massontrichrome (Figure 1b) stained sections as described in Materials and Methods. Microscopic analysis of the histological sections of WAT demonstrated significantly increased levels of infiltrating immune cells, loss of lipid droplets, and evidence of increased fibrosis in CoV-2 infected hACE2 mice compared to uninfected mice ( Figure 1). Between uninfected male and female mice, the size of adipocytes was relatively larger in females ( Figure 1a). However, female mice lost a significant amount of body fat compared to males during CoV-2 infection (Figure 1a) [31,32]. We observed increased fibrosis in adipose tissue in infected mice compared to uninfected mice (Supplemental Figure S2). These data suggest that adipose tissue undergoes significant morphological changes, including increased immune cell infiltration and loss of lipid droplets, which can alter the local and systemic immune and metabolic homeostasis during CoV-2 infection.
Sex Differences in the Tissue CoV-2 Tropism in the Lungs and Visceral Fat Pads
ACE2 protein is a well-recognized receptor for CoV-2 entry into the host cell [33,34]. Earlier we showed by Western blotting that CoV-2 infection increases the expression levels of ACE2 protein in the lungs of hACE2 mice [30]. The levels of ACE2 were significantly higher in the lungs of both male (p ≤ 0.0001) and female (p ≤ 0.01) mice infected with SARS-CoV-2 compared to sex-matched uninfected (control) mice [30]. Here, we analyzed whether CoV-2 infection also alters the levels of ACE2 in WAT. In WAT, the levels of ACE2 were significantly higher in male (p < 0.05) CoV-2 infected mice compared to sex-matched control mice (Figure 2a). We analyzed the viral loads in the lung and WAT by qPCR analysis. Lung viral loads were significantly greater in male CoV-2-infected mice compared to female CoV-2-infected mice (Figure 2b), which may be due to increased ACE2 levels in male mice [30]. However, qPCR analysis demonstrated significantly higher levels of viral load in the WAT of female CoV-2 infected mice (64-fold, p ≤ 0.005) compared to male CoV-2 infected mice, although the levels of ACE2 were not significantly increased (Figure 2c). We also performed immunohistochemistry (IHC) analysis of SARS-CoV-2 using a monoclonal antibody against the SARS-CoV-2 nucleocapsid protein, which demonstrated the presence of SARS-CoV-2 nucleocapsid protein in adipose tissue around the lipid droplets in infected mice ( Figure 2d). These data demonstrate that: (i) CoV-2 infection alters ACE2 levels and viral loads differently in male and female mice; (ii) SARS-CoV-2 infects and persists in adipose tissue; (iii) adipose tissue in females may act as a sink/reservoir for CoV-2; and (iv) an inverse relationship exists between the viral loads in the lungs and adipose tissue.
Sex Differences in the Tissue CoV-2 Tropism in the Lungs and Visceral Fat Pads
ACE2 protein is a well-recognized receptor for CoV-2 entry into the host cell [33,34]. Earlier we showed by Western blotting that CoV-2 infection increases the expression levels of ACE2 protein in the lungs of hACE2 mice [30]. The levels of ACE2 were significantly higher in the lungs of both male (p ≤ 0.0001) and female (p ≤ 0.01) mice infected with SARS-CoV-2 compared to sex-matched uninfected (control) mice [30]. Here, we analyzed whether CoV-2 infection also alters the levels of ACE2 in WAT. In WAT, the levels of ACE2 were significantly higher in male (p < 0.05) CoV-2 infected mice compared to sexmatched control mice (Figure 2a). We analyzed the viral loads in the lung and WAT by qPCR analysis. Lung viral loads were significantly greater in male CoV-2-infected mice compared to female CoV-2-infected mice (Figure 2b), which may be due to increased ACE2 levels in male mice [30]. However, qPCR analysis demonstrated significantly higher levels of viral load in the WAT of female CoV-2 infected mice (64-fold, p ≤ 0.005) compared to male CoV-2 infected mice, although the levels of ACE2 were not significantly increased (Figure 2c). We also performed immunohistochemistry (IHC) analysis of SARS-CoV-2 using a monoclonal antibody against the SARS-CoV-2 nucleocapsid protein, which demonstrated the presence of SARS-CoV-2 nucleocapsid protein in adipose tissue around the lipid droplets in infected mice ( Figure 2d). These data demonstrate that: (i) CoV-2 infection alters ACE2 levels and viral loads differently in male and female mice; (ii) SARS-CoV-2 infects and persists in adipose tissue; (iii) adipose tissue in females may act as a sink/reservoir for CoV-2; and (iv) an inverse relationship exists between the viral loads in the lungs and adipose tissue.
SARS-CoV-2 Infection Alters Immune Signaling in the Adipose Tissue Differently in Male and Female hACE2 Mice
Immunoblot analysis of WAT lysates demonstrated significant differences in the protein levels of immune cell markers indicating altered levels of CD4 + cells CD8 + cells and F4/80 + cells; and inflammatory cytokines such as TNFα, IL-6, and IL-10 between the sexes during CoV-2 infection ( Figure 3). Uninfected female mice showed significantly lower levels of resident CD4 + cells (p < 0.05) and CD8 + cells (p < 0.05) compared to uninfected male mice ( Figure 3a). CoV-2 infection significantly increased the infiltration of CD4 + and CD8 + cells in WAT in both males (p < 0.05 and p < 0.005, respectively) and females (p < 0.0001 and p < 0.0001, respectively) compared to their respective sex-matched uninfected mice. The levels of F4/80 + cells in WAT were significantly elevated (p < 0.01) in the WAT of CoV-2 infected mice compared to uninfected mice, irrespective of their sex ( Figure 3a). Overall, the levels of CD4 + cells and CD8 + cells) were significantly increased (p < 0.0001) in the WAT of female CoV-2 mice compared to male CoV-2 mice.
SARS-CoV-2 Infection Alters Immune Signaling in the Adipose Tissue Differently in Male and Female hACE2 Mice
Immunoblot analysis of WAT lysates demonstrated significant differences in the protein levels of immune cell markers indicating altered levels of CD4 + cells CD8 + cells and F4/80 + cells; and inflammatory cytokines such as TNFα, IL-6, and IL-10 between the sexes during CoV-2 infection ( Figure 3). Uninfected female mice showed significantly lower levels of resident CD4 + cells (p < 0.05) and CD8 + cells (p < 0.05) compared to uninfected male mice (Figure 3a). CoV-2 infection significantly increased the infiltration of CD4 + and CD8 + cells in WAT in both males (p < 0.05 and p < 0.005, respectively) and females (p < 0.0001 and p < 0.0001, respectively) compared to their respective sex-matched uninfected mice. The levels of F4/80 + cells in WAT were significantly elevated (p < 0.01) in the WAT of CoV-2 infected mice compared to uninfected mice, irrespective of their sex (Figure 3a). Overall, the levels of CD4 + cells and CD8 + cells) were significantly increased (p < 0.0001) in the WAT of female CoV-2 mice compared to male CoV-2 mice. There was no significant difference between the levels of proinflammatory TNFα in the WAT of male and female control mice (Figure 3b). However, CoV-2 infection significantly increased the levels of TNFα in female mice compared to their sex-matched controls (p < 0.01) and infected male counterparts (p < 0.05). Similarly, the levels of IL-6 were significantly elevated in CoV-2-infected female mice compared to their male counterparts (p < 0.001) and sex-matched controls (p < 0.0001). No significant change in the levels of IL-10 was observed in either male or female CoV-2-infected mice compared to the corresponding sex-matched control groups. These data demonstrated that CoV-2 infection induces stronger proinflammatory signaling in the WAT of female mice compared to male mice. . Immune signaling in the WAT during CoV-2 infection is altered differently between the sexes. Immunoblot images of (a) immune cell markers (CD4, CD8, F4/80) and (b) inflammatory markers (TNFα, IL-6, IL-10). β-actin was used as loading control. Fold changes in the protein levels were normalized to β-actin expression and are shown as bar graphs. The error bars represent standard error of the mean. * p < 0.05, ** p < 0.01, *** p < 0.001, and **** p < 0.0001 compared to uninfected sex-matched mice and between the infected groups (n = 4/sex/group) (M, male; F, female).
There was no significant difference between the levels of proinflammatory TNFα in the WAT of male and female control mice (Figure 3b). However, CoV-2 infection significantly increased the levels of TNFα in female mice compared to their sex-matched controls (p < 0.01) and infected male counterparts (p < 0.05). Similarly, the levels of IL-6 were significantly elevated in CoV-2-infected female mice compared to their male counterparts (p < 0.001) and sex-matched controls (p < 0.0001). No significant change in the levels of IL-10 was observed in either male or female CoV-2-infected mice compared to the corresponding sex-matched control groups. These data demonstrated that CoV-2 infection induces stronger proinflammatory signaling in the WAT of female mice compared to male mice.
SARS-CoV-2 Infection Alters Immune Signaling in the Adipose Tissue Differently in Male and Female hACE2 Mice
Immunoblot analysis of WAT lysates demonstrated significant differences in the protein levels of lipases (ATGL and p-HSL) between the sexes in hACE2 mice and during CoV-2 infection (Figure 4). Uninfected female mice showed significantly lower levels of Figure 3. Immune signaling in the WAT during CoV-2 infection is altered differently between the sexes. Immunoblot images of (a) immune cell markers (CD4, CD8, F4/80) and (b) inflammatory markers (TNFα, IL-6, IL-10). β-actin was used as loading control. Fold changes in the protein levels were normalized to β-actin expression and are shown as bar graphs. The error bars represent standard error of the mean. * p < 0.05, ** p < 0.01, *** p < 0.001, and **** p < 0.0001 compared to uninfected sex-matched mice and between the infected groups (n = 4/sex/group) (M, male; F, female).
SARS-CoV-2 Infection Alters Immune Signaling in the Adipose Tissue Differently in Male and Female hACE2 Mice
Immunoblot analysis of WAT lysates demonstrated significant differences in the protein levels of lipases (ATGL and p-HSL) between the sexes in hACE2 mice and during CoV-2 infection (Figure 4). Uninfected female mice showed significantly lower levels of ATGL (p < 0.01) and p-HSL (p < 0.01) expression compared to uninfected male mice ( Figure 4). Furthermore, CoV-2 infection significantly increased the levels of ATGL (p < 0.05) and p-HSL (p < 0.01) in females compared to female uninfected mice. However, the levels of ATGL significantly decreased (p < 0.05), and the levels of p-HSL were not altered in infected male mice compared to uninfected male mice. These data indicate that CoV-2 infection differently activates lipases in WAT between male and female hACE2 mice. 4). Furthermore, CoV-2 infection significantly increased the levels of ATGL (p < 0.05) and p-HSL (p < 0.01) in females compared to female uninfected mice. However, the levels of ATGL significantly decreased (p < 0.05), and the levels of p-HSL were not altered in infected male mice compared to uninfected male mice. These data indicate that CoV-2 infection differently activates lipases in WAT between male and female hACE2 mice.
SARS-CoV-2 Infection Causes a Loss of Fat Cells in hACE2 Mice
Histological analysis demonstrated a significant loss of lipid droplets and adipocytes in CoV-2 infected mice compared to their control groups (Figure 1). We analyzed whether the cause for the loss of adipocytes was due to apoptosis or necrosis by quantitating the protein levels of cleaved caspase 3 and Bnip3, respectively, in the WAT ( Figure 5). In the WAT of uninfected female mice, the levels of cleaved caspase 3 and Bnip3 were slightly elevated compared to uninfected male mice; however, this difference was not statistically significant. In contrast, CoV-2 infection significantly increased the levels of cleaved caspase 3 (p < 0.0001) (Figure 5a) and Bnip3 (p < 0.001) (Figure 5b) in females compared to uninfected controls. Interestingly, the levels of cleaved caspase 3 in the WAT of CoV-2 females were significantly higher (p < 0.0001) compared to their male counterparts, suggesting that cell death in the WAT of female mice may be predominantly driven by apoptosis (Figure 5a). In addition, the levels of necrotic cell death markers in the WAT of CoV-2 infected mice were also significantly elevated (p < 0.0001) in females compared to males (Figure 5b). These data indicate that during CoV-2 infection adipose tissue is lost via both apoptotic and necrotic cell death in females more so than in males.
SARS-CoV-2 Infection Causes a Loss of Fat Cells in hACE2 Mice
Histological analysis demonstrated a significant loss of lipid droplets and adipocytes in CoV-2 infected mice compared to their control groups (Figure 1). We analyzed whether the cause for the loss of adipocytes was due to apoptosis or necrosis by quantitating the protein levels of cleaved caspase 3 and Bnip3, respectively, in the WAT ( Figure 5). In the WAT of uninfected female mice, the levels of cleaved caspase 3 and Bnip3 were slightly elevated compared to uninfected male mice; however, this difference was not statistically significant. In contrast, CoV-2 infection significantly increased the levels of cleaved caspase 3 (p < 0.0001) (Figure 5a) and Bnip3 (p < 0.001) (Figure 5b) in females compared to uninfected controls. Interestingly, the levels of cleaved caspase 3 in the WAT of CoV-2 females were significantly higher (p < 0.0001) compared to their male counterparts, suggesting that cell death in the WAT of female mice may be predominantly driven by apoptosis (Figure 5a). In addition, the levels of necrotic cell death markers in the WAT of CoV-2 infected mice were also significantly elevated (p < 0.0001) in females compared to males (Figure 5b). These data indicate that during CoV-2 infection adipose tissue is lost via both apoptotic and necrotic cell death in females more so than in males. Western blot images of (a) Cleaved caspase 3 (apoptosis marker) and (b) Bnip3 (necrosis marker). GDI was used as loading control. Fold changes in the protein levels were normalized to GDI expression and are shown as bar graphs. The error bars represent standard error of the mean. *** p < 0.001 and **** p < 0.0001 compared to uninfected sex-matched mice (n = 4/sex/group) (M, male; F, female).
Discussion
The epidemiological findings reported globally indicate higher morbidity and mortality in males than in females with SARS-CoV-2 infection [35][36][37]. Although women also get infected with CoV-2, many clinical studies indicate that males are more susceptible to developing severe COVID-19 compared to females, and many researchers have attributed this difference to sex-specific hormones [38][39][40][41]. A few reports have also suggested a difference in immune responses between the sexes [42][43][44]. However, how exactly the immune response may change between males and females during CoV-2 infection is not well understood. In our previous studies, we have demonstrated that pathogens such as parasites, such as Trypanosoma cruzi, and bacteria, such as Mycobacterium tuberculosis, can infect and persist in adipose tissue [30,45,46]. Recently, we and others have shown that CoV-2 can also infect adipose tissue [28,30,47,48]. In particular, biopsies have demonstrated the presence of CoV-2 in subcutaneous thoracic fat [28] and abdominal fat [29] in COVID-19 patients. These studies have shown that adipose tissue can be a significant reservoir for SARS-CoV-2 and an important source of inflammatory mediator IFN-γ [29]. The present study investigated sex differences in: (i) SARS-CoV-2 viral loads in adipose tissue; and (ii) immune signaling due to the presence of CoV-2 in adipose tissue. Moreover, this study assessed whether the relationship between lung and adipose tissue viral loads differs between male and female infected hACE2 mice. Our study revealed for the first time that: (a) viral loads in adipose tissue and the lungs differ between males and females; (b) an inverse relationship exists between the viral loads in the lungs and adipose tissue, and it differs between the males and females in hACE2 mice; and (c) CoV-2 infection alters immune signaling, lipolysis, and cell death signaling differently in the adipose tissue of SARS-CoV-2 infected male and female mice.
Earlier we showed that the viral loads in the lungs of female CoV-2 infected mice were significantly lower compared to male CoV-2 infected mice, which is reminiscent of the observations made in COVID-19 patients [30,49]. The increased lung pathology Western blot images of (a) Cleaved caspase 3 (apoptosis marker) and (b) Bnip3 (necrosis marker). GDI was used as loading control. Fold changes in the protein levels were normalized to GDI expression and are shown as bar graphs. The error bars represent standard error of the mean. *** p < 0.001 and **** p < 0.0001 compared to uninfected sex-matched mice (n = 4/sex/group) (M, male; F, female).
Discussion
The epidemiological findings reported globally indicate higher morbidity and mortality in males than in females with SARS-CoV-2 infection [35][36][37]. Although women also get infected with CoV-2, many clinical studies indicate that males are more susceptible to developing severe COVID-19 compared to females, and many researchers have attributed this difference to sex-specific hormones [38][39][40][41]. A few reports have also suggested a difference in immune responses between the sexes [42][43][44]. However, how exactly the immune response may change between males and females during CoV-2 infection is not well understood. In our previous studies, we have demonstrated that pathogens such as parasites, such as Trypanosoma cruzi, and bacteria, such as Mycobacterium tuberculosis, can infect and persist in adipose tissue [30,45,46]. Recently, we and others have shown that CoV-2 can also infect adipose tissue [28,30,47,48]. In particular, biopsies have demonstrated the presence of CoV-2 in subcutaneous thoracic fat [28] and abdominal fat [29] in COVID-19 patients. These studies have shown that adipose tissue can be a significant reservoir for SARS-CoV-2 and an important source of inflammatory mediator IFN-γ [29]. The present study investigated sex differences in: (i) SARS-CoV-2 viral loads in adipose tissue; and (ii) immune signaling due to the presence of CoV-2 in adipose tissue. Moreover, this study assessed whether the relationship between lung and adipose tissue viral loads differs between male and female infected hACE2 mice. Our study revealed for the first time that: (a) viral loads in adipose tissue and the lungs differ between males and females; (b) an inverse relationship exists between the viral loads in the lungs and adipose tissue, and it differs between the males and females in hACE2 mice; and (c) CoV-2 infection alters immune signaling, lipolysis, and cell death signaling differently in the adipose tissue of SARS-CoV-2 infected male and female mice.
Earlier we showed that the viral loads in the lungs of female CoV-2 infected mice were significantly lower compared to male CoV-2 infected mice, which is reminiscent of the observations made in COVID-19 patients [30,49]. The increased lung pathology observed in male mice is likely due to increased viral loads and infiltrated immune cells in the lungs. Interestingly, in female mice, CoV-2 levels were significantly reduced in the lungs but significantly increased in the WAT compared to infected male mice. It has been shown that estrogen reduces the levels of ACE2 [50]. Thus, although ACE2 is more highly expressed in adipose tissue than in the lungs [51], females may have reduced levels of ACE2 in WAT because of their higher levels of estrogen. However, SARS-CoV-2 can also infect and invade cells via other receptors and cellular mechanisms [34,52]. For example, SARS-CoV-2 can infect cells through the cholesterol-rich lipid rafts [53][54][55], which may be the case in adipose tissue in female mice. Our data suggested that in female mice adipose tissue may act as a sink/reservoir for SARS-CoV-2 and thus spares the lungs from a greater viral load, preventing pulmonary damage due to infiltrated immune cells and activated pro-inflammatory cytokines. The reduced viral load in the lungs of female mice may also be attributed to an increased pro-inflammatory environment in female mice caused by increased IL-6 and TNF-a levels in adipose tissue, which increases the levels of circulating pro-inflammatory cytokines.
We observed an increased average size of adipocytes in uninfected females compared to uninfected males in the adipose tissue of hACE2 mice, which may be attributed to the lower levels of lipases in female mice. However, the increased levels of lipases in the adipose tissue of infected female mice compared to infected male mice may cause a loss of lipid droplets. CoV-2 infection causes a loss of lipid droplets and promotes cell death in adipose tissue. Our histological and Western blotting analysis demonstrated that the loss of lipid droplets and increased cell death due to lipolysis, necrosis, and apoptosis were significantly higher in the WAT of infected female mice compared to infected male mice. Like other viruses and parasites, SARS-CoV-2 utilizes host lipids for its biosynthetic needs [56]. It has been shown that lipid droplets increase the replication of SARS-CoV-2 [56]. Isolated monocytes from COVID-19 patients showed an increased accumulation of intracellular lipid droplets compared to SARS-CoV-2 negative donors [56], suggesting that CoV-2 manipulates cellular metabolism to acquire lipid resources from the host. Thus, adipocytes, which are rich in lipid droplets, provide the necessary fuel for viral replication. In female hACE2 mice, the presence of CoV-2 in adipose tissue increased the loss of lipid droplets and caused cell death, which likely resulted in the infiltration of immune cells and the elevation of cytokines such as IL-6 and TNF-α. The difference in viral load and immune cell activation can be attributed to lipid droplets. The loss of lipid droplets due to deregulated lipolysis has been linked to the infiltration of immune cells, immune cell activation, and cell death (apoptotic or necrotic) [57][58][59][60]. The process of cell death initiates the infiltration of immune cells and the release of TNFα, which in turn further elevates lipolysis [61]. In general, male mice have more fat compared to female mice and male mice are more susceptible to developing obesity [62,63]. However, the levels of body fat in hACE2 mice were not measured. These basic metabolic differences in fat tissue between males and females likely contribute to the greater levels of CoV-2 in females, leading to higher levels of pro-inflammatory cytokines in adipose tissue. The cytokines released in adipose tissue contribute to the elevated cytokine levels in circulation [64]; thus, in infected female mice, TNF-α and IL-6 released from the adipose tissue could activate immune cells and contribute to the observed reduction of viral load in the lungs [65,66].
Biosafety
All aspects of this study were approved by the Institutional Animal Care and Use Committee (IACUC) and Institutional Biosafety Committee of Center for Discovery and Innovation (CDI)-Hackensack University Medical Center and adhered to the National Research Council guidelines.
Animal Model and Experimental Design
The transgenic mice expressing human angiotensin-converting enzyme 2 (hACE2) were purchased from Jackson Laboratories, Bar Harbor, ME and bred at CDI animal research facility. Both male and female mice (n = 8) were intra-nasally infected with 1 × 10 4 pfu SARS-CoV-2 (NR-52281, Isolate USA-WA1/2020 CoV-2 virus, NIH-BEI Resources, Manassas, VA, USA). After 10 days post infection (DPI), the animals (n = 4/sex) were euthanized, and samples such as blood, lungs, spleen, and mesenteric white adipose tissue (WAT) were collected. Age and sex-matched uninfected hACE2 mice served as controls (Supplementary Figure S1). The lungs and WAT samples alone were used in the present study.
Histological Analysis of Adipose Tissue
Freshly isolated WAT were fixed with 10% neutral-buffered formalin for a minimum of 48 h and then embedded in paraffin wax (n = 4/sex). Hematoxylin and eosin (H&E) and Masson's trichrome staining were performed, and the images were captured as previously published [46]. Four to six sections of each WAT were analyzed in this study. For each WAT section, the histological evidence of adipose tissue pathology was classified in terms of the presence of infiltrating immune cells, loss of lipid droplets, and fibrosis [46,67].
Determination of SARS-CoV-2 Load in the Tissue
Total RNA was isolated from the lungs and WAT of SARS-CoV-2 infected hACE2 mice using TRIzol reagent. The number of SARS-CoV-2 copies was quantified using a 2019-nCoV_N2 primer/probe mix and One-Step PrimeScript RT-PCR kit (Takara Bio Inc., San Jose, CA, USA). All assays were performed on Agilent AriaMx Real-time PCR System according to the following cycling conditions: 15 min at 42 • C (1 cycle, reverse transcription), followed by 10 sec at 95 • C (1 cycle, hot start) and continuing with 5 sec at 95 • C, and 30 sec at 55 • C (40 cycles, PCR amplification).
Immunohistochemistry Analysis of SARS-CoV-2
Freshly isolated WAT tissues were fixed with 10% neutral-buffered formalin for a minimum of 48 h and then embedded in paraffin wax (n = 4/sex) and sectioned for immunohistochemistry analysis (IHC). IHC was performed using a rabbit monoclonal anti-SARS-CoV-2 nucleocapsid protein (#NR-53791, Sino Biological, Wayne, PA, USA) with a dilution of 1:1000 followed by biotinylated secondary antibody using VECTASTAIN Elite ABC-HRP kit (#PK-6101, Vector Laboratories, Newark, CA, USA). The sections were then washed and incubated with peroxidase substrate and counterstained with hematoxylin.
Immunoblot Analysis
Tissue lysates were prepared as previously described [30]. The protein concentration quantitation was performed using a Pierce BCA protein assay kit (#23225, ThermoFisher Scientific, Waltham, MA, USA). Then, 30 µg total protein from each sample was loaded and resolved on 8% or 15% SDS-PAGE as appropriate and transferred onto nitrocellulose membrane for immunoblot analysis.
Statistical Analysis
Data represent means ± S.E. Data were pooled, and statistical analysis was performed on GraphPad Prism software version 9.4.1 using two-way ANOVA and Student's t-test as appropriate and significant differences were determined as p values between <0.0001 and <0.05 as appropriate.
Conclusions
In conclusion, our studies suggest that CoV-2 infection affects adipose tissue physiology which could alter systemic metabolic and immune homeostasis during COVID-19. It will be of great importance to further investigate the link between adipose tissue pathophysiology and pulmonary viral load and COVID-19 severity in COVID-19 research. Thus, further mechanistic studies are warranted to understand the role of the pathophysiology of adipose tissue in the pathogenesis of CoV-2 infection and COVID-19 outcomes. Further studies may determine the mechanistic roles of various fat tissues in regulating immune and metabolic signaling in male and female COVID-19 patients. | 7,151.2 | 2023-01-01T00:00:00.000 | [
"Medicine",
"Environmental Science",
"Biology"
] |
Bayesian Energy Measurement and Verification Analysis
: Energy Measurement and Verification (M&V) aims to make inferences about the savings achieved in energy projects, given the data and other information at hand. Traditionally, a frequentist approach has been used to quantify these savings and their associated uncertainties. We demonstrate that the Bayesian paradigm is an intuitive, coherent, and powerful alternative framework within which M&V can be done. Its advantages and limitations are discussed, and two examples from the industry-standard International Performance Measurement and Verification Protocol (IPMVP) are solved using the framework. Bayesian analysis is shown to describe the problem more thoroughly and yield richer information and uncertainty quantification results than the standard methods while not sacrificing model simplicity. We also show that Bayesian methods can be more robust to outliers. Bayesian alternatives to standard M&V methods are listed, and examples from literature are cited.
Introduction
This study argues for the adoption of the Bayesian paradigm in energy Measurement and Verification (M&V) analysis.As such, no new Bayesian methods will be developed.Instead, the advantages, limitations, and application of the Bayesian approach to M&V will be explored.Since the focus is on application, a full explanation of the underlying theory of the Bayesian paradigm will not be given.Readers are referred to Sivia and Skilling [1] or Kruschke [2] for a basic introduction, or von der Linden et al. [3] or Gelman et al. [4] for more complete treatments.
The argument made below is not that current methods are completely wrong or that the Bayesian paradigm is the only viable option, but that the field can benefit from a increased adoption of Bayesian thinking because of its ease of implementation and accuracy of the results.
This paper is arranged as follows.After discussing the background of current M&V analysis methods and the opportunities for improvement in Section 1.1, the Bayesian paradigm is introduced and its practical benefits and some caveats are discussed in Section 2. Section 3 offers two well-known examples and their Bayesian solutions.We also discuss robustness and hierarchical modelling.Section 4 gives a reference list of Bayesian solutions to common M&V cases.
Background
M&V is the discipline in which the savings from energy efficiency, demand response, and demand-side management projects are quantified [5], based on measurements and energy models.A large proportion of such M&V studies quantify savings for building projects, both residential and commercial.The process usually involves taking measurements or sampling a population to create a baseline, after which an intervention is done.The results are also measured, and the savings are inferred as the difference between the actual post-intervention energy use, and what it would have been, had no intervention taken place.These savings are expressed in probabilistic terms following the International Standards Organization (ISO) Guide to the Expression of Uncertainty in Measurement (GUM) [6].M&V study results often form the basis of payment decisions in energy performance contracts, and the risk-implications of such studies are therefore of interest to decision makers.
The Bayesian option will not affect the foundational M&V methodologies such as retrofit isolation or whole facility measurement, but only the way the data are analysed once one of these methods has been decided upon.
M&V guidelines such as the International Performance Measurement and Verification Protocol (IPMVP) [5], the American Society of Heating, Refrigeration, and Air Conditioning Engineers (ASHRAE)'s Guideline 14 on Measurement of Energy, Demand, and Water Savings [7], or the United States Department of Energy's Uniform Methods Project (UMP) [8], as well as most practitioners, use frequentist (or classical) statistics for analysis.Because of its popularity in the twentieth century, most practitioners are unaware that this is only one statistical paradigm and that its assumptions can be limiting.The term 'frequentist' derives from the method that equates probability with long-run frequency.For coin flips or samples from a production line, this assumption may be valid.However, for many events, equating probability with frequency seems strained because a large, hypothetical long-run population needs to be imagined for the probability-as-frequency-view to hold.Kruschke [2] gives an example where a coin is flipped twenty times and seven heads are observed.The question is then: what is the probability of the coin being fair?The frequentist answer will depend on the imagined population from which the data were obtained.This population could be obtained by "stopping after 20 flips", but it could also be "stopping after seven heads" or "stopping after two minutes of flipping" or "to compare it to another coin that was flipped twenty times".In each case, the probability that it is a fair coin changes, even though the data did not-termed incoherence [9].In fact, the probabilities are dependent on the analyst's intention.By changing his intention, he can alter the probabilities.This problem becomes even more severe in real-world energy savings inference problems with many more factors.The hypothetical larger population from which the energy use at a specific time on a specific day for a specific facility was sampled is difficult to imagine.That is not to say that a frequentist statistical analysis cannot be done, or be useful.However, it often does not answer the question that the analyst is asking, committing an "error of the third kind".Analysts have become used to these 'statistical' answers (e.g., "not able to reject the null hypothesis"), and have accepted such confusion as part of statistics.For example, consider two mainstays of frequentist M&V: confidence intervals (CIs) and p-values.CIs are widely used in M&V to quantify uncertainty.According to Neyman, who devised these intervals, they do not convey a degree of belief, or confidence, as is often thought.Frequentist confidence intervals are produced by a method that yields an interval that contains the true value only in a specified percentage (say 90%) of cases [10].This may seem like practically the same thing, but an explanation from most frequentist statistics textbooks will then seem very confusing.Consider Montgomery and Runger's Applied Statistics and Probability for Engineers [11], under "Interpreting a Confidence Interval" (CI).They explain that, with frequentist CIs, one cannot say that the interval contains the true number with a probability of e.g., 90%.The interval either contains the value, or it does not.Therefore, the probability is either zero or one, but the analyst does not know which.Therefore, the interval cannot be associated with a probability.Furthermore, it is a random interval (emphasis theirs) because the upper and lower bounds of the interval are random variables.
Consider now the p-value.Because of the confusion surrounding this statistic, the American Statistical Association issued a statement regarding its use [12], in which they state that p-values neither signify probabilities of the hypothesis being true or false, nor are they probabilities that the result arose by chance.They go on to say that business (or policy) decisions should not be based on p-value thresholds.p-values do not measure effect sizes or result importances, and by themselves are not adequate measures of evidence.Such statements by professional statisticians leave most M&V practitioners justifiably confused.It is not that these methods are invalid, but that they have been co-opted to answer different kinds of questions to what they actually answer.The reason for their popularity in the 20th century has more to do with their computational ease, compared to the more formal and mathematical Bayesian methods, than with their appropriateness.The Bayesian conditional-probability paradigm is much older than the frequentist one but used to be impractical for computational reasons.However, with the rise in computing power and new numeric methods for solving Bayesian models, this is no longer a consideration.
The Bayesian Paradigm
Instead of approaching uncertainty in terms of long-run frequency, the Bayesian paradigm views uncertainty as a state of knowledge or a degree of belief, the sense most often meant by people when thinking about uncertainty.These uncertainties are calculated using conditional-probability logic and calculus, proceeding from first principles.For example, consider two conditions M and S. Let Pr() denote a probability and | "conditional on" or "given".Furthermore, let I be the background information about the problem.Bayes' theorem states that: Now, as stated previously, M&V is about verifying the savings achieved, based on some measurements and an energy model, and quantifying the uncertainty in this figure.If we let S be the savings, and M the measurements, Bayes' theorem as stated above answers that question exactly: it supplies a probability of the savings given the measurements and any background information that might be available; Pr(S|M).Bayes' theorem is, therefore, the natural expression of the M&V aim: Verification|Measurement ≡ Pr(S|M).
Whereas the frequentist paradigm views the data as random realisations of a process with fixed parameters, the Bayesian paradigm views the data (measurements) as fixed, and the underlying parameters as uncertain (thereby avoid the incoherence of the coin flip example [9]).This seems like a trivial distinction at first but is significant: the frequentist only solves for Pr(M|S): the probability of observing that data, given the underlying savings value.However, that is not the question M&V seeks to answer.In the frequentist paradigm, the analyst does not invert this as Bayes' theorem does to find the probability distribution on the savings, given the data.Therefore, in the frequentist case, the wrong question is being answered, as alluded to above (Technical note: to be fair, we note that, for constant priors, the likelihood may be equivalent to the posterior.When it is the case, the frequentist likelihood may borrow from Bayesian theory and be interpreted as a probability).
It is this inversion process that has often been intractable in higher dimensions until the advent of Markov Chain Monte Carlo (MCMC) techniques and increased computing power (Technical note: other Monte Carlo-based inversion techniques such as rejection or importance sampling are only efficient enough to be practical in low-dimensional settings.Note that we use Monte Carlo here in the sense of a straightforward sense of generating random numbers according to standard distributions [13]).MCMC software has allowed users to specify a model (e.g., a linear regression model), supply the observations or data (measurements), and infer the values on the model parameters probabilistically.This is called probabilistic programming.Probabilistic programming is compelling because, instead of working with point estimates on all unknown parameters (e.g., slope and intercept in a straight-line regression model), one describes the system in terms of probability distributions.Working with probability distributions rather than point estimates is preferable, since it is well known that doing calculations with point estimates can lead to erroneous conclusions [14].When doing forward-calculations as illustrated in Figure 1, it is therefore desirable to use distributions on unknown variables and then apply a Monte Carlo simulation or Mellin Transform Moment Calculation method [15,16] to obtain a probability distribution on the result.MCMC allows one to do the inverse: inferring parameter distributions from given data and a model.Therefore, MCMC is to regression what Monte Carlo simulation is to deterministic computation.The adoption of the Bayesian paradigm therefore allows the analyst to move from deterministic to probabilistic M&V, as shown in Figure 1.
Parameters
a, b Deterministic and probabilistic calculation, simulation, and inverse modelling.The notation ∼ N[•] denotes a normal distribution as a convenient substitute for any distribution.Note that this figure does not illustrate or recommend a cyclic work flow; usually, only one of the for processes is of interest for a particular problem.Indeed, continually updating, or "fiddling", a Bayesian prior based on the posterior (i.e., treating the illustration as a cycle) is poor modelling practice.We recommend that M&V analysts set, state, and defend their prior, and not change it to achieve a different outcome.
For the inversion described above to work, the Pr(S|I) term, called the prior, needs to be specified.Although the prior can be used to incorporate information into the model, which is not available through the data alone, it is, in essence, merely a mathematical device allowing inversion.The prior is often specified as "non-informative"-a flat probability distribution over the region of interest, allowing the data to "speak for itself" through the likelihood term.This will be discussed in more detail below.The other term, Pr(M|I), need not be specified in numeric MCMC models-it is a normalising factor ensuring that the right-hand side of the equation can integrate to unity, making it a proper probability density function (Technical note: this term becomes important in more sophisticated Bayesian analyses where model selection or experimental design is done [1]).The left-hand side of the equation is called the posterior distribution and is proportional, therefore, to the product of the prior and the likelihood.
Advanced Bayesian models may be nuanced, but the fundamental mechanics as described above stay the same for all Bayesian analyses: specify priors, describe the likelihood, and solve to find the posterior on the parameters of interest.
Practical Benefits
Besides the theoretical attractiveness discussed above, the Bayesian paradigm also offers many practical benefits for energy M&V: 1.Because Bayesian models are probabilistic, uncertainty is automatically and exactly quantified.2. Uncertainty calculations in the Bayesian approach can be much less conservative than standard approaches.Shonder and Im [17] show a 40% reduction in uncertainty in one case.Since project payment is often dependent on savings uncertainties being within certain bounds, using the Bayesian approach can increase project feasibility.3.By making the priors and energy model explicit, the Bayesian approach ensures greater transparency-one of the five key principles of M&V [5].4. The Bayesian approach is widely used and is rapidly gaining popularity in other scientific fields.Lira [18] relates that even the GUM (adopted by many societies of physics, chemistry, electrotechnics, etc.) is being rewritten to be more consistent with this approach.Since M&V reports uncertainty according to the GUM, Bayesian calculations would be useful.5. Bayesian models are more universal and flexible than standard methods.Bayesian modelling can be highly sophisticated, but the core of probabilistic thinking is consistent throughout.This is different to frequentist statistics where knowledge of one or even many tests will not necessarily aid the analyst in understanding a new metric, or approach to a problem not seen before.Many frequentist tests are ad hoc and apply only to specific situations.For example, t-tests have little to do with regression in frequentism, but, in Bayesian thinking, they are expressions of the same idea.6. Being modular, Bayesian modelling is more flexible.Ordinary least squares (OLS) linear regression assumes residuals are normally distributed and that the variance is constant for all points.In a probabilistic Bayesian model, the parameters can be distributed according to any distribution, but the posterior for each will be determined by the data (if the prior is appropriately chosen).Models are also modular and can be designed to suit the problem.For example, it is no different to create terms for serial correlation, or heteroscedasticity (non-constant variance) than it is to specify an ordinary linear model.This also allows for easy specification of non-routine adjustments, the handling of missing values, and the incorporation of unmeasured yet important quantities such as measurement error, often problematic for energy models.For the retrofit isolation with a key parameter measurement approach, the unmeasured parameters (the estimates) can also be incorporated in this way.7. Bayesian models can account for model-selection uncertainty.There are often multiple reasonable energy models which could describe a specific case-for example: time and dry-bulb temperature; occupancy and dry-bulb temperature; temperature, humidity, and occupancy, etc.The analyst usually chooses one model, discards the rest, and reports the uncertainty produced in that specific model.However, this uncertainty does not account for model selection.In other words, there is an uncertainty associated with choosing that specific model above another reasonable one.Bayesian model averaging allows many models to be specified simultaneously, and averages their results by automatically weighting each model's influence on the final result by that model's explanatory power.This gives a far more realistic uncertainty value [4].8.Because uncertainty is automatically quantified, CIs can be interpreted in the way most people understand them: degrees of belief about the value of the parameter.9.The Bayesian approach is well-suited to "small data" problems.This seems like a minor point in developed countries where questions surrounding big data are more pressing.However, big (energy) data is a decidedly "first-world problem".In developing countries, a lack of meters makes M&V expensive, and it is useful to have a method that is consistent on smaller data sets as well.10.Bayesian approaches allow real-time or online updating of estimates [19][20][21].For many other machine learning techniques, the data need to be split into testing and training sets, the model trained on the training set, and then used to predict the testing set period.As new data becomes available, the model needs to be retrained in many cases (Technical note: Artificial Neural Networks (ANNs), stochastic gradient descent and passive-aggressive algorithms, as well as Dynamic Linear Models can also be updated online), making it computationally expensive to keep a model updated.In a Bayesian paradigm, previous data can be summarised by the prior so that the model need not be retrained.11.The Bayesian approach allows for the incorporation of prior information where appropriate.
The danger in this will be discussed in Section 2.2.However, in cases where it is warranted, known values or ranges for certain coefficients can be specified in the prior.This has been done successfully for energy projects [22][23][24][25].Prior information is also useful in longitudinal studies, where measurements or samples from previous years can be taken into account [20,21].12.When the savings need to be calculated for "normalised conditions", for example, a 'typical meteorological year', rather than the conditions during the post-retrofit monitoring period, it is not possible to quantify uncertainty using current methods.However, Shonder and Im [17] have shown that it can be naturally and easily quantified using the Bayesian approach.
Caveats
The Bayesian approach also comes with certain caveats that M&V practitioners and policy makers should bear in mind.
1. Modelling is non-generic.In point 5 above, it was stated that the Bayesian approach is more universal.This is true in the sense that the same basic approach is used for many different kinds of problems.However, the inherent modularity of the method as described in point 6 means that there is not a one-size-fits-all generic template in Bayesian modelling, the way there usually is in frequentist modelling.This necessitates more thinking from the analyst.However, we believe this to be an advantage: frequentist approaches make it easier to think less, but as a consequence, also to build poor models, which has led to the current replication crisis seen in research [26] and a general mistrust of statistical results [27].High quality models require some thought and care, in any paradigm.2. As with any method, it is not immune to abuse.The most popular criticism is that, by having a prior distribution on the savings, the posterior may be biased in a way not warranted by the data, making the result subjective.This is certainly possible.However, having a prior in an M&V analysis is actually an advantage.
(a) As stated above, it allows for greater modelling transparency.The Bayesian form forces the analyst to be explicit about his or her modelling assumptions, and to defend them.Such assumptions cannot be imported by (accidentally or purposefully) choosing one test over another, as in the frequentist case.(b) It is sometimes necessary to include priors to avoid bias.Ioannidis [28] and Button [29] have shown that many medical studies contain false conclusions due to biased results.The bias that was introduced was to consider positive and negative outcomes from a clinical trial equally likely.However, the prior odds of an experimental treatment working is much lower than the odds of that treatment not working.Ignoring these prior odds leads to a high false-positive rate, since many of the positive results are actually false and due to noise.In M&V, the situation is reversed: the prior odds of energy projects saving energy are high.
Having a neutral prior would therefore bias a result towards conservatism (Technical note: conservatism is one of the key principles of M&V [5], but we do not hereby advocate for neutral priors in all cases).Nevertheless, Button's study is an excellent illustration of why priors are an important part of probability calculus.(c) Because the assumptions and distributions used are clearly stated, it precludes hedging the M&V result with phrases such as "however, from previous studies/experience, we know that this is a conservative figure . . .".Because the prior was stated and defended at the outset, the final result should already incorporate it and should not be hedged.(d) The thorough analyst will test the effect of different priors on the posterior, demonstrating the bias introduced through his modelling assumptions, and justifying its use.
3. Bayesian methods can be computationally expensive for large datasets and complex models.It is true that numerical solvers are becoming more efficient and computational power is increasing.However, in comparison with matrix inversion techniques used for linear regression, for example, Bayesian methods are much slower and may be inappropriate for real-time applications [30].4. The forecasting accuracy of other machine learning (ML) methods can be higher than regression in some cases [31,32], although regression-based approaches such as time-of-week-and-temperature [33] still perform very well [32,34] and may be preferred for simplicity.Note that this is a limitation of regression, not the overall Bayesian paradigm, although regression is the way most M&V analysts would use Bayesian methods.Many ML techniques also have Bayesian approaches, for example Bayesian tree-based ensemble methods [35] or Bayesian Artificial Neural Networks [36,37].It also depends on the problem: it is not possible to know beforehand which model will work the best [38].ML algorithms without Bayesian implementations also still only produce point estimates.Therefore, they cannot be compared to the full probabilistic approach, which provides much richer information and is not just a forecasting technique, but a full inference paradigm.5.The parametric from of the model needs to be specified.Parametric Bayesian models as described in most of this study can only be correct in so far as their functional form describes the underlying physical process.Functional form misspecification is a real possibility.This is different to the machine learning methods described in the previous paragraph, which do not rely on a functional form being specified.Non-parametric models have their own benefits and limitations: for cases where the underlying physical process is well-understood, a parametric model can be more accurate.However, non-parametric methods such as Gaussian Processes (GPs) [22,39] or Gaussian Mixture Models [40] still require some model specification at a higher level (hyperparameters).GP models, for example, rely on an appropriate covariance function for valid inference.For more information on GPs for machine learning, see Rasmussen and Williams [41].
Bayesian M&V Examples
To demystify the Bayesian approach, two basic M&V calculations will be demonstrated.The reader will notice the recurring theme of expressing all variables as (conditional) probability distributions.
Sampling Estimation
Consider the following example from the IPMVP 2012 [5] (Appendix B-1).Twelve readings are taken by a meter.These are reported as monthly readings, but are assumed to be uncorrelated with any independent variables or other readings, and are therefore construed to be random samples.The values are: D = [950, 1090, 850, 920, 1120, 820, 760, 1210, 1040, 930, 1110, 1200]. ( The units are not reported and the results below are therefore left dimensionless, although kWh would be a reasonable assumption.These data were carefully chosen, and have a mean µ = 1000, sample standard deviation s s = 150.
IPMVP Solution
The standard error is SE = 43.The confidence interval on the mean is calculated as: Since t 90%,11 = 1.80, the 90% confidence interval on the mean was calculated as 1000 ± 1.80 × 43 = (933, 1077), or a 7.7% precision.Metering uncertainty is not considered in this calculation.
Bayesian Solution
The Bayesian estimate of the mean is calculated as follows.First, prior distributions on the data need to be specified.Vague priors will be used: A t-distribution will be used for the likelihood below, and the degrees of freedom parameter (ν) of this distribution will, therefore, need to be specified.One could fix ν for the t-distribution at 12, since there are twelve data points and traditionally ν has been taken to signify this number.However, if outliers are present or if the data has more or less dispersion than the standard t-distribution with as many data points, this would not be realistic.It is therefore warranted to indicate the uncertainty in the data by specifying a prior distribution on ν also: a hyperprior.Kruschke [42] recommends an exponential distribution with the mean equal to the number of data points.This allows equal probability of ν being higher or lower than the default value: If the vector of the parameters is θ = (µ, σ, ν), then the likelihood can be written as: Note that the t-distribution is not used because of the t-test, but because its heavier tails are more accommodating of outliers.Any distribution could have been specified if there was good reason to do so.The posterior on µ is plotted in Figure 2. It was simulated in PyMC3 using the Automatic Differentiation Variational Inference (ADVI) algorithm with 100,000 draws, which is stable and converges on the posterior distribution in 10.76 s on a middle-range laptop computer.Although the mathematical notation may seem intimidating to practitioners who are not used to it, writing this in the probabilistic Python programming package PyMC3 [43] It is important to note that no probability statements about the values inside the frequentist interval can be made, nor can one fit a distribution to the interval.The distribution indicated is strictly a Bayesian one.The Bayesian (highest density) interval is slightly wider than the frequentist confidence interval, at a precision of 8.5%.If ν were fixed at 12 (indicating that we are certain that the data does indeed reflect a t-distribution with 12 degrees of freedom exactly), Bayesian and frequentist intervals correspond exactly.However, the Bayesian alternative allows for a more realistic value.
With comparisons between two groups (two-sample t-tests), the effect of uncertainty in the priors becomes even more pronounced [42].The posterior distribution can now be used to answer many interesting questions.For instance, what is the probability, given the data at hand, that the true mean is below 900?Or, is it safe to assume that the standard value of 950 is reflected by this sample, or should the null hypothesis be rejected?(If previous data to this effect is available, it could be included in the prior, maybe using the equivalent prior sample size method [44]).The frequentist may say that there is not enough evidence to reject the null, but cannot accept it either.In the Bayesian paradigm, 950 falls comfortably within the 90% confidence range, and can therefore be accepted at that level.As a further question, if this is an energy performance contracting project, and we assume that the data points are different facilities rather than different months, would it be worthwhile taking a larger sample to increase profits, if we believe that the true mean is 1100 (on which see Lindley [45], Bernardo [46] and Goldberg [47]).
It is therefore evident that the Bayesian result yields richer and more useful information using intuitive mathematics.
Regression
In M&V, one often uses the baseline data (D b ) to infer the baseline (pre-retrofit) model parameters θ through an inverse method: where f (•) is a function relating the independent variables (energy governing factors) to the energy use of the facility, and τ is time.The model parameters describe the sensitivity of the energy model to the independent variables such as occupancy, outside air temperature, or production volume.
As an aside, this section will discuss an elementary parametric energy model using Bayesian regression, similar to standard linear regression.In practice, a two-parameter linear regression model seldom captures the different states of a facility's energy use, for example, heating at low temperatures, a comfortable range, and cooling at high temperatures.Piecewise linear regression techniques are often used [48][49][50][51][52], and they tend to work reasonably well if their assumptions are satisfied, but they are not stable in all cases, are approximate, and the assumptions are often restrictive.Shonder and Im [17] provide a Bayesian alternative.A non-parametric model using a Gaussian Process could also be used, and since one does not need to specify a parametric model, it allows very flexible models to be fit while still quantifying uncertainty.This is especially useful for models where energy use is a nonlinear function of the energy governing factors.However, to keep the example simple and focussed, only a simple parametric model will be considered below.
Example
Suppose one has a simple regression model where the energy use of a building E is correlated with the outside air temperature through the number of Cooling Degree Days (CDD).One cooling degree day is defined as an instance where the average daily temperature is one degree above the thermostat set point for one day, and the building therefore requires one degree of cooling (Technical note: a more accurate description would be the "building balance point", where the building's mass and insulation balance external forcings [53]).Let the intercept coefficient be θ 0 , the slope coefficient θ 1 , and the Gaussian error term .One could then write: In standard linear regression, one would write θ as the vector of two coefficients and do some linear algebra to obtain their estimates.There would be a standard error on each, which would indicate their uncertainties, and if the assumptions of linear regression, such as normality of residuals, independence of data, homoscedasticity, etc. hold, then it would be accurate.In Bayesian regression, one would describe the distributions on the parameters: where σ is the vector of the standard deviations on the estimates.Generating random pairs of values from the posterior, at a given value of CDD, according to the appropriate distributions, will yield the posterior predictive distribution.This is the distribution of energy use at a given temperature, or over the range of temperatures.Overlaying such realisations onto the actual data is called the posterior predictive check (PPC).Now, consider a concrete example.The IPMVP 2012 [5] (Appendix B-6) contains a simple regression example of creating a baseline of a building's cooling load.The twelve data points themselves were not given, but a very similar data set yielding almost identical regression characteristics has been engineered and is shown in Table 1.A linear regression model was fit to the data, and yielded the result shown in Table 2. 1.The coefficient of determination is R 2 = 0.93, which is identical to the IPMVP case.These results may be compared to Bayesian summary statistics in Table 3.
IPMVP Solution
The IPMVP then proceeds to calculate the uncertainty in the annual energy figure by multiplying the standard error on the estimate (the average standard error) by t 95% and the average consumption in the average month, and assumes that this value is constant for all months.As discussed in this study, this approach is problematic, and can at best be seen as approximate.Since it is treated in some detail in the IPMVP, the analysis will not be repeated here.
Bayesian Solution
The key to the Bayesian method is to approach the problem probabilistically, and therefore view all parameters in Equation ( 9) as probability distributions, and specify them as such.In this regression model, there are three parameters of interest: the intercept (θ 0 ), slope (θ 1 ), and the response (E).This response is the likelihood function, familiar to most readers as the frequentist approach.These distributions need to be specified in the Bayesian model.First, consider the priors on the slope and intercept.These can be vague.Technical note: the uniform prior on θ 0 in Equation ( 11) is actually technically incorrect: it may seem uniform in terms of gradient but is not uniform when the angle of the slope is considered.It is therefore not "rotationally invariant" and biases the estimate towards higher angles [54].The correct prior is Pr(θ|I) ∼ (1 + θ 2 ) − 3 2 ; this is uniform on the slope angle.The reason that Equation (11) works in this case is that the exponential weight of the likelihood masks the effect.However, this is not always the case, and analysts should be careful of such priors in regression analysis: Now, consider the likelihood.In frequentist statistics, one needs to assume that E in Equation ( 9) is normally distributed.In the Bayesian paradigm, one may do so, but it is not necessary.A Student's t-distribution is often used instead of a Normal distribution in other statistical calculations (e.g., t-tests) due to its additional ("degrees of freedom") parameter, which accommodates the variance arising from small sample sizes more successfully.As in Section 3.1.2,an exponential distribution on the degrees of freedom (ν p ) is specified.It has also been found that specifying a Half-Cauchy distribution on the standard deviation (σ p ) works well [55].Therefore, the hyperpriors are specified as: and: The mean of the likelihood is the final hyperparameter that needs to be specified.This is simply Equation ( 9), written with the priors: The full likelihood can thus be written as: The PyMC3 code is shown below: import pymc3 as pm with pm.Model() as bayesian_regression_model: # Hyperpriors and priors: nu = pm.Exponential('nu', lam=1/len(CDD)) sigma = pm.HalfCauchy('sigma', beta=1) slope = pm.Uniform('slope', lower=0, upper=20) intercept = pm.Uniform('intercept', lower=0, upper=10000) # Energy model: regression_eq = intercept + slope*CDD # Likelihood: y = pm.StudentT('y', mu=regression_eq, nu=nu, sd=sigma, observed=E) # MCMC calculation: trace = pm.sample(draws=10000,step=pm.NUTS(), njobs=4) The last line of the code above invokes the MCMC sampler algorithm to solve the model.In this case, the No U-Turn Sampler (NUTS) [56] was used, running four traces of 10,000 samples each, simultaneously on a four-core laptop computer, in 3.5 min fewer samples, could also have been used.
A discussion of the inner workings and tests for adequate convergence of the MCMC is beyond the scope of the study and has been done in detail elsewhere in literature [4].The key idea for M&V practitioners is that the MCMC, like MC simulation, must converge, and must have done enough iterations after convergence to approximate the posterior distribution numerically.For most simple models such as the ones used in most M&V applications, a few thousand iterations are usually adequate for inference.Two popular checks for posterior validity are the Gelman-Rubin statistic R [57,58] and the effective sample size (ESS).The Gelman-Rubin statistic compares the four chains specified in the program above, started at random places, to see if they all converged on the same posterior values.If they did, their ratios should be close to unity.This is easily done in PyMC3 with the pm.gelman_rubin(trace) command, which indicates R equal to one to beyond the third decimal place.However, even if the MCMC has converged, it does not mean that the chain is long enough to approximate the posterior distribution adequately because the MCMC mechanism produces a serially correlated (autocorrelated) chain.It is therefore necessary to calculate the effective sample size: the sample size taking autocorrelation into account.In PyMC3, one can invoke the pm.effective_n(trace) command, which shows that the ESSs for the parameters of interest are well over 1000 each for the current case study.As a first-order approximation, we can therefore be satisfied that the MCMC has yielded satisfactory estimates.
The MCMC results can be inspected in various ways.The posteriors on the parameters of interest are shown in Figure 3.If a normal distribution is specified on the likelihood in Equation ( 16) rather than the Student's t, the posterior means are identical to the linear regression point estimates-an expected result, since OLS regression is a special case of the more general Bayesian approach.Using a t-distributed likelihood yields slightly different, but practically equivalent, results.The mean or mode of a given posterior is not of as much interest as the full distribution, since this full distribution will be used for any subsequent calculation.However, the mean of the posterior distribution(s) is given in Table 3 for the curious reader.
Two brief notes on Bayesian intervals are necessary.As discussed in Section 1.1, the frequentist 'confidence' interval is a misnomer.To distinguish Bayesian from frequentist intervals, Bayesian intervals are often called 'credible' intervals, although they are much closer to what most people think of when referring to a frequentist confidence interval.The second note is that Bayesians often use HDIs, also known as highest posterior density intervals.These are related to the area under the probability density curve, rather than points on the x-axis.In frequentist statistics, we are used to equal-tailed confidence intervals since we compute them by taking the mean, and then adding or subtracting a fixed number-the standard error multiplied by the t-value, for example.This works well for symmetrical distributions such as the Normal, as is assumed in many frequentist methods.However, real data distributions are often asymmetrical, and forcing an equal-tailed confidence interval onto an asymmetric distribution leads to including an unlikely range of values on the one side, while excluding more likely values on the other.An HDI solves this problem.It does not have equal tails but has equally-likely upper and lower bounds.3. Notice how the slope and intercept estimates are correlated: as the slope increases, the intercept decreases.The Markov Chain Monte Carlo (MCMC) algorithm explores this space, resulting in the real joint two-dimensional posterior distribution on the slope and intercept.
The posterior distributions shown in Figure 3 are seldom of use in themselves and are more interesting when combined in a calculation to determine the uncertainties in the baseline as shown in Figure 4, also known as the adjusted baseline.To do so, the posterior predictive distribution needs to be calculated using the pm.sample_ppc() command, which resamples from the posterior distributions, much like the MC simulation forward-step of Figure 1.The Bayesian model can also be used to calculate the adjusted baseline, or what the postimplementation period energy use would have been, had no intervention been made.The difference between this value and the actual energy use during the reporting period is the energy saved.For the example under consideration, the IPMVP assumes that an average month in the post-implementation period: one with 162 CDDs.It also assumes that the actual reporting period energy use is 4300 kWh, measured with negligible metering error.
To calculate the savings distribution using the Bayesian method, one would do an MC simulation of: where θ 0 and θ 1 are the distributions shown in Figure 3.Note that they are correlated and so using the PPC method described above would be the correct approach.Running this simulation with 10,000 samples yields the distribution shown in Figure 5.The 95% HDI is [2229, 2959], while the frequentist interval is [1810,3430] for the same data-a much wider interval.Furthermore, the IPMVP then assumes averages and multiplies these figures to get annual savings and uncertainties.In the Bayesian paradigm, the HDIs can be different for every month (or time step) as shown in Figure 4, yielding more accurate overall savings uncertainty values.
Robustness to Outliers
As alluded to above, using the Student's t-distribution rather than the normal distribution allows for Bayesian regression to be robust to outliers [59].The heavier tails more easily accommodate an outlying data point by automatically altering the degrees-of-freedom hyperparameter to adapt to the non-normally distributed data.Uncertainty in the estimates is increased, but this reflects the true state of knowledge about the system more realistically than alternative assumptions of light tails, and is therefore warranted.The robustness of such regression does not give the M&V practitioner carte blanche to ignore outliers.One should always seek to understand the reason for an outlier; if the operating conditions of the facility were significantly different, the analyst should consider neglecting (or 'condoning') the data point.However, it is not always possible to trace the reasons for all outliers, and inherently robust models are useful (Technical note: the treatment here is very basic, and for illustration.More advanced Bayesian approaches are also available.For example, if there are only a few outliers, a mixture model may be used [60].If there is a systematic problem such an unknown error variable, one can "marginalise" the offending variable out.The right-hand and top distributions of Figure 3 are marginal distributions: e.g., the distribution on the slope, with the intercept marginalised out, and vice versa.For an M&V example of marginalisation where an unknown measurement error is marginalised out, see Carstens [61] (Section 3.5.3).von der Linden et al. provides a thorough treatment of all the options for dealing with outliers [3] (Ch. 22)).
To demonstrate the robustness of such a Bayesian model, consider the regression case above.Suppose that for some reason the December cooling load was 3250 kWh and not 8250 kWh, indicated by the red point in the lower right-hand corner of Figure 6.If OLS regression were used, and this point is not removed, it would skew the whole model.However, the t-distributed likelihood in the Bayesian model is robust to the outlier.The effect is demonstrated in Figure 6.Four lines are plotted: the solid lines are for the data set without the outlier.The dashed lines are for the data set with the outlier.In the Bayesian model, the two regression lines are almost identical and close to the OLS regression line for the standard set.However, the OLS regression on the outlier set is dramatically biased and would underestimate the energy use for hot months due to the outlier.
Hierarchical Models
A further advantage in the Bayesian paradigm is the use of hierarchical, or multilevel models.This is a feature of the model structure rather than the Bayesian calculation itself (it also works for MLE) [2], but it is nevertheless useful in M&V.Suppose that multiple measures are installed at multiple sites so that the IPMVP Option C: Whole Building Retrofit is used for M&V.The UMP Chapter 8 [62] reports that there are two ways to analyse such data.The two-stage approach involves first analysing each facility separately and then using these results for the overall analysis in stage two.The fixed effects approach analyses all buildings simultaneously but assumes that the effect sizes are constant across facilities, using an average effect for all buildings.Hierarchical modelling considers both the individual facility's energy saving and the overall effect simultaneously.It does this by assuming that the group effects are different realisations of an overarching distribution with a mean and variance, which is used as a prior.This can lead to 'shrinkage' in the parameter uncertainty estimates because the group effects are mutually informative.For groups with little data, the overarching effect distribution plays a larger role, and for groups with more data, a smaller role.In addition, the overall variance is reduced because the sources of inter-facility variance are isolated from that of inter-measure variance.The result for a hierarchical model is that the effect estimation for an individual facility is influenced by the overall estimate of the measured effect, as well as by the data for the facility.As another example, consider a program that retrofits air conditioning units in different provinces in South Africa.One could fix the savings effect across all facilities, but this will underestimate some and overestimate others.Otherwise, one could analyse by facility, then by province, and then overall.The hierarchical model provides a better alternative in these cases, and comprises the bulk of many Bayesian data analysis texts [2,4].Booth, Choudhary, and Spiegelhalter have provided an excellent example of using hierarchical Bayesian models in energy M&V [63].
Bayesian Alternatives for Standard M&V Analyses
At this point, an M&V analyst may want to try the Bayesian method for an M&V problem, but where to start?In Table 4, some Bayesian alternatives to standard M&V analyses are given.The references cited are mostly from M&V studies, although some general statistical sources are also listed where applicable.
Conclusions
The Bayesian paradigm provides a coherent and intuitive approach to energy measurement and verification.It does so by defining the basic M&V question-the savings inference given measurements-using conditional probabilities.It also provides a simpler and more intuitive understanding of probability and uncertainty because it allows the analyst to answer real questions in a straightforward manner, unlike traditional statistics.Due to recent technological and mathematical advances being incorporated into software, analysts need not be expert statisticians to harness the power and flexibility of this method.
The probabilistic nature of Bayesian analysis allows for automatic and accurate uncertainty quantification in savings models.The richer nature of the Bayesian result is shown in a sampling and a regression problem, where it is found that the Bayesian method allows for more realistic modelling and a greater variety of questions that can be answered.Its flexibility is also demonstrated by constructing a robust regression model, which is much less sensitive to outliers that standard ordinary least squares regression traditionally used in M&V.
Figure 3 .
Figure 3. Joint plot of posterior distributions on the parameters of interest.The summary statistics are given in Table3.Notice how the slope and intercept estimates are correlated: as the slope increases, the intercept decreases.The Markov Chain Monte Carlo (MCMC) algorithm explores this space, resulting in the real joint two-dimensional posterior distribution on the slope and intercept.
Figure 4 .
Figure 4. Measured data with overlaid Bayesian baseline model and its 95% HDI.
Figure 5 .
Figure 5. Distribution on the savings for a month with 162 Cooling Degree Days (CDDs).
Figure 6 .
Figure 6.Demonstration of robustness of t-distributed Bayesian regression.Note that the two Bayesian regression lines (solid and dashed) coincide almost perfectly.
Table 1 .
Cooling Degree Day (CDD) Data for International Performance Measurement and Verification Protocol (IPMVP) Example B-6.Note that these data were reverse-engineered to yield the same regression results as reported in the IPMVP.The original data were not reported in the IPMVP.
Table 3 .
Summary statistics for Bayesian posterior distributions shown in Figure3when a Student's t-distribution is used on the likelihood.Compare to linear regression results in Table2.HDI: Highest Density Intervals.
Table 4 .
Common M&V (Measurement and Verification) cases and their Bayesian alternatives. | 10,434.2 | 2018-02-06T00:00:00.000 | [
"Engineering",
"Environmental Science",
"Computer Science"
] |
On scale-free extensions of massive (bi-)gravity
We discuss a scale-free model of bigravity, in which the mass parameter of the standard bigravity potential is promoted to a dynamical scalar field. This modification retains the ghost-free bigravity structure, in particular it remains free of the Boulware-Deser ghost. We investigate the theory's interaction structure, focusing on its consistent scaling limits and strong coupling scales. Furthermore we explore the model's quadratic action, both around generic background configurations and paying special attention to cosmological backgrounds and to the associated background evolution. Finally we consider the possibility of realizing a phase of late-time acceleration as well as a quasi-de Sitter inflationary stage at early times, when the promoted"mass scalar"becomes the inflaton.
1 Introduction The discovery of healthy massive and bi-gravity models ( [1-3] and [4, 5] respectively) paved the way for the exciting possibility that late-time cosmic acceleration could be driven by massive spin-2 degrees of freedom.However, such theories generically come with a very low strong coupling scale, which makes extracting the prediction of (a UV completion of) these theories at high energies/early times very difficult, if not impossible.For example, around Minkowski massive (bi-)gravity has a strong coupling scale Λ 3 = (m 2 M Pl ) 1/3 , where m is the (technically natural) mass of the graviton.When this mass is of order the Hubble scalean identification phenomenologically motivated by the desire to have this theory playing the role of dark energy at late times -we have that Λ 3 ∼ 1000km −1 .While such a low strong coupling scale does not impact our ability to find cosmological solutions for this theory at late times 1 , it seriously calls into question the predictivity of the theory at small scales (e.g.solar system tests of gravity) and at high energies (early times).
An obvious modification of ghost-free massive and bigravity that may improve this situation is to promote the small coupling constant of the theory -the mass of the graviton m -to a field Φ and render the theory scale-free up to the residual presence of M Pl . 2 This is what we investigate in this paper.Theoretically the hope is to gain better (perturbative and weakly coupled) control of the theory via a strong coupling scale, which depends on the (local) background/vev value of the scalar field Φ and indeed we will find such a dependence.As such we will present the interaction structure of the resulting theory and show that the presence of the new dynamical scalar degree of freedom Φ leads to interesting modifications also at low energies.Cosmologically speaking the hope is that we obtain an extended bigravity model, which is capable of realising late-time accelerated expansion as well as making reliable predictions for the early universe and an associated potential inflationary period.We note that our approach is somewhat analogous to what has been done in a more generic setting for massive gravity in the context of "mass-varying massive gravity" models [14] 3 , with tight additional restrictions arising from our requirement of scale-freeness.
While this mass-varying nature of our model is what will allow us to have a "running" strong coupling scale of the theory (i.e. one that depends on the evolution of Φ), this feature of course replaces the technically natural mass scale m with an evolving field.As such we are faced with a mass hierarchy problem, since at late times we will require Φ ∼ H 0 in order for a well-behaved dark-energy contribution to arise, yet H 0 M Pl .Scale free models can be powerful frameworks in addressing such mass hierarchy problems [7-13] and as such the hope here is that, after promoting m to be a scalar field, we can dynamically generate the correct scales without the need to introduce additional scales into the action by hand.Of course, and as briefly mentioned above, our approach is only the first step in rendering the theory fully scale free, even at the classical level.Rendering the classical action fully-scale free one would need to pai our work with that of [7-13] in order to promote the residual scale M Pl → Ψ, where Ψ is a dynamical field as well and supplement this with a mechanism to dynamically recover the Planck scale, i.e. a Higgs mechanism for Ψ based on spontaneous symmetry breaking that allows this field to settle to a value Ψ ∼ M Pl .However, we re-emphasise that here we only tackle the first part of this problem and probe the most cosmologically interesting scale m and how this can be promoted to a field in a scale-free way. 4 Also note that, even classically and in spirit with the scale-generation via spontaneous symmetry breaking argument above, around a given non-trivial cosmological background a scale will of course be generated spontaneously, as we will see explicitly in section 5. Finally a comment on loop corrections: Once our model has been fully embedded in a fully scale-free classical theory, with all explicit mass scales in the action promoted to fields and effective scales arising via symmetry breaking, it may still be the case that loop corrections will generate an effective scale.Examples where loop corrections may break scale freeness by introducing such a mass scale include [18], but notice that this does not always have to be the case [8] and one can in principle build theories which are scale free both at classical and quantum level.Here we will focus on the first step -constructing a scale-free classical model -and will leave loop corrections and the stability of scale-freeness under these to future work.
Outline: In section 2 we introduce and motivate scale-free bigravity.This is followed by an investigation of its interaction structure, strong coupling scales and scaling limits in section 3.Then, in section 4, we study the general quadratic perturbative action of the theory, both for general backgrounds and specialised to cosmological Friedmann-Lemaître-Robertson-Walker (FLRW) backgrounds.In section 5 we finally consider specific realisations of the theory and investigate whether they give rise to accelerated expansion in the early and/or late universe, before we conclude in 6.We also collect some additional useful results in the appendices.
Notation and conventions: Throughout we use the following conventions.We set c = = k Boltzmann = 1.M Pl = 1/ √ 8πG 2.4 × 10 18 GeV is the reduced Planck mass.We work with the metric signature (−, +, +, +), and we restrict to D = 4 spacetime dimensions.With and with • we indicate derivatives with respect to conformal time and cosmic time, respectively.We use Greek letters µ, ν, . . . to denote spacetime indices, which are raised and lowered as specified.Capital Latin letters A, B, . . .are reserved for Lorentz indices and are raised and lowered with the Minkowski metric η AB .Bracketed indices (i), (j), . .., label different fields -label indices are not automatically summed over; whether they are upper or lower indices carries no meaning.
Scale-free Bigravity
Ghost-free bigravity [4, 5] typically comes with two hierarchically ordered scales: Firstly the (in principle) two Planck masses M Pl , directly associated to the kinetic interactions of the two spin-2 fields in the theory, which are in principle distinct but which will be identified for the purposes of this paper.As such the first scale is Pl .In addition there is the mass scale m, i.e. the parameter controlling the mass of the massive graviton mode in the theory. 5Note that m is technically natural and protected by diffeomorphism symmetry.This ensures that the (late-)cosmologically motivated scenario with a hierarchy m M Pl can be realised, with dark energy-like self-accelerating solutions.Here we present and discuss a very simple extension of ghost-free bigravity in which the mass scale m is promoted to be a dynamical field, as motivated in the introduction above.We do this in such a way that no mass scale is introduced in the theory other than M Pl , which makes this approach different from the closely related general mass-varying massive gravity approach [14] (on top of the obvious fact that we also consider bi-and not massive gravity, thereby also promoting a fiducial fixed reference metric to a dynamical field -we will come back to the massive gravity limit later though).We can write our theory down in two equivalent formulations, the vielbein and metric formulations.We will now briefly discuss both and their equivalence, since both will be useful in different contexts discussed later in the paper.
Vielbein and metric formulations of the theory
The vielbein version: The theory we propose is a very straightforward generalisation of standard ghost-free bigravity [4, 5], closely related to models of mass-varying massive gravity [14].We promote the graviton mass parameter m to be a scalar field of mass dimension one and endow that field with a canonical kinetic term and a potential.As such our model has the following action formulated in terms of 2 vielbeins/spin-2 fields E (1) and E (2) and the corresponding vielbein one-forms A µ dx µ .This means each spin-2 field comes equipped with an Einstein-Hilbert term (first line), we have massive bigravity interactions with a graviton mass that has been promoted to be a field Φ (second and third line), we have an additional piece of the action giving Φ dynamics (first term in the last line) and finally we have a minimal coupling of matter, via the matter Lagrangian L m containing the matter fields Ψ i , to one of the vielbeins E (1) (second term in the last line). 6Note that there are five dimensionless coupling constants β i in addition to the dimensionful coupling constant M Pl .In an effective field theory spirit we will consider the β i to be constant O(1) parameters.The metric corresponding to each vielbein satisfies and comes with an associated covariant derivative ∇ (i) , while the wedge product ∧ in (2.1) has been defined as totally anti-symmetrising space-time indices as usual.
The potential for Φ, W (Φ) is in principle unrestricted.However, if we insist that there are no other dimensionful scales in the theory other than M Pl , i.e. we forbid any dimensionful scales from hiding in W (Φ), this means we can write where λ is a dimensionless parameter of arbitrary size 7 .Note that the constraint structure of healthy massive and bi-gravity models carries over and ensures that no ghostly Boulware-Deser degrees of freedom propagate [14].As such, around a flat Minkowski background, we have 8 propagating degrees of freedom: 5 (massive graviton) + 2 (massless graviton) + 1 (the new scalar Φ), one dimensionful scale/mass parameter M Pl and six dimensionless parameters β i , λ.For a more detailed discussion regarding degree of freedom counting for analogous models see [22].
The metric version: For comparison we can also write down the metric version of our theory.In the presence of the symmetric vielbein condition
B
µ η AB , which we discuss further below, the two versions become physically equivalent.In the metric picture our theory takes on the form where we will take D = 4 in what follows and for later convenience we define a potential β n e n g −1 (1) g (2) . (2.5) The β i are the same as above and the e n are elementary symmetric polynomials satisfying (for some matrix X) where we have defined As such, the elementary symmetric polynomials can explicitly be written as where square brackets [• • • ] denote taking the trace.While we will use the metric formulation of the theory when computing cosmological solutions later, we will find the vielbein formulation more useful when probing the interaction structure of the theory.
Equivalence of formulations: Above we have discussed both the vielbein and metric formulations of our model.Working in different formulations will be useful in what follows below, but we want to briefly recap why these two formulations are equivalent in our context.On certain branches of solutions (the ones we will consider -for a more complete discussion including alternative branches see [23, 24]) the "symmetric vielbein condition" can be enforced.This is equivalent to the statement that we can set the so-called DvN (Deser-van Nieuwenhuizen) gauge 8 which imposes the following relation between two distinct vielbeins E (i) and E (j) (in matrix notation) where η denotes the flat Minkowski metric as before.We can then use this condition and the expressions of the metrics in terms of their vielbeins to find [25] which relates our two formulations and identifies the two actions (2.1) and (2.4) (and in particular the mass terms and the β i coefficients) as equivalent upon noticing that we can re-write the mass terms in the following way where we have picked one particular mass term and β i for illustration, but have kept all numerical arguments as explicit as possible to emphasize that an analogous argument follows through for all other mass terms too.Notice how all residual factorial factors are swallowed up into e 3 in moving to the third line.In moving from the second to the third line we have also extracted an overall factor of det E (1) , where this choice is arbitrary (i.e.we could just as well have extracted det E (2) ).
Equations of motion and constraints
Equations of motion: We now move on to consider the dynamics of our model at the level of the equations of motion.We will do so in the metric language and, in order to keep notation clean, will define g (1) = g and g (2) = f .The equations of motions for g µν and f µν are then given by ) where to simplify the notation we have introduced the following tensors µν is the energy momentum tensor of matter and The definition of the Y ν (n)µ (X) matrices closely mimics that of the elementary symmetric polynomials and is as follows: (2.17) The equation of motion for the field Φ can be written as where W ,Φ ≡ dW/dΦ.
Bianchi constraints: As a consequence of the Bianchi identity, we find the following Bianchi constraints (for each one of the two metrics) where the overbar indicates covariant derivatives with respect to the f metric.Both these constraints follow from the invariance of the action under the diagonal subgroup of the general coordinate transformations of the two metrics.
It is easy to show that the Bianchi constraint (2.21) is equivalent to the covariant conservation of the total energy momentum tensor where T Φ µν is the energy momentum tensor for the scalar field.The lagrangian for Φ is Therefore, the energy momentum tensor for the scalar field is given by It follows that where the last identity follows from eq. (2.21).
Interaction structure and strong coupling scales
We now take our model (2.1) and make the propagating degrees of freedom explicit in order to better understand the interaction structure of the theory.For this it will turn out to be useful to work in the vielbein formulation.A priori one might expect that the interaction structure is very different with respect to the "standard" bi-gravity case, especially since scalar modes are expected to mix already at the level of the quadratic action, which would result in a different diagonalisation procedure and different dynamics for the propagating degrees of freedom.Also, several of the interactions which vanish up to total derivatives in the standard bigravity case will now remain, since the "mass scale prefactor" is now dynamical.
As such we will take particular care in going through the derivation and will not simply port expressions or field normalisations from the analogous bigravity calculation [6].
The field content
Stückelberg fields and degrees of freedom: We want to restore diffeomorphism invariance in our action in order to make the dynamics of the different helicity modes explicit (as the helicity 0, 1 and 2 modes are all bundled together in h (1) and h (2) which are perturbations around the background for E (1) and E (2) respectively).As such let us begin by briefly recapping the use of Stückelberg fields to restore diffeomorphism invariance.We have two vielbeins in the theory, E (1) and E (2) , transforming under two copies of general coordinate transformations, GC (1) and GC (2) .The mass interaction term(s) break this invariance down to the diagonal subgroup GC (1) × GC (2) .The Stückelberg trick then amounts to restoring the full unbroken invariance at the expense of introducing additional gauge fields, which will eventually turn out to capture the different helicity degrees of freedom of the graviton(s) in the theory.In effect the diffeomorphism Stückelberg replacement amounts to a field transformation of one of the vielbeins Here we have chosen to transform E (2) , but this choice is of course arbitrary.For a discussion of dualities and ambiguities in the context of choosing Stückelberg transformations for bi-and multi-gravity models see [26, 27]. 9 The kinetic, Einstein-Hilbert, terms are gauge-invariant under diffeomorphisms, so remain unmodified under this replacement.We may now expand the vielbeins and Stückelberg fields as effectively choosing to expand our theory around a Minkowski background.In (3.2), h (1) , h (2) , B, π are the fields which will capture the two helicity-2 modes as well as helicity-1 and -0 modes of the massless and massive graviton respectively.Note that we have already chosen to canonically normalise the h fields in the above, since this normalisation will be controlled by the known Einstein-Hilbert term.The normalisation of the other fields is left for later, since this will be determined by the quadratic action for those fields.In what follows for simplicity we will drop the combined (i, j) indices, that keep track of the symmetry group(s) the Stückelberg fields know about, since having chosen to transform E (2) here, there will only be one π and one B field.Another note is in order before we proceed: in the vielbein formulation it is not just copies of general coordinate invariance which interactions break down to their diagonal subgroup, but the same also happens for Lorentz invariance.The Lorentz Stückelberg fields will crucially modify the interactions of the helicity-1 mode, which is why in the following we contain ourselves to investigating the helicity-2/0 interactions and we leave an investigation of interactions involving helicity-1 modes for future research -for an analogous calculation in the standard massive (bi-)gravity setting, see [6, 29].From here on we will therefore set B = 0.
A local field expansion and scaling limits:
There is an inherent tension in what we are trying to achieve here.On the one hand we have intentionally built an, except for M Pl , scalefree theory.Yet on the other hand we are here trying to obtain a perturbative understanding of the interaction structure of the theory.The helicity-0 mode will inherit its normalisation from the mass term, which now comes with a time-dependent "mass scale" φ.From the form of the interactions one should therefore expect that the scales determining when any particular perturbative expansion of the theory is valid (strong coupling scales), will now depend on the background value of Φ (or, in a different language, on its vev).In order to make this explicit and understand the evolving strong coupling scale while simultaneously maintaining our scale-free theory, we will perform a local expansion of Φ around some fixed reference value φ 0 .We emphasise that φ 0 is fixed, so it is not a dynamical background field.In other words we will perform the split The condition δφ φ 0 ensures that we can normalise modes coming from the mass term using φ 0 at leading order and have a well-defined perturbative expansion in powers of δφ.Obviously this will only give a locally valid expansion, as there is no guarantee that the evolution of Φ will not eventually lead to δφ φ 0 for an arbitrary previously chosen φ 0 .However, locally (by which we mean: local in space-time, but particularly "local" in time) this will be a useful expansion to use.In this way we will get a handle on what interactions exist locally, for which configurations the perturbation theory breaks down and what the relevant strong coupling scales are.
Propagating degrees of freedom
Tadpole cancellations: Armed with the above Stückelberg and field expansion schemes, we can now go through the action order-by-order.Throughout we will ignore contributions coming from W (Φ) -these can straightforwardly be added once a concrete form for this potential is specified. 10First up are terms linear in the fields, i.e. tadpole terms.We would like to remove these terms so that the backgrounds we have chosen really are solutions of the theory 11 .This will impose a condition on the dimensionless order one coefficients β i of the theory.Using the above expansions we find that the resulting linear terms are given by where we have defined h ≡ h (1) and l ≡ h (2) to avoid clutter.Removing these terms imposes the following conditions (which we choose to express as conditions on β 0 and β 4 ): In what follows we will impose those conditions, so that we are in effect left with three dimensionless O(1) parameters: The quadratic action: Next up is the quadratic action, which importantly will determine how we have to normalise the π field.We should expect mixing not just between the h fields and π (scalar-tensor mixing) but also between δφ and π (scalar-scalar mixing), both of which should be removed via diagonalising transformations.We begin by ignoring mass terms (i.e.quadratic non-derivative interactions) and look at the kinetic interactions at the quadratic level.We split these into pure scalar, pure tensor and scalar-tensor interactions S kin 2 = S kin scalar + S kin tensor + S kin scalar−tensor .
We first look at pure scalar interactions, involving the Stückelberg field π and the scalar δφ.The field π does not have its own kinetic term and in the standard bigravity case obtains its kinetic term via demixing from the tensors.Here scalar interactions are in principle also mixed, which (after demixing the scalars) would give rise to an apparent ghost.Explicitly we find where we have used the shorthand π ν µ ≡ ∂ µ ∂ ν π.This immediately looks dangerous, since the associated kinetic mixing matrix has opposite sign eigenvalues, so one of the two modes would behave as a ghost.However, a closer look shows that the tadpole cancellation requirements from above in fact eliminate the scalar mixing term and as a result the scalar action simply reduces to This means that π will have to inherit its kinetic term from scalar-tensor mixing terms as usual and that δφ is automatically decoupled from the other fields at quadratic level.As such the rest of this section can proceed just as for the standard bigravity case.
Moving on we now consider pure tensor and scalar terms together, where we recall that we defined h ≡ h (1) and l ≡ h (2) .We focus on the h − π mixing (the argument will be the same for l − π).Pure tensor interactions for h (and analogously for l) are given by i.e. a linearised Einstein-Hilbert term, whereas the scalar-tensor mixing interactions between the scalar π and h at quadratic order are Note that here we have already substituted in all the expressions above the expression for β 0 , β 4 in eq.(3.5), coming from tadpole cancellation requirements, as we will in what follows throughout this section.Demixing these h−π interactions and the analogous l−π interactions amounts to performing the following two linearised conformal transformations where η denotes the flat Minkowski metric as usual.Finally we can canonically normalise π by sending which then results in the fully demixed kinetic quadratic action Finally we look at the potential interactions at quadratic order.After the replacements for tadpole cancellation, demixing kinetic modes and normalising the fields, we find The mass matrix between the different modes remains mixed just as in the standard bigravity case, with all residual terms proportional to powers of φ 2 0 .Note that δφ is completely decoupled, but h, l, π are all mixed.
Non-linear interactions and strong coupling
Cubic interactions: We can now finally move on to higher order interactions, which in particular will set the strong coupling scales of the theory and describe its true "interaction structure".The same tensor-scalar interactions (and resulting pure scalar interactions via (3.11)) are present as for the standard bigravity theory.However, in addition new tensorscalar and scalar-scalar interactions are present in our theory as well.
In order to disentangle these two types of interactions, and their different physical properties, we will use two types of scaling limits.We begin by taking the following scaling limit, which will eliminate all cubic interactions involving tensors (3.15) This limit isolates pure scalar-scalar interactions at cubic order, which are given by where we have suppressed constant dimensionless O(1) factors in going to the second line.These pure scalar interactions immediately underline the need for δφ φ 0 in order for our perturbative approach to be valid.Otherwise e.g. the second term above immediately becomes larger than the (quadratic order) kinetic term for π, invalidating a perturbative expansion like ours here, which implicitly assumes that higher orders are subsequently more suppressed than lower orders (otherwise we in general need to keep track of arbitrarily large orders and can never truncate).Also note the first term, which is simply a non-derivative potential-type term, has not disappeared here since φ 0 cannot simply be taken to zero without invalidating the perturbative approach.Note that one can, however, take φ 0 → 0 if one is willing to scale (and in principle eliminate) δφ at the same time (see below).As long as δφ φ 0 and, as inspection of the above action shows, also |δφ(2π) 2 | |φ 3 0 π µ π µ |, the cubic action is under control.This is effectively a restriction on the validity of our local Φ → φ 0 +δφ expansion.Since φ 0 can be chosen arbitrarily, we can always (at least for a 'short time') satisfy these conditions. 12Even though it may therefore be tempting to turn these conditions into a 12 When expanding around the value taken by Φ at a given time, instantaneously (i.e. at that given time) δφ = 0 and the inequality is trivially satisfied for any non-zero Φ.How long the expansion around φ0 remains valid will depend on the evolution of Φ and hence on the choice of potential and mass interactions and coupling constants in the action.However, for a smoothly and continuously evolving Φ and hence δφ the expansion will always remain valid for a finite and non-zero length of time.
new additional "cutoff", one should refrain from doing so, since this is purely a result of the initial choice of φ 0 and a choice that satisfies the above inequalities can always be made. 13econdly we consider another scaling limit, which essentially recovers the standard decoupling limit of bigravity.Here we eliminate the new dynamical scalar δφ altogether and afterwards (the ordering is important) take a scaling limit resembling the bigravity Λ 3 decoupling limit, where φ 0 plays the role of the bigravity mass parameter m.The limit we take is therefore where δφ → 0 before the remaining scaling limit is taken, as discussed above.Focussing on the scalar interactions that arise from the scalar-tensor interactions via the demixing transformation (3.11), we find where we have suppressed constant dimensionless O(1) factors in going to the second line.These interactions unsurprisingly are precisely analogous to those found for standard bigravity, with m → φ 0 and an associated strong coupling scale Λ3 .
Having considered two particular scaling interactions, let us now pull everything together and look at the complete set of interactions at cubic order involving scalars only (postdemixing via (3.11)).We find where the additional terms that are suppressed in the two scaling limits considered above are pure π interactions suppressed by scales larger than Λ3 , as they would exist in standard bigravity as well.In summary, the final result for the cubic action shows that we have the same cubic interactions as for standard bigravity, with m → φ 0 , supplemented by perturbative corrections suppressed by 1/φ p 0 , where p is some power p ≤ 3. When φ 0 is chosen such that our perturbative expansion is valid 14 , Λ3 therefore is the strong coupling scale of 13 For example, consider a monotonically growing φ.Once the perturbative description around a given initially chosen φ0 becomes strongly coupled (since δφ becomes larger and larger and eventually dominates over φ0), we simply choose to expand around a new more 'recent' φ0, where φ0 = Φ(t1), φ0 = Φ(t2) and t2 > t1, and can recover a valid perturbative description in the process.In this sense we suggest thinking of φ0 as a 'reference value' -while it does instantaneously satisfy the background equations of motion for Φ, φ0 once chosen and as defined by us here, has no dynamics (i.e. it is not a dynamical background variable).It is a constant reference value useful to keep track of the dominant normalising effects for the fields, but all the dynamics for Φ resides in δφ. 14Recall that this requires δφ φ0 as well as a restriction on the relation between δφ and φ 3 0 , as discussed above.
the theory, as may have been guessed naively.We emphasize that, just as the discussion of the quadratic action, this hinges on enforcing the tadpole cancellation requirements (3.5).Otherwise a whole new host of interactions at different scales would apparently be present.
Higher order interactions: The structure we observed for cubic interactions is generic.Consider as a second explicit example interactions at quartic order.Taking our first scaling limit SL 1 we then find where as before we have suppressed constant dimensionless O(1) factors in going to the second line, we have a potential-term like contribution and extra derivative interactions suppressed by powers of φ 0 .Note that the same conditions as for the quadratic and cubic interactions still ensure that our perturbative expansion is valid at this order.Moving on to look at SL 2 for quartic interactions we have where we now suppress constant dimensionless O(1) factors from the start to avoid clutter and we can read off the effective strong coupling scale Λ3 again and see the same type of interactions as for the standard bigravity decoupling limit.Note that the pure-scalar interactions from before de-mixing, which come in at lower scales ( Λ5 for cubic order, Λ4 for quartic order etc.) cancel up to total derivatives due to the anti-symmetric structure of the interaction potential, just as for standard massive and bi-gravity.
The above interactions are supplemented by other scalar interactions that vanish in the limits considered above, i.e. suppressed by scales larger than Λ3 and/or powers of φ 0 .All the interactions are (Boulware-Deser) ghost-free, as shown by the constraint analyses [14], even though the corresponding equations of motion at higher orders naively (i.e.without applying additional transformations) become higher-order in derivatives (and hence naively lead to Ostrogradski instabilities), just as for the standard bi-and multi-gravity cases [27, 28].
Given that this overall structure stays in place also at other generic higher orders, it makes sense to write Λ strong coupling = Λ3 , which is the scale where perturbative unitarity is lost 15 .We re-emphasise that this result is highly non-trivial, given that the terms with the new dynamical scalar Φ = φ 0 + δφ change the structure of interactions (by providing additional vertices) and could have changed the relevant suppressing energy scales as well.What was crucial for Λ3 to become the effective strong coupling scale was that the extra scalar δφ decoupled at quadratic order due to the tadpole cancellation conditions (3.5), so that no extra de-mixing at this order was necessary and the field normalisations therefore stayed as they were in standard bigravity.
Vainshtein screening and the equations of motion
In order to see what phenomenological effects the new scaling limit interactions might have, we now compute the contribution to the π equations of motion from the different limits presented above.We do so in the case of a spherically symmetric and static field configuration (e.g.around a central point-like matter source), in close analogy to what is done for galileons [31].
We focus on the cubic order contributions and find that the contribution to the π equations of motion coming from (3. 16) is where we have suppressed constant O(1) dimensionless constants from the start this time and ≡ ∂/∂ r .From (3.18) we have The contribution seen in (3.24) are exactly as for standard bigravity with m → φ 0 , as expected.Note the higher-derivative nature of the equations of motion -this does not lead to an Ostrogradski ghost, since the cubic order action is complemented by infinitely many higher order terms and the full action written in this way is therefore degenerate.We will discuss this issue at the level of the action in the following subsection.The new terms in (3.23), suppressed by powers of φ 0 as expected, give new non-linear contributions in the spherically symmetric and static case considered here.This is consistent with the standard Vainshtein screening (since we can make δφ arbitrarily small for the initial evolution from any point onwards by choosing φ 0 appropriately), but the terms in (3.23) will modify the non-linear background solution for π and hence also modify the Vainshtein radius and screening effects.How this takes place again will be highly dependant on the evolution of Φ and hence on the choice of potential and initial conditions for Φ.
The massive gravity limit
Having discussed the interaction structure for our "scale free" model of bigravity above, we can easily deduce what the interaction structure would be for an analogous model of scale-free massive gravity, which would be a particular model of the so-called "mass-varying massive gravity" type [14].It corresponds to freezing one of the dynamical vielbeins in (2.1) -for definiteness (this is an arbitrary choice) we freeze E (2) by sending E (2) A µ → δ A µ or equivalently by setting g (2) µν = η µν in (2.4).We still introduce Stückelberg fields via this now fixed reference metric.We emphasise that what we mean by the "massive gravity limit" here literally consists of freezing one metric/vielbein and we do not try to obtain this limit as a decoupling limit of the full action, but we do keep the β 4 term, which now becomes a simple standard mass term for Φ in flat space.In the following we briefly go through the same steps as above to show what the interaction structure of the corresponding scale-free massive gravity model is and what changes in comparison to the bigravity case considered above.
Tadpoles and the quadratic action: Inspection of (3.4) suggests that the tadpole conditions do not change in the (single) massive gravity case and an explicit check verifies that we still require for the linear tadpole terms to cancel.Moving on to the quadratic action, we see that scalarscalar mixing is again forbidden by implementing the tadpole conditions (otherwise it would still take on the form (3.5)).Scalar-tensor mixing at quadratic order is still eliminated by the linearised conformal transformation and of course no transformation for the second tensor (l) is needed any more, since l is not a dynamical degree of freedom in massive gravity.Finally we can canonically normalise π by sending π → π which then results in the fully demixed kinetic quadratic action and where we note that we have an extra factor of √ 2 in comparison to the bigravity case, owing to the fact that we only demixed from one and not from two tensors.
Non-linear interactions (cubic):
We will again utilise the two scaling limits SL 1 , SL 2 defined above in order to disentangle interactions.At cubic order we now have where nothing has changed in comparison with the bigravity case except for some numerical factors due to the changed normalisation of π for the quadratic action.However, for our second scaling limit, i.e. the one resembling the standard bigravity decoupling limit, we have We notice two differences when comparing with (3.18): (1) Firstly the absence of a term like π µ π µ 2π.This is due to the fact that now we are Stückelberging a fixed reference metric, whereas previously we had to Taylor-expand E (2) post-Stückelberging, which gave rise to a non-local dependence on π via terms such as the one missing here. 16Note that at cubic order scalar-tensor mixing, and hence the appearance of terms like the one missing here, could also be removed by a local field re-definition in the bigravity case, but at higher orders this is not the case.We will see the difference between the scale-free massive and bi-gravity cases related to these terms even more clearly at quartic order below.( 2) The now non-dynamical nature of E (2) also leads to a different β-dependence when compared with (3.18).Unsurprisingly the interactions found in the SL 2 limit here are precisely analogous to those found for standard massive gravity, with m → φ 0 and an associated strong coupling scale Λ3 .Pulling everything together at cubic order we find that the complete set of interactions at this order is where comparison with (3.19) reveals a modified β-dependence compared with the bigravity case as discussed above.
Non-linear interactions (quartic): Moving on to quartic interactions, in our first scaling limit SL 1 we find In this limit we again see no differences to the bigravity case except for numerical factors coming from the slightly different normalisation for π.Differences to the bigravity case are more pronounced in the SL 2 scaling limit, where we obtain and comparison with (3.21) empasises the point discussed for cubic interactions above.Namely that additional higher-derivative interactions coming from the dynamical nature of both vielbeins in the bigravity case are absent in the massive gravity case.As before, at quartic order the above interactions are supplemented by other scalar interactions that vanish in the limits considered above, i.e. suppressed by scales larger than Λ3 and/or by powers of φ 0 .
Quadratic action on generic backgrounds
In the previous section we have investigated the interaction structure of scale-free bigravity around flat-space configurations for the metrics and a constant configuration for the scalar field.We will now turn to analyze the structure of the quadratic action of the model, expanded around generic background configurations.To derive the quadratic action for generic backgrounds, we generalize the method introduced in [32] for massive gravity and applied in [33] to the (standard) bigravity case.We then specialize to homogeneous and isotropic backgrounds (FLRW) for the metrics and we write down the most general parametrization for the quadratic lagrangian in this context.We conclude commenting on the background evolution of the model in the cosmological ansatz.
The perturbed metrics are defined as where ḡµν and fµν indicate generic background solutions and h µν and µν are canonically normalized variables.From now on, the indices of the tensor h µν and h µν will be raised and lowered with the physical background metric ḡµν , whereas the indices of the tensor l µν and µν will be raised and lowered with the background metric fµν .The scalar field is expanded around a background configuration as We underline that in the equation above, φ is a dynamical field, solution of the background equation of motion for the scalar field Φ. 17 Using the method illustrated in appendix B and based on the results of [33], we derive the general expression for the perturbed action, quadratic in the canonically normalized metric perturbations h µν and µν and δφ 17 We emphasize that our approach here is different from that of section 3. There, in the context of studying the interaction structure of the theory around Minkowski backgrounds, we considered the split Φ = φ0 + δφ, with φ0 being a fixed reference configuration for the scalar field.
where the tensors M µναβ
••
and M µν •• are defined in appendix B and E µναβ (ḡ) is the Lichnerowicz operator in curved space-time, whose explicit expression can be found in appendix B.
We observe that when the massive gravity limit µν → 0 is taken, we recover a specific implementation of the mass-varying massive gravity model proposed in [14].The resulting mass term in this limit is the one derived in [32] for (standard) massive gravity, with an additional contribution mixing the scalar field with the metric perturbation h µν .
Cosmological background case
We now want to specialize our results for the quadratic action (4.4) to the case of cosmological backgrounds.The kinetic structure of the linearized theory is standard (two copies of GR plus a scalar field).We will focus on the parametrization of the mass term in the case of homogeneous and isotropic background solutions.
Cosmological ansatz: We consider solutions of bigravity where both metrics are spatially isotropic and homogeneous.For simplicity, we also assume that both metrics have flat spatial sections, K = 0. Modulo time re-parameterizations, the most general form for the metrics (in conformal time τ ) is fµν Here a and b are the scale factors of the two metrics and c is a lapse function for f .It is convenient to define both the conformal Hubble parameter (H) and the standard one (H) for both metrics where denotes the derivative with respect to the conformal time τ .We introduce also the ratio between the two scale factors r = b a .(4.10) We indicate with φ the background value of the scalar field Φ.
In the matter sector, we consider the energy-momentum tensor of a covariantly conserved perfect fluid with equation of state p = wρ and 4-velocity u µ .Explicitly, Background equations: The equation of motion for the background value of the scalar field, φ ≡ φ(τ ) can be written as where It is useful to introduce an effective potential The quantity V (r, c) gives a time-dependent correction to the scalar field mass.We observe that if we set the potential of the scalar field to zero from the very beginning, W = 0, we still get a quadratic potential from the coupling to the matter sector, W = 1/2M 2 Pl V φ 2 .18As already shown, the Bianchi constraint (2.21) is equivalent to the covariant conservation of the total energy momentum tensor.In the cosmological ansatz it can be written as where ρ tot = ρ m + ρ φ and ρ φ is the energy density of the scalar field.Explicitly The associated pressure p φ ≡ ω φ ρ φ is given by Note that both p φ and ρ φ include contributions coming from the bigravity potential, which would still be relevant if φ were not a dynamical field, but just a fixed mass scale.In the limit when φ's evolution is frozen this will be the dominant contribution together with the stationary value of W (φ), so in a slight abuse of notation we will still refer to these contributions via p φ and ρ φ even when there is (effectively) no dynamical φ.It is easy to show that the Bianchi constraint eq.(2.22) is equivalent to which reduces to the standard constraint in bi-gravity for constant φ e.g.see equation (59) in [33].We distinguish in the following two branches of solutions according to how the Bianchi constraint (4.20) is realized.We can either implement the constraint extracting e.g. the lapse c or asking that the combinations of β i and r in the round parenthesis are vanishing.Explicitly First Branch : Second Branch : The first branch is the analogue of the algebraic branch in the standard bi-gravity formulation while the second one corresponds to the so called dynamical branch.For standard bi-gravity, the existence of two branches of solutions has been pointed out for the first time in [34].In the standard case, the evolution of perturbations in the second branch has been intensively studied in [35-39] while the evolution of tensor perturbations in the first branch is presented in [33].In the next section we will analyze the main features of the two branches (4.21) and (4.22).The equations of motion (the Friedman equation and the acceleration equation) for the metric g are given by 3H while for the f metric we find the equations of motion 2 First branch: In the first branch the ratio between the two scale factors is constant r = r and there are the following two constraints We assume one can solve both the equations simultaneously.This imposes a relation between/restriction on the β i and r, which would not be satisfied by an arbitrary choice of β i .However, by looking at (4.25,4.26)we see that the above constraints impose H f = 0 and H f = 0 respectively.Using the definition (4.9) this results in a constant b.Consequently for r = r = cnst we have a constant scale factor a and thus H = 0.This branch is therefore not viable to describe (homogeneous and isotropic) background cosmology.
Second branch: In this branch (4.22), the Bianchi constraint (4.20) can be used to extract the lapse c.We get It follows that in general in this branch the correction to the mass of the scalar field is a time-dependent quantity V (r, c) given by eq.(4.15).The Friedmann equations in this branch are given by eqs.(4.23) and (4.25) with The state parameter ω φ ≡ p φ /ρ φ is given by If the scalar field φ is slowly varying, the background evolution in this second branch will be very close to the one of standard bigravity in the dynamical branch.
Mass term on cosmological backgrounds
With the ansatz (4.7, 4.8) for the background metrics, homogeneity and isotropy request that the tensors M αβµν and M µν • in eq.(4.6) admit the following general parametrization.For the gg and f f terms of M αβµν where • stands for either g or f .For the mixed terms gf , the parametrization takes the form For the tensors M µν • the parametization takes the form where • stands for either g or f .
The functions α ) depend on conformal time through the ratio between the two scale factors, r, and the lapse function c.Their explicit expressions are given in appendix C. Note that contrary to gg and f f , M ij00 gf = M 00ij gf and we have introduced γ gf = γ f g .Given this parametrization it is straightforward to write the mass term for any type of perturbations on a cosmological background, The explicit form of the last term in eq. ( 4.49) depends on the choice of the potential for the scalar field while V = V (ḡ, f ).We have at this point all the ingredients needed to study perturbations of the theory: it is just a matter of varying the total quadratic action (4.4),where S kin 2 is the kinetic action evaluated on cosmological backgrounds and S m 2 is given by eq.(4.43).We observe that taking the massive-gravity limit µν → 0 in (4.43), i.e. setting L (2) f φ to zero in eq.(4.43), we get the generic parametrization of the mass term in a cosmological setting for a specific implementation of the "mass-varying massive gravity" model proposed in [14], as discussed above.On the other hand, the results presented in [33] for the standard bi-gravity context are exactly recovered once the limit δφ → 0 is taken in (4.43).
As pointed out in [40], in the context of standard bigravity, gradient exponential instabilities may arise in the scalar sector, therefore making the model not viable to describe the process of structure formation.In [39] anyway it was shown that there exists a choice of parameters of the bigravity potential such that in the sub horizon limit, exponential gradient instabilities are absent in the scalar sector of perturbations.In this last work a model (the so-called β 1 − β 4 model) was identified to be the only one with both a viable background evolution and exponential gradient instabilities absent in the scalar sector.However, further investigations (see e.g [37], [35]) pointed out that this sub-model suffers from another problem: in the scalar sector the Higuchi bound is violated during an early de Sitter inflationary phase, rendering it impossible to use the model for primordial cosmology, e.g. to embed the model in inflation.
In our scale-free model, an additional scalar field is present, which at the perturbation level is mixing with the scalar perturbations of the metric.The mixing is only in the mass matrix (the kinetic structure is standard) of scalar perturbations.In principle, one would expect to find an analogous situation as before: for a special choice of parameters, gradient exponential instabilities are absent.Once a sub model (i.e.identified by the β i non vanishing) with such a good behaviour is pointed out, it would be interesting to consider the Higuchi bound for it.A full analysis of this type is quite involved and deserves a separate investigation, which we are planning to present in a future work.
A scale-free model of inflation and dark energy
In this section we focus on the background evolution of scale-free bigravity in the cosmological ansatz of Sec.4.1.In particular we want to analyze if the model can be effectively used as a model of dark-energy at late times.Indeed, we know that if the scalar field is non-dynamical (i.e. in the standard bigravity scenario), in the cosmological ansatz, a phase of accelerated expansion can be recovered at late-times.The dark energy contribution becomes constant at late-times, when ρ → 0, and it drives a quasi-de Sitter expansion phase.In Sec.5.2, we will then turn to consider the case in which the scalar field is promoted to be the inflaton field and we study if it is possible to recover a viable inflationary scenario in this way.We focus on the second branch, which is the only one which can give rise to a viable cosmology.
Late-time accelerated expansion
We start exploring which conditions need to be satisfied in order to get a late-time phase of accelerated expansion.For convenience we will here use cosmic time t as the time variable (dt ≡ a dτ ) and indicate with • derivatives with respect to cosmic time.We want the energy density ρ φ defined in (4.18) to play the role of dark energy at late times.We underline that in ρ φ there is a contribution coming from the fact that we are dealing with a modified gravity model, and proportional to the bi-gravity potential V (r, c) together with a contribution coming from the kinetic and potential terms of the scalar field 19 .
If we want accelerated expansion at late times to be driven by the (bigravity) mass term, we need (1) to choose the parameters of the model in such a way that ρ φ gives the dominant contribution to the total energy density at late times (2) to recover at late time a quasi de Sitter stage, i.e. ρ φ −p φ .Note that in some sense this is an abuse of notation, since we really just want φ to freeze and let the massive interactions for the tensor (whose potential contributions are also captured by ρ φ , p φ as defined in (4.18) and (4.19)) drive accelerated expansion in the same way as for standard bigravity.Indeed, when φ is frozen, from an inspection of eq.(4.28), we see that the expression defining the lapse c in terms of the other background quantities is exactly the standard bigravity one.As a consequence, in this limit, eqs.(4.29) and (4.30), which give the energy density and pressure of the scalar field, have exactly the same form of the dark energy density and pressure in standard bigravity, with the addition of a constant contribution coming from the potential W . 20 In this sense we can enforce the essence of our requirement via these conditions, which can be achieved choosing at some time t f , φ(t f ) ∼ H 0 and We observe that, assuming φ(t f ) M Pl , this last condition implies where in the last equality we have used the Friedmann equation for the g-metric.In the regime (5.1), the Bianchi constraint reduces to which, once it is substituted in the Friedmann equation for the f -metric (4.26) gives Substituting in (5.4) H from the Friedmann equation (4.23) (for ρ → 0 and in the regime (5.1)), we get the following condition From this equation we read that if the condition (5.1) holds, the ratio between the two scale factors r has to be constant, independently of the value of the β i and of the parameters of the potential W .Therefore, from the Friedmann equation (4.23), it follows H cnst and we recover a late-time de Sitter phase.In particular, since c 1, we get an equation of state (4.31) for the fluid p φ ∼ −ρ φ .Anyway, we observe that the condition (5.1) at late times can be satisfied only by fine-tuning the parameters of the model.Indeed, deriving eq.(5.2) and substituting it in the equation of motion for the scalar field (4.14), we get φ(t f ) which is compatible with the slow-roll condition (5.1)only if the parameters of the bigravity potential are chosen in a such a way that V (r, c) ∼ H 2 (t f )/M 2 Pl , i.e.V is (severely) finetuned to be suppressed in this way.It follows that using this model at late times as an effective model for dark energy requires a price to pay.The first option is to accept the above fine-tuning of the model parameters. 21Alternatively another possible way out is to give up our requirement on the model to be scale-free and introduce in the potential W a constant contribution to play the role of dark energy at late times, thus essentially reintroducing an explicit cosmological constant.Needless to say that both options do not really present an improvement over the standard (cosmological constant problem plagued) ΛCDM solution.Anyway, even if recovering viable dynamics at late times is not trivial in this model, if the scalar field is promoted to be the inflaton, this model can be used at early times as a model of inflation, with interesting phenomenological features, as we will explain in Sec.5.2.
Early-time inflationary evolution
This scale-free model of bigravity constitutes a generalization of the standard bigravity model, in which the mass parameter in front of the bigravity potential is promoted to a (dynamical) scalar field.The next step is to promote this scalar field to be the inflaton field and to study if it is possible to recover a viable inflationary scenario in this way.The remainder of this section is devoted to exploring this intriguing possibility.
For definiteness, we specialize to the case of a quartic potential for the inflaton field in eq.(2.3).The field φ can in principle interact with other fields such as fermions, gauge bosons, etc., but we assume that this interaction can be neglected during inflation and that energy and pressure are dominated by the contribution from the inflaton.The energy-momentum tensor of φ is given by eq.(2.25).The effective potential defined in (4.16) reads where we have defined a time-dependent mass for the inflaton and V (r, c) is defined in eq.(4.15).Since the effective inflaton mass is a time-dependent quantity, the shape of the effective potential (5.7) changes with time.
At early times we now impose the standard slow-roll condition on φ and we show that it is sufficient to get an early de Sitter stage.We assume that at a given time τ i , there exists a region of space in which φ 2 (τ i ) a 2 (τ i ) W(φ) . (5.8) It follows that the Friedman equation (4.24) reduces to (considering ρ → 0 at early time) 3H 2 8πG W(φ) . (5.9) Using the slow-roll condition (5.8), it follows where the last inequality follows from the standard assumption that at an early inflationary stage φ(τ i ) M Pl .We therefore see that at early time the condition (5.1) which guarantees the existence of a de Sitter stage is automatically implemented as soon as the standard slowroll conditions (5.8) are imposed.Therefore, the same reasoning presented in section 5.1 applies and as a direct consequence of (5.8) we obtain i.e. at early-time, a de Sitter-like inflationary stage is recovered. 22he evolution of the time-dependent mass depends on the details of the background evolution and in general it is different for different choices of the values of the parameters of the bigravity potential, β n .We distinguish two different regimes.If we are in the regime in which m 2 φ (τ ) ≥ 0, the minimum of the effective potential is constant and given by φ = 0.If instead we have m 2 φ (τ ) < 0 , then the shape of the effective potential is a double well and at a given instant of time τ , the minimum is given by φ(τ ) = ±m φ (τ )/ √ λ.In full generality, a transition between the two regimes is possible.If the evolution of m 2 φ is such that approaching the end of inflation it goes to positive values, then we recover the standard scenario, with the inflaton field oscillating around its constant (and vanishing) minimum configuration.After inflation, since then φ = 0, the coupling between the two metrics is vanishing and each of the two gravity sectors is evolving independently.
The opposite situation, i.e. m 2 φ < 0 at late inflation, gives rise to a richer cosmology: in this case the expectation value of the inflaton field is non vanishing and (in general) a timedependent quantity.Therefore the cosmological dynamics of the background after inflation is more complicated, with the two gravity sectors interacting through the potential term.This second scenario in the limit of m φ ∼ const corresponds to the so called dynamical branch in standard bigravity. 23After inflation the energy density of the inflaton defined in eq.(4.29) is still a time dependent quantity and plays the role of a dynamical dark energy contribution.However, we stress that the only way to get a positive dark energy contribution at the end of inflation here, is to add to the inflaton potential W a constant contribution, i.e. to introduce a cosmological constant-like term in the action, which also adds a new scale to the theory (and hence destroys its 'scale-freeness').
Conclusions
In this paper we have investigated a "scale-free" extension of massive (bi-)gravity models, where the mass parameter m is promoted to be a dynamical scalar field.Our model is completely captured by the actions (2.1) and (2.4) and its main features are the following: • Strong coupling scales: Perturbatively investigating the interaction structure of the theory around Minkowski, we find a strong coupling scale Λ3 3 = M Pl φ 2 0 in analogy 22 The slow-roll condition (5.8) used in the equation of motion for the inflaton leads to (5.6).This last equation at early times is consistent with the slow-roll condition assumed, for a proper choice of the model parameters (not necessarily fine-tuned in this case). 23We observe that the condition m φ ∼ const after inflation is automatically realized if after inflation there exists a region of space in which the slow-roll condition (5.8) is satisfied.
with standard bi-and massive gravity (see e.g.equations (3.17) and (3.18)).Here we have employed a perturbative expansion of Φ = φ 0 + δφ around a fixed and nondynamical reference value φ 0 .Different to the standard massive (bi-)gravity cases, enforcing tadpole cancellation conditions is crucial for this strong coupling scale to be made explicit.
• Modified low-energy physics: Additional interactions, not present in standard massive and bi-gravity decoupling limits, can be found in our model due to the new dynamical scalar degree of freedom Φ.They generically affect scaling limits and the low-energy physics of the model.We capture these new interactions in a scaling limit (see e.g.equations (3.15), (3.16) and (3.20)) different from the standard decoupling one, which clearly illustrates the regimes where our pertubative expansion is valid and the conditions necessary to satisfy it.
• Cosmological framework: Exploiting the method presented in [33], in section 4 we derived the quadratic action of our theory around both generic and explicitly FLRW background configurations.We find the precise form of new interactions due to the additional scalar Φ complementing the standard bigravity ones derived in [33].This will also enable the detailed study of cosmological perturbations in future work.Furthermore we have derived the background dynamics and established the nature of the two different branches of solutions in our model.
• Dark Energy and Inflation: Finally we explicitly study how periods of early and late-time acceleration, i.e. an inflationary and dark energy phase, can be realised at the background level in our model.Inflation can be successfully (and without fine-tuning parameters) realized, with the scalar field Φ acting as a slowly-rolling inflaton and leading to an early-time quasi-de Sitter inflationary stage (see section 5.2).Surprisingly, generating a period of late-time acceleration is significantly more difficult and requires either extreme fine-tuning of parameters or the (re-)introduction of an explicit additional (mass) scale in the potential for Φ (see section 5.1). 24This restriction will also apply to our massive gravity limit and generic mass-varying models such as [14].
Throughout this paper we have considered both a scale-free extension of bigravity and also its massive gravity limit.Various extensions are worthy of further investigation, ranging from extending the work presented here to fully-fledged multi-gravity models (see appendix A) to considering couplings of matter and/or the additional scalar Φ to more than one metric (i.e.going beyond the minimal coupling of GR).The perturbative properties of the model in a cosmological setting as well as a study of the explicit evolution of strong coupling scales in different background configurations and throughout different phases are also left for future work.Finally, and in the spirit of scale-freedom, it would be interesting to embed our approach in a fully scale-free framework where the Planck mass(es) are also promoted to become dynamical (scalar) fields and their present-day fixed nature arises via spontaneous symmetry breaking along the lines of [7, 9-13].
We conclude by summarising and emphasising the defining features of the scale-free extension to massive (bi-)gravity considered here.This extension eliminates one of the mass scales in the original theory, replacing it by a dynamical field and in the process can alleviate low strong-coupling scale problems at early times which hinder the predictivity of the theory then, essentially via having Φ H 0 at early times whilst Φ eventually transitions towards smaller values at late times.This does enable us to nicely describe inflationary physics within this model, although a successful period of late-time acceleration (i.e.obtaining Φ ∼ H 0 at late times) requires resorting to either fine-tuning or the (re-)introduction of a separate mass scale in the potential for Φ.We hope that our work both helps to clarify the nature of scalefreeness in and mass-varying extensions of massive bigravity and paves the way to understand and fully extract the physical signatures of these models.
C Parametrization of the cosmological mass term
We give here the explicit expressions for the functions which parametrize the mass tensor on cosmological backgrounds, as presented in Section 4.2:
4
-linear interactions and strong coupling 13 3.4 Vainshtein screening and the equations of motion 16 3.5 The massive gravity limit 16 Quadratic action on generic backgrounds 19 4.1 Cosmological background case 20 4.2 Mass term on cosmological backgrounds 23 5 A scale-free model of inflation and dark energy 25 5 | 14,737.8 | 2016-08-23T00:00:00.000 | [
"Geology",
"Physics"
] |
Certificateless Multisignature Scheme Suitable for Network Coding
Network coding can save the wireless network resources and improve the network throughput by combining the routing with coding. Traditional multisignature from certificateless cryptosystem is not suitable for the network coding environment. In this paper, we propose a certificateless multisignature scheme suitable for network coding (NC-CLMSS) by using the sequential multisignature and homomorphic hash function. NC-CLMSS is based on the CDH and ECDL problems, and its security is detailedly proved in the random oracle (RO) model. In NC-CLMSS, the source node generates a multisignature for the message, and the intermediate node linearly combines the receiving message. NC-CLMSS can resist the pollution and forgery attacks, and it has the fixed signature length and relatively high computation efficiency.
Introduction
As the network information interaction technology, the network coding [1] has routing and coding functions and allows the router to encode the received data. Network coding has the merits of high transmission efficiency, fast speed, strong robustness, and good stability, but it is vulnerable to the pollution attacks in the data transmission process. In recent years, the researchers have proposed a series of network-coding signature schemes [2][3][4][5][6] to solve the network coding contamination, where the schemes in [4,5] effectively solved the replay attacks by using the time stamps; the certificateless network-coding homomorphism signature [6] is designed by using the homomorphic hash function; it can resist the replay attacks with forgery attacks at the same time and has lower computational overhead with the communication cost.
In real scenario, there are many applications to use the signature technology. With the development of communication technology, the scholars proposed many signature varieties (including multisignature) suitable for various application scenarios, such as medical field [7][8][9][10], privacy security [11], vehicle-mounted network [12,13], multicast network [14,15], e-government [16], e-commerce [17], and campus management facilities [18]. Multisignature first generates the partial signature of the same message, and then, the signature collector integrates the partial signatures into a signature. In terms of the order of partial signatures, multisignature can be divided into sequential multisignature [19] and broadcast multisignature [20,21]. Compared with ordinary multisignature, the sequential multisignature has the following characteristics: (1) the signature length has nothing to do with the number of signatures; (2) instead of using the public key of each signer, the group public key can be used to verify the signature; (3) signers sign the messages in a concrete order, otherwise a valid multisignature cannot be obtained; (4) it is not computationally feasible to obtain the valid signatures without the joint operation of all signers. From now on, there is no sequential multisignature suitable for network coding, as described in Figure 1, so we will devise such a scheme to resist the pollution and forgery attacks in wireless networks.
Contributions.
For the above reasons, a new certificateless multisignature scheme for the network coding (NC-CLMSS) is devised by combining the certificateless public key with sequential multisignature. In NC-CLMSS, the users at the source node generate the sequential multisignatures for the messages in a fixed order and transfer the signed messages from the router to the intermediate node. Intermediate node performs the linear combination of received information. Meanwhile, the destination node can verify the correctness of the signature without knowing the signer private key. Destination node filters out the contaminated information and forwards the validated data to the next receiving node. NC-CLMSS overcomes the key escrow and certificate management issues; moreover, it can resist the forgery attacks with pollution attacks in the multisource network-coding environment and has relatively better transmission efficiency.
Bilinear Pairing.
Assume G 1 and G 2 are additive and multiplication cyclic groups with the prime order q, respectively. P is a generator of the cyclic group G 1 . e: G 1 × G 1 ⟶G 2 is an admissible bilinear pairing if e is a map with the following properties: e (aP, bP) � e (P, P) ab , for any a, b ∈ z * q , and P ∈ G 1 ; e (P, P) ≠ 1; there exists an efficient algorithm to compute e (P, Q), for any P, Q ∈ G 1 . Definition 1. (ECDL problem). Given (P, aP) ∈ G 1 , for any a ∈ z * q , the ECDL (elliptic curve discrete logarithm) problem is to calculate a ∈ z * q .
Multisource Network
Model. Multisource network coding [22] has a set of source nodes. In the multisource model, each encoding message has a uniformly assigned two-dimensional index. Model for multisource transmission network is shown in Figure 2.
Multisource network coding is regarded as a directed acyclic graph R � (E′, V), where E′ is the set of edges in the network and V is the set of all nodes. U � u 1 , u 2 , . . . , u m ⊂ V is the set of the source nodes and D � d 1 , d 2 , . . . , d k ⊂ V is the set of the sink nodes; m multicast messages are expressed by v � (v 1 , v 2 , . . . , v m ); the source nodes' set U sends v � (v 1 , v 2 , . . . , v m ) to the sink nodes D, where each message vector v i is composed of n elements over finite field F, where v i is written as Let j be the unique index uniformly assigned to each message, and the same multicast message sent by different source nodes has the same index. Each packet w � (w 1 , w 2 , . . . , w l ) can be sent by arbitrary intermediate node in network, and w is the linear combination of l messages received by this node. Table 1, the readers can see the meaning of notations relevant to this article.
Algorithm Definition.
A NC-CLMSS is defined by six polynomial time algorithms as follows.
Setup: input a security parameter ρ and finally output the master key s with a system parameter set μ. Extract: input μ with the user identity ID i and finally output a pair (R i , D i ) of partial public/private keys. KeyGen: input μ with the user identity ID i and finally output a pair (x i , P i ) of public/private keys. Multisignature: input μ, the master key s, the message v t , the private key (D i , x i ), and public key (R i , P i ) and finally output a signature σ i .
Combination: input the message vector w 1 , . . . , w m and finally output a combined signature σ. Verification: input μ, σ i , and σ, the public key (R i , P i ), and the message v t ; the verifier outputs a result based on the verification case.
Security Model.
A NC-CLMSS must meet the existential unforgeability against the adaptive chosen-message attacks (UF-CMA). For the UF-CMA security model of NC-CLMSS, we think about the game EXP1/EXP2 between a challenger C and a polynomial time adversary A 1 or A 2 .
where A 1 is a malicious user who can change any user public key but cannot know the master private key; A 2 is a malicious KGC who knows the system master key but cannot change any user public key. After that, A 1 or A 2 carries out the adaptive queries as follows:
Security and Communication Networks
Finally, A 1 /A 2 outputs a forged signature σ * . In the adaptive queries, A 1 should not request the full private key of ID s ; A 2 cannot request the private key of ID s . In addition, σ * should not be returned by any multisignature oracle.
Definition 3.
A NC-CLMSS is said to be UF-CMA secure if no polynomial time adversary A 1 /A 2 succeeds in EXP1/ EXP2 with a non-negligible advantage.
Setup.
Given a security parameter ρ, KGC (key generation center) chooses cyclic groups G 1 and G 2 with the prime order q, as described in Section 2.1. P is a generator of G 1 and e: G 1 × G 1 ⟶G 2 . KGC selects secure hash functions: KGC chooses a master key s ∈ R Z * q and maintains its secret and then calculates the system public key P pub � sP. Finally, KGC publishes the system parameter set: μ � G 1 , G 2 , q, P, e, P pub , H 0 , H 1 , H 2 .
Extract.
Given the identity ID i of the user N i and μ, KGC randomly chooses r i ∈ Z * q and calculates R i � r i P, . ., ID n }, D i is the partial private key of N i , and R i is the partial public key of N i .
KeyGen.
Given the identity ID i of the user N i and μ, this user N i (i∈{1, 2, . . ., n}) randomly chooses a secret value x i ∈ Z * q and calculates the public key P i � x i P. Note that . ., ID n } is an identity set of n users and N 1 ⟶N 2 ⟶. . .⟶N n denotes the signature sequence of n users. In other words, the user N i (i ∈ {1, 2, . . ., n}) signs the message v t with the sequence N 1 ⟶N 2 ⟶. . .⟶N n . Firstly, N 1 calculates where σ 1 is the partial signature of the message v t from the user en, the signature of the user N n is σ n � n i�1 SIGN i . Finally, σ � (σ 1 , σ 2 , . . . , σ d ) and v t are sent to the intermediate code and sink node.
Combination.
Given the local coding vector α � (α 1 , . . . , α m ) and global vector β � (β 1 , . . . , β m ), the intermediate node combines the message vector as follows: en, the message vector v t is also denoted as w � m j�1 β j v j , and the signature corresponding to the 4.6. Verify. After receiving the multisignature and combination signature, the verifier calculates If the equality e(σ n , P) � e(T, n i�1 (l i P i + R i + h i P pub )) holds, the multisignature is valid and invalid otherwise.
Single Signature Verification.
Given the signature σ i of the message v t , then the signature verification process of the user N i (i ∈ {1, 2, . . ., n}) is as follows:
Combination Verification. Given the message
is the multisignature corresponding to w. In the verification phase, it is necessary to check the correctness of the following equality: where h i � H 0 (ID i , R i ). In the multisource network coding, the intermediate nodes combine the messages from different source nodes and form a combination signature. Different source nodes may send the same message. In order to distinguish the possible combination of the same message vector, the global coding vector is expressed as where the global coding vector β j (u k ) ∈ β j (u 1 ), . . . , β j (u d ) and source node user u k ∈ {u 1 , u 2 , . . ., u d }.
en, the message vector is expressed as w � m j�1 d k�1 β j (u k )v j . Hence, the multisignature of message vector w can be expressed as σ � m j�1 d k�1 (σ j (u k )) β j (u k ) , and then, the i-th component in the multisignature can be expressed as en, the relevant equality is verified as follows: From the verification process of single message, we know e(σ n , P) � e(T, n i�1 (l i P i + R i + h i P pub )). en, the verification process is denoted as Proof. C receives a random instance (P, aP, bP) ∈ G 1 of CDH problem, and its aim is to use A 1 (the subroutine of C) to calculate abP ∈ G 1 . C maintains the initially empty lists L 0 , L 1 , L 2 , and L 3 to store the query-answer values of several oracles. Firstly, O setup C (ρ) ⟶ μ A 1 , where P pub � aP. en, A 1 adaptively issues the polynomial time queries as follows.
Security Analysis
H 0 queries: A 1 issues an H 0 query. C outputs h i to A 1 if the relevant tuple is in the list L 0 ; otherwise, C returns a random h i ∈ R Z * q and stores (ID i , R i , h i ) in L 0 . H 1 queries: A 1 issues an H 1 query. C returns l i if a matching tuple is in the list L 1 ; otherwise, C returns l i ∈ R Z * q and stores (ID i , L, P i , R i , v t , l i ) in L 1 . H 2 queries: A 1 issues an H 2 query. If it is not the θ-th query (θ ∈ {1, 2, . . ., q 0 } (q 0 is the query times relevant to the H 0 oracle) and a matching tuple is in the list L 2 , C outputs T � lP (l ∈ R Z * q ) and stores (v t , l i , P pub , l, T) in L 2 ; otherwise, C returns T � bP and stores (v t , l i , P pub , -, T) in L 2 . Partial private key queries: A 1 requests a partial private key of ID i . If it is not the θ-th query, C chooses r i ∈ R Z * q to calculate R i � r i P such that D i satisfies D i P � R i + h i P pub and finally returns D i as the answer and stores (ID i , r i , R i , D i ,-,-) in the list L 3 ; otherwise, C fails and aborts the game. Public key queries: A 1 requests a public key of ID i . C calculates P i � x i P (x i ∈ R Z * q ) and finally returns PK i � (R i , P i ) and updates the list L 3 with (ID i , r i , R i , D i , x i , P i ). Secret value queries: A 1 requests a secret value of ID i . C returns x i from L 3 if the corresponding public key has not been replaced.
Public key replacement: if it is not the θ-th query, the public key of ID i is replaced by A 1 ; otherwise, C fails and aborts the game. Multisignature queries: for a multisignature query of message v t , C runs the relevant algorithm and returns a result if it is not the θ-th query; otherwise, C signs v t Security and Communication Networks 5 with the sequence N 1 ⟶N 2 ⟶. . .⟶N n . Firstly, C calculates for N 1 as follows: T � H 2 v t , L, P pub , where σ 1 is the partial signature of v t for N 1 . en, C calculates for N i (i ∈ {1, 2, . . ., n}) relevant to (v t , σ i−1 ) as follows: If e(σ i−1 , P) � e(T, i−1 j�1 (l j P j + R j + h j P pub )) holds, C calculates for N i as follows: Finally, C calculates σ n � n i�1 SIGN i and delivers σ � (σ 1 , σ 2 , . . . , σ d ) which is sent to A 1 . Combination queries: A 1 requests a combination query. For the local coding vector α � (α 1 , . . . , α m ), global vector β � (β 1 , . . . , β m ), and message vector (w 1 , w 2 , . . . , w m ), C combines the message vector w � m i�1 α i w i . en, the message vector is also denoted as w � m j�1 β j v j , and the signature process relevant to w is σ j � m i�1 σ α i i,j , where σ i, j (1 ≤ i ≤ m and 1 ≤ j ≤ l) denotes the j-th element of σ i . Finally, C outputs a combined signature σ � m i�1 σ α i i . Verification queries: A 1 requests a verification query. C runs the verification algorithm and returns a result if it is not the θ-th query; otherwise, C calculates If the equality e(σ n , P) � e(T, n i�1 (l i P i + R i + h i P pub )) holds, C returns σ and ⊥ otherwise.
Finally, A 1 outputs a forgery signature σ * . In the adaptive queries, A 1 cannot request a full private key of ID i , and σ * is not returned by any multisignature oracle. If it is not the θ-th query, C fails and aborts the game; otherwise, C calls the H 0 , H 1 , and H 2 oracles and then searches the list L 3 . Finally, C verifies the following equality: From the above equality, we can obtain the solution of CDH problem: □ 6.1. Probability Estimation. Probability that C succeeds in the above-mentioned game is estimated as follows. Here, it is necessary to think about three events: E 1 is the event that C does not abort the game E 2 is the event that A 1 successfully forge a signature E 3 is the event that there exists at least one record of nontarget identity in successful forgery case In E 1 , there exists one time not querying the target identity, and then, Pr [E 1 ] ≥ 1/(l s + l r ), where l s is the times of secret value query and l r is the query times of public key replacement, E 2 denotes that A 1 wins in the game, then Pr [E 2 |E 1 ] ≥ ε, and E 3 at least occurs once time in n queries, then Pr [E 3 |E 1 ∧E 2 ] ≥ 1/n. Hence, the success probability that C solves the CDH problem is
Theorem 2. In the RO model, if the polynomial time adversary A 2 can break the UF-CMA-II security of NC-CLMSS, a challenge algorithm C must be able to solve the CDH problem.
Proof. C receives a random instance (P, aP, bP) ∈ G 1 of CDH problem, and its aim is to utilize A 2 (the subroutine of C) to determine the value of abP ∈ G 1 . C maintains the initially empty lists L 0 , L 1 , L 2 , and L 3 to save the queryanswer values of several oracles. Firstly, O setup C (ρ) ⟶ μ , s A 2 .
6 Security and Communication Networks en, A 2 adaptively performs the polynomial time queries as below: H 0 queries: for an H 0 query, if (ID i , R i , h i ) is in the list L 0 , C returns h i ; otherwise, C returns h i ∈ R Z * q and stores (ID i , R i , h i ) in L 0 . H 1 queries: for an H 1 query, if the matching tuple is in the list L 1 , C returns l i ; otherwise, C returns l i ∈ R Z * q and stores (ID i , L, P i , R i , v t , l i ) in L 1 . H 2 queries: for an H 2 query, if it is not the θ-th query (θ ∈ {1, 2, . . .,q 0 } (q 0 is the query times relevant to H 0 oracle) and the relevant tuple is in the list L 2 , C randomly outputs T � lP ∈ G 1 (l ∈ R Z * q ) as the answer; after that, C stores (v t , l i , P pub , l, T) in L 2 , otherwise, C returns T � bP ∈ G 1 and stores (v t , l i , P pub ,-,T) in L 2 . Partial private key queries: for a partial private key query for identity ID i . C calculates R i � r i P, D i � r i + h i s (r i ∈ R Z * q ) and returns D i and stores (ID i , r i , R i , D i , -, -) in the list L 3 .
Public key queries: for a public key query for identity ID i , if it is not the θ-th query, C calculates P i � x i P (x i ∈ R Z * q ) and finally returns PK i � (R i , P i ) and updates L 3 with (ID i , Signature queries: A 2 issues a multisignature query for message v t . If it is not the θ-th query, C runs the multisignature algorithm to output a result; otherwise, C signs v t with the sequence N 1 ⟶N 2 ⟶. . .⟶N n . Firstly, C calculates for N 1 as follows: T � H 2 v t , L, P pub , where σ 1 is the partial signature of v t for N 1 . en, C calculates for N i (i ∈ {1, 2, . . ., n}) relevant to (v t , σ i−1 ) as follows: If e(σ i−1 , P) � e(T, i−1 j�1 (l j P j + R j + h j P pub )) holds, C calculates for N i as follows: Verification queries: for a verification query, C runs the verification algorithm and returns a result if it is not the θ-th query; otherwise, C calculates (1 ≤ i ≤ n) and T � H 2 (v t , L, P pub ). If e(σ n , P) � e(T, n i�1 (l i P i + R i + h i P pub )) holds, C returns σ and ⊥ otherwise.
Finally, A 2 outputs a forgery signature σ * . In queries, A 2 cannot query the secret value of ID i , and σ * is not returned by signature oracle. If it is not the θ-th query, C fails and aborts the game; otherwise, C calls the H 0 , H 1 , and H 2 oracles and then searches the list L 3 and then verifies as follows: CDH problem solution can be obtained from equation (19): Theorem 3. Our NC-CLMSS can prevent the pollution attacks in the multisource network coding environment.
Proof. In NC-CLMSS, the signature process takes place at the source node and intermediate node. For the source node, the attacker can capture any node in the network and uses it Security and Communication Networks to launch the attacks; this node sends the polluted information to the next node, but it is equivalent to solving the elliptic curve discrete logarithm (ECDL) problem for the attacker obtaining the signer private key from the public key. For the intermediate nodes, the attacker captures the signature from source node and tries to forge a signature; then, the attacker must own the user private key, and it is also equivalent to solving the ECDL problem. NC-CLMSS can resist the pollution attacks in the network-coding environment because solving the ECDL problem is computationally infeasible.
Performance Analysis
In this section, the performance comparison is made between NC-CLMSS and existing schemes in [19][20][21] based on the computational complexity. Schemes in [19][20][21] cannot resist the pollution attacks; the schemes in [20,21] are not sequential multisignature. Our NC-CLMSS is a sequential multisignature and can resist pollution attacks. Table 2 describes the time complexity of main cryptography operations. Experimental environment for the performance analysis in this section: the processor is Intel (R) Core (TM) i7-6700HQ CPU @2.60GHz; the system type is the 64-bit operating system. Based on this system, we use C programming language, PBC library, and OpenSSL program to obtain the cryptography operation time, as shown in Table 2. Table 3 describes the computational efficiency of several schemes. From Table 3, the computational complexity of NC-CLMSS is relatively lower than other schemes in [19][20][21].
Simulation curves of signature time-consuming of comparison schemes are shown in Figure 3. Simulation curves of verification time-consuming comparison are shown in Figure 4. Simulation curves of total algorithm time comparison are shown in Figure 5. Assume the number n of signature members is 10, 20, 30, 40, 50, and 60, respectively. Experiment results show the running time of different schemes increases linearly with the increase of the number of signed members. As shown in Figure 3, in the signature phase, the growth rate of NC-CLMSS is relatively slower than other schemes. From Figure 4, the computational efficiency of NC-CLMSS is the highest. In terms of total time in Figure 5, NC-CLMSS takes the least time. Hence, NC-CLMSS is a relatively better cryptography algorithm in several schemes.
Summary
Network encoding cryptography has many merits, but there exists the inevitable problem how to resist the pollution attacks and forgery attacks in the message transmission process. By using the techniques of the certificateless multisignature and multisource network coding cryptosystem, we construct a certificateless multisignature scheme suitable for network coding (NC-CLMSS). Under the ECDL and CDH assumptions, this algorithm is proved to satisfy the UF-CMA security and can resist the pollution attacks; its computational complexity is relatively lower.
Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
e authors declare that they have no conflicts of interest.
Authors' Contributions
Huifang Yu worked on the security model, instance design, and security proof; Zhewei Qi worked on the instance design and simulation experiment; Danqing Liu worked on the introduction and formal algorithm definition; Ke Yang estimated the probability. | 6,294.4 | 2021-11-16T00:00:00.000 | [
"Computer Science"
] |
Non-linear vibration of Euler-Bernoulli beams
In this paper, variational iteration (VIM) and parametrized perturbation (PPM) methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found for nonlinear problems. Comparison of VIM and PPM with Runge-Kutta 4th leads to highly accurate solutions.
INTRODUCTION
The demand for engineering structures is continuously increasing.Aerospace vehicles, bridges, and automobiles are examples of these structures.Many aspects have to be taken into consideration in the design of these structures to improve their performance and extend their life.One aspect of the design process is the dynamic response of structures.The dynamics of distributedparameter and continuous systems, like beams, were governed by linear and nonlinear partialdifferential equations in space and time.It was difficult to find the exact or closed-form solutions for nonlinear problems.Consequently, researchers were used two classes of approximate solutions of initial boundary-value problems: numerical techniques [28,31], and approximate analytical methods [2,26].For strongly non-linear partial-differential, direct techniques, such as perturbation methods, were not utilized to solve directly the non-linear partial-differential equations and associated boundary conditions.Therefore first partial-differential equations are discretized into a set of non-linear ordinary-differential equations using the Galerkin approach and the governing problems are then solved analytically in time domain.
Kopmaz et al. [20] considered different approaches to describing the relationship between the bending moment and curvature of an Euler-Bernoulli beam undergoing a large deformation.Then, in the case of a cantilevered beam subjected to a single moment at its free end, the difference between the linear and the nonlinear theories based on both the mathematical curvature and the physical curvature was shown.Biondi and Caddemi [8] studied the problem of the integration of the static governing equations of the uniform Euler-Bernoulli beams with discontinuities, considering the flexural stiffness and slope discontinuities.
The vibration problems of uniform Euler-Bernoulli beams can be solved by analytical or approximate approaches [10,21].Pirbodaghi et al. [25] studied non-linear vibration behaviour of geometrically non-linear Euler-Bernoulli beams subjected to axial loads using homotopy analysis method.Also, the effect of vibration amplitude on the non-linear frequency and buckling load is discussed.Burgreen [9] investigated the free vibrations of a simply supported buckled beam using a single-mode discretization.He pointed out the natural frequencies of buckled beams depend on the amplitude of vibration.Eisley [11,12] used a single-mode discretization to investigate the forced vibrations of buckled beams and plates.He considered both simply supported and clamped-clamped boundary conditions.For a clamped-clamped buckled beam, Eisley [11,12] used the first buckling mode in the discretization procedure.He obtained similar forms of the governing equations for simply supported and clamped-clamped buckled beams.
The main purpose of this study is to obtain the analytical expression for geometrically non-linear vibration of clamped-clamped Euler-Bernoulli beams fixed at one end.Geometric non-linearity arises from non-linear strain-displacement relationships.This type of nonlinearity is most commonly treated in the literature.Sources of this type of nonlinearity include midplane stretching, large curvatures of structural elements, and large rotation of elements.First, the governing non-linear partial differential equation using Galerkin method was reduced to a single non-linear ordinary differential equation.It was then assumed that only fundamental mode was excited.The later equation was solved analytically in time domain using VIM and PPM.Ultimately, VIM and PPM methods are compared with Runge-Kutta 4th method.
DESCRIPTION OF THE PROBLEM
Consider a straight beam on an elastic foundation with length L, a cross-section A, a mass per unit length µ, moment of inertia I , and modulus of elasticity E that subjected to an axial force of magnitude F as shown in Fig. 1.It is assumed that the cross-sectional area of the beam is uniform and its material is homogenous.The beam is also modeled according to the Euler-Bernoulli beam theory.Planes of the cross sections remain planes after deformation, straight lines normal to the mid-plane of the beam remain normal, and straight lines in the transverse direction of the cross section do not change length.The first assumption ignores the in plane deformation.The second assumption ignores the transverse shear strains and consequently the rotation of the cross section is due to bending only.The last assumption, which is called the incompressibility condition, assumes no transverse normal strains.The last two assumptions are the basis of the Euler-Bernoulli beam theory [27].
The equation of motion including the effects of mid-plane stretching is given by: Where C is the viscous damping coefficient, Kis a foundation modulus and U is a distributed load in the transverse direction.Assume the non-conservative forces were equal to zero.Therefore Eq. ( 1) can be written as follows: For convenience, the following non-dimensional variables are used: Where R = (I/A) 0.5 is the radius of gyration of the cross-section.As a result, Eq. ( 2) can be written as follows: Assuming W (X, t) = ϕ(X)ψ(t)whereϕ(X)is the first eigenmode of the beam [32] and applying the Galerkin method, the equation of motion is obtained as follows: Where α = α 1 + α 2 F + K and α 1 , α 2 and β are as follows: The Eq. ( 5) is the governing non-linear vibration of Euler-Bernoulli beams.The center of the beam subjected to the following initial conditions: where A denotes the non-dimensional maximum amplitude of oscillation.
BASIC IDEA OF VARIATIONAL ITERATION METHOD
To illustrate the basic concepts of the VIM, we consider the following differential equation: Where L is a linear operator, N a nonlinear operator and g(t) an inhomogeneous term.According to VIM, we can write down a correction functional as follows: Where λ is a general Lagrange multiplier which can be identified optimally via the variational theory [17].The subscript n indicates the nth approximation and ũn is considered as a restricted variation [17], i.e. δ ũn = 0.
APPLICATION OF VARIATIONAL ITERATION METHOD
To solve Eq. ( 5) by means of VIM, we start with an arbitrary initial approximation: From Eq. ( 5), we have: Integrating twice yields: Equating the coefficients of cos(ωt) in ψ 0 and ψ 1 , we have: Latin American Journal of Solids and Structures 8(2011) 139 -148 And therefore, Where δ ũn = 0 is considered as restricted variation.
Its stationary conditions can be obtained as follows: Therefore, the multiplier, can be identified as As a result, we obtain the following iteration formula: By the iteration formula (20), we can directly obtain other components as: Where ω is evaluated from Eq. ( 13).
In the same manner, the rest of the components of the iteration formula can be obtained.
APPLICATION OF PARAMETRIZED PERTURBATION METHOD
Equation of motion, which reads: We let By substituting Eq. ( 23) in Eq. ( 22): We suppose that the solution of Eq. ( 24) and the constant α, can be expressed in the forms: Substituting Eqs. ( 25) and ( 26) into Eq.( 24) and equating coefficients of same powers of ε yields the following equations: Solving Eq. ( 27) we obtain: Therefore, Eq. ( 28) can be re-written as: Avoiding the presence of a secular terms needs: Substituting Eq. ( 31) into Eq.( 26) Solving Eq. ( 30), we obtain: Its first-order approximation is sufficient, and then we have: Where the angular frequency can be written by Eq. (32).
RESULTS AND DISCUSSIONS
The behavior of ψ(A, t) obtained by VIM and PPM at α = π and β = 0.15 is shown in Figs. 2 and 3. Influence of coefficients β and α on frequency and amplitude has been investigated and plotted in Figs. 4 and 5, respectively.The comparison of the dimensionless deflection versus time for results obtained from VIM, PPM and Runge-Kutta 4th order has been depicted in Fig. 6 for α = π and β = 0.15, with maximum deflection at the center of the beam equal to five (A=5 ).The solutions are also compared for t=0.5 in Table 1.It can be observed that there is an excellent agreement between the results obtained from VIM and PPM with those of Runge-Kutta 4th order method [1].
CONCLUSIONS
In this paper, nonlinear responses of a clamped-clamped buckled beam are investigated.Mathematically, the beam is modeled by a partial differential equation possessing cubic non-linearity because of mid-plane stretching.Governing non-linear partial differential equation of Euler-Bernoulli's beam is reduced to a single non-linear ordinary differential equation using Galerkin method.Variational Iteration Method (VIM) and Paremetrized Perturbation Method (PPM) have been successfully used to study the non-linear vibration of beams.The frequency of both methods is exactly the same and transverse vibration of the beam center is illustrated versus amplitude and time.Also, the results and error of these methods are compared with Runge-Kutta 4th order.It is obvious that VIM and PPM are very powerful and efficient technique for finding analytical solutions.These methods do not require small parameters needed by perturbation method and are applicable for whole range of parameters.However, further research is needed to better understanding of the effect of these methods on engineering problems especially mechanical affairs.
Figure 1 A
Figure 1 A schematic of an Euler-Bernoulli beam subjected to an axial load.
Figure 4
Figure 4 Results of frequency versus amplitude associated with influence of β at α = π, for PPM or VIM.
Figure 5 Figure 6
Figure 5 Results of frequency versus amplitude associated with influence of α at β = 0.15, for PPM or VIM. | 2,144.8 | 2011-06-02T00:00:00.000 | [
"Engineering",
"Physics"
] |
A general framework for parametric survival analysis
Parametric survival models are being increasingly used as an alternative to the Cox model in biomedical research. Through direct modelling of the baseline hazard function, we can gain greater understanding of the risk profile of patients over time, obtaining absolute measures of risk. Commonly used parametric survival models, such as the Weibull, make restrictive assumptions of the baseline hazard function, such as monotonicity, which is often violated in clinical datasets. In this article, we extend the general framework of parametric survival models proposed by Crowther and Lambert (Journal of Statistical Software 53:12, 2013), to incorporate relative survival, and robust and cluster robust standard errors. We describe the general framework through three applications to clinical datasets, in particular, illustrating the use of restricted cubic splines, modelled on the log hazard scale, to provide a highly flexible survival modelling framework. Through the use of restricted cubic splines, we can derive the cumulative hazard function analytically beyond the boundary knots, resulting in a combined analytic/numerical approach, which substantially improves the estimation process compared with only using numerical integration. User‐friendly Stata software is provided, which significantly extends parametric survival models available in standard software. Copyright © 2014 John Wiley & Sons, Ltd.
Introduction
The use of parametric survival models is growing in applied research [1][2][3][4][5], as the benefits become recognised and the availability of more flexible methods becomes available in standard software. Through a parametric approach, we can obtain clinically useful measures of absolute risk allowing greater understanding of individual patient risk profiles [6][7][8], particularly important with the growing interest in personalised medicine. A model of the baseline hazard or survival allows us to calculate absolute risk predictions over time, for example, in prognostic models, and enables the translation of hazards ratios back to the absolute scale, for example, when calculating the number needed to treat. In addition, parametric models are especially useful for modelling time-dependent effects [4,9] and when extrapolating survival [10,11].
Commonly used parametric survival models, such as the exponential, Weibull and Gompertz proportional hazards models, make strong assumptions about the shape of the baseline hazard function. For example, the Weibull model assumes a monotonically increasing or decreasing baseline hazard. Such assumptions restrict the underlying function that can be captured, and are often simply not flexible enough to capture those observed in clinical datasets, which often exhibit turning points in the underlying hazard function [12,13].
Crowther and Lambert [14] recently described the implementation of a general framework for the parametric analysis of survival data, which allowed any well-defined hazard or log hazard function to be specified, with the model estimated using maximum likelihood utilising Gaussian quadrature. In this article, we extend the framework to relative survival and also allow for robust and cluster robust standard errors. In particular, throughout this article, we concentrate on the use of restricted cubic splines to demonstrate the framework, and describe a combined analytic/numeric approach to greatly improve the estimation process.
Various types of splines have been used in the analysis of survival data, predominantly on the hazard scale, which results in an analytically tractable cumulative hazard function. For example, M-splines, which by definition are non-negative, can be directly applied on the hazard scale, because of the positivity condition. Kooperberg et al. [15] proposed using various types of splines on the log hazard scale, such as piecewise linear splines [15,16]. In this article, we use restricted cubic splines to model the log hazard function, which by definition ensures that the hazard function is positive across follow-up, but has the computational disadvantage that the cumulative hazard requires numerical integration to calculate it. Restricted cubic splines have been used widely within the flexible parametric survival modelling framework of Royston and Parmar [17,18], which are modelled on the log cumulative hazard scale. The switch to the log cumulative hazard scale provides analytically tractable cumulative hazard and hazard functions; however, when there are multiple time-dependent effects, there are difficulties in interpretation of time-dependent hazard ratios, because these will vary over different covariate patterns, even with no interaction between these covariates [18].
In Section 2, we derive the general framework and extend it to incorporate cluster robust standard errors and incorporate background mortality for the extension to relative survival. In Section 3, we describe a special case of the framework using restricted cubic splines to model the baseline hazard and time-dependent effects, and describe how the estimation process can be improved through a combined analytical and numerical approach. In Section 4, we apply the spline-based hazard models to datasets in breast and bladder cancer, illustrating the improved estimation routine, the application of relative survival, and the use of cluster robust standard errors, respectively. We conclude the paper in Section 5 with a discussion.
A general framework for the parametric analysis of survival data
We begin with some notation. For the i th patient, where i = 1, … , N, we define t i to be the observed survival time, where t i = min(t * i , c i ), the minimum of the true survival time, t * i , and the censoring time, c i . We define an event indicator d i , which takes the value of 1 if t * i ⩽ c i and 0 otherwise. Finally, we define t 0i to be the entry time for the i th patient, that is, the time at which a patient becomes at risk.
Under a parametric survival model, subject to right censoring and possible delayed entry (left truncation), the overall log-likelihood function can be written as follows: with log-likelihood contribution for the i th patient where f (t i ) is the probability density function and S(.) is the survival function. If t 0i = 0, the third term of Equation (2) can be dropped. Using the relationship where h(t) is the hazard function at time t, substituting Equation (3) into Equation (2), we can write Now given that The log-likelihood formulation of Equation (6) implies that, if we specify a well-defined hazard function, where h(t) > 0 for t > 0, and can subsequently integrate it to obtain the cumulative hazard function, we can then maximise the likelihood and fit our parametric survival model using standard techniques [19]. When a standard parametric distribution is chosen, for example, the exponential, Weibull or Gompertz, and for the moment assuming proportional hazards, we can directly integrate the hazard function to obtain a closed-form expression for the cumulative hazard function. As described in Section 1, these distributions are simply not flexible enough to capture many observed hazard functions. If we postulate a more flexible function for the baseline hazard, which cannot be directly integrated analytically, or wish to incorporate complex time-dependent effects, for example, we then require numerical integration techniques in order to maximise the likelihood.
Numerical integration using Gaussian quadrature
Gaussian quadrature is a method of numerical integration, which provides an approximation to an analytically intractable integral [20]. It turns an integral into a weighted summation of a function evaluated at a set of pre-defined points called quadrature nodes or abscissae. Consider the integral from Equation (6) To obtain an approximation of the integral through Gaussian quadrature, we first must undertake a change of interval using Applying numerical quadrature, in this case Gauss-Legendre, results in where v = {v 1 , … , v m } and z = {z 1 , … , z m } are sets of weights and node locations, respectively, with m as the number of quadrature nodes. Under Gauss-Legendre quadrature, the weights v j = 1. We must specify the number of quadrature nodes, m, with the numerical accuracy of the approximation dependent on m.
As with all methods that use numerical integration, the accuracy of the approximation can be assessed by comparing estimates with an increasing number of nodes. We return to the issue of choosing the number of quadrature points in Section 3.
Excess mortality models
In population-based studies where interest lies in mortality associated with a particular disease, it is not always possible to use the cause of death information. This may be due to this information not being available or it considered too unreliable to use [21,22]. In these situations, it is common to model and estimate excess mortality by comparing the mortality experienced amongst a diseased population with that expected amongst a disease-free population. The methods have most commonly been applied to population-based cancer studies and have also been used in studies of HIV [23] and cardiovascular disease [24]. The total mortality (hazard) rate, h i (t), is partitioned into the expected mortality rate, h * i (t), and the excess mortality rate associated with a diagnosis of disease, i (t).
Transforming to the survival scale gives where R i (t) is known as the relative survival function and S * i (t) is the expected survival function. The effect of covariates on the excess mortality rate is usually considered to be multiplicative, and so, covariates, X i , are modelled as where 0 is the baseline excess hazard function and is a vector of log excess hazard ratios (also referred to as log excess mortality rate ratios). This model assumes proportional excess hazards, but in populationbased cancer studies, this assumption is rarely true and there has been substantial work on methods to fit models that relax the assumption of proportionality [24,[26][27][28]. A common model for analysing excess mortality is an extension of Royston-Parmar models [24]. These models are fitted on the log cumulative excess hazard scale. With multiple time-dependent effects, interpretation of hazard ratios can be complicated, and so, there are advantages to modelling on the log hazard scale instead. For example, in a model on the log cumulative excess hazard scale where both age group and sex are modelled as time-dependent effects, but with no interaction between the covariates, the estimated hazard ratio for sex would be different in each of the age groups. In a model on the log excess hazard scale, this would not be the case [18]. Previous work by Remontet et al. [29] used numerical integration but used quadratic splines, limited to only two knots, with no restriction on the splines.
The log-likelihood for an excess mortality model is as follows: Because the terms log do not depend on any model parameters, they can be omitted from the likelihood function for purposes of estimation. This means that in order to estimate the model parameters, the expected mortality rate at the time of death, h * (t i ), is needed for subjects that experience an event.
Cluster robust standard errors
In standard survival analysis, we generally make the assumption that observations are independent; however, in some circumstances, we can expect observations to be correlated if a group structure exists within the data, for example, in the analysis of recurrent event data, where individual patients can experience an event multiple times, resulting in multiple observations per individual. In this circumstance, we would expect observations to be correlated within groups. Failing to account for this sort of structure can underestimate standard errors.
GivenV, our standard estimate of the variance covariance matrix, which is the inverse of the negative Hessian matrix evaluated at the maximum likelihood estimates, we define the robust variance estimate developed by Huber [30] and White [31,32] where u i is the contribution of the i th observation to log L∕ , with N as the total number of observations. This can be extended to allow for a clustered structure. Suppose the N observations can be classified into M groups, which we denote by G 1 , … , G M , where groups are now assumed independent rather than individual level observations. The robust estimate of variance becomes 33 5280-5297 where u (G) i is the contribution of the j th group to log L∕ . More specifically, Rogers [33] noted that if the log-likelihood is additive at the observation level, where We follow the implementation in Stata, which also incorporates a finite sample adjustment ofV * r = {M∕(M − 1)}V r .
Improving the estimation when using restricted cubic splines
The very nature of the modelling framework described earlier implies that we can specify practically any general function in the definition of our hazard or log hazard function, given that it satisfies h(t) > 0 for all t > 0. To illustrate the framework, we concentrate on a particular flexible way of modelling survival data, using restricted cubic splines [34].
We begin by assuming a proportional hazards model, modelling the baseline log hazard function using restricted cubic splines where X i is a vector of baseline covariates with associated log hazard ratios , and s(log(t)| , k 0 ) is a function of log(t) expanded into restricted cubic spline basis with knot location vector, k 0 , and associated coefficient vector, . For example, if we let u = log(t), and with knot vector, k 0 s(u| , k 0 ) = 0 + 1 s 1 + 2 s 2 + · · · + m+1 s m+1 (19) with parameter vector , and derived variables s j (known as the basis functions), where 3 if the value is positive and 0 otherwise, and In terms of knot locations, for the internal knots, we use by default the centiles of the uncensored log survival times, and for the boundary knots, we use the minimum and maximum observed uncensored log survival times. The restricted nature of the function imposes the constraint that the fitted function is linear beyond the boundary knots, ensuring a sensible functional form in the tails where often data are sparse. The choice of the number of spline terms (more spline terms allow greater flexibility) is left to the user. A recent extensive simulation study assessed the use of model selection criteria to select the optimum degrees of freedom within the Royston-Parmar model (restricted cubic splines on the log cumulative hazard scale), which showed no bias in terms of hazard ratios, hazard rates and survival functions, with a reasonable number of knots as guided by AIC/BIC [13].
Complex time-dependent effects
Time-dependent effects, that is, non-proportional hazards, are commonplace in the analysis of survival data, where covariate effects can vary over prolonged follow-up time, for example, in the analysis of registry data [9]. Continuing with the special case of using restricted cubic splines, we can incorporate time-dependent effects into our model framework as follows: where for the p th time-dependent effect, with p = {1, … , P}, we have x p , the p th covariate, multiplied by some spline function of log time, s(log(t)| p , k p ), with knot location vector, k p , and coefficient vector, Once again, degrees of freedom, that is, number of knots, for each time-dependent effect can be guided using model selection criteria, and/or the impact of different knot locations assessed through sensitivity analysis.
Improving estimation
Given that the modelling framework is extremely general, in that the numerical integration can be applied to a wide range of user-defined hazard functions, the application of Gaussian quadrature to estimate the models may not be the most computationally efficient. For example, in Crowther and Lambert [14], we compared a Weibull proportional hazards model, with the equivalent general hazard model using numerical integration.
In the restricted cubic spline-based models described earlier, the restricted nature of the spline function forces the baseline log hazard function to be linear beyond the boundary knots. In those areas, the cumulative hazard function can actually be written analytically, as the log hazard is a linear function of log time. Defining our boundary knots to be k 01 , k 0n , we need only conduct numerical integration between k 01 , k 0n , using the analytical form of the cumulative hazard function beyond the boundary knots.
We define 0i and 1i to be the intercept and slope of the log hazard function for the i th patient before the first knot, k 01 , and 0i and 1i to be the intercept and slope of the log hazard function for the i th patient after the final knot, k 0n . If there are no time-dependent effects, then { 0i , 1i , 0i , 1i } are constant across patients. The cumulative hazard function can then be defined in three components If we assume t 0i < k 01 and t i > k 0n , then before the first knot, we have and after the final knot, we have and H 2i (t) becomes The alternative forms of the cumulative hazard function for situations where, for example, t 0i > k 01 , are detailed in Appendix A. This combined analytical/numerical approach allows us to use far fewer quadrature nodes, which given numerical integration techniques are generally computationally intensive, is a desirable aspect of the estimation routine. We illustrate this in Section 4.1.
Improving efficiency
In this section, we conduct a small simulation study to compare the efficiency of the Kaplan-Meier estimate of the survival function with a parametric formulation using splines, in particular, when data are sparse in the right tail. We simulate survival times from a Weibull distribution with scale and shape values of 0.2 and 1.3, respectively. Censoring times are generated from a U(0,6) distribution, with the observed survival time taken as the minimum of the censoring and event times, and an administrative censoring Copyright Table I.
From Table I, we see that at both 4 and 5 years, the mean squared error is lower for the parametric approach, compared with the Kaplan-Meier estimate. Bias is essentially negligible for all estimates. This indicates a gain in efficiency for the parametric approach in this particular scenario. Of course, this simulation setting is limited to a simple case of a Weibull, but note that we do not fit the correct parametric model, but an incorrect flexible model still does better than the Kaplan-Meier.
Example applications
We aim to show the versatility of the framework through three different survival modelling areas, utilising splines, whilst providing example code in the appendix to demonstrate the ease of implementation to researchers.
Breast cancer survival
We begin with a dataset of 9721 women aged under 50 years and diagnosed with breast cancer in England and Wales between 1986 and 1990. Our event of interest is death from any cause, where 2847 events were observed, and we have restricted follow-up to 5 years, leading to 6850 censored at 5 years. We are interested in the effect of deprivation status, which was categorised into five levels; however, in this example, we restrict our analyses to comparing the least and most deprived groups. We subsequently have a binary covariate, with 0 for the least deprived group and 1 for the most deprived group.
In this section, we wish to establish the benefit of incorporating the analytic components, described in Section 3.2, compared with the general method of only using numerical integration, described in Section 2. We use the general Stata software package, stgenreg, described previously [14], to fit the full quadrature-based approach, and a newly developed Stata package, strcs, which implements the combined analytic and numeric approach when using splines on the log hazard scale. We apply the spline-based models shown in Equation (18), with five degrees of freedom (six knots), that is, five spline variables to capture the baseline, incorporating the proportional effect of deprivation status, with an increasing number of quadrature points, until estimates are found to have converged to three, four and, finally, five decimal places. Table II compares parameter estimates and standard errors under the full numerical approach, across varying number of quadrature nodes, and Table III presents the equivalent results for the combined analytic/numeric approach. From Table II, we still observe variation in estimates and the log-likelihood to five or six decimal places between 500 and 1000 nodes, whilst for the combined approach shown in Table III, the maximum difference between 100 and 1000 nodes is 0.000001. For the combined approach, the loglikelihood does not change to three decimal places between 100 and 1000 nodes, whilst the log-likelihood for the full numerical approach is only the same to one decimal place.
We found that with the full numerical approach, it required 23 nodes and 50 nodes, to establish consistent estimates to three and four decimal places, respectively. We compare that to 18 nodes and 27 nodes under the combined analytic and numerical approach. Final results for the combined approach using 27 nodes are presented in Table IV. Table II. Comparison of estimates when using different numbers of nodes for the fully numeric approach. From Table IV, we observe a statistically significant hazard ratio of 1.309 (95% CI: 1.212, 1.414), indicating an increased hazard rate in the most deprived group, compared with the least deprived group. Comparing computation time, the general approach with 50 quadrature nodes took 20.5 s on a standard laptop, compared with 17.5 using the combined approach with 27 nodes. Figure 1 shows the fitted survival functions from the full numerical approach (using stgenreg), the combined analytic/numerical approach (using strcs) and the Cox model. It is clear that all three models yield essentially identical fitted survival functions, although from a visual inspection all three appear to fit poorly.
We can investigate the presence of a time-dependent effect due to deprivation status, by applying Equation (23). We use five degrees of freedom to capture the baseline and use three degrees of freedom to model the time-dependent effect of deprivation status. Figure 2 shows the time-dependent hazard ratio, illustrating the decrease in the effect of deprivation over time. The improved fit when incorporating the time-dependent effect of deprivation status is illustrated in Figure 3.
Example Stata code to fit time-independent and time-dependent models presented in this section is included in Appendix B.
Excess mortality model
For the excess mortality model, we use the same data source as in Section 4.1. However, we now include women aged over 50 years. Expected mortality is stratified by age, sex, calendar year, region and deprivation quintile [25]. As for the analysis in Section 4.1, we only include the least and most deprived groups for simplicity. Age is categorised into five groups: < 50, 50-59, 60-69, 70-79 and 80+ years. There are 41 645 subjects included in the analysis, with a total of 17 057 events before 5 years post-diagnosis.
Proportional excess hazards model.
We initially fit a model where the excess mortality rate is assumed to be proportional between different covariate patterns. We compare the estimates with a model Copyright using restricted cubic splines on the log cumulative hazard scale [24]. In both models, six knots are used with these placed evenly according to the distribution of log death times, with results presented in Table V. From Table V, we observe very similar hazard ratios and their 95% confidence intervals between the models on different scales.
Time-dependent effects.
A model is now fitted where the assumption of proportional excess hazards is relaxed for all covariates. This is carried out by incorporating an interaction between each covariate and a restricted cubic spline function of log time with four knots (three degrees of freedom). The knots are placed evenly according to the distribution of log death times. The estimated excess hazard ratio for deprivation group can be seen in Figure 4. If there is not an interaction between deprivation group and age group, then this hazard ratio is assumed to apply for each of the five age groups. If the model was fitted on the log cumulative excess hazard scale, then this would not be the case. This is illustrated in Figure 5 where the same linear predictor has been fitted for a model on the log cumulative excess hazard scale and the estimated excess hazard ratio is shown for two age groups and is shown to be different. The impact of the default interior knot locations can be assessed through sensitivity analyses, varying the knot locations. In Figure 6, we compare the default choice (interior knots at 1.024 and 2.660), with three other choices, illustrating some minor variation in the tails of the estimated shape of the timedependent excess hazard ratio; however, the functional form is generally quite robust to knot location.
Example Stata code to fit time-independent and time-dependent excess mortality models presented in this section is included in Appendix C.
Cluster robust errors
To illustrate the use of cluster robust standard errors, we use a dataset of 85 patients with bladder cancer [35,36]. We fit a model for recurrent event data, where the event of interest is recurrence of bladder cancer. Each patient can experience a total of four events, shown in Table VI. A total of 112 events were observed. Covariates of interest include treatment group (0 for placebo, 1 for thiotepa), initial number of tumors (range 1 to 8, with 8 meaning 8 or more) and initial size of tumors (in centimetres, with range 1 to 7).
To allow for the inherent structure, events nested within patients, we fit a parametric version of the Prentice-Williams-Peterson model, allowing for cluster robust standard errors. This model uses nonoverlapping time intervals; thus, for example, a patient is not at risk of a second recurrence until after the first has occurred. The baseline hazard for each event is allowed to vary; that is, there is a stratification factor by event. We use five knots for a shared baseline between the events but allow departures from this baseline using restricted cubic splines with three knots for each of the subsequent events. For comparison, we also fit a Cox model, stratified by event number, with cluster robust standard errors [37]. Results are presented in Table VII.
From Table VII, we observe similar estimates from the spline-based model, compared with the Cox model with cluster robust standard errors. We can compare estimated baseline hazard rates for each of the four ordered events, from the spline-based model, shown in Figure 7. We can see from Figure 7 that those patients who go on to experience a third and fourth event have a high initial hazard rate, demonstrating the fact that they will likely be a more severe subgroup.
Example Stata code to fit the cluster robust spline model is included in Appendix D.
Discussion
We have described a general framework for the parametric analysis of survival data, incorporating any combination of complex baseline hazard functions, time-dependent effects, time-varying covariates, delayed entry (left truncation), robust and cluster robust standard errors, and the extension to relative survival. Modelling the baseline hazard, and any time-dependent effects parametrically, can offer a greater insight into the risk profile over time. Parametric modelling is of particular importance when extrapolating survival data, for example, within an economic decision modelling framework [11]. In this article, we concentrated on the use of restricted cubic splines, which offer great flexibility to capture the observed data, but also a likely sensible extrapolation if required, given the linear restriction beyond the boundary knots. In particular, we described how the general framework can be optimised in special cases with respect to the estimation routine, utilising the restricted nature of the splines to incorporate the analytic parts of the cumulative hazard function, in combination with the numerical integration. This provided a much more efficient estimation process, requiring far fewer quadrature nodes to obtain consistent estimates, providing computational benefits. However, it is important to note that although we have concentrated on the use of splines in this article, essentially any parametric function can be used to model the baseline (log) hazard function and time-dependent effects. Copyright In application to the breast cancer data, we showed that the general numerical approach requires a large number of quadrature nodes, compared with the combined analytic/numeric approach, in order to obtain consistent estimates. This is due to the numerical approach struggling to capture high hazards at the beginning of follow-up time. Given that hazard ratios are usually only reported to two/three decimal places, the large number of nodes used in Section 4.1 will often not be required. In further examples not shown, where the hazard is low at the beginning of follow-up, often < 30 nodes are sufficient with the full numerical approach.
We have chosen to use restricted cubic spline functions of log time, because in many applications we have found this to provide an equivalent or better fit, compared with using splines of time. However, in studies with age as the timescale, it may be more appropriate to use spline functions of untransformed time.
Other approaches to modelling the baseline hazard and time-dependent effects include using the piecewise exponential framework, through either a Bayesian [38] or classical approach [39]. Han et al. [39] developed a reduced piecewise exponential approach that can be used to identify shifts in the hazard rate over time based on an exact likelihood ratio test, a backward elimination procedure and an optional presumed order restriction on the hazard rate; however, it can be considered more of a descriptive tool, as covariates cannot currently be included. The piecewise approach assumes that the baseline and any time-dependent effects follow a step function. Alternatively, using splines, as described in this article, would produce a more plausible estimated function in continuous time, with particular benefits in terms of prediction both in and out of sample, compared with the piecewise approach.
In this article, we have only looked at fixed effect survival models; however, future work involves the incorporation of frailty distributions. User-friendly Stata software, written by the authors, is provided, which significantly extends the range of available methods for the parametric analysis of survival data [14].
If t 0i < k 01 and k 01 < t i < k 0n , then we have | 6,931.4 | 2014-12-30T00:00:00.000 | [
"Mathematics"
] |
A novel non-dominated sorting genetic algorithm for multi-objective optimization: DSGA
Non-dominated sorting is a critical component of all multi-objective evolutionary algorithms (MOEAs). A large percentage of computational cost of MOEAs is spent on non-dominated sorting. So the complexity of nondominated sorting method in a large extent decides the efficiency of the MOEA. In this paper, we present a novel non-dominated sorting method called the dynamic non-dominated sorting (DNS). It is based on the sorting of each objective instead of dominance comparisons. The computational compelxity of DNS is O ( mN log N ) ( m is the number of objectives, N is the population size), which equals to the best record so far. Based on DNS, we introduce a novel multi-objective genetic algorithm (MOGA) called the dynamic nondominated sorting genetic algorithm (DSGA). Then, some numerical comparisons between different non-dominated sorting method are presented. The results shows that DNS is efficient and promising. Finally, numerical experiments on DSGA are also given. The results show that DSGA outperforms some other MOEAs both on general-scale and large-scale multi-objective problems.
Introduction
Multi-objective optimization has extensive application in engineering and management. Many optimization problems in the real-world can be modeled as multi-objective optimization problems (MOPs) [10], [23], [35]. However, due to the theoretical and computational challenges, it is not easy to solve MOPs. Therefore, numerical multi-objective optimization attracts a wide range of research over the last decades.
One popular way to solve MOP is to reformulate it into a single-objective optimization problem. We call this technique the indirect method. Typical indirect methods are weighted sum method [31], ε−constraint method [7] and their variations [11]. One difficulty for the weighted sum method is the selection of proper weights so as to satisfy the decision-maker's preference. Since the weighted sum is a linear combination of the objective functions, the concave part of the Pareto frontier cannot be obtained using the weighted sum method. The ε−constraint method converts multiple objectives, except one, to constraints. However, it is difficult to determine the upper bounds of these objectives. On the one hand, small upper bounds could exclude some Pareto solutions; on the other hand, large upper bounds could enlarge the searching area, which yields some sub-Pareto solutions. Additionally, indirect method can only obtain a single Pareto solution in each run, but in the real-world application, decision-makers often prefer a number of optional strategies so that they can choose one according to their preference.
Another strategy to solve MOP is to explore the entire objective function value space directly in order to obtain its Pareto frontier. We call this strategy the direct method. Population-based heuristic methods are ideal direct methods, because their iterative units are populations instead of a single point, so they can obtain a set of solutions in a single run. In the past few years, many heuristic methods were applied to solve MOP, such as the evolutionary algorithm [19], [25], [39], genetic algorithm [34] and differential evolution [22], [24]. Among them, genetic algorithm attracted a great deal of attention and lots of good methods has been presented [3], [13], [16], [17].
A combination of direct and indirect methods is another strategy to solve MOP. We call this type the hybrid method. A representative of this type is MOEA/D [36]. It combines the evolutionary algorithm and three scalarization methods.
When solving MOP using direct methods, two important issues [42] need to be addressed: -Elitism: In the process of multi-objective evolutionary algorithm (MOGA), we always prefer solutions whose function values are closer to the real Pareto frontier. In the selection procedure, these solutions should be selected as parents for the next generation, which leads the task of non-dominated sorting in each iteration. According to the definition of efficient point, numerous amount of comparisons are needed to identify the non-dominated state of each point. Therefore, reasonably reducing the computational cost is one of the key research issues in designing MOEA.
-Diversity: Diversity reflects the distribution of the obtained Pareto frontier. Obviously, a uniformly distributed Pareto frontier is preferred than a unevenly distributed one. In other words, a good algorithm should avoid obtaining solutions which are excessively concentrate on one or two isolated areas.
Among them, elitism is realized by non-dominated sorting whose core operation is comparison. Since non-dominated sorting is needed in each iteration, the efficiency of non-dominated sorting method is very important for the performance of MOEA. In this paper, we first propose a novel non-dominated sorting method called the dynamic non-dominated sorting (DNS), and then a new multiobjective genetic algorithm (MOGA) based on DNS. The rest of the paper is organized as follows: In Section 2, we review some existing non-dominated sorting methods and the framework of genetic algorithm. In Section 3, we proposed DNS and a new MOGA based on DNS. In Section 4, we compare DNS with other existing non-dominated sorting methods. In Section 5, we test the proposed MOGA using some numerical benchmarks and compare its numerical performance with other MOEAs. Section 6 concludes the paper.
Related works
In this section, we first review some basic definitions of multiobjective optimization, then some existing non-dominated sorting methods, and finally propose the framework of genetic algorithm.
Some basic definitions of MOP
The general mathematical model of MOP is Here F : R n → R m is a vector function and X ⊆ R n is a box constraint.
Obviously, if y ≺ z, then y z. In this paper, if y z, we say y dominates z or z is dominated by y; if y z and z y, we say y and z are non-dominated.
Let Y ⊆ R m and y * ∈ Y , if there is no y ∈ Y such that y y * (or y ≺ y * ), then y * is called an efficient point (or weakly efficient point) of Y . Suppose that F (x * ) is an efficient point (or weakly efficient point) of the objective function value space F (X), then x * is called an efficient solution (or weakly efficient solution) of Problem (1).
Efficient and weakly efficient solutions can also be defined using cone or partial order. Another name of the efficient solution is Pareto solution. The meaning of Pareto solution is that, if x * is a Pareto solution, there is no feasible solution x ∈ X, such that f i (x) ≤ f i (x * ) for all i ∈ {1, 2, · · · , m} and there is at least one i 0 ∈ {1, 2, · · · , m} such that f i0 (x) < f i0 (x * ). In other words, x * is the best solution in the sense of " ". Another intuitive interpretation of Pareto solution is that it cannot be improved with respect to any objective without worsening at least one of the others. Weakly efficient solution means that if x * is a weakly efficient solution, then there is no feasible solution x ∈ X, such that any f i (x) of F (x) is strictly better than that of F (x * ). In other words, x * is the best solution in the sense of "≺". Obviously, an efficient solution is also a weakly efficient solution. The set of efficiet solutions is denoted by P * , its image set F (P * ) is called the Pareto frontier, denoted by PF * .
Existing non-dominated sorting methods
Non-dominated sorting is one of the critical step in MOEAs. A large percentage of computation cost is spent on non-dominated sorting for it involves numerous comparisons. Until now, there are more than ten different non-dominated sorting methods [18]. The earliest one is the naive non-dominated sorting [26]. In this method, in order to find if a solution is dominated, the solution has to do dominance comparisons with all the other solutions, which leads a numerical complexity of O(mN 3 ) in the worst case. Here, m stands for the number of objectives, N stands for the population size, the same below. The naive approach does not record any dominance comparison result, which in return cause a lot of repeated computation. The fast non-dominated sorting [3] overcomes this drawback by calculating two entities for each solution p: (i) domination count n p , the number of solutions which dominate the solution p; and (ii) dominate set S p , a set of solutions that the solution p dominates. This modification reduces the computational complexity of the fast non-dominated sorting to O(mN 2 ).
In [20] McClymont and Keedwell proposed climbing sorting and deductive sorting. The climbing sorting is similar to the bubble sorting for real number sequence. In order to locate a non-dominated solution, the candidate is shifted from dominated solution to the dominating one until all the solutions in the current population are visited. The final candidate must be a non-dominated solution. The deductive sorting is similar to the selection sorting for real number sequence. In the deductive sorting, one successively check each solution, once the current solution is found to be dominated, abandon it. If the current solution dominates all the other solutions, or is non-dominated with the others, then it is identified as a non-dominated solution. The climbing sorting works well on populations with large number of Pareto frontiers. On the contrary, the deductive sorting is good at sorting population with small number of Pareto frontiers. The average computational complexity of the climbing sorting and deductive are both O(mN 2 ).
Another idea to save dominance comparisons is to discard the identified non-dominated solutions, Corner sorting [30] applies this idea. Some of the non-dominated sorting method consider the partial order of the solutions in the populations. For example, the efficient non-dominated sorting [38] first sorts solutions using the common partial order of m−dimensional vector. This sorted population has a very important feature: solution p m will never be dominated by a solution p n if m < n. As shown in Table (III) in [38], computational complexity of the efficient non-dominated sorting is O(mN 2 ) in the worst case, while O(mN √ N ) or O(mN log N ) in the best case (depends on the different methods used in partial order.) In order to avoid repeated dominance comparisons, one can record the results of dominance comparisons in a matrix. This idea is applied in the dynamic non-dominated sorting [18] where a N × N matrix with entries 1, −1, 0 is used to record the dominance relationships between solutions. The computational complexity of the dynamic non-dominated sorting is O(mN 2 ). Another method applying this idea is the dominance degree sorting [41]. This method first calculate a comparison matrix for each objective, then builds a dominance degree matrix by adding these comparison matrixes together. The dominance relationship can be found in the dominance degree matrix. In the dominance degree sorting, only the real number sequence sorting is needed. This makes it much faster than the method based on dominance comparison. In this paper, we improve the dynamic non-dominated sorting by hybridizing it with the dominance degree sorting. The computational complexity of the improved dynamic non-dominated sorting will decrease to O(mN log N ).
Genetic algorithm
In computer science and operations research, genetic algorithm (GA) which is inspired by the process of natural selection, is one of the most popular evolutionary algorithms. It is introduced by John Holland in 1960s, and then developed by his students and colleagues at the University of Michigan between 1960s and 1970s [9]. Over the last two decades, GA was increasingly enriched by plenty of literatures [12], [33], [21]. Nowadays, GA are applied in a wide range of areas, such as mathematical programming, combinational optimization, automatic control, image processing, etc.. Suppose P (t), O(t) and S(t) represent parents, offsprings and selection pool of the t th generation, respectively. The general structure of GA is described in Algorithm 1.
Algorithm 1: Genetic algorithm
Input: Population size N p , crossover rate α c , mutation rate α m , maximal generation number t max and problem parameters. Output: Obtained population and their corresponding evaluation.
Step 2: While t has not reached t max , do Step 2.1: Crossover operator: generate crossover offspring O c (t), Step 2.2: Mutation operator: generate mutation offspring O m (t), Step 2.3: Evaluation: evaluate O c (t) and O m (t) and build the selection pool by Step 2.4: Selection operator: select P (t + 1) from S(t), Step 2.5 Let t ← t + 1, go back to Step 2.
The implementation of GA may be various in different situations. For example, some implementation generate O c (t) and O m (t) independently based on P (t), while some implementation first generate O c (t) based on P (t), then yields O m (t) based on O c (t). Furthermore, crossover, mutation and selection operators are alterable in GA. Different designs of these operators lead to different numerical performance of GA.
It is worth to notice that, for notation P (t), O(t) and S(t), we do not specify whether they are decision variables (i.e., P (t)/O(t)/S(t) ⊂ X) or objective function values (i.e., P (t)/O(t)/S(t) ⊂ F (X)) since they are bijection through objective function F (x). One can distinguish them according to the contexts. For example, when calculating the Pareto frontier, they are seen as objective function values; when running crossover and mutation, they are seen as decision variables.
Dynamic sorting genetic algorithm
In this section, we first propose an improved dynamic non-dominated sorting, then based on the improved dynamic non-dominated sorting, design a novel multiobjective optimization genetic algorithm titled the dynamic sorting genetic algorithm.
Dynamic non-dominated sorting
According to the definition of efficient point, in order to detect the nondominated points in a selection pool, each solution must compare with the others in the selection pool to find if it is dominated. In the naive sorting [2], the non-dominated points in different Pareto frontiers are detected one by one, so there exists numerous repetitive dominance comparisons between some candidate pairs, which in a large extent increases the computational complexity of native sorting. In this subsection, we tackle this shortage by recording the result of dominance comparison between each candidate pairs, which in return, avoids any repeated comparison. This idea is inspired by the dynamic programming, so we call it the dynamic non-dominated sorting.
Suppose S(t) is the current selection pool who has N solutions. The aim of non-dominated sorting is to identify all the Pareto frontiers in S(t). We denote the i th Pareto frontier l i (1 ≤ i ≤ i max ). Obviously, we have 1 ≤ i max ≤ N , i max = 1 means that all the solutions in S(t) are non-dominated, i max = N means that each Pareto frontier has only one solution. We use a N × N matrix D to record the dominance relationship in S(t), where The non-dominated solutions can be detected using D. Each row of D stands for a solution. If there is no −1 in the i th row, that means y i is not dominated by any other solution, i.e., y i is non-dominated. Finding all rows with this feature, we can detect all the non-dominated solutions. These solutions consist the first Pareto frontier of the selection pool S(t). Assign l i = 1 to these points. When detecting the second Pareto frontier, solutions on the first Pareto frontier (already identified) should not be involved any more. So before detecting the second Pareto frontier, we first shrink D by discarding the rows and columns whose solutions are already identified as in the first Pareto frontier. Then repeat the same process to detect the second Pareto frontier and so forth, until all the solutions are identified, i.e., the matrix D becomes empty.
The procedure of the dynamic non-dominated sorting is presented in Algorithm 2. The input is the current selection pool S(t), its size is N ; the output is the Pareto frontier index l i , i = 1, 2, · · · , N . Step 1 computes the N × N dynamic matrix D.
Step 2 detects the current non-dominated solution using the current D.
Step 3 shrinks the matrix D by removing rows and columns corresponding to the detected non-dominated solutions in Step 2. Then if D is not empty, go back to Step 2 to detect non-dominated solution in the next Pareto frontier; otherwise, the process of non-dominated detection finishes. It is worth to note that after some rows and columns have been removed, the index of the matrix D and the index of solution in the selection pool are not corresponding any more. So in Algorithm 2, we use an index set I ij to virtually shrink the matrix D. Here the index i always means the index of a solution in the selection pool.
Step 1: Compute a N × N dynamic matrix D whose element is Step 2: Let k := k + 1, search by rows, find set Step 3: Shrink the matrix D by removing indexes I from the index set I ij , i.e., I ij = I ij \ I.
Step 4: If I ij is not empty, go back to Step 2; otherwise stop the loop.
The index l i is called the Pareto frontier index. The smaller l i is, the better elitism y i is, i.e., the solution with smaller Pareto frontier index is closer to the real Pareto frontier.
Dynamic matrix
The computation of the dynamic matrix D is the core step of the dynamic non-dominated sorting, most of the computational cost is spent on this step. If use the dominance comparison to calculate the dynamic matrix D, N (N −1)/2 times of dominance comparisons are needed, which makes the computational complexity of the dynamic non-dominated sorting O(mN 2 ). Through the transitivity of dominating can be used in practice, it still cannot reduce the computational complexity dramatically. In this subsection, we apply the idea presented in the dominance degree sorting [41], introducing a faster method to calculate the dynamic matrix.
The process of calculating the dominance matrix is as follows. Firstly, for each objective, we calculate a N × N comparison matrix C f k (1 ≤ k ≤ m) which records the comparison relationship of solutions on this objective. Take the first objective for example, suppose vector w f1 = (p f1 C f1 can be obtained very fast by sorting the members of w f1 .
Secondly, adding all the comparison matrix together to get a dominance degree matrix C, i.e., To eliminate the effect of these solutions with identical values for all objectives, we set the corresponding element of C to be zero. For example, if p i and p j are identical respect to all objectives, we set C ij = 0. Obviously, according to this rule, C ii = 0 for all i = 1, 2, · · · , N .
Thirdly, the elements of C reflect the dominance relationship between solutions. For example, The pseudocode of calculating the dynamic matrix is presented in Algorithm 3
Algorithm 3: Dynamic matrix
Input: Selection pool S(t) and its size N = |S(t)|, number of objectives m, an iteration counter k = 1. Output: Dynamic matrix D. Step then let Step 2: If k + 1 ≤ m, then let k = k + 1, go back to step 1; otherwise, let Step 3: Build dynamic matrix D. If Cij = m, then let Dij = 1 and Dji = −1; otherwise, let Dij = 0.
Step 4: Output the dynamic matrix D.
The main computational effort of the dynamic matrix is on the computation of the comparison matrixes C f k (k = 1, 2, · · · , m). Intuitively, for each objective, function values are compared with each other, so N (N − 1)/2 real number comparisons are needed, which makes the numerical complexity of dynamic matrix O(mN 2 ). However, this process can be improved by applying a real number sequence sorting method, such as quick sort [41]. The computational complexity of the quick sort is O(N log N ), so the computational complexity of dynamic matrix is O(mN log N ).
Dynamic sorting genetic algorithm (DSGA)
In this subsection, we present a novel multi-objective genetic algorithm. Nondominated sorting in this algorithm applies the dynamic non-dominated sort-ing presented above, so we call this algorithm the dynamic sorting genetic algorithm, abbreviated as DSGA. The process of DSGA is presented in Fig. 1. In the step of crossover and mutation, self-adaptive simulated binary crossover operator (SSBX) [4] and power mutation operator (PM) [6] are applied. The SSBX operator is a real-parameter recombination operator which is commonly used in the evolutionary algorithm (EA) literature. The operator involves a parameter which dedicates the spread of offspring solutions vis-a-vis that of the parent solutions. The PM operator is based on the power distribution. It is proved to have the same performance as the widely used non-uniform mutation operator [6].
For the selection step, the binary tournament selection operator used in NSGA-II is still applied in DSGA. The binary tournament selection operator is mainly constituted by the fast non-dominated sorting and the crowdedcomparison operator. In DSGA, we replace the fast non-dominated sorting by the dynamic non-dominated sorting proposed above.
Comparison of non-dominated sorting methods
In order to clarify the improvement of the dynamic non-dominated sorting (DNS), this subsection compares it with other non-dominated sorting methods. Except DNS proposed in this paper, four other referential non-dominated sorting methods are considered: the fast non-dominated sorting (FNS) [3], climbing sorting (CS) [20], deductive sorting (DS) [20] and the dominance degree non-dominated sorting (DDNS) [41]. FNS is one of the earliest Pareto sorting approaches. It is updated from the naive non-dominated sorting [2]. The computational complexity of FNS is O(mN 2 ). CS follows dominating relationships between solutions and climbs up the graph toward the Pareto frontier. The key process of CS is to change the considering solution from any dominated one to dominating one until a non-dominated solution (at the current Pareto frontier) has been identified. The computational complexity of CS is O(mN 2 ). DS accesses each solution based upon the natural order of the population. The candidate solution compares with all its following solutions but not with its previous ones. The average numerical complexity of DS is O(mN 2 ), but in the best case that each Pareto frontier has only one solution, it decreases to O(mN ). DDNS is one of the state-of-the-art non-dominated sorting algorithms. Differently from the other non-dominated sorting algorithms, DDNS does not compare two solutions to identify dominating relationship. Instead, it constructs a comparison matrix which stores the relationship of all solutions with respect to each objective. Then a dominance degree matrix can be obtained by adding these comparison matrices together. Finally, Pareto ranking of the population can be obtained by analyzing the dominance degree matrix. If use quick sort in ranking each objective, the computational complexity of DDNS is O(mN log N ).
We compare DNS with the other referential non-dominated sorting methods introduced above. For metrics of numerical performance, time consumption and number of comparisons are considered. Experiments are divided into three groups: (i) performance with respect to the variation of the the population size, (ii) performance with respects to the variation of the number of Pareto frontiers, and (iii) performance with respect to the variation of the number of objectives. We use the fixed features population generator [18] to generate test populations. This generator can generate test populations with certain features, such as having prefixed number of points, prefixed number of Pareto frontier and prefixed number of points in each Pareto frontier. The generated test populations are listed in Table 1 where m stands for the number of objectives, k stands for the number of Pareto frontiers and N is a vector standing for the number of points in each Pareto frontiers. In the series (i) test populations, the number of objectives and Pareto frontiers are fixed, while the number of points in each Pareto frontier are even and increases from 12 to 30 with a step of 2. In the series (ii) test populations, the number of objectives is fixed, while the number of Pareto frontiers increases from 1 to 10 with step of 1, each test population has 150 points in total evenly distributed in each Pareto frontier. In the series (iii) test populations, the number of Pareto frontiers and number of points in each Pareto frontier are fixed, while the number of objectives arises from 2 to 10 with step of 1.
Results of the numerical experiments are illustrated in Fig. 2, 3 and 4. In Fig. 2(b), FNS needs much more comparisons than the other four methods, CS and DS need exact the same amount of comparisons, DDNS and DNS too but less than CS and DS. As the increase of population size, number of comparisons for FNS increases much faster than the other four method, then DS and CS, the increasing trend of DDNS and DNS are relative gentle. The same features demonstrated in Fig. 2(a) for time consumption. It is worth to note that DDNS spent slightly less time than DNS. Fig. 3 shows that, as the number of Pareto frontiers increase, the time consumption and number of comparisons decrease for CS and DS. DDNS and DNS stay in a lower level stably, while FNS is stably appears in a very high level.
It is showed in Fig. 4 that the time consumption and the number of comparisons increase as the arise of the number of objectives. This is reasonable, because the increase of the number of objectives must increases the number of comparisons, which in return increases the time consumption. But the increase rates are different. FNS has the steepest trend, CS and DS are less, DDNS and DNS only have slight increase.
In summary, the computation complexity of DNS keeps stable if the population size is fixed, and has a slight increase if the population size and number if objectives increase. This statement agrees with the theoretical complexity analysis of DNS. DNS outperforms FNS, CD and DS, and performs the same as DDNS which is considered as the most efficient non-dominated sorting method [41].
Numerical experiments
In this section, we investigate the numerical performance of DSGA. Firstly, we further compare the sorting methods FNS and DNS by embedding them into the same MOEA (NSGAII [3]). Secondly, we compare DSGA with some of the other popular MOEAs, including MOEA/D [36], SparseEA [28], PPS [8] and LSMOP [29]. Finally, we investigate the numerical performance of DSGA when scaling the number of variables.
Test problems
We use five series of test problems in the numerical experiments. They are ZDT series [42], DTLZ series [5], UF series [37], BT series [15] and LSMOP series [1]. Features of these test problems including number of objective functions m, number of dimensions n, variable bounds X and references are demonstrated in Table 2. All test problems are scalable respect to the number of dimensions, the DTLZ series is also scalable respect to the number of objective functions. Numbers in the brackets are the number of dimensions or the number of objectives we set in our experiments. Details of the objective functions, referential Pareto frontiers and Pareto solutions refer to the references.
Referenial algorithms and parameter setting
We use five referential MOEAs in the numerical experiments. They are NS-GAII [3], MOEAD [36], SparseEA [28], PPS [8] and LSMOF [29]. Among them, NSGAII is one of the most popular MOEA based on genetic algorithm. In the past decades, NSGAII got thousands of citations. MOEAD is a successful multiobjective optimization method based on decomposition, it is often used as a [14] standard in numerical experiments. SparseEA, PPS and LSMOF are three of the latest MOEAs, note that SparseEA and LSMOF are originally designed for solving large-scale multiobjective optimization problems. Among the five referential algorithms, NSGAII is used to verify the improvement of the sorting method DNS comparing with the traditional one FNS, while the other four referential algorithm are used to investigate the numerical performance of the proposed method DSGA. The implementation of these algorithms are based on the PlatEMO [27]. For the sake of fair comparison, parameters for all algorithms are uniformly set as far as possible. To be specific, the population size is set to be 100, the maximum number of objective function evaluations is set to be 100000, the maximum number of iterations is set to be 500. The maximum number of objective function evaluations and iterations are taken as stop criteria for all algorithms. In order to achieve statistic performance, all the test are run 30 times independently, and the mean and standard deviation of the performance metrics are recorded. The other parameters for certain algorithms are set as the default in PlatEMO.
Performance metrics
Many performance metrics have been proposed to evaluate the numerical performance of MOGAs [40]. There are two goals for evaluation metrics: (i) measure the convergence of the obtained Pareto frontier, and (ii) measure the diversity of the obtained Pareto frontier.
We use the performance metric IGD [17] to evaluate the numerical performance. Suppose that P * is a set of uniformly distributed points belonging to the real Pareto frontier. It can be taken as a standard representation of the real Pareto frontier. Let A be a set of solutions obtained by a certain solver, then IGD is defined as the average distance from P * to A: where d(v, A) is the minimum Euclidean distances between v and the points in A, i.e., In fact, P * is a sample set of the real Pareto frontier. If |P * | is large enough to approximate the Pareto frontier very well, IGD(A, P * ) could measure both the diversity and convergence of A. This is also the reason that we choose IGD as the evaluation metric for this paper. A smaller IGD(A, P * ) means the set A is closer to the real Pareto frontier and has better diversity. Another well-known performance metric is the hypervolume value (HV) [32] of the obtained non-dominated solutions. The calculation of HV value do not need a referential Pareto frontier P * , but is more complicated than the calculation of IGD value, especially when the number of objectives is large. In this paper, we use IGD instead of HV since the referential Pareto frontiers of the test problems are all known and evenly distributed ones can be generated using PlatEMO.
NSGAII with FNS and DNS
In this subsection, we compare FNS and DNS by embedded them into the same MOEA. Since FNS is originally used in NSGAII, we replace FNS in NSGAII by DNS to build a new MOEA. In the following, we call the NSGAII with FNS NSGAII-FNS, and call the NSGAII with DNS NSGAII-DNS. Note that NSGAII-FNS and NSGAII-DNS are only different in the non-dominated sorting method.
In order to achieve fair competition and statistical performance, all the tests are run for 30 times independently, and the mean and standard deviation of two performance metrics, CPU time and IGD value, are recorded. In the following tables, the best record for a certain performance metric is marked as in grey cell. Besides, the Wilcoxon rank sum test with a significant level of 0.05 is adopted to perform statistical analysis the experimental results, where the symbols "+","-" and "=" indicate that the result by NSGAII-FNS are significantly better, significantly worse and statistically similar to that obtained by NSGAII-DNS, respectively.
As shown in Table 3, NSGAII-DNS spends significantly less CPU time than NSGAII-FNS on all test problems, which further verifies that DNS is faster than FNS. As for the IGD value, Table 3 shows that 38 out of the total 39 test problems are statistically similar. This is reasonable for that NSGAII-FNS and NSGAII-DNS are only different in the non-dominated sorting method, which affects the CPU time but not the final solutions.
In Figure 5, we demonstrate the decrease curve of IGD of the first test problem in each series. Because inside a series, the test problems have more or less the same structure, the IGD curve of one problem can represent the others. For each test problem, 10 samples of IGD value are taken evenly from 1000 to 10000 times of objective function evaluations. From Figure 5, the IGD value of NDGAII-DNS and NSGAII-FNS converge to almost the same value for problems ZDT1 and DTLZ1. Figures 5(d) and 5(e) show that NSGAII-DNS outperforms NSGAII-FNS for problems BT1 and LSMOP1. For problem UF1, Figure 5(c) shows that NSGAII-FNS outperforms NSGAII-DNS. | 7,641.2 | 2021-04-12T00:00:00.000 | [
"Computer Science"
] |
SYNTHESIS, CHARATERIZATION AND BIOLOGICAL ACTIVITIES OF UREAS AND THIOUREAS DERIVATIVES
Abstract: Urea, a naturally occurring compound, became the first organic compound which was synthesized in lab by Wohler in 1928, and played important physiological and biological roles in animal kingdom. Synthesis of urea became a revolutionary step in the history of synthetically organic chemistry. [1]. et al explained its use as topical drug; urea is absolutely none toxic, undesirable actions occur if skin state and concentration of urea are on a misbalance. It is most valuable substance for restoring hydration in skin and in eczemas due to skin dryness.
Introduction
Replacement of oxygen atom in urea by sulphur atom produces Thiourea which has been successfully used in many diseases.Mitchell et al explained that 'Thiourea' the sulphur analogue of urea has been known for over a century and a quarter during which time it has found a variety of uses, some within the biological field.Most noted of these have been their employments as a plant growth stimulator to break bud dormancy and increase crop yield and more recently as a therapeutic agent to treat thyroid dysfunction .
Thiourea, itself has been used as stimulator to break bud dormancy.Prepared sulphonyl urea derivatives and evaluated them as synergistic herbicides [4].
Experimental
The following compounds were synthesized according to the scheme as given before under plan of study.Elemental analysis was done by using carbon and nitrogen analyzers.Melting points were determined in open capillary and are uncorrected.The IR spectral study of the synthesized compounds was done by using JASCO infra-red spectrophotometer.K Br disc method was used.The UV spectral study was done by using UV/ VIS Spectrophotometer.Spectral grade ethanol is used as solvent... NMR spectral study was performed on JEOL, FX90Q, FOURIER, Transform NMR spectrometer.
Preparation of phenyl Thiourea:-0.1mol(9.3g) of aniline was dissolved in 10 ml. of conc.HCl acid, diluted to 100 ml with water in a 250 ml.conical flask.To this added 0.1 mol (7.6g) of NH4SCN solution (in 50 ml.warm water) with constant stirring and mixture was refluxed for 30-45 minutes.It is allowed to cool in ice for 30 minutes and the obtained white crystals were filtered, washed with water and recystallised.
Preparation of 4-sulphonyl phenyl Thiourea, sodium salt:-0.1mol() of sulphanilic acid was diluted to 100 ml with water in a 250 ml conical flask.To this added 0.1 mol (7.6g) of NH 4 SCN solution (in 50ml warm water) with constant stirring.Reaction mixture was refluxed on water bath for 30-45 minutes.Sodium carbonate solution was added to adjust pH alkaline and mixture was again heated on water bath for 10 min.It is allowed to cool in ice for few minutes.The obtained white crystals were filtered, washed and recystallised from alcohol. .
Preparation of 4-carboxy-phenyl Thiourea:-
0.1mol () of 4-carboxy phenyl aniline was diluted to 100 ml with water in a 250 ml conical flask.To this added 0.1 mol (7.6) of NH 4 SCN solution ( in 50ml warm water ) with constant stirring.Reaction mixture was refluxed on water bath for 30-45 minutes.
Sodium carbonate solution was added to adjust proper alkaline pH to achieve maximum product formation .The mixture was again heated on water bath for about 10 minutes and was allowed to cool in ice for few minutes.The obtained yellowish-brown product was filtered, washed and recystallised.
Results and Discussions
Chemical structure and biological activity: It was observed that biological activity of a compound is associated with a particular structural unit or group and hence if this structural unit or group is present in other Compound, the latter also becomes biologically active.Such a part of drug, which is responsible for biological action, termed as pharmacophore group.Urea and Thiourea displaying biological activities possess specific binding sites, known as hydrogen binding area, complementary area and auxiliary binding area shown in the given figures.
Proposed binding sites in Thiourea
Size and shapes of various groups in these molecules co-related positively with the biological activity.The x-ray crystallographic data suggested that the distal aryl/ heterocyclic ring, present in complementary area, occupies different positions depending on bond angles and in the atomic distances, affects the potency of a drug.
The aim of investigation of new drug is based to investigate and optimize the auxiliary binding area for producing more potent biological activities.The bioactivity of compounds depends on 'Bioisosteric'.Isosteric modifications involve the replacement of an atom, or group of atoms in a molecule by another atom or group of atoms with similar electronic and steric configurations.Thus 'Burger' explained, the isosteric pairs have similar peripheral electronic arrangements with similar shapes and similar volumes, and which exhibits similar chemical & physical properties.Since the biological properties of classically related isosteric compounds, often turned out to be more similar than their chemical and physical properties.
The synthesized compounds were characterized by elemental analysis, IR, UV and NMR spectral studies.Elemental analysis data were found within ± 0.4% of the theoretical values.Melting point of phenyl Thiourea was compared with the literature value and was in agreement with the observed value.All the physical and analytical data are given in Table -1 The IR, UV and NMR spectral methods are the important tools for the structural elucidation of the synthesized compounds.All the spectral data of the synthesized compounds are given below-
Infrared Spectral Studies of Synthesized Thioureas:
Infrared radiation refers broadly to that part of the electromagnetic radiation spectrum between the visible and microwave regions.Of greatest practical use to organic chemistry is the limited portion between 4000 and 400 cm -1 .
Even a very simple molecule can give an extremely complex spectrum.Although the IR spectrum is characteristic of entire molecule, it is true that certain groups of atom give rise to bonds at or near the same frequency regardless of the rest of the molecule.
The persistence of these characteristic bonds permits to obtain useful information about the compounds synthesized.
The infrared spectral study was done on JASCO infrared spectrophotometer IR report100.KBR disc method was used.The spectra data are given below in cm -1
Ultra-violet Spectral Studies of Synthesized Thioureas:
Molecular absorption in the ultra-violet (UV) and visible region of the spectrum is dependent on the electronic structure of the molecule.Absorption of energy is quantized; resulting in the elevation of electrons from orbital in the ground state to higher energy orbital's in the excited state.In practice, UV spectroscopy is limited to conjugated systems.
Characteristic groups with diverse electronic environment absorb at selective wavelengths, and this helps in recognizing characteristic groups in molecules of widely varying complexity.
UV spectra were taken on Jasco model 7800, UV/VIS Spectrophotometer.Spectral grade methanol and ethanol were used as solvents.All the above compounds were synthesized according to the scheme as mentioned under plan of study.The methods of preparation are described in experimental part .wasproved by the elemental analysis and spectral data of the synthesized compounds.The data reveal and confirm the proposed planned structure of synthesized compounds with satisfactory elemental data within ± 0.4 limit to the theoretical values, satisfactory UV λ max values, -NCON-and N-CS-N absorption peaks in IR spectra and satisfactory aromatic and NH proton signals in NMR spectra.
C O N C L U S I O N S
Biological importance of Thiourea is well known as mentioned earlier under the review of literature.This prompted us to synthesize Thiourea derivatives.The synthesis of the proposed Thiourea was done according to the plan successfully as evident from the relevant elemental data, melting points and spectral data.
The observed elemental data for C and N are almost compatible with the calculated values.Melting point of phenyl Thiourea is found to be similar to the reported value given in literature.The λ max values as apparent in UV spectra are well agreed to the structure of the compounds.IR spectral absorption frequencies are appeared in similar pattern to the structures of the compounds.NMR proton signals data are consistent with the protons environment as found in the corresponding compound.
The above study thus concludes that the synthesized compounds are aryl/ 4-substituted Thiourea as evident by elemental and UV, IR and NMR spectral data.
UV spectral data for synthesized Thiourea are given below.The value of λ max is given belowis an important tool for determining the structure of a molecule.An NMR spectrum can give almost unbelievably detailed information about molecular structure.(a) The number of signals, which tells us how many different kinds of protons there are in molecule.(b) The positions of the signals, which tells us something about the electronic environment of each kind of proton.(c) The intensities of the signals, which tells us how many protons of each kind there are, and (d) The splitting of a signal into several peaks, which tells us about the environment of a proton with respect to other, nearby protons... NMR spectral study was done on JEOL, FX90Q, Fourier, and Transform NMR Spectrometer.NMR (CDCl 3 ) signal values on $ scale are given below- | 2,041.2 | 2010-10-31T00:00:00.000 | [
"Chemistry"
] |
Software-Defined Optimal Computation Task Scheduling in Vehicular Edge Networking
With the development of smart vehicles and various vehicular applications, Vehicular Edge Computing (VEC) paradigm has attracted from academic and industry. Compared with the cloud computing platform, VEC has several new features, such as the higher network bandwidth and the lower transmission delay. Recently, vehicular computation-intensive task offloading has become a new research field for the vehicular edge computing networks. However, dynamic network topology and the bursty computation tasks offloading, which causes to the computation load unbalancing for the VEC networking. To solve this issue, this paper proposed an optimal control-based computing task scheduling algorithm. Then, we introduce software defined networking/OpenFlow framework to build a software-defined vehicular edge networking structure. The proposed algorithm can obtain global optimum results and achieve the load-balancing by the virtue of the global load status information. Besides, the proposed algorithm has strong adaptiveness in dynamic network environments by automatic parameter tuning. Experimental results show that the proposed algorithm can effectively improve the utilization of computation resources and meet the requirements of computation and transmission delay for various vehicular tasks.
Introduction
With the development of the intelligent connected vehicles, more and more vehicular terminal devices have begun to participate in data task collection and processing [1][2][3][4], such as autonomous driving, virtual reality, and computation-intensive tasks. [5] presented a traffic management service, called ABATIS, to optimize the routes for vehicles. In cloud computing paradigm, the collected data and processing tasks have been uploaded to a centralized data center far away from Internet of vehicles [6]. After the task execution is completed, the processing results will be transmitted back to the task initiator. Hence, enormous sensed data and the encapsulated computation-intensive tasks transmission have put severe strain on the mobile network, especially in terms of bandwidth consumption. With the ever-increasing amount of network traffic, the network congestion frequently happens and degrades the quality of service (QoS) for delay-sensitive tasks [7][8][9].
Recently, a Vehicular Edge Computing (VEC) paradigm was presented, as shown in Figure 1. A vehicle can offload some complex delay-sensitive tasks to edge cloud due to the limited computing, storage, communication capacity [8,10,11], as shown in the limited computing, storage, communication capacity [8,10,11], as shown in Figure 2. There are existing works focusing on the task offloading and resource allocation. For example, [12] exploits Lyapunov optimization theory to maximize the long-term performance of networking system, such as lower task execution delay and task migration delay. Although Lyapunov optimization algorithm can be designed and implemented, it is not suitable to complex and highly dynamic network environments. Literature [13] proposed the Cloud Computing Management Unit (CCMU) to optimize the allocation of computing resources. In [13], CCMU uses the Markov decision process to give the optimization decisions. Although the MDP has been developed a general algorithm (Bellman Equation), the convergence speed of MDP is still slow for the state space of continuous variables. Overall, it is difficult to achieve the load balancing effect for the existing task offloading and resource allocation algorithms. How to reasonably allocate computing and communication resources is still a challenge for the VEC networking. In our previous research, our work is the exploiting the modern control theory to model the computation task optimal scheduling in vehicular edge networks [14]. This paper is the extension of the conference paper [14]. In this paper, we proposed an Optimal Control-based computing Task Scheduling algorithm (OCTS). The proposed OCTS method has significantly improved the previous work in the following aspects: (1) Introducing VEC architecture and assumptions; (2) using the software-defined network (SDN)/OpenFlow to collect the necessary network parameters for task scheduling; (3) optimizing task migration delay and avoiding network congestion by adjusting the weight value . When the network delay is higher than the threshold value, it can be reduced by increasing weight value ; (4) enhancing the experimental verification; and (5) comparisons with the existing approaches. The remainder of this paper is organized as follows. Section II gives the related work. Section III describes the network scenario and system model. Section IV presents the vehicular task queuing model. Section V proposes the optimal control-based computing task scheduling algorithm. Section VI presents our empirical studies. Section VII concludes this paper. The remainder of this paper is organized as follows. Section 2 gives the related work. Section 3 describes the network scenario and system model. Section 4 presents the vehicular task queuing model. Section 5 proposes the optimal control-based computing task scheduling algorithm. Section 6 presents our empirical studies. Section 7 concludes this paper.
Related Works
With the development of Internet of vehicles, more and more vehicular applications have been developed to meet the QoS requirements of mobile users. Due to the limited computing, storage, and communication capacities of mobile terminals, the vehicle itself cannot be able to meet the QoS requirements of various applications. Although cloud computing has large computing power, the transmission delay between vehicles and cloud computing platform is significant [15]. Hence, it is not sufficient for the latency-sensitive applications. The edge computing servers are closer to the mobile terminals, which can effectively reduce task execution and migration delay [8].
Nowadays, some researchers have focused on the mobile task offloading and resource allocation. A previous study [16] proposed a joint optimal VEC server selection and offloading (JSCO) Algorithm to address resource allocation for a multiuser multi-server VEC system. Fan [17] proposed a collaborative optimization migration and caching model to improve the performance of edge task execution. Then, the optimization problem with two independent sub-problems was solved. Next, the resource management algorithm was designed to jointly schedule task and its migration. The experimental results show that the proposed model can reduce the latency of task execution. Another study [18] studied the average delay minimization problem for component-based linear applications in vehicular ad-hoc networks and proposed a delay-optimization based ant colony optimization algorithm (DoACO). This optimization problem with the stringent constraint conditions has been proved a NP hard problem. Liu [19] presented the optimization problem with the energy consumption, execution delay, and price cost constraints. Specifically, energy consumption, execution delay, and computing capacity were explicitly and jointly considered. On the basis of theoretical analysis, a multi-objective optimization problem with joint conditions was presented. To minimize the power consumption, execution delay, and price cost, the multi-objective optimization problem was solved by the scaling scheme and the interior point method. Another study [20] proposed a resource-sharing scheme for data center collaboration, which stipulated that each data center uses buffer to store service requests for local execution. When the buffer is full, the request is migrated to an adjacent data center and accepted if the current queue length is below the pre-defined threshold in the data center. In this way, the blocking state and task execution latency of the data center can be effectively reduced. Furthermore, previous research [21] studied three load sharing schemes, namely no-sharing, random sharing, and minimum load sharing. After the comparisons, they find that the minimum load sharing scheme is most suitable for making full use of the cooperation among servers to realize the load balancing. Another study [22] proposed another edge computing task scheduling model, which transformed the waiting time minimization problem into an overall planning problem, and then carried out optimal scheduling through dynamic programming. A previous study [23] proposed an improved chaotic bat swarm algorithm. Based on the bat algorithm, chaos factors and second-order oscillation were introduced to accelerate the update of dynamic parameters and thus improve the convergence of the algorithm.
However, the proposed methods [12,[20][21][22][23][24][25][26][27][28] result in unbalancing resource allocation for vehicular tasks due to dynamic network environment driven by humans. In order to achieve the load-balancing, literatures [29,30] used the idea of software defined network to obtain the more network status parameters. SDN is an innovative network design, implementation, and management method, which separates network control from forwarding process to achieve better user experience [31]. Next, the collected network status parameters are the input vector of the proposed optimization model. Experiments show that the proposed algorithms can significantly reduce task execution time. Although the proposed algorithms can achieve the better results, the number of iterations being solved is still large due to the high dimension input vector. Hence, the presented solving algorithms are not fundamentally suitable for delay-sensitive vehicular task execution.
VEC Architecture and Assumptions
In this section, we first introduce the networking layer architecture. Then, the softwaredefined vehicular edge networking (SD-VEC) architecture and computation models are elaborated. Figure 3 shows the SD-VEC networking layer architecture. In the user layer, when the vehicles in the area covered by a Roadside Unit (RSU), they can send vehicular tasks to the RSU with wireless connections. In the VEC layer. Each VEC server is connected with an RSU. The RSU will forward these tasks to the VEC servers and then the VEC server will execute these tasks and send them back to the requesting vehicles. The VEC servers in different area are connected by the wired cables in the same local area network. The VEC servers can send or receive tasks to or from other servers by these wired cables. In the control layer, the SDN controller can connect with the VEC servers through wired cables. The SDN controller can not only obtain the status information of servers and network, such as the CPU utilization, memory usage, but also control the task migration among the servers. The descriptions of symbols are shown in Table 1.
Symbols Description
The CPU frequency of VEC server The CPU clock period of VEC server The number of the tasks arriving at VEC server at time The task execution time on server at time The processing time to run tasks on server The number of the tasks sent form server to server The task transmission time with no network
Network Model Assumptions
We assume that the second layer includes N VEC servers, which are deployed near the RSU. Each VEC server is equipped with an RSU thus the VEC servers and RSUs share the same index. When the vehicles move into the coverage of the RSUs, they can offload their computation tasks to corresponding RSUs via wireless link. The CPU frequency of a VEC server i is denoted as f i and the corresponding clock period is h i = 1/ f i . All of the CPU frequencies for VEC servers can be denoted as f = { f 1 , · · · · · · , f i } and the corresponding CPU clock periods can be denoted as h = {h 1 , · · · · · · , h i }, i ∈ N.
Secondly, we assume that the received tasks by server i follow a Poisson distribution. We denote λ i (t) as the number of the tasks arriving at the VEC server i at time t, and the task execution time on server i at time t is denoted as m t i . = ρ λ i (t) is denoted as the processing time to run tasks on a server i. All tasks arriving at the VEC servers are denoted as λ(t) ∈ {λ 1 (t), · · · · · · , λ i (t)}, i ∈ N and their corresponding processing time can be To simplify the computation, we assume that the task execution time is m t i × h i for a VEC serve i. Hence, the server i can take h i × m t i × λ i (t) to process the tasks at time t. Table 1. Description of the symbols.
Symbols Description
The number of the tasks arriving at VEC server i at time t m t i The task execution time on server i at time t ρ λ i The processing time to run tasks on server i u ij (t) The number of the tasks sent form server i to server j τ The task transmission time with no network congestion ND i The task transmission time on server i CD i The task execution time on server i x i State variable for VEC server i J The convergence cycle of the system at time t x * (t) The optimal routing trajectory at time t u * (t) The optimal control vector at time t C max Threshold value of CPU utilization ϕ The optimum range of CPU utilization for a VEC server G The vector form of ϕ D The execution time and transmission time incurred by offloaded task scheduling ξ A coefficient which is used to adjust the weight of the offloaded task transmission time Thirdly, during the work of this system, the network delay cannot be easily calculated. In order to adjust and optimize the task schedule via the network state, we use the SDN to obtain the network state. The network delay obtained by SDN is defined as D a , and the maximum network delay defined by a user is defined as D a max .
Vehicular Task queuing Model
Due to the limited computation capacity of a VEC server and the burst of task arrivals, some VEC servers are busy, while others are free. The load imbalance will lead to a low computation resources utilization and extra computation time. Hence, we have to schedule tasks among VEC servers to alleviate the load imbalance.
We assume that we send tasks of server i to server j and the number of the tasks can be denote as u ij (t). Specifically, if server i needs to process a large number of tasks at time t while server j has to process a small number of tasks, the u ij (t) could be positive number. Thus, the number of tasks which server i send to others can be denoted as According to the presented computation model, at time t the to process these tasks. Vehicular task queuing model is shown as Figure 4. Next, we describe the task queuing model and task computation model. transmission time, we assume that the tasks arrive at server i from other servers follow a Poisson distribution. We also assume that the task transmission time is τ when there is no network congestion. As shown in Figure 4a, we use M/M/1 queuing model to build the vehicular task queuing model. The task transmission time can be denoted as Equation (1), network delay computing delay Un-Compute task RSU VEC Figure 4. Vehicular task queuing model.
Task Computation Model
As shown in Figure 4b, we use M/M/1 to build the vehicular task queuing model. The task execution time is denoted as Equation (2).
Task Queuing Model
Task scheduling not only can effectively decrease the task execution time of high load servers, but also can increase computation resource utilization. However, the task scheduling will increase the task transmission time of the VEC network. To calculate the task transmission time, we assume that the tasks arrive at server i from other servers follow a Poisson distribution. We also assume that the task transmission time is τ when there is no network congestion. As shown in Figure 4a, we use M/M/1 queuing model to build the vehicular task queuing model. The task transmission time can be denoted as Equation
Task Computation Model
As shown in Figure 4b, we use M/M/1 to build the vehicular task queuing model. The task execution time is denoted as Equation (2).
where CD i is denoted as task execution time on a server i.
Problem Formulation and Optimal Task Scheduling Solving
Our goal is to reduce the load on each server as much as possible while satisfying the network delay and computing delay of vehicular tasks.
The problem formulation with constraints is shown as Formula (3).
In the Formula (3), is the performance index of the VEC system. ND(u(t)) and CD(u(t)) is the execution time and transmission time incurred by offloaded task scheduling. When D a > D max a , the increasing value of ξ is to decrease D a . ξ is a coefficient to adjust the weights of the offloaded task transmission time. If we increase the value of ξ, the task transmission time will decrease while the task execution time will increase. The adjustment of the ξ value is used for dealing with the stringent time constraint vehicular tasks. Formula (3) can be resolved by calculus of variations method, but before that, we need to set up the corresponding state equations and state variables. Firstly, the CPU utilization of a VEC server is denoted as a state variable. Next, the various tasks with different QoS requirements from both vehicles and other mobile terminals (laptop, smart phones, etc.) are denoted as the inputs of the system framework. The inputs of the network system have clearly influenced on running state variables of this system. The state variables of a VEC server i can be denoted as Equation (5). Consequently, the running state vectors of the VEC system can be defined as Equation (6).
Secondly, the running state equation of the VEC system is used to describe the relationship between the input of this system and the system state. The running state equation of this system can be obtained, as shown in Equation (7).
where the matrix A(t) represents the relationship among the state variables within the VEC system. The matrix B(t) represents the state control variable, which is used to control and track the variations of running states. The CPU utilization over time can be represented by the vector x(t). The vector x(t) is referred as the trajectory of the VEC system. The scheduled tasks among the VEC servers can be denoted as u(t), namely the control vector. Through scheduling tasks among VEC servers, we can effectively control the CPU utilization of VEC servers from the initial running state to the final running state. In the entire running process, the offloaded task execution time and migration time can be controlled in an optimum range during the convergence cycle. Then, the convergence cycle of the VEC system can be denoted as a functional variable J. If we get the minimum value of the vector f by using control vector u(t) to control vector x(t) from the original state x(0) to the destination state x(t f ), we could get an optimal routing trajectory for all offloaded tasks in the VEC system. Here, the optimal routing trajectory is denoted as x * (t). t f is the time consumption for the optimization process. The corresponding control vector is called optimal control vector, which is denoted as u * (t).
Next, the status information of the servers, such as the CPU utilization and the network bandwidth, is collected by the SDN controller. The offloaded task among these servers is totally scheduled through the designed load-balancing app on a SDN controller. Optimized task scheduling among VEC servers can improve the load imbalance for the VEC virtual resources. Specifically, the VEC servers with higher load will migrate their tasks to that with lower load. Furthermore, the CPU utilization of all the optimized VEC servers will keep on optimum status level.
Finally, a threshold value C max % for CPU utilization is pre-defined. When the CPU utilization of a VEC server has just exceeded the pre-defined value, this time is set as the initial state indexed by 0. In addition, the CPU utilization of a VEC server is assumed as the optimization object. After time T, we can obtain the final optimization state. Hence, we can the optimal range for all of the VEC servers between the initial state and the final optimization state through tasks scheduling. Here, the optimum range of CPU utilization for a VEC server is denoted as ϕ(x(T), T) = 0, and the vector form of ϕ(x(T), T) = 0 is represented as G(x(t)) = 0 and the range of x(T) is set as S = {x(T)|G(x(t)) = 0}.
At last, the proposed Algorithm 1 is shown as below.
Input: Task arrival numbers, CPU usage of all SBSs, Control parameter ξ, J(u(t))
Output: Optimal control u * (t), optimal trajectory x * (t) 1. For t = 0; t ≤ T do 2. Calculate the expected CPU usage of SBSs C e %; 3. Calculate the fitted curve λ(t) and ρ λ (t) based on task arrival numbers; 4. Establish the state vector .
Experiment Setup
In this section, the simulation experiments are designed and implemented to evaluate the performance for the proposed optimal control-based computation task scheduling in software-defined vehicular edge networking in terms of CPU utilization and delay. The minimum configuration of a server is Core i3 CPU and 4G memory for performing the experiment in real time.
We have presented the software-defined vehicular edge networking (SD-VEC) environments, as shown in Figure 5. As shown in this figure, the vehicle nodes firstly communicate with its RSU node, and then the RSU node can obtain the flow tables through the RSU controller, the vehicle nodes can route by the flow rules at last. Here, we choose the floodlight v1.2 as the SDN controller. The combination of simulation of urban mobility (SUMO v1.8) with instant virtual network (Mininet v2.2) as the base software platform are installed on a computer equipped with i7 CPU and 8GB memory. SUMO can generate the mobility pattern of the vehicles that is used by the Mininet. We chose the city of Luxembourg in European cities as the simulation scenario. That is because Luxembourg SUMO Traffic Scenario is well-known and frequently used to evaluate the VANETs communication system. In this network experiment, there is an SDN controller, there are 5 VEC servers and 100 vehicles in a SD-VEC network. As shown in Figure 5, one VEC server can connect 20 vehicles at the beginning. To simplify the calculation, the computation capacity of every VEC server is set to 1GHz and the task transmission time in the LAN is set to 10 ms without network congestion. The event of vehicular task arrivals on a VEC server follows the Poisson distribution, and every task will take 10 6 CPU cycles. The captured network traffic in this paper is the time series with white Gaussian noise. The rest of simulation experimental parameters are shown in Table 2. follows the Poisson distribution, and every task will take 6 10 CPU cycles. The captured network traffic in this paper is the time series with white Gaussian noise. The rest of simulation experimental parameters are shown in Table 2. Figure 6 shows the network topology of the experiment. In the figure, the SDN Controller is connected with VEC by these cables, and the VECs is connected with the vehicles by wireless. Figure 6 shows the network topology of the experiment. In the figure, the SDN Controller is connected with VEC by these cables, and the VECs is connected with the vehicles by wireless. As shown in Figure 7, the initial average CPU utilization of the edge servers 1 to 4 is 20% and CPU utilization of the edge server 5 is 90%. The initial average memory utilization of the edge servers 1 to 4 is 25% and memory utilization of the edge server 5 is 100%. The initial average disk utilization of the edge servers 1 to 4 is 23% and memory utilization of the edge server 5 is 93%. The total experiment duration is 1000 s. The experiments show As shown in Figure 7, the initial average CPU utilization of the edge servers 1 to 4 is 20% and CPU utilization of the edge server 5 is 90%. The initial average memory utilization of the edge servers 1 to 4 is 25% and memory utilization of the edge server 5 is 100%. The initial average disk utilization of the edge servers 1 to 4 is 23% and memory utilization of the edge server 5 is 93%. The total experiment duration is 1000 s. The experiments show that the usages of network load are uneven. Next, we simulated the Lyapunov optimization algorithm to improve the efficiency of the task scheduling on the edge servers. The average CPU utilization of servers 1 to 4 have increased from 20% to 30% and server 5 has decreased from 90% to 55%. The measurements of CPU utilization in this figure show the CPU utilization curves of the five edge servers are closer than that of without using any optimization. These results show the Lyapunov optimization algorithm can achieve the goal of computation load balancing. Then, we used the proposed OCTS optimization algorithm to schedule the offloaded task on the edge servers. As shown in Figure 7, the CPU utilization of servers 1 to 4 have increased from 20% to 35%, and the CPU usage of server 5 has decreased from 90% to 45%. The measurements of CPU utilization in Figure 7 show the CPU utilization curves of the five edge servers are closer than that of no optimization and using Lyapunov optimization. These experimental results prove that our proposed OCTS method is better than the Lyapunov optimization and no optimization methods in terms of computation load balancing. With the Lyapunov optimization, the average memory utilization of servers 1 to 4 have increased from 25% to 32% and server 5 has decreased from 100% to 65% while with the OCTS optimization, the average memory utilization of servers 1 to 4 have increased from 25% to 38% and server 5 has decreased from 100% to 53%. With the Lyapunov optimization, the average disk utilization of servers 1 to 4 have increased from 23% to 32% and server 5 has decreased from 93% to 63% while with the OCTS optimization, the average memory utilization of servers 1 to 4 have increased from 23% to 35% and server 5 has decreased from 93% to 50%. terms of computation load balancing. With the Lyapunov optimization, the average memory utilization of servers 1 to 4 have increased from 25% to 32% and server 5 has decreased from 100% to 65% while with the OCTS optimization, the average memory utilization of servers 1 to 4 have increased from 25% to 38% and server 5 has decreased from 100% to 53%. With the Lyapunov optimization, the average disk utilization of servers 1 to 4 have increased from 23% to 32% and server 5 has decreased from 93% to 63% while with the OCTS optimization, the average memory utilization of servers 1 to 4 have increased from 23% to 35% and server 5 has decreased from 93% to 50%.
As shown in Figure 7, in the early stage of optimization, the effect of OCTS is not as good as that of Lyapunov. This is because if too many vehicular tasks are migrated at that time, there will be a high migration delay. When the load of the server drops, the optimization effect of OCTS is obviously better than that of Lyapunov, because when the computing delay of the server drops, the migration of a large number of vehicular tasks will not lead to too high migration delay. Hence, we can get a conclusion that the optimization effect for the proposed OCTS algorithm is about 10% to 15% higher than the Lyapunov optimization method under the same status conditions. Furthermore, the optimization effect for the proposed OCTS algorithm is about 30% to 40% higher than no optimization method under the same status conditions. Secondly, we compare the CPU utilization among the no optimization, the local optimization, and global optimization, as shown in Figure 8. Global optimization means that we can get load and delay information for each server through the SDN controller. In this figure, when the system runs without optimization, server 2 is about 20% CPU utilization As shown in Figure 7, in the early stage of optimization, the effect of OCTS is not as good as that of Lyapunov. This is because if too many vehicular tasks are migrated at that time, there will be a high migration delay. When the load of the server drops, the optimization effect of OCTS is obviously better than that of Lyapunov, because when the computing delay of the server drops, the migration of a large number of vehicular tasks will not lead to too high migration delay.
Hence, we can get a conclusion that the optimization effect for the proposed OCTS algorithm is about 10% to 15% higher than the Lyapunov optimization method under the same status conditions. Furthermore, the optimization effect for the proposed OCTS algorithm is about 30% to 40% higher than no optimization method under the same status conditions. Secondly, we compare the CPU utilization among the no optimization, the local optimization, and global optimization, as shown in Figure 8. Global optimization means that we can get load and delay information for each server through the SDN controller. In this figure, when the system runs without optimization, server 2 is about 20% CPU utilization and server 4 is about 30% CPU utilization. When the system is under local optimization, server 2 is about 20% CPU utilization and server 4 is about 45% CPU utilization. At this time, server 5 offloads a large number of tasks to server 4, and server 2 remains idle due to the lack of global performance status information. Tasks from server 5 is denied when server 4's CPU utilization is approaching the threshold. and server 4 is about 30% CPU utilization. When the system is under local optimization, server 2 is about 20% CPU utilization and server 4 is about 45% CPU utilization. At this time, server 5 offloads a large number of tasks to server 4, and server 2 remains idle due to the lack of global performance status information. Tasks from server 5 is denied when server 4's CPU utilization is approaching the threshold. Hence, when the system is under the global optimization, the CPU utilization of server 2 is about 33%, and that of server 4 is about 34%. The experimental results show that our proposed algorithm can achieve more excellent load balancing effect than another two methods.
Thirdly, we compare the no optimization with the OCTS optimization methods in the terms of the delay metric in unit of millisecond. As shown in Figure 9, the proposed OCTS method is compared with no optimization method in terms of both the task migration time and the task processing time. The experimental results show that both the task Hence, when the system is under the global optimization, the CPU utilization of server 2 is about 33%, and that of server 4 is about 34%. The experimental results show that our proposed algorithm can achieve more excellent load balancing effect than another two methods.
Thirdly, we compare the no optimization with the OCTS optimization methods in the terms of the delay metric in unit of millisecond. As shown in Figure 9, the proposed OCTS method is compared with no optimization method in terms of both the task migration time and the task processing time. The experimental results show that both the task processing and task migration time for the servers 1 to 8 slightly increases when our proposed OCTS method enables. Besides, although the task migration time for servers 9 and 10 have also slightly increases, the task processing time of server 9 and 10 has obviously decreased. After the OCTS optimization finished, the task processing time and the task migration time among the edge servers have become approximately equal. The experimental results prove that our proposed OCTS method can obviously improve the computation and network load balancing. However, the task migration time needs to further optimize. In this evaluation, we set the parameter ξ equal to 1. Next, we try to adjust the value of parameter ξ to optimize the solving. The parameter ξ is used to adjust the proportion of network delay in the load balancing optimization process for reducing the task migration delay. That is because the improvement of load balancing needs too large a number of task migrations from one edge server to another edge server. Fourthly, we study the parameter optimization to reduce the task migration time.
Here, we set a counter for an edge server to count the number of vehicular tasks arriving at the edge server. When the number of the offloaded task is up to 100, the counter will be reset to 0. Besides, the task execution time and task migration time will be calculated again. Then, we try to increase the value of parameter to show the variations of task execution time and task migration time. As shown in Figure 10, compared with no optimization method, the experimental results show that both the task processing time and the task migration time of servers 1 to 8 decreases with the increasing of the value of when our proposed OCTS method enables. Additionally, the task execution time of servers 9 and 10 are significantly reduced after the OCTS optimization. That is because a large number of tasks are scheduled from edge servers 9 and 10 to other edge servers. Meanwhile, the task migration time is doubled. That is because with the increasing value of parameter , the OCTS optimization method appears over fit. As the experimental results show, we can come to the conclusion that there exists an optimal tradeoff between task execution time and task migration time when is equal to 3. Fourthly, we study the parameter ξ optimization to reduce the task migration time. Here, we set a counter for an edge server to count the number of vehicular tasks arriving at the edge server. When the number of the offloaded task is up to 100, the counter will be reset to 0. Besides, the task execution time and task migration time will be calculated again. Then, we try to increase the value of parameter ξ to show the variations of task execution time and task migration time. As shown in Figure 10, compared with no optimization method, the experimental results show that both the task processing time and the task migration time of servers 1 to 8 decreases with the increasing of the value of ξ when our proposed OCTS method enables. Additionally, the task execution time of servers 9 and 10 are significantly reduced after the OCTS optimization. That is because a large number of tasks are scheduled from edge servers 9 and 10 to other edge servers. Meanwhile, the task migration time is doubled. That is because with the increasing value of parameter ξ, the OCTS optimization method appears over fit. As the experimental results show, we can come to the conclusion that there exists an optimal tradeoff between task execution time and task migration time when ξ is equal to 3. the task migration time of servers 1 to 8 decreases with the increasing of the value of when our proposed OCTS method enables. Additionally, the task execution time of servers 9 and 10 are significantly reduced after the OCTS optimization. That is because a large number of tasks are scheduled from edge servers 9 and 10 to other edge servers. Meanwhile, the task migration time is doubled. That is because with the increasing value of parameter , the OCTS optimization method appears over fit. As the experimental results show, we can come to the conclusion that there exists an optimal tradeoff between task execution time and task migration time when is equal to 3. Commented [m correct. Figure 10. The impact on delay for servers 1 to 10.
Conclusions
In this paper, we propose an optimal control-based resource allocation algorithm, called OCTS, and exploit the software-defined networks framework to achieve the computation and network load balancing among the VEC servers in vehicular edge networking. Our contributions are that 1 SD-VEC networking layer architecture is presented; 2 the calculus of variations method in modern control theory is introduced to solve the optimal load balancing strategy for the offloaded edge computation tasks; 3 the parameter adjustment can optimize the task processing time and task migration time and meet the service requirements of vehicular users. Simulation experimental results prove that our proposed OCTS method can effectively reduce the load imbalance and improve the resource utilization of idle edge servers. Our future work is to study the user behavior and predict the load imbalance position in advance. According to the load utilization estimation, we can effectively schedule the vehicular tasks to the idle VEC servers. | 8,478.4 | 2021-02-01T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
Till austerity do us part? A survey experiment on support for the euro in Italy
The COVID-19 pandemic worsened Italy’s fiscal outlook by increasing public debt. If interest rates were to rise, it would become more likely that Italy experiences a financial crisis and requires a European bailout. How does making EU funds conditional on austerity and structural reforms affect Italians’ support for the euro? Based on a novel survey experiment, this article shows that a majority of voters chooses to remain in the euro if a bailout does not involve conditionality, but the pro-euro majority turns into a relative majority for ‘Italexit’ if the bailout is contingent on austerity policies. Blaming different actors for the fiscal crisis has little effect on support. These results suggest that conditionality may turn Italian voters against the euro.
Introduction
The COVID-19 pandemic has led to a severe deterioration of the fiscal outlook of eurozone governments, particularly in Italy. Italian public debt increased to nearly 160% of gross domestic product (GDP) in 2020. Furthermore, for the past 25 years, Italy's growth rate has usually been lower than the interest rate it pays on the stock of debt. If such circumstances were to persist, financial markets may perceive Italy's public debt to be unsustainable. This makes a resurgence of tensions in sovereign bond markets and a revival of the euro crisis a distinct possibility.
According to the rules introduced in the first stage of the euro crisis, a country that is unable to finance its debt at acceptable interest rates should apply for an emergency loan from the European Stability Mechanism (ESM). To reduce moral hazard, countries that receive financial assistance have to sign a Memorandum of Understanding with the ESM (and possibly with the International Monetary Fund (IMF) and the European Central Bank (ECB) as well), pledging to introduce a series of austerity measures and structural reforms as a condition for assistance. An ESM program is a prerequisite for Outright Monetary Transactions (OMT) by the ECB, 1 i.e., potentially unlimited purchases of government bonds by the central bank.
One of the problems with this crisis resolution mechanism is that the austerity measures imposed on crisis countries are highly unpopular Kuo, 2016, 2020;Franchino and Segatti, 2019;Jurado et al., 2020) and lead to electoral volatility, public protests, and the emergence of anti-system forces (Bojar et al., 2021;Bremer et al., 2020;Hu¨bscher et al., 2020). Still, existing research shows that voters in most crisis-ridden countries strongly support the euro and are unwilling to leave it despite the costs associated with austerity (Clements et al., 2014;Hobolt and Wratil, 2015;Roth et al., 2016). In July 2015, Greek voters rejected the European Union (EU) bailout package in a popular referendum, but research shows they still wanted to remain in the common currency (Jurado et al., 2020;Walter et al., 2018;Xezonakis and Hartmann, 2020). This unwillingness to leave, despite the costs of austerity, strengthened the hand of 'creditor' countries and allowed them to shift the burden of adjustment on 'debtor' countries during the euro crisis (Copelovitch et al., 2016;Frieden and Walter, 2017).
In this article, we ask how Italian voters would evaluate the trade-off between remaining in the euro and implementing austerity in case of a fiscal crisis. To what extent would they accept the costs of austerity for the promise of a bailout and continued membership in the common currency? Italy is the third-largest economy in the eurozone, which makes it systemically important. Many commentators, therefore, believe that the euro stands or falls with Italy, and the possibility of exit is far from purely academic. In the wake of the euro crisis, Eurosceptic parties emerged that questioned Italy's membership in the eurozone. The Five Star Movement (M5S) included the promise of a referendum on the permanence in the euro in its electoral manifesto of 2014, 2 while the Lega proposed a negotiated exit from the eurozone in its 2018 and 2019 manifestos. 3 Moreover, support for the euro before and after the COVID-19 outbreak was significantly lower in Italy than in other crisis-ridden countries (as we show below). Still, we know little about how Italians weigh the costs and benefits of staying in the euro in case of a financial crisis.
We use a novel framing experiment that exposes individuals to six different hypothetical scenarios to elicit preferences for the trade-off between austerity and euro membership. Some scenarios mention that the bailout package comes with the standard set of austerity policies included in previous European bailouts, while other scenarios do not. 4 Moreover, some scenarios suggest that the Italian government is responsible for the crisis due to its fiscal profligacy, while others hint that the EU, led by Germany and other northern European countries, has precipitated the crisis due to its fiscal inflexibility. The study is based on a large survey (n ¼ 4200) fielded among a representative sample of Italian voters in October 2019, in the wake of a standoff between the Italian government and the European Commission over the country's government deficit.
We find that in the control group, a majority of respondents favours remaining in the euro. However, informing participants about the conditionality associated with a bailout package changes the majority for remaining in the euro into a majority for 'Italexit'. In contrast, foreign blame attribution and domestic blame attribution do not significantly influence preferences. Overall, our results suggest that opposition to further austerity trumps support for the euro in Italy. This implies that the European approach to crisis resolution, based on fiscal consolidation and structural reform in exchange for financial support, may lead to greater resistance in Italy than it did in other countries and even to a break-up of the eurozone.
Preferences for eurozone membership and exit during the euro crisis
The 2008 financial crisis and its aftermath fundamentally shook the political and economic system in Europe and led to an exceptional politicisation of the euro (Copelovitch et al., 2016;Matthijs and Blyth, 2015). The Maastricht Treaty did not foresee any mechanisms for financial assistance to member states and even included an explicit no-bailout clause (Article 125 of the Treaty on the Functioning of the European Union (TFEU)). However, when Greece lost access to financial markets in 2010 and several other member states followed suit, the EU decided to bail them out. The bailouts helped countries to service their debt and avoid bankruptcy, but they came with strict conditionality. The euro crisis was perceived as issuing primarily from government profligacy (Buti and Carnot, 2012), and the existing mechanisms of fiscal surveillance (the Stability and Growth Pact (SGP)) were further strengthened through the introduction of the Fiscal Compact. Countries receiving financial assistance were required to sign a Memorandum of Understanding, committing them to structural reforms and austerity policies (Frieden and Walter, 2017;Walter et al., 2020).
The bailout packages were controversial in both creditor and debtor countries. Voters in creditor countries were sceptical about financial transfers to other countries (e.g., Bechtel et al., 2014;Beramendi and Stegmueller, 2020;Kleider and Stoeckel, 2019;Stoeckel and Kuhn, 2018;Walter et al., 2020), whereas voters in debtor countries opposed the conditionality attached to the bailouts Kuo, 2016, 2020;Franchino and Segatti, 2019). Overall, the eurozone crisis further politicised the EU and the euro (Hutter and Kriesi, 2019) and substantially increased dissatisfaction with the EU (De Vries, 2018;Guiso et al., 2016;Hobolt and De Vries, 2016).
Remarkably, however, support for euro membership remained high across the continent (Clements et al., 2014;Hobolt and Wratil, 2015;Roth et al., 2016). In some countries, the adverse effect on growth and unemployment was severe, and the incremental approach in resolving the crisis proved 'catastrophic for the citizens of many crisis-plagued member states' (Jones et al., 2016(Jones et al., : 1010). Yet, existing research finds that even in the crisis-ridden south, voters still fundamentally supported the euro despite austerity and a prolonged recession. There was a broad consensus in debtor countries that a unilateral exit from the euro should be avoided at all costs, not just in Greece but also in other countries (Walter et al., 2020: 4). Even pro-euro individuals were not enthusiastic about austerity, but they 'believe [d] it [was] preferable to alternatives and worth the costs, particularly regarding maintaining the benefits of the EU and euro' (Ferna´ndez-Albertos and Kuo, 2020: 216). As citizens compared the status quo against possible alternatives (De Vries, 2018), the prospect of leaving the euro was even less attractive than austerity for voters in the south.
Events around the third Greek bailout in 2015 illustrate how popular support for the euro reduced the room for manoeuvre of national negotiators. In his reconstruction of the negotiation process, the Greek chief negotiator, finance minister Yannis Varoufakis (Varoufakis, 2017: 478). However, Jurado et al. (2020) show that while the far-left government led by Syriza was trying to renegotiate the terms of the agreement with the creditors (the 'Troika'), support for the euro remained very high in Greece (around 75%) despite the negative consequences of austerity for the Greek population (Xezonakis and Hartmann, 2020). Survey evidence suggests that, in summer 2015, when a majority of voters rejected the third bail-out package in a popular referendum, more than three-quarters of respondents wanted to keep the euro, and only 13% preferred exit (Walter et al., 2018: 982). In the course of the negotiation, the Greek government never explicitly threatened exit but tried to convince the counterpart that exit may come about by accident (Pitsoulis and Schwuchow, 2017). Popular support for the euro thus deprived the Greek government of a credible exit option and reduced its bargaining power. This made it easier for the creditor countries to shift the burden of adjustment on debtor countries during the euro crisis (Copelovitch et al., 2016;Frieden and Walter, 2017).
Overall, previous episodes of crisis suggest that voters have conflicting preferences: on the one hand, they strongly support the euro; on the other hand, they strongly oppose austerity (Clements et al., 2014;Kuo, 2016, 2020;Franchino and Segatti, 2019). Due to the parlous state of Italian public finances, voters in Italy may have to face exactly this dilemma at some point. Given that support for the euro is significantly lower in Italy than in other crisis-ridden countries according to data from the Eurobarometer shown in Figure 1, it is important to ask: how would they respond to the prospect of having to agree to a structural adjustment plan as a condition for financial support?
Framing effects on support for the euro Preferences for euro remain or exit are unlikely to be fixed. A large literature has shown that framing effects substantially affect individual-level preferences (Amsalem and Zoizner, 2020;Druckman, 2007a, 2007b;Lupia, 1994;Slothuus and de Vreese, 2010) as individuals update their preferences based on new information (Zaller, 1992). This literature has highlighted both the effect of equivalence frames, which 'present the same information in either a positive or negative light', and emphasis frames, which 'vary how the information is presented and its content' (Amsalem and Zoizner, 2020: 4; also see Cacciatore et al., 2016;Chong and Druckman, 2007b). Emphasis frames usually have a stronger effect than equivalence frames because they provide information the receivers may not possess or focus their attention on aspects they may not be attentive to when considering an Note: The graph shows the percentage of respondents who say they are for: 'A European economic union with one single currency, the euro'. It reports results from Eurobarometer wave 92 and 93, which are based on nationally representative samples.
issue. 5 These effects also have been found in more realistic settings involving natural experiments (King et al., 2017;Slothuus, 2010), and they can persist over time beyond the immediate experimental setting (Lecheler et al., 2015). We expect framing effects to influence support for euro membership and exit in Italy. Research on international disintegration shows that elites have a central role in shaping public discourse and mobilizing opposition to international integration (De Vries et al., 2021;Walter, 2021). Although the eurozone crisis strongly politicised the currency union, it remains a complex arrangement. Cognitively, it is difficult for individuals to fully evaluate the costs and benefits of a policy change. Bechtel et al. (2017) thus find that only some individuals are fundamentally opposed to bailouts in creditor countries. Most citizens rather have contingent attitudes, i.e., their attitudes 'depend on the specific features of the policy and could shift if those features are altered' (Bechtel et al., 2017: 864). More generally, European voters are likely to use benchmarking to compare possible reform scenarios to the status quo (De Vries, 2018). For example, Bansak et al. (2020: 510) show that preferences towards Grexit and the European bailouts are shaped by 'different views about the likely effect of Grexit on the larger European economy'. These expectations about alternative states of the world change based on new information, and therefore, preferences for euro membership and exit should be susceptible to framing. Specifically, we focus on two different mechanisms: information about the costs associated with continued membership and blame attribution.
First, support for euro exit may decline when respondents are alerted to the conditionality associated with euro bailout packages. During the recent economic crises, financial assistance to debtor countries was conditional on highly contentious policies being implemented in receiving countries, including spending cuts, tax increases, and structural reforms, such as industrial relations liberalisation and pension cuts (Frieden and Walter, 2017: 372). Although elites and media were successfully able to sell austerity to voters in some countries like the United Kingdom (Barnes and Hicks, 2018) or Denmark (Bisgaard and Slothuus, 2018), most evidence suggests that voters in the crisis-ridden southern European countries oppose austerity policies Kuo, 2016, 2020;Franchino and Segatti, 2019;Hu¨bscher et al., 2020). The experience of the crisis and austerity did not only contribute to a large amount of electoral volatility and protests (Alonso and Ruiz-Rufino, 2020; Bremer et al., 2020), but it also weakened support for the euro (Hobolt and Wratil, 2015) and influenced the result of the 2015 Greek referendum on the bailout package (Jurado et al., 2020;Xezonakis and Hartmann, 2020). Given that utilitarian considerations remain strong predictors of public support for European integration (Foster and Frieden, 2021), we expect that individuals presented with a scenario that requires Italy to implement austerity due to EU conditionality would increase their support for euro exit. It remains an open question whether the decline in support is large enough to tip the balance in favour of exit. H1: Public support for Italexit is higher when voters are informed that the government is required to implement EU-enforced austerity measures as a condition for financial assistance.
Second, the eurozone is a complex institutional architecture, which blurs lines of responsibility. This makes it difficult for voters to hold governments accountable, conditioning the extent to which governments are sanctioned for economic outcomes (Hellwig and Samuels, 2008;Hobolt and Tilley, 2014;Powell and Whitten, 1993). This opens the door for strategies of blame-shifting: by assigning responsibility, elites can cue voters (Zaller, 1992) and avoid blame (Weaver, 1986). In the case of EU intervention in national politics, governments often attempt to 'play the blame game' by criticizing the EU and shifting responsibility (Schlipphak and Treib, 2017). This strategy was also used by national actors during the recent economic crisis, often successfully. Bellucci (2014) shows that in the 2013 Italian national election, blaming the EU (or the former Berlusconi government) was an effective strategy that influenced party choice. Similarly, Ferna´ndez-Albertos et al. (2013) found that in Spain, blaming globalisation and other European governments for the economic crisis reduced the responsibility attributed to the domestic government (among supporters of the government). This process also occurred in Germany, where citizens followed party cues on international bailouts, as Stoeckel and Kuhn (2018) demonstrate. Moreover, Del Ponte (2020) finds that rhetoric by foreign leaders can influence policy preferences for austerity and the EU in Italy, although this is conditional on national and European identity. We thus expect that blame attribution influences support for euro exit. If foreign actors are blamed for the crisis, voters may be more likely to view the euro as the problem (because it limits the perceived national sovereignty and increases the influence of these foreign actors); if the national government is blamed for the crisis, the reverse should be true.
H2: Public support for Italexit is higher when voters receive information that attributes responsibility for the fiscal crisis to foreign actors.
H3: Public support for Italexit is lower when voters receive information that attributes responsibility for the fiscal crisis to the national government.
Our hypotheses should hold for all respondents, but the strength of the effects may differ between subgroups due to heterogeneous treatment effects. In particular, more knowledgeable individuals are likely to be better informed and to have more manifest preferences, which reduces the informational impact of the frames. As a consequence, frames should have larger effects for individuals with low knowledge, both general knowledge and specific economic knowledge (Chong and Druckman, 2007). Moreover, preferences for the euro should vary with individual-level differences. Existing research has highlighted the role of both material interest (Banducci et al., 2009;Gabel, 1998;Hobolt and Wratil, 2015) and political preferences (Bansak et al., 2020;Stoeckel and Kuhn, 2018) in shaping attitudes. Such variables may also moderate the impact of frames due to 'motivated reasoning' (Taber and Lodge, 2006). Individuals are more likely to process and accept those frames that correspond to their prior political orientations, and thus framing effects should be greater for these individuals (vice versa for frames that are conflicting with prior political orientations).
Data and methods
Our study is based on an original survey fielded in Italy in October 2019, at a time when the Italian government was under pressure from the European Commission for not complying with the fiscal rules of the EU and shortly after the antiestablishment government coalition between the Lega and M5S had broken up over the wisdom of challenging the European Commission on the European fiscal rules. 6 The survey was conducted among a large sample of Italian adult citizens (n ¼ 4200) by SWG, a leading polling company in Italy. Respondents were sampled from a pool of more than 60,000 individuals, who were recruited online and by telephone to ensure a balanced composition of the population. Sample quotas were used to ensure a representative sample based on age, gender, and economic sector. We used survey weights to further correct for deviations in our sample from the true population on other dimensions (region, age, gender, education, and past vote choice) as explained in the Online appendix. However, results do not depend on whether or not we use weights, and on the type of weights.
Experiment design and dependent variable
In the survey, we used a pre-registered 3x2 factorial experiment to study attitudes towards Italexit. We asked all respondents to imagine the following scenario: Italy faces a crisis of confidence in financial markets. The European Central Bank is no longer willing to lend to Italian banks; capital flows out of the country; customers try to withdraw their deposits from banks; and the interest rate spread with Germany increases. As a result, the Italian government is unable to meet its financial obligations. Other European countries and European institutions offer a bailout package.
Before deciding whether or not to accept the bailout package, the government calls a referendum. The referendum asks citizens whether they want to stay in the euro and thus accept the bailout package, or whether they want to reject the bailout package and therefore exit the euro In designing the basic scenario, we drew inspiration from the Greek scenario of June 2015: freezing of liquidity provisions by the ECB; capital flight and depositors' run on banks; rapid increase of risk premia on government bonds; and ensuing financing problems for the treasury due to mounting interest rates. This kind of scenario is considered realistic by Italian economists who have studied the issue of a possible exit of Italy from the eurozone (e.g. Manasse, 2019).
At the time the survey was fielded, the Italian public debt was by no means considered a safe asset. In fact, it was rated BBB, just two notches above junk status (see Buiter, 2020: 142). This means that an unfavourable shock could deprive it of its investment-grade status, which is an assessment given by rating agencies and is frequently used by institutional investors to manage their portfolios. If Italian bonds were to lose investment status, institutional investors would have to sell them. Even the ECB would not be able to accept Italian sovereign bonds as collateral if their rating went below the minimum requirement of BBB- (Orphanides, 2017), at least according to the ECB's collateral policy before the COVID-19 outbreak. In brief, an unfavourable development, such as the Italian public deficit increasing above European targets, could unleash a crisis of confidence and cause the Italian government to lose access to international financial markets. This would either lead to a request for a European bailout or Italexit.
After the basic scenario, we asked respondents how they would vote in a hypothetical referendum about euro membership. This was a heuristic device aimed at eliciting preferences about a real decision-making situation as opposed to simply expressing an opinion (Landa and Meirowitz, 2009: 494). In reality, it seems unlikely (but not impossible) that a decision about Italexit would be preceded by a popular referendum. Nonetheless, the possibility of such a referendum has been repeatedly discussed by key political actors in Italy before and after the Greek referendum of 2015 and is highly salient in the Italian public sphere. 7 Our basic scenario diverts from the Greek course of events in 2015 in one crucial way. In Greece, the consequence of a no vote was ambiguous because it was not clear whether it implied renegotiation of the bailout package or euro exit (Walter et al., 2018). We eliminated the ambiguity and created a stark choice between accepting the bailout package and remaining in the euro or rejecting it and exiting the euro. We use vote choice in this hypothetical referendum as our dependent variable. The dependent variable has four categories: 'accept the bailout plan and remain in the euro', 'reject the bailout plan and exit the euro', 'would not vote', and 'don't know'. To simplify the analysis, we merge respondents from the last two answers categories in the analyses below. We randomly combined the basic scenario with variation in blame attribution for triggering the crisis (national government/foreign countries/no attribution) and variation in the conditionality associated with the bailout (austerity frame/absence thereof). This resulted in six different scenarios, as summarised in Table 1. Some experimental groups received the information that the offer of a bailout package was contingent on the implementation of policy changes. This austerity scenario was written trying to replicate the experience of other countries in the past. It mentions several different policies that were requested from countries that were bailed out during the euro crisis (Jacoby and Hopkin, 2020) and incorporates the recent rules about depositors' participation (bail-in) in case of bank resolution (Quaglia, 2019).
Moreover, for some experimental groups, the basic scenario was preceded by one of two blame attribution frames. These emphasis frames had the same basic informational content -Italy's public deficit increases and this induces the rating agencies to downgrade Italian public bonds -but tried to stimulate two plausible interpretations of the informational content, i.e., why the financial crisis came about and who was primarily responsible for it. In the foreign blame frame, the EU is the culprit since it 'launches an excessive deficit procedure against Italy', while the government tries to 'rekindle growth and reduce unemployment'. In the national blame frame, the Italian government is the culprit because 'it has decided to ignore the European fiscal rules and has allowed the public deficit to exceed the figure agreed with the European Commission', even though Italian public debt is 'already very high to begin with'.
We decided not to introduce a frame about the costs of exit in our study for the following reasons. First, adding another frame would have necessitated a 3Â2Â2 factorial design and a much larger sample than we had available. Second, while it is possible to specify with some degree of assurance the kind of conditionality that would be included in a bailout package for Italy based on previous bailouts, a scenario emphasizing the costs of exit is more difficult to specify because there is no precedent for it. The costs of exiting the euro would depend on several assumptions: orderly vs. disorderly exit; how other countries would respond; the type of exchange rate regime that would be chosen (a flexible exchange rate or entry into the European Exchange Rate Mechanism); whether there is a return to the lira or the creation of a smaller southern eurozone, etc. Third, the literature on Brexit suggests that the perceived costs of exit and international disintegration may be less important than the perceived costs of remaining (Carreras, 2019;Grynberg et al., 2020). Therefore, we decided to focus on the cost of austerity and blame attribution in this article.
Note that, in an effort to be as realistic as possible, our frames combine various elements. Thus, while we can identify any overall treatment effect of the frames thanks to randomisation (which ensures exogeneity by design), we are unable to specify the role that specific elements of our frames play. For example, for the austerity frame, we are not able to determine to what extent any shift in preferences is due to easier rules for layoffs, expenditure cuts, privatisation, etc. This is acceptable, in our view, because these elements have historically been bundled together in bailout packages.
The specific wording of the frames is included in the Online appendix. All frames were written as pure issue frames and provided no information about endorsements by parties or other political actors.
Independent variables
To estimate the experimental treatment effect, the key independent variables of interest are the six different scenarios that result from our factorial design. We present results both without controls and with the following controls: gender, age, age squared (to capture non-linear effects of age), educational attainment, household income, respondents' assessment of the export dependence of their firm or organisation, employment contract (indeterminate duration, fixedterm, part-time, or agency work or having no work contract), economic knowledge (based on responses to three economic knowledge questions) and region (North versus South). In an additional model, we add past vote choice as a separate variable to assess how variation in preferences towards the euro might be correlated with party choice. The detailed coding and summary statistics of all variables are presented in the Online appendix.
Empirical strategy
Our analysis proceeds in three steps. First, we analyse the experimental treatment effects of austerity and variation in blame attribution. Since our dependent variable can take three values ('remain', 'exit', and 'don't know') and since we are interested in how the frames change support for each option, we estimate multinominal probit regression models. The results do not change if we use dichotomous transformations of the dependent variable and estimate linear probability models or logit or probit models instead, as shown in the Online appendix. Due to random assignment to treatment, we present results without control variables, but they are unchanged if we include control variables (reported in the Online appendix). We calculate and plot the average marginal effects of the frames and the associated predicted probabilities of vote choice in the hypothetical Italexit referendum. Second, to examine how preferences towards the euro vary by individual socio-economic background and political orientations, we add other independent variables to the model specifications. Third, as a synthesis of the two preceding steps, we examine whether the experimental treatment effects vary by respondents' characteristics.
Results from the survey experiment
How strong is support for the euro when respondents are faced with the Greek-style scenario of a financial crisis? And how susceptible are individuals to information about austerity requirements and about who is to blame for the crisis? Figure 2 reports the average treatment effects of the austerity frame, the domestic blame and the foreign blame frames, and their combinations. The results show that the austerity frame has the strongest effect: it reduces support for remain by about 20% and increases support for exit by about 15%, which is in line with hypothesis 1.
However, our expectations are not confirmed for the domestic and the foreign blame frames, for which the effects are insignificant. Interestingly, the percentage of respondents who are uncertain increases by a significant margin when the EU and other governments are blamed for the fiscal crisis. It similarly increases when the domestic government is blamed, but this effect is not statistically significant. These insignificant findings are in line with evidence from Greece, where blame attribution is found not to have significantly influenced electoral vote choice during the euro crisis either (Karyotis and Ru¨dig, 2015;Kosmidis, 2018). It is possible, however, that the frames for blame attribution were not formulated strongly enough to have an effect on preferences. 8 The dominant effect of austerity also stands out in the combined treatment conditions. When the domestic and foreign blame frames are presented together with the austerity frame (the two lower treatment conditions in Figure 2), the effects are similar to the treatment effect of austerity alone (Table 1). This is confirmed by a formal test, which shows that the interaction effects between the austerity (Table 1) lower under the combination of austerity and the government blame frame than under the combination of austerity and the foreign blame frame. This is in line with hypotheses 2 and 3, but the difference between these two treatment conditions is statistically insignificant. Do the frames shift democratic majorities? Figure 3 shows the predicted probabilities of voting in the referendum by treatment group. In the control group, where respondents did not receive any treatment, 51.4% of respondents would vote to accept the bailout package and remain in the euro. In contrast, 30.4% of respondents would vote to reject the bailout package and exit the euro. This confirms existing findings that, in principle, the euro is still relatively popular in southern Europe despite the euro crisis. Yet, the share of undecided respondents is also large (18.2%), which indicates that politicians have substantial room for manoeuvre. The distribution of preferences is similar in the two blame attribution treatments which do not include information about conditionality. Yet, the situation changes drastically when respondents receive the austerity frame: a relative majority of 45.9% of respondents now prefer exit, 31.2% still support remain, while 22.9% are uncertain. Variation in blame attribution does not alter this relative majority for Italexit under austerity.
Overall, these findings suggest that support for euro membership and exit is contingent upon the costs of continued membership in Italy. Apparently, Italians are strongly opposed to austerity, and this opposition trumps support for the euro. Note: Predicted probabilities of voting in a hypothetical referendum and 95% confidence intervals based on multinomial probit models presented in the Online appendix.
Individual-level determinants of the vote in the referendum
How does support for Italexit vary by socio-economic background and political orientations? In Table 2, we examine how the vote in the hypothetical referendum relates to individual characteristics, controlling for our frames. Higher educational attainment and a higher position in the income distribution are associated with stronger opposition to Italexit. Moving from an individual with a university degree to an individual with lower secondary education increases support for Italexit by 13 percentage points. Similarly, moving from the highest to the lowest income decile increases the likelihood of supporting Italexit by 13 percentage points. These results suggest that support for the euro increases with the respondents' socioeconomic position. We do not find significant effects for other individual-level predictors except age. Gender, export exposure, employment contract, and region are not associated with euro preferences, but there is a curvilinear effect of age. Middle-aged individuals (between 40 and 60) are more supportive of exit than remain, whereas younger and older age cohorts are more supportive of remain (see the Online appendix for an illustration). We can only speculate about the reason for this pattern. Younger individuals have no memory of the pre-euro phase; hence, they may be more likely to want to remain in the euro. In contrast, older, retired individuals are less directly exposed to the difficult labour market situation in Italy than individuals below 60, and they are more likely to fear the loss of purchasing power that may be brought about by exit from the euro due to devaluation.
Finally, in Model 1, higher economic knowledge is associated with stronger support for remain, but this effect disappears when we control for partisan preferences in Model 2. 9 According to this model, preferences are strongly associated with respondents' partisan preferences. Voters of the Lega (the reference category) are the strongest supporters of Italexit (although the difference with Fratelli d'Italia is statistically insignificant), while voters of the Partito Democratico (PD) are least likely to support Italexit. The marginal effect of shifting from the Lega to the PD, keeping all other individual characteristics (including frames) constant, decreases the probability of voting for Italexit in the referendum by 47%. The marginal effects of the M5S and Forza Italia reduce the probability of voting for Italexit by 9 and 12% relative to Lega, while the marginal effects of no party (which accounts for 37% of the sample) and other party are 33 and 21%, respectively.
Heterogeneous framing effects
In this section, we check whether some of the individual variables associated with attitudes towards the euro moderate the treatment effects of our experimental frames (austerity, government blame, and foreign blame). For most interactions with individual-level predictors, heterogeneous treatment effects are absent. For example, we did not find heterogeneous effects for the role of trade exposure, neither at the individual (perceived export dependence) nor at the regional level. Still, effects for three variables are worth highlighting, namely knowledge (education and economic knowledge), material interest (income) and political (partisan) preferences. Note: Predicted probabilities of voting in a hypothetical referendum and 95% confidence intervals based on multinomial probit models presented in the Online appendix. Income is included as a linear and quadratic term to account for possible non-linear heterogeneous treatment effects. Figure 5. Heterogeneous domestic government blame treatment effects for partisan preferences.
Note: Predicted probabilities of voting in a hypothetical referendum and 95% confidence intervals based on multinomial probit models presented in the Online appendix.
First, for some frames, effects are larger for individuals with low economic knowledge and low education, as shown in the Online appendix. However, the differences are small and do not alter our assessment of the degree of empirical support and non-support for our hypotheses. In particular, even high-knowledge individuals still react strongly to the austerity frame. Overall, this suggests that knowledge plays a limited role for preferences (see also Armingeon, 2021).
Second, Figure 4 shows that the effect of the austerity frame on the propensity to vote for exit is muted for individuals at the upper end of the income distribution, and it is much stronger for individuals at the lower end. In particular, the effect of austerity on the likelihood to vote for remain is insignificant for the two highest income deciles, and it is insignificant for the three highest income deciles for the likelihood to vote for exit. This finding suggests that information about austerity resonates more strongly with less well-off individuals, who are more likely to think that they will be negatively affected by the scenario, than richer individuals, who probably consider themselves immune from the negative consequences of austerity.
Although partisan choice is a strong predictor of the referendum vote (Table 2), it only modifies the effect of the treatments in one instance: PD and M5S supporters react differently to the blame attribution treatments than Lega supporters ( Figure 5). While the government blame frame tends to increase support for exit among the Lega supporters, it decreases support among voters of the PD and M5S, who were in government when we fielded the survey. For the PD, this effect is non-negligible (seven percentage points) and statistically significant. Thus, PD voters are not only the most supportive of Italy's membership in the euro (Table 2, Model 2), but they are also likely to further reduce their support for Italexit when the Italian government is blamed for the crisis.
Conclusion
The literature on the euro crisis has found that voters in southern European countries are cross-pressured: on the one hand, they are opposed to austerity; on the other hand, they are attached to the euro. So far, the attachment has trumped the opposition: despite the high costs of structural adjustment policies, no democratic majority has supported exit in any eurozone country. This situation strengthened the bargaining position of northern governments: as southern governments were constrained by domestic preferences for remaining in the euro, they had to accept the terms of the northern European countries.
Using a survey experiment, we presented a large representative sample of Italian voters with the trade-off between accepting the conditionality of a European bailout plan or exiting the euro. Our results suggest that Italian public opinion is strongly sensitive to the costs of remaining in the euro (Franchino and Segatti, 2019). If voters are informed that eurozone membership comes at the cost of austerity, support for exit increases by 15% and support for remain decreases by almost 20%. Importantly, the pro-euro majority that we find in the control group turns into a relative majority for Italexit if Italy's continued membership comes at the expense of austerity. In contrast, we do not find any significant effect of blame attribution. Apparently, Italian voters do not care much about whose fault the crisis is but they strongly oppose further austerity. This opposition is strong enough for them to consider leaving the common currency.
The large effect of the austerity treatment indicates that eurozone membership can easily become contested in Italy. Support for the euro is lower in Italy than in other countries, but public opinion is also malleable by elite framing. Moreover, there is a large share of undecided voters who are likely to follow elite cues about the euro. Preferences towards the euro in Italy are, therefore, contingent and likely to shift depending on how the issue is framed. Individuals who are better-off and who support the PD are less likely to react to the threat of austerity, but their number is not large enough to ensure Italy's continued membership in the eurozone. Therefore, European policymakers may hit the limits of their preferred crisis resolution strategy if there was a fiscal crisis in Italy: conditional financial support, provided by the ESM or other European institutions, may antagonise voters and push them out of the common currency.
Our findings have to be interpreted with caution, however. First, we did not present respondents with a frame that highlights the cost of exiting the euro, which narrows our findings. Although it is uncertain how such an exit would unfold and it is likely that its economic consequences would differ dramatically depending on whether exit is negotiated with the European partners or not, it is possible that preferences for remain would increase significantly if the costs of exit were to be emphasised and they could counterbalance the decline due to the emphasis on the costs of remain (austerity). At the same time, if the case of Brexit is any guide, it is also possible that citizens discount the costs of exit in formulating their preferences (Carreras, 2019;Grynberg et al., 2020). Therefore, we plan to analyse how citizens evaluate the cost of remain vs. exit in the future, given that considerations about alternative states are crucial to explain support for European integration (De Vries, 2018).
Second, preferences for the euro are likely to change over time depending on the economic situation of a country. We ran our survey before the COVID-19 pandemic hit Italy. Although preferences towards the euro did not change according to the Eurobarometer (Figure 1), other surveys indicate that in spring 2020, when Italians felt they had been left alone by the other European countries in responding to the first wave of the pandemic, sentiments towards the EU became less favourable in Italy. 10 Our research indicates that attitudes towards the euro are likely to deteriorate in these circumstances, but future research should verify that this is the case.
Third, in this article, we studied the case of a southern European country. However, the possibility that a systemically important member state could exit the euro will have knock-on effects and may shift preferences in northern EU member states as well. Future research should also investigate whether the threat of disintegration increases popular support for institutional reform and a more equitable sharing of the burden of adjustment in 'creditor' countries such as Germany or the Netherlands. 10. For example, one poll in spring 2020 found that 83% of citizens rejected Europe's behaviour towards Italy after the COVID-19 outbreak (see https://www.termometropo litico.it/1522328_sondaggi-politici-piepoli-coronavirus-italiani-criticano-comporta mento-ue.html, accessed on December 7, 2020), while another poll found that support for leaving the EU had increased by 20 percentage point to 49% (see https://www.dire. it/10-04-2020/446061-sondaggio-dire-tecne-aumentano-gli-italiani-che-vorrebberouscire-dallue/, accessed on December 7, 2020). | 9,571.8 | 2021-04-08T00:00:00.000 | [
"Economics"
] |
Modern Ab-Initio Calculations on Modified Tomas-Fermi-Dirac Theory
Thomas-Fermi theory is an approximate method, which is widely used to describe the properties of matter at various hierarchical levels (atomic nucleus, atom, molecule, solid, etc.). Special development is achieved using Thomas-Fermi theory to the theory of extreme states of matter appearing under high pressures, high temperatures or strong external fields. Relevant sections of physics and related sciences (astrophysics, quantum chemistry, a number of applied sciences) determine the scope of Thomas-Fermi theory. Popularity Thomas-Fermi theory is related to its relative simplicity, clarity and versatility. The latter means that the result of the calculation by Thomas-Fermi theory applies immediately to all chemical elements: the transition from element to element is as simple scale transformation. These features make it to be a highly convenient tool for qualitative and, in many cases, and quantitative analysis.
Introduction
Thomas-Fermi theory is originally proposed by Thomas and Fermi [1]- [4] to describe the electron shell of a heavy atom, which is characterized by a relatively uniform distribution of the electron density.
Thomas-Fermi theory is the semi-classical (WKB) limit in relation to self-consistent Hartree field equations, and therefore the modification of this model is associated with a more detailed account of the correlation, exchange, quantum and multi-shell effects.
Initial approximate nature of Thomas-Fermi theory has a dual nature.Remain outside the model, firstly, correlation effects, reflecting the inaccuracy of the Hartree method and the associated self-consistent difference (average) true interaction from the true physical interaction.Secondly, in Thomas-Fermi theory quantum effects are not considered responsible approximate nature of the semi-classical description of the atom.The report examines the theory of these effects, allowing to find the limits of applicability of Thomas-Fermi theory in its original form and to generalize the model beyond the scope of its applicability.
The presence of correlation corrections is caused by difference of self-consistent Hartree field of the actual field inside the atom.These corrections are the result of the anti-symmetry of the electron wave functions and are interpreted as the exchange correlation effects.Additionally, appear also the effects of the power correlation.
We begin by considering the effects of correlation, which in turn are divided into two classes.This is primarily the effects of statistical correlation (exchange effects), describing the effect of the Pauli principle on the interaction of particles.Electrons with parallel spins are hold at a greater distance from each other than in the singlet state, and the radius of such a correlation coincides with the de Broglie wavelength of an electron.
Correlation effects of the second class (called correlation effects of power or simply correlation effects) reflect the inaccuracy of the principle of independent particles, i.e., the inability to talk about the state of a single electron in the effective average field of the other particles because of their mutual influence, beyond the self-consistent description.Being the power effects, this kind of correlation effects characterized by a dimensionless parameter is equal to the ratio of perturbation theory of the average energy of the Coulomb interaction between pairs of particles to their average kinetic energy.In Thomas-Fermi [3] [4] theory which introduces accounting Dirac correlation effects [2], this expansion has been called the theory of Thomas-Fermi-Dirac.
The report shows that the total energy of the electrons can be expressed in terms of the spatial dependence of the electron density according to the Thomas-Fermi-Dirac theory.In report calculation, the energy of the atom is based on nuclear-electron and electron-electron interactions (which can also be represented as a function of the electron density).
Quantum corrections arise from the use of the semi-classical formalism and reflect the presence of non-local electron density communication to the potential in consequence of the "uncertainty principle".
Theoretical Procedures
A variational technique can be used to derive the Thomas-Fermi equation, and an extension of this method provides an often-used and simple means of adding corrections to the statistical model [5] [6].Thus, we can write the Fermi kinetic energy density of a gas of free electrons at a temperature of zero degrees absolute in the form: ( )( ) 3 where 3 10 3π2 2 3 The electrostatic potential energy density is the sum of the electron-nuclear and the electron-electron terms.We can write this as: , where v n is the potential due to the nucleus of charge Z, v e is the potential due to the electrons, and the factor of 1/2 is included in the electron-electron term to avoid counting each pair of electrons twice.With x denoting distance from the nucleus, the total energy of the spherical distribution is given by The expression for density on the Thomas-Fermi model, ( ) with ( ) , is obtained by minimizing Equation (1) subject to the auxiliary condition that the total number of particles N, remains constant.
The potential energy V, is a function of position in the electron distribution.E' is the Fermi energy, or chemical potential, and is constant throughout a given distribution.The Thomas-Fermi equation follows from Equation ( 2) and Poisson's equation.
The tendency for electrons of like spin to stay apart because of exclusion principle is accounted for by the in-clusion in Equation ( 1) of exchange energy, the volume density of which is given by: ( )( ) ( ) ρ .From this equation we get ( ) ( ) Now Poisson equation with the density given by Equation ( 3) leads to the Thomas-Fermi-Dirac (TFD) equation.In the following two slides we propose additional energy terms to be included in Equation (l).The incorporation of these terms leads to a simple quantum-and correlation-corrected TFD equation.
The quantum-correction energy density follows from a slight change in the derivation due to March and Plaskett [6].March and Plaskett have demonstrated that the TF approximation to the sum of one-electron eigenvalues in a spherically symmetric potential is given by the integral: where the number of states over which the sum is carried is written as ( ) Here E(n r , l) is the expression for the WKB (quasi-classic) eigen-values considered as functions of continuous variables [1] [6]; n r is the radial quantum number; l is the orbital quantum number; And the region of integration is bounded by n r = −1/2, l = −1/2, and E(n r , l) = E'.
We have included a factor of two in these equations to account for the spin degeneracy of the electronic states.The Fermi energy E' is chosen so that Equation (5) gives the total number of states being considered, the N electrons occupying the N lowest states.With considerable manipulation, Equation (4) becomes TF energy equation: and Equation ( 5) reveals the TF density through the expression 3 2 2 4π d 3π both integrals being taken between the roots of E' = V(x).We have written these results in atomic units, so that P, the Fermi momentum, is defined by ( ) It is pertinent to examine the error in the TF sum of eigen-values, as given by Equation ( 6), for case of pure Coulomb field.The WKB eigen-values in Coulomb field given by ( ) And let us consider the levels filled from n = 1 to n = v, where n is the total quantum number defined by n = nr + l + 1.Then, for any value of v we can evaluate the error in the TF approximation to the sum of eigen-values, comparing always with the correct value, −Z 2 v. Scott correction to the total binding energy is obtained by letting v become very large.
Although the sum of one-electron eigen-values is not the total energy of the statistical atom because of the electron-electron interaction being counted twice, we might expect to improve the calculated binding energy greatly by correcting this sum in some manner, since the chief cause of the discrepancy is certainly the large error in the electron-nuclear potential energy.
This correction can be performed by imposing a new lower limit on l in the integrations above.When we introduce a new lower limit l min and a related quantity which we call the "modification factor", min 1 2 a l = + we obtain, after more manipulation, slightly different expressions corresponding to Equation ( 6) and Equation (7).
From these revised expressions we can identify a quantum-corrected TF density expression, and corrected kinetic energy density Revised lower limit on the volume integrals, say x 1 , is the lower root of for x < x l , ρ must vanish (stay zero), and we have thus termed x 1 the "inner density cutoff distance".We can call the second term on the right-hand side of Equation (10) the "quantum-correction energy density" and write it in the more consistent form: 2 2 by defining , 2 The modification factor a, is determined by the initial slope of the potential function.
For interpreting these results it is helpful to consider just what we have done in changing the lower limit of the orbital quantum number.
Since the lower limit l = −1/2 must correspond to an orbital angular momentum of zero, we have, clearly, eliminated states with angular momentum of magnitude between zero and a cutoff value L c = aħ.Corresponding to L c at every radial distance is now a linear cutoff momentum: P c = aħ/x, and we can rewrite Equation (9) in terms of the Fermi momentum and cutoff momentum: At radial distances less than x l , momenta are prohibited over the entire range from zero to P, so the electron density vanishes.This interpretation must be modified somewhat when exchange and correlation effects are included; for then the Fermi momentum is no longer simply given by Equation ( 8), except very near the nucleus.
We can define x 1 as in the absence of interactions, i.e., as the lower of the roots of Equation ( 11), but it is not correct to demand that the density vanish at the upper root.Instead, we require only that the density be real.
Correlation Correction [1] [5] [6].The original TF equation describes a system of independent particles, while the introduction of exchange energy, which leads to the TFD equation, represents a correction for the correlated motion of electrons of like spin.The remainder of the energy of the electron gas is termed the correlation energy.By its inclusion we are recognizing that electrons, regardless of spin orientation, tend to avoid one another.
In extensions of the statistical model there have been suggested at least two different expressions, for the correlation energy that approach, in the appropriate limits, Wigner's low-density formula and the expression due to Gell-Mann and Brueckner at high densities.In addition to these, Gombas and Tomishima [6] have utilized ex-pansions of the correlation energy per particle in powers of ρ 1/3 about the particle density encountered at the outer boundary of the atom or ion.In this expansion, the term of first-order can be considered as a correction to the exchange energy, and it follows that the TFD solutions for a given Z then correspond to correlation-corrected solutions for a modified value of Z.
Aside from rather poor approximation of the correlation energy, a drawback to this procedure is that the TFD solutions must be at hand.If solutions representing specified degrees of compression are desired, the method would appear to be impractical.It is interesting and fortunate that over density range of interest it is apparently possible to approximate the correlation energy per particle quite closely by an expression of form: where we have set c c = 0.0842, and compared this approximation with the values due to Carr and Maradudin [5].
Derivation and Discussion
From the results of the preceding slides, we can now express the total energy per unit volume of the charge distribution in the form: where all quantities appearing in the equation have been previously defined.By minimizing the integral of U over the volume occupied by the charge, while requiring that the total number of electrons be fixed, we obtain the following equation: 6 The electron density is found as a function of R by solving Equation ( 14), a quartic in ρ 1/6 .
To accomplish this we write a "resolvent cubic equation" in terms of another variable, say y: ( ) Let us use the same symbol y, to denote any real root of this cubic equation.We can then express the four roots of the quartic, and hence four expressions for the electron density, in terms of y.One of these expressions possesses the proper behavior in reducing to previously obtained results in the neglect of correlation and exchange effects, namely: ( ) where ( ) We note that ψ vanishes when correlation is neglected, since y = −τ 1 is then root of Equation (15).In the familiar manner we now define a modified TFD potential function θ by the relation: and from Poisson equation and Equation ( 16) we obtain: ( ) .
Equation (20), Equation (15), Equation (17), and Equation ( 19) constitute the differential relationship to be satisfied at each step in the integration.We could, of course, write immediately the solutions of Equation (15) in analytic form, but it proves convenient in the numerical treatment to obtain a root by the Newton-Raphson method, since a good first guess in the iteration is available from the previous integration step.
The boundary conditions on Equation ( 19) are: First-as nucleus approached the potential must become that nucleus alone, or θ(0) = 1; Second-at outer boundary x 2 , of distribution of N electrons, In addition to potential and density distributions, total binding energies of atoms are of special interest to us here.For the proper evaluation of energies, the arbitrary constant that is present originally in both the electrostatic potential energy and the Fermi energy must be specified.The state of infinite separation of the constituent particles is normally taken to have zero energy.
We therefore follow the usual convention and fix the potential at the edge of the neutral atom at zero for all values of x 2 .For an ion the potential energy of an electron at the boundary is taken as: The defining relation, Equation (18), now gives at the boundary: ( ) or, solving for the Fermi energy, ( ) The total electron-nuclear potential energy given by ) Other energy integrals are, with an obvious notation:
Results and Conclusions
It was pointed out in the introduction that the quantum-corrected TFD equation yields atomic binding energies in good agreement with experimental values and with the results of Density Functional Theory (DFT) calculations [5].
Multi-shells effects reflect irregularities physical quantities due to the discrete energy spectrum, but in the case of the continuous spectrum of these effects may occur as a result of interference of de Broglie waves and allow the model to take into account the shells structure of the atom.Multi-shells effects associated with the discrete spectrum of bound electrons in atomic systems (atom, ion, atomic cell, etc.).
Multi-shells effects, unlike quantum-exchange effects, affect to the chemical potential E', but practically have no effect on the value of self-consistent potential V [7].Therefore, when they account for the calculation of a corresponding shells correction is not necessary to solve the Poisson equation.Just use the normalization condition with the same self-consistent potential in Thomas-Fermi model.
For shell corrections E' sh primary role of shell effects reduces to a shift of the chemical potential E' [8], ( ) ( ) ∑ where v = n r + 1/2, λ = l + 1/2.Software implementation of this modified Thomas-Fermi theory and calculations (for example, rare gas atoms, Table 1 and Table 2) taking into account quantum, exchange and correlation corrections showed that the this Table 2.The electron density (external shells) of the rare atoms-helium, neon, argon, krypton, computed on the present model agree closely with their crystal radii.
He Ar
Ne Kr corrections really lead to a rapprochement and converge results with experimental data, and also the results obtained by the DFT approximation [5].Total energy calculations by Thomas-Fermi, DFT and experimental data are shown in the summary Table 1.Next step of this work is included program realization for multi-shell and gradient corrections also [1] [6].
Minimization of the total energy now leads to the equation: | 3,746.4 | 2015-06-05T00:00:00.000 | [
"Physics"
] |
A QoS Enhancement Scheme through Joint Control of Clear Channel Assessment Threshold and Contending Window for IEEE 802.11e Broadcasting
In a WLAN, when a great many nodes coexist, the network may readily be congested, thus causing packets dropping and network performance degradation. To solve this issue, a lot of schemes have been proposed. However, most of the previous works attempt to avoid the possible channel congestion by controlling the packets generation rate and/or transmitting power of nodes, while the effects of Clear Channel Assessment (CCA) threshold are not well examined. In our paper, a Joint CCA threshold and contending window control algorithm (JCCA) is proposed to avoid channel congestion or reduce the congestion probability of broadcasting in an IEEE 802.11e network. Both the network conditions and the priorities of messages are taken into account to improve the broadcasting performance in our paper. According to the simulation results, it can be concluded that our scheme can significantly increase the network throughput as well as packets delivery ratio and reduce the packet transmission delay compared to the IEEE 802.11e and Adaptive Carrier Sensing-Based MAC Designs (ACSBM) protocol.
Introduction
Over the past few years, our society has incessantly tended towards the use of wireless communications and social networking technologies.In this regard, the IEEE developed the 802.11 standard [1] in order to define a protocol for offering local area interconnectivity between different wireless devices.The importance of Wireless Local Area Networks (WLANs) has grown considerably due to their simplicity of deployment, low cost, and multimedia content support.To further improve the differentiation of services in IEEE 802.11 networks, the IEEE 802.11e [2] amendment was then developed.As a prioritization method, this amendment introduced a new contention-based channel access method, that is, Enhanced Distributed Channel Access (EDCA), to enable Quality of Service (QoS) guarantee for the original CSMA/CA mechanism [3] used in IEEE 802.11 networks.
However, the broadcasting in IEEE 802.11e networks still adopts the Binary Exponential Backoff (BEB) scheme for collisions resolutions, which actually cannot reflect the degree of channel competitions and is unfair to those nodes that did not transmit successfully [4].Although the IEEE 802.11e standard specifies a set of recommended values of the contention parameters by which the channel competitions among different prioritized services could be alleviated, its static setting is usually unable to meet various QoS requirements in highly complicated and dynamic networks with different traffic loads [5].For instance, the high network load generally implies an acute channels competition and a high probability of collisions among traffic flows, resulting in the decrease of system performance.On the other hand, under a light network load, the fixed contention parameters may lead to expanded delay and lower channel utilization during channel accessing.Therefore, to achieve a satisfying 2 Mobile Information Systems EDCA performance, an adaptive adjustment protocol is very beneficial to balance the requirements between traffic load awareness and protocol complexity according to the network conditions.
Actually, to increase the performance regarding medium access in IEEE 802.11 networks, many efforts have been made before to improve the BEB based schemes [6].Some authors also proposed to dynamically adapt CW according to the channel congestion state [7] in order to enhance the network throughput.Based on the previous works, it can be found that there are few works trying to improve the system performance regarding the combination of throughput, channel utilization ratio, packets delivery ratio, and average transmission delay at the same time.
To fill this gap, in our paper, a scheme to improve the IEEE 802.11eWLAN broadcasting performance in terms of the above indexes is proposed through the joint control of the CCA threshold and contending windows.As we know for the original CCA mechanism, when one node is transmitting, all other nodes must wait until it finishes.To check whether the channel is busy or idle, a node has to perform a CCA check.The decision is based on the value of the CCA threshold.If the in-band signal energy crosses this threshold, CCA is held busy until the medium energy is below the threshold [8].In our work, by adaptively setting the CCA threshold and initial value of the contending windows according to the network condition and priorities of messages, the network performance is significantly enhanced.In summary, the contributions of our work are generalized as follows: (1) At first, we set different initial values of CCA threshold based on different priorities of messages.After that, we use the channel utilization ratio to determine the CCA threshold for a node when transmitting.
(2) Both network condition and priorities of messages are taken into consideration to improve the broadcasting performance in a WLAN, via the joint control of the CCA threshold and contending window.
The remainder of this paper is organized as follows.In Section 2, we outline some related works regarding the performance improvement in WLANs.In Section 3, our proposed joint control algorithm is given with reasonable assumptions.In Section 4, our proposed algorithm has been theoretically analyzed using a 1D Markov chain model.Section 5 gives the numerical results and performance evaluations of our model.Our paper is concluded in Section 6 followed by acknowledgements and cited references.
Related Work
A classic article by Bianchi [9] presented the notion that the performance of the traditional DCF (Distributed Coordination Function) strongly depends on the network conditions, mainly the minimum contending window and number of active stations.In addition, the author further confirmed that the parameters of EDCA are very important for collisions resolution, where different parameter settings not only determine the choice of services' priorities, but also influence the overall performance of a network [10].Specifically, under a complicated network condition, the static parameter configuration of EDCA cannot well optimize the system performance [11].Additionally, some works also demonstrated that the network has a high collision probability in case of heavy traffic load which would lead to an unsatisfying EDCA performance [12,13].
In [14], the authors proposed a scheme to balance the requirement between throughput and fairness through the estimation to the number of completing nodes and the optimal contending window.This scheme proved that the probability of successful transmission of a broadcasted frame could be improved by up to 50% [15].In addition, Calì et al. [16] applied the p-persistent backoff algorithm to the IEEE 802.11 networks and showed that it is possible to tune the backoff window size at run time to obtain a capacity very close to the theoretical limit for stations.Their results show that the capacity of the enhanced protocol is very close to the theoretical upper bound [16] in all the configurations analyzed.However, their scheme needs a station to have an exact knowledge of the network contention level which would be very difficult in practice.As a result, a distributed collision resolution scheme, Asymptotically Optimal Backoff (AOB) [17], is proposed based on the estimation of the network contention level in an IEEE 802.11 wireless LAN.The AOB dynamically adapts the backoff window size according to the estimated network load level and guarantees that a WLAN could asymptotically achieve its optimal channel utilization.In [18], the authors proposed a delay-aware self-adaption scheme for the cumulative improvement of both the throughput and the channel access delay at run time.Although the aforementioned works have their cons and pros in terms of system performance improvement under various traffic loads, there are few works studying the schemes to enhance the network performance with respect to the combination of throughput, channel utilization ratio, packets delivery ratio, and average transmission delay in the meantime.
As for the performance optimization upon CCA adjustment, there are also some previous works for IEEE 802.11 networks.Jamil et al. [19] proposed a CCA threshold adaptation scheme to improve the overall throughput in high density WLANs.Their numerical results showed a global gain of 190% in the aggregate throughput compared to the upper bound assumed by the present MAC protocol.In [20], a patent is proposed to dynamically adjust the CCA threshold depending on the type of interferences detected.Numerical results show that the self-adaption of the CCA threshold can considerably improve the network performance at the cost of a longer delay for the processor node to access the channel.The patent also demonstrates that there is no fixed threshold suited simultaneously to both heavy and light channel loads.Therefore, it is very necessary to introduce the dynamic CCA mechanism into present IEEE 802.11 protocol stacks.
In summary, it can be concluded that it is still an active topic even today to enhance the broadcasting performance with varying network loads via the self-adaption of the IEEE 802.11e protocol.From our perspective, the adjustment of the CCA threshold should take the following principles into account: (1) A higher CCA threshold results in more hidden nodes, smaller radio range, and shorter channel access delay.
(2) A lower CCA threshold will correspondingly result in lower spatial multiplexing ratio, reduced bandwidth utilization, longer channel access delay, and smaller collision probability.
(3) Due to the rapid change of the number of nodes, network topology, and environment, instead of being fixed, the CCA of a network should be adapted to the load conditions for network performance improvement.
(4) The CCA threshold should be decided by taking the priorities of messages into account such that the prioritized messages can access the channel at a higher probability.
In our paper, by taking the aforementioned principles into consideration, a model is proposed via the joint control over the contending window and CCA.We first computed the channel utilization ratio according to (1).After that, we set different initial CCA thresholds and contending windows according to the different types of services.Then, the CCA threshold of a specific service is dynamically adjusted according to the observed channel utilization ratio to decide whether the channel is sensed busy or idle.Finally, we set an appropriate CW based on the channel state for a station.
The Algorithm for Joint Control over Clear Channel Assessment Threshold and Contending Window
In this section, we will describe our proposed algorithm in detail.To implement our algorithm, the channel utilization ratio is used to classify the network conditions into three categories, that is, low utilization, intermediate utilization, and high utilization cases.In our work, different CCA thresholds and contending windows are set up according to different network conditions and QoS requirements.For readability, the proposed algorithm has been framed as three parts as shown in Figure 1: (1) compute the channel utilization ratio to discriminate the present network condition, (2) initialize the CCA threshold and contending window based on the observed network conditions and messages priorities, and (3) adapt the CCA threshold and contending window to the network conditions by following some specific policies, which will be given later.Each process shown in Figure 1 will be described in detail in Sections 3.1, 3.2, and 3.3, respectively.
Compute the Channel Utilization Ratio.
The channel utilization ratio in our work is defined as where denotes the channel utilization ratio, is the number of slots, BUSY indicates the channel's busy time, AIFS is the value of AIFS, Backoff denotes the node backoff
Types of services
Initial values of the CCA thresholds 0 duration, and CCH indicates the executing interval of our control algorithm, respectively.With (1), we then could get the channel utilization ratio while estimating the network congestion level.In our work, the network conditions are classified into three categories according to two predefined utilization ratio thresholds, say low and high .
Initialize the CCA Threshold and Contending Window.
In our work, we define different initial values of the CCA thresholds for messages with different priorities.If the channel utilization ratio is low and the channel resource is underused, a small value of CW min should be chosen to increase the probability of the node successfully accessing the channel.On the contrary, if the channel utilization ratio is high, the transmission attempts from nodes are likely to cause the network to be congested.In this case, assigning a larger value of CW min may reduce the possibility of collisions.Based on the above analysis, the configuration criterion of the contending windows in our work is listed in Table 1.
To reduce the complexity of our algorithm, we only consider priorities of messages while setting up the CCA threshold and neglect the difference between different network conditions.The setting of the CCA threshold for four different prioritized messages is demonstrated in Table 2.
The CCA thresholds for these four types of messages range from CCA min () to CCA max (), where CCA min () and CCA max () denote the minimum and maximum value of the CCA threshold of the th type services, respectively.
Mobile Information Systems
Adjustment of the CCA Threshold and Contending Window.
When the node density is low, the channel utilization ratio is usually low and the spectrum resource is underused.In this case, a higher CCA threshold and a smaller CW min are preferred for the node to increase the probability of successfully accessing the channel.In our work, if the channel is sensed busy, the contending window is increased by a step value larger than 1 but less than 2. On the other hand, in the case of the channel being used efficiently, a smaller CCA and a larger CW min will be employed to avoid the possible collisions.Accordingly, after the node transmits successfully, instead of directly resetting the contending window to CW min , we choose a step value to gradually reduce the contending window until it reaches CW min .The detailed procedure for adjusting the CCA threshold and CW is described as follows.
(1) In the State of Low Channel Utilization Ratio ( < ).Under this state, the number of nodes is generally small and the channel loads are light.To make full use of the network spectrum, a larger CCA and a smaller initial value of CW min must be chosen to enable the node to access the channel with a higher probability.Meanwhile, while the channel is sensed busy, the contending window will not be increased in a binary manner, but with by a step value larger than 1 and less than 2 until it reaches the maximum value CW max , in order to increase the channel utilization ratio.The details of this procedure are given as follows: (1) At first, the CW of messages with different priorities will be set to their initial values, that is, CW low ().And CW min is set to its minimum value, that is, CW low min ().To make the node access the channel with a higher probability, the CCA threshold is then set to CCA = CCA max () . ( (2) While the channel is sensed busy, the contending window will not be increased in a binary manner, but by a step value as where is a smoothing factor ranging from 1 to 2 and the CW is the value of the contending window before sensing the channel.After the CW is gradually increased to CW low max , the CW will remain unchanged if the channel is still sensed busy.Whenever CW is updated, the node's backoff timer should be recomputed with where CW new denotes the value of the contending window when the node backs off again and () indicates a function randomly generating a decimal range from 0 to 1.
(2) In the State of Intermediate Channel Utilization ( < < ℎℎ ).Under this state, the channel is properly utilized, so the original backoff scheme is used for the collision resolution as follows: (1) At first, the CW of messages with different priorities are set to their initial values, that is, CW low (), and CW min is set to its minimum value CW low min ().The CCA threshold is set to (2) When the channel is sensed busy, its contending window is doubled in a binary manner as When CW is gradually increased to CW low max , the CW will remain unchanged if the channel is still busy.Whenever CW is updated, the node's backoff timer is recomputed according to (4).
(3) In the State of High Channel Utilization Ratio ( > ℎℎ ).In this case, there are usually numerous nodes contending the channel simultaneously.If the node's contending window is directly restored to CW min after a successful transmission, the channel competition will be still acute and the average transmission delays will be expanded with a high risk.Therefore, on this occasion, a higher value of CW min should be assigned to each node to alleviate the channel competition.In this way, after a successful transmission, instead of directly resetting the node's contending window to CW high min (), we halve it step by step.To reduce the collisions among nodes, the CCA threshold must also be set to a smaller value.The corresponding procedure for CCA adjustment under the high channel utilization case is described as follows: (1) At first, the CWof messages with different priorities are set to their initial values, that is, CW high ().And CW min is set to its initial value CW high min ().Correspondingly, the CCA threshold is set to (2) When the channel is sensed busy, the contending window is doubled in a binary manner as After CW is gradually increased to CW low max , let its value remain unchanged when collisions happen again.
(3) After a successful transmission of the message, instead of directly restoring the node's contending window to CW high min (), we decrease it linearly via a parameter, that is, 0.5, in our paper: After CW is gradually decreased to CW high min (), let its value also remain unchanged after a successful transmission.Whenever CW is updated, the node's backoff timer is recomputed with (5); that is, = CW × () × .
The pseudocode of our whole algorithm is shown in Algorithm 1.At first, we calculate the channel utilization ratio according to the given parameters and set the initial value of CCA threshold and CW by types of messages and channel conditions.Then, the CCA threshold and CW were adjusted based on observed channel conditions.Finally, we could derive the backoff timer from the value of CW.
Theoretical Analysis
In this section, we will give out the theoretical analysis regarding our proposed algorithm.We assume that there are contending nodes in the discussed network.The sending buffers of all stations are saturated; thus, each station always has packets to be sent.Next, we will analyze our algorithm using the 1D Markov chain model [21] as follows.
Let a discrete-time Markov chain () denote the node's backoff timer at time . indicates the th type services. 0 () denotes the initial contending window for service which is equal to CW status min ().The value of CW status min () can be one of the CW low min (), CW mid min (), and CW high min () statuses depending on the observed channel status.We assume the probability ( = 1, 2, 3 . ..), which indicates a station transmitting a packet of the th type service in a virtual slot , is independent of the backoff procedure.Let {} express the state of each node and indicate the value of the station's backoff timer in the range (0, 1, 2, 3, . . ., 0 () − 2, 0 () − 1).Then, the state transition diagram of our discussed scenario can be given as shown in Figure 2.
As Figure 2 shows, the transition probability from state to state − 1 is 1.When is equal to 0, the station begins to transmit data and choose a random backoff timer to access the channel.The one-step transition probabilities are given as follows: Let () be the stationary distribution of the introduced Markov chain which is the node's backoff timer in state .Then, we have Therefore, in the steady state, we have With ( 12), we can derive 0 () as follows: Since the station will begin to transmit data when the backoff timer is equal to 0, the probability of a station transmitting data in any time slot is denoted as Therefore, the probability that the channel is sensed busy is given by Furthermore, the probability that a successful transmission occurs within a slot time is derived as Let denote the probability that a collision happens.Then, we have With the aforementioned analysis, once is given, the throughput can be derived as follows: where is the MAC payload size (in bits), is the duration of an empty slot time, is the duration during which the channel is still sensed busy due to a successful transmission, and is the time wasted by a collision, respectively.Note that = =DIFS + DATA + SIFS + ACK.Thereupon, the average experienced delay can be estimated as follows.Assume that the total throughput given by ( 18) is fairly shared by contending stations; thus, the average packet delay is given by
Performance Evaluation
Our model is implemented on the NS-2.34 platform [22].
The algorithm is evaluated with the metrics in terms of the average packet transmission delay, packet delivery ratio, and network throughput by varying the vehicular densities.The parameters for network performance evaluation are listed in Table 3.The related thresholds of contending windows referred to in Section 3 are given in Table 4.
In order to accurately evaluate the performance of our proposed model, we have compared our JCCA method with IEEE 802.11e and ACSBM algorithm [23].The effect of JCCA on packet delivery ratio is shown in Figure 3.It can be noted that, with the increasing of nodes in the network, the packet delivery ratio begins to decline, no matter which method we take.However, the decreasing of the packet delivery ratio of both IEEE 802.11e and ACSBM algorithm is sharper than our JCCA model.Actually, when there are only few nodes contending the network bandwidth, the difference of packet delivery ratio among different methods is very small.However, when there are a great many nodes in the network, the contending window of IEEE 802.11e and ACSBM will be quickly restored to its initial value after successful transmissions.This makes the access competition among nodes more acute due to heavy network load and then causes the packet delivery ratio to decline.Instead, the CW will decrease gradually to its initial value after successful transmissions using our JCCA protocol, thus reducing the number of contending nodes, as well as increasing the packet delivery ratio.
In Figures 4 and 5, we analyze the impact of our JCCA on average packet transmission delay and network throughput.As shown in Figure 4, at the beginning, the difference of average packet transmission delay among three protocols is smaller.Actually, since only few nodes compete for the channel, the average packet transmission delay will not be expanded too much considering few collisions.When the node density continuously grows, our scheme begins to show the superiority of delay decreasing compared to the other two protocols.Because of lower node density and channel utilization ratio, the contending window of JCCA will not be increased two times but by a parameter larger than 1 and less than 2. In this way, the opportunities for nodes accessing the channel have been increased and the average delay correspondingly decreases.When the node density is higher, unlike IEEE 802.11e and ACSBM, our CCA adaptive and CW slow decreasing mechanisms not only bring more opportunities for nodes to transmit concurrently but also reduce the number of possible collisions through CW control.In Figure 5, when the number of nodes increases, our JCCA always outperform IEEE 802.11e and ACSBM protocol in throughput.The reason is the same as given for Figure 4, where the CCA adaptive adjustment and load-aware CW control bring more chances for nodes to transmit successfully at the same time, therefore increasing the throughput compared with other two schemes.
To show the impact of our CCA adjustment strategy on the packets reception, we also evaluate the packets reception ratio among three protocols in Figure 6 with radio range or distance varying.As shown in Figure 6, the packet reception ratio reduced with the increasing of radio distance for all three protocols.However, it is worth noting that the reduction of packet reception ratio is slower for JCCA compared to IEEE 802.11e and ACSBM protocols.In fact, the adjustment of CCA according to the channel utilization ratio will make our JCCA efficiently use the spectrum resource through intelligent determination of the channel busy/idle state.As a result, although the radio distance setting is directly influencing the packet delivery ratio considering the signal fading and more/few introduced interferences, our JCCA with variable CCA thresholds could outperform the other two protocols at any radio distance.
In Figure 7, the channel utilization ratio of three protocols has been drawn in the box-plot form.A box spans from the first to the third quartile and the median is marked with a line.With the use of congestion or load-aware contention strategy, our JCCA shows the highest channel utilization ratio compared with the other two.This means that our JCCA is competent under different load levels and has better scalability considering node densities, transmitting power, channel fading, and so on.
Conclusions
In the traditional WLANs, the fix setting of the CCA threshold leads to issues such as higher packets collisions and lower channel utilization ratios.In this paper, through the adaptive adjustment of the CCA threshold according to the network conditions and message priorities, the level of spatial reuse is improved by which the performance can be significantly enhanced for an IEEE 802.11e network.In addition, since the load-aware contention resolution is introduced, the channel utilization ratio using our JCCA scheme is improved to avoid network congestion.Numerical results show that our schemes could outperform the IEEE 802.11e and ACSBM in terms of packet delivery ratio, average transmission delay, and throughput.
In our future work, we will study the proactive congestion control schemes via transmitting power and packets generation rate control in high dynamic networks such as VANETs.
Figure 3 :
Figure 3: Comparison of packet delivery ratio.
Figure 4 :
Figure 4: Comparison of average transmission delay.
Figure 6 :
Figure 6: Comparison of packets delivery ratio under different radio distances.
Figure 7 :
Figure 7: Comparison of the channel utilization ratio among three protocols.
Table 1 :
Configuration of the contending window. is selected from [0, 3] denoting four types of services in IEEE 802.11e; indicates the channel utilization ratio; CW low min () is the minimum contending window of the th type of service when the network is in the low channel utilization case.
Table 2 :
Initial values of the CCA thresholds for different types of services.
Table 3 :
Simulation parameters of network performance.
Table 4 :
Setting of the contending window for different message priorities. | 6,126.4 | 2017-01-29T00:00:00.000 | [
"Computer Science"
] |
BUSINESS MODEL AND CORE COMPETENCE REFINEMENT: GOOGLE CASE STUDY
Negotiations on the Internet have increased dramatically. Therefore, new strategies and competitive business models are crucial factors to consolidate a firm‟s leadership position. In essence, a company that offers its services to a broader number of users and complementary companies will have its strategic position strengthened. Google has focused on achieving a leadership position offering two distinct services: the search engine and the advertisement service on the Web. Those services are the base on which the company‟s core competence was built, i
INTRODUCTION
With the mission of "organizing the world"s information and making it universally accessible and useful" (DAWSON; HAMILTON, 2006), the Google phenomenon can be an impressive example to be followed by any manager who wants to transform its enterprise into a successful business.Some facts illustrate this statement: Google originated from the project of two Stanford University doctorate students that, in approximately a decade of existence, led the company to reach the position of the most profitable and innovative of the world (BATTELLE, 2006); Google"s search tool became very popular in very little time, to the point of routinely providing 500,000 searches a day, in 1998, a few months after being founded.By late 1999, Google was averaging about seven million searches per day.By the middle of 2000, it was handling 15 million searches per day (VISE; MALSEED, 2007); In five years, the company managed to revert a situation of US$14,7 million net loss to achieve a profit of US$1,5 billion (VISE; MALSEED, 2007); The company filed with the SEC (Securities and Exchange Commission) for an initial public offering (IPO) in 2004, the highest IPO ever accomplished in Nasdaq (BATTELLE, 2006), and ever since, its stock value increased by more than 500% within a period of only three years.Moreover, it is estimated that, despite its short existence, Google was rated the world"s number one brand name, above Apple, Coca-Cola, Samsung, Ikea and Nokia.(DAWSON; HAMILTON, 2006).
So it is possible to affirm that the Google phenomenon reveals new dynamics that occurred at a very fast pace in a new business environment: the company found a way to manage the chaos of continuous growth of information on the Web.Google transformed its technological tool into a profitable business, associating its core competence with an innovative way to generate revenue flows and structuring its business as a correct mix of technology and innovation in business.
Thus, some questions might be asked by people who want to manage a business within a similar context: How do you establish a company"s business model that will permit the exploitation of the full potential of a technological innovation?How can a business model transform a new technology into value for the company and its clients?
The aim of this study is to tackle those questions through the conceptual approach of business models and core competency refinement.
In general lines, this case study is based on the hypothesis that Google"s success is due to the synergy among two strategic factors: a business model based on search and publicity in the Internet and a great capacity for refining core competency through network effects.
THEORETICAL REFLECTIONS
A lot of discussion has arisen about the construct known as business model.In the 90"s, with the commercial ascension of the Internet, many firms presented their descriptions of business models in order to obtain financing (SHAFER;SMITH;LINDER, 2005).The term has been studied and defined.However, in spite of its appealing approach within the _______________________________ RAI -Revista de Administração e Inovação, São Paulo, v. 6, n. 3, p. 46-62, set./dez.2009.literature, there is not very much consensus about a common definition to the term (CHESBROUGH; ROSENBLOOM, 2002;HEDMAN;KALLING, 2003;OSTERWALDER, 2004;SHAFER;SMITH;LINDER, 2005).
Since the mid-1990s, studies have begun to associate the construct to the context of the knowledge economy, the information society, or the age of revolution (HAMEL, 2000;OSTERWALDER, 2004;OSTERWALDER;PIGNEUR;TUCCI, 2005;SHAFER;SMITH;LINDER, 2005), where it is seen as an analytical tool that helps managers and strategists to understand and communicate a company"s logic in creating sustainable revenues.
According to several authors, the new economy ruled by the technological paradigm of the information technologies allows for a series of new business configurations and partnerships among companies and increases the number of stakeholders, as well as the company"s complexity, making it difficult for managers and strategists to intervene (DRUCKER, 1993;HAMEL, 2000;KIM;MAUBORGNE, 1999;LASTRES;ALBAGLI, 1999;OSTERWALDER, 2004).
It is possible to verify the diversity of definitions for the term in the literature in the study carried out by Amit andZott (2001), Reis, Proença andProença Junior (2003), Shafer, Smith and Linder (2005) and Tsalgatidou and Pitoura (2001).
Reis, Proença and Proença Junior ( 2003) define a business model as the structure and the logic of the transactions that pertain to the operation of an enterprise and the way in which that enterprise positions itself on the market.
On the other hand, Tsalgatidou and Pitoura (2001), see the business model as a logical architecture for product, service and information flow, including a description of the business actors involved and their roles, as well as revenue sources.
To Amit and Zott (2001), a business model can be described as an architectural configuration of the components of commercial transactions developed to explore businesses opportunities.Shafer, Smith and Linder (2005) affirm that the basis of a business model is a company"s essential logic to create and sustain value.They pointed out four main categories present in a company"s business model: i) strategic choices; ii) value creation; iii) value network; iv) value capture.
Regarding the definitions above and other definitions found in the literature, some consensus can be reached in relation to two elements that seem to be present in the concepts of business model: it helps understand a company"s business 'logic' and it mentions which components are involved in value creation.Amit and Zott (2001) stated that if a firm creates value, it does so because of its business model.The authors found empirical support for the belief that the firm"s business model is relevant for its performance and proposed that the business model should be understood as a unit of analysis.In other words, the business model describes the ways in which the company qualifies the transactions that create value for all participants, including partners, suppliers and customers.A business model deals with value creation while a revenue model is concerned with value appropriation.Joel Yutaka Sugano, Eduardo Jardel Veiga Gonçalves e Mariane Figueira _______________________________ RAI -Revista de Administração e Inovação, São Paulo, v. 6, n. 3, p. 46-62, set./dez.2009.
For Kanai and Tsunoda (2002) a business model is dynamic, as the company keeps developing its activities through the combination of three elements that the author defined as: 1) WHO the company intends to reach -the customers, 2) WHAT value it intends to createthe customers" needs, 3) HOW the company proceeds to deliver the value created to its customers -resources and processes.
The contributions of Amit and Zott (2001) and Kanai and Tsunoda (2002) help understand the business model as a tool that enables the company to create value.However, those authors focus only on value creation leaving aside those components of a business model that might help understand how value appropriation occurs.
Hamel (2000) proposed a generic business model that tries to explain a company"s performance in the present, which is when, in his opinion, companies should focus on business concept innovation.The terms business concept and business model are synonymous.The author explains that a business model is a business concept that has been put into practice.
For the author, business concept innovation is what will define the competitive advantage in the present.He explains that business concept innovation is the capacity of reconceiving existing business models in ways that will enable a company to create new value for its customers, surprise its competitors and create new wealth for its investors.
Osterwalder ( 2004) created a generic ontology for the term, making it less difficult to describe a company"s business model.He defined a business model as: a conceptual tool that contains a set of elements and their relationships and allows expressing a company"s logic of earning money.It is a description of the value a company offers to one or several segments of customers and the architecture of the firm and its network of partners for creating, marketing and delivering this value and relationship capital, in order to generate profitable and sustainable revenue streams (OSTERWALDER, 2004, p. 15).Chesbrough and Rosenbloom (2002) emphasized that the role of the business model is to assure that the technological core of an innovation is translated into economic value.Thus, without an appropriate business model, the new technology does not turn into economic value.
The concept of business model has become relevant in the context of change brought about by the information technology paradigm that demands disruptive innovation in companies.The business model incorporates the comprehension of how a company can benefit from new opportunities.On the one hand, it defines the way a company combines several strategic approaches.On the other, the business model consists of a definition, as well as the components that have to be present for a company to create and deliver value to members, customers and itself in a sustainable way.
RESEARCH PROCEDURES
The present study is a case study that aimed at enlarging knowledge about an object through the comprehension of questions such as How and Why, in relation to its functioning (JUNG, 2004).
According to Yin (1994), in case studies five components of research design are specially important: A study"s questions: 1 -How did Google establish its business model to enable the company to fully exploit the potential of its technological innovation? 2 -How did Google"s business model transform a new technology into value for the company and _______________________________ RAI -Revista de Administração e Inovação, São Paulo, v. 6, n. 3, p. 46-62, set./dez.2009.
its customers?Its propositions: Clarify matters related to the importance of adequate business models to allow the exploitation of a technological innovation and to translate the technological innovation into value for companies and customers.Its units of analysis: Google"s business model and Google"s core competency refinement; The logic linking the data to the propositions: the hypotheses that Google"s success is due to the synergy between two strategic factors (a business model based on search and advertising on the Internet and a great capacity for refining the core competency through network effects) guided the study; The criteria for interpreting the findings: the study applied Triviños" (1987) definition of one of the types of case studies (historical and organizational case study) where the researcher is interested basically in an organization"s life and history, helping to meet the study objectives.
Data were collected from secondary sources, which have been defined by the University of Maryland Libraries ( 2009) as interpretations and evaluations of primary sources.They are not evidence, but rather commentary on and discussion of evidence.Secondary sources might be bibliographies, biographical works, commentaries, critiques, dictionaries, encyclopedias, histories, journal articles, magazine and newspaper articles, monographsother than autobiographytextbooks, web site (UNIVERSITY OF MARYLAND LIBRARIES, 2009).
THE CASE STUDY
The present section states Google"s case study.It describes the company"s emergence, as well as its business model and evolution.
THE ORIGINS OF THE INTERNET 'SEARCH AND ADVERTISING' BUSINESS MODEL
Throughout the 1990s, there was a huge and 'disordered' increase in the content of the World Wide Web, thanks to the growing popularity of personal computers, and a strong need for organizing that vast content emerged, to assist Internet users.
The search tools of the time, however, used simple algorithms that sorted the search results according to the number of times certain key-words appeared on the pages.That system was unable to classify the sites according to the best content, because most of the time those results were confused by spams (repeated words on the page), which disturbed the search tool at the time of the indexation.
At that time, most of the Internet traffic was controlled by large portals that were able to filter and produce diversified contents in their domains.For those large portals, offering effective search tools was of little interest, since they might conduct their users to other independent sites, outside the portals.Battelle (2006) explains that in the late 1990s, search was not a priority for most Internet executives.The search tool was just a commodity -an attribute that was only satisfactory and at that time, the goal was not to send people out of one"s portal, as search tools did, but to keep them in.
Thanks to intense traffic, the large portals also acted as important Internet advertising vehicles.However, advertising was unable to differentiate specific traffic (in other words, the traffic where users would be predisposed to act in response to advertisements of the products Joel Yutaka Sugano, Eduardo Jardel Veiga Gonçalves e Mariane Figueira _______________________________ RAI -Revista de Administração e Inovação, São Paulo, v. 6, n. 3, p. 46-62, set./dez.2009. or services of a company) from non-specific traffic (the common traffic that did not get translated into customers for advertising companies).
Since the substantial volume of traffic in the large portals consisted mostly of nonspecific traffic, the advertising companies were not obtaining the expected response to the investments they were making on the Internet.
In an attempt to solve those problems, GoTo emerged, offering a new search tool based on a new business model: the search results obtained were the paid advertising announcements themselves.For the final user, that meant that spamming could be fought, because non deliberate results were eliminated.At the same time, there was no waste for the companies involving the investments they had made, since the advertising was geared to the specific traffic.Moreover, in the GoTo model, the announcers would only pay for the advertisements according to their performance.In other words, payment would be due when a user effectively entered the announcer's site through the advertising link, which was called cost per click (CPC).
The first problem of GoTo, however, lay on the announcers" critical mass creationput in a different way, a chain reaction in which the announcers' volume grows automatically, attracted by the new customers -to fill out its lists of search results, owing to the novelty of its advertising model.Most companies were not yet convinced that their investments would indeed turn into new businesses.
GoTo then devised an aggressive strategy of critical mass creation, offering the advertising service linked to the search results at the minimum cost of a cent of a dollar per click.GoTo believed that very soon companies would begin to compete for the paid announcements, so that the company that was willing to pay more would have its announcement better positioned when a certain keyword was typed into its search tool.The results of this strategy were quickly observed, and in six months the revenues generated by its advertising service had surpassed service maintenance expenses.
The company also adopted a strategy for traffic acquisition.Through partnership agreements, GoTo placed a search tool inside other sites of great audience.This way, it developed two business lines: the search service through the main GoTo site, and a distribution business that generated smaller revenues, but on a much larger scale through the traffic generated by third parties" sites.
GOOGLE EMERGENCE
In January 1996, Larry Page and Sergey Brin began to work on a doctorate project on Computer Science at Stanford University.Such a project consisted of the creation of a Web tool called BackRub that aimed at assimilating the connections between different Web sites.According to Battelle (2006, p. 61), BackRub would be "a system that would discover connections in the Web, store them for analysis, and replicate them in a way that enabled anyone to see who was connecting to any Web page".
With the development of the BackRub project, the PageRank algorithm was created.It was capable of counting all the connections between different sites and then ranking them according to their degree of importance.According to UP Blog, Google explains its PageRank technology in the following way: The classification of the pages (PageRank) relies on the exceptionally democratic nature of the Web, using its vast link structure as an indicator of each individual page value.Essentially, Google interprets a link between page A and page B as a vote from page A to page B. But Google looks beyond the volume of votes, or links, that a page receives; it also analyzes _______________________________ RAI -Revista de Administração e Inovação, São Paulo, v. 6, n. 3, p. 46-62, set./dez.2009.
the page that gives the vote.The votes given by "important" pages weigh more and help make other pages "important" (UPBLOG, 2008, p. 1) Based on PageRank and other refinements, Google was the most sophisticated search tool when compared to others at that time.Page and Brin, its creators, tried to license the technology to several Silicon Valley companies (including Yahoo and Excite) over a period of eighteen months for the amount of US$ 1,2 million, but no satisfactory agreement was reached.The reason for that, as explained above, was that a search tool was not a priority for Internet executives at the time.
After failing to obtain success in licensing their technology, they decided to set up a company and, after presenting the Google technology to Andy Bechtolsheim, a venture capitalist and one of the founders of Sun, Page and Brin got US$ 100,000.Some weeks later, on September 7, 1998, Google Inc. was formally incorporated.Its core competency was to provide a search service to Internet users; in the beginning, they had only three employees and the main office was located at a rented room beside a garage.
GOOGLE"S BUSINESS MODEL
Unlike GoTo, Google"s main objective was not to provide an advertising tool, but rather a search tool that offered Internet users the best results according to the degree of relevance of each site"s content, with the help of advanced algorithms.
That strategy allowed the company to secure an intense volume of traffic in very little time.Only two years after its foundation, Google had already registered approximately sixty million daily searches.
However, even with the vast audience they had attracted, the company had negative revenues until the end of 2000, since it did not yet have a sustainable business model.It was then, in an attempt to change that situation, that Google launched a new service called AdWords, which Battelle (2006) describes as follows: In essence, Google replicated the GoTo approach, building an automated self-service model that allowed the announcers to buy on-line text announcements using a credit card.However, unlike GoTo, Google already had plenty of traffic for its natural search results (results that classified the sites by the best content) and Brin and Page insisted on separating them from the advertising results, a key distinction of Google in relation to GoTo, which was launched as a purely commercial tool (BATTELLE, 2006, p. 107) In October 2000, Google introduced a new service, called AdWords.An announcement on the main site promoted the new service: "Do you have a credit card and five minutes?Place your announcement on Google today" (BATTELLE, 2006, p. 107) As it can be seen, AdWords is a service through which Google transmits advertisements on its result page with a crucial difference: Google separated publicity results from 'natural' search results.Figure 1 shows that AdWords are ordered on the right side of Google"s search page.Joel Yutaka Sugano, Eduardo Jardel Veiga Gonçalves e Mariane Figueira _______________________________ RAI -Revista de Administração e Inovação, São Paulo, v. 6, n. 3, p. 46-62, set./dez.2009.
Google was aware that most of the users were much more interested in natural search results than in advertising results; and the company knew that when mixing those two types of results the quality of its services could be seriously affected.
The first versions of AdWords adopted a CPT (Cost per Thousand) system, in which the announcers paid for the number of impressions (or announcements) and not for the click, as in GoTo.But in February of 2002, Google launched a new version of AdWords that offered not only the advertising service by performance (CPC or Cost per Click), but also an auction system that classified and evaluated a paid announcement according to its level of popularity.In other words, the company that paid more for a certain keyword would have its announcement ranked better in the AdWords section when that word was typed in Google.However, it could lose that position if another company"s Web page got a larger number of clicks in that same section over time.
Some months after introducing the new version of AdWords, Google made public an agreement with AOL in which AOL would use Google"s search technology in the AOL portal.Such an agreement, together with others with several small companies, demonstrated that Google had opened a new business line: the distribution of AdWords.
That business model permitted synergistically combining search and advertising services.It succeeded at rescuing Google from a loss situation in the years of 1999 and 2000 and turning it into one of the most profitable companies in the history of business.Table 1 shows the company"s financial performance from 1999 to 2005.According to Vise and Malseed (2007) the secret of the effectiveness of Google"s businesses model is discussed by its founders, Larry Page and Sergey Brin, in the following text: Google exhibits only text announcements addressed by keywords.That means you won't see the announcement unless you are looking for information on that specific topic.And for that, there are not animated banners competing for your attention, the text announcements are read carefully by the users, who frequently think they are as valuable as the search results themselves (VISE; MALSEED, 2007, p. 116).
BUSINESS MODELS: GOOGLE VERSUS GOTO
In spite of the similarities between the GoTo and Google business models (since both offered advertising linked to a search tool), it is important to observe differences that were crucial and that culminated in Google's success when compared to GoTo.
In general, in their business models, companies develop dynamic activities through the combination of three factors that Kanai and Tsunoda (2002) defines as: 1) WHO the company intends to reach -the customers, 2) WHICH value it intends to create -the needs, 3) HOW the company works in order to deliver the value created to its customers -the resources and the processes.Bearing those factors in mind, it is possible to distinguish between the GoTo and the Google business models more accurately.Figure 2 As can be seen, in terms of reaching customers (WHO the company wants to reach), Google was more effective, focusing on the group formed by all Internet users, offering them a service of greater value, classifying Internet sites according to the relevance of their content.This resulted in the rapid increase in the mass of users that would soon propel the development of other strategic actions by Google.
In terms of value created (WHICH needs the company should meet), Google distinguished natural search results from those based strictly on advertisements, while GoTo focused mainly on commercial results.
The great difference between the two business models, however, lies in the resources and processes used by the two companies (HOW the company works to deliver the value created).While GoTo developed a search tool based upon paid advertising to assist mainly those companies that wanted to announce on the Internet, Google developed the best existing search tool, enabled through technologically advanced algorithms, focusing on assisting Internet users mainly.
That becomes evident when Google launches Adwords and insists on separating the results of advertisements from those obtained through its search technology.A businesses model is not static.On the contrary, it is dynamic and because of that Google is trying to adapt itself and continuously create new value to satisfy clients' needs.
GOOGLE"S BUSINESS MODEL EVOLUTION
In 2003, for instance, Google launched AdSense, a service for distributing AdWords in the web sites of third parties.In this service, site editors, through registration with Google, allow advertising announcements (usually of correlated content) from the Google net announcers to appear beside the content of their sites.In that case, the editor responsible for that site may receive a portion of the revenue that is generated by the click of an Internet user who was attracted by AdSense.
According to Battelle (2006, p. 130), in that new service there was a significant difference in relation to AdWords, since AdSense "was not addressed by the consumers' consultations based on intentions, but by a site content".The author asserts that "the supposition was that if a reader was visiting a site related to flowers, for instance, flower announcements from the Google nets inside the current Web page would be the most appropriate" (BATTELLE, 2006, p. 130) Also according to Battelle (2006, p. 130) "AdSense was by almost any measure a great success -thousands of editors enrolled to use the service.Most were responsible for small sites that had not previously had a way of turning the small traffic they had into money".
Thus, AdSense has created an important net of distribution of Google announcements directly into independent sites, characterizing an evolution in the company"s business model, as the advertisements were only transmitted within the search results.
Ever since then, Google has been developing its businesses model through the expansion of its portfolio of services offered to Internet users.That happens because for each new service offered, the company generates more traffic and opens up new space to expand its advertising services.Some examples are the transmission of advertisements in new services such as Gmail (the email service) and Orkut (the relationship site).
Another example in the evolution of Google"s business model is the acquisition of the video site YouTube by Google, in 2006.At an interview to Folha Online (the website of one of the most prestigious newspapers in Brazil), the president of Google Brazil, Alexandre Hohagen, announced that in the United States the company is already offering a new form of advertisement: in-video ads, with advertisements inserted in YouTube videos.
The next section explains how the Google business model evolution has become possible.
GOOGLE'S CORE COMPETENCY REFINEMENT
The concept of a firm"s core competency has its origins on the Resource Based View (RBV) theory.It is defined as the consolidation of the company's technical and productive abilities and it can be perfected with the addition of the customer's competencies (PRAHALAD; HAMEL, 2005).
Google's core competency is based on the technology used in the search service, which is capable of building and organizing a database that makes it possible for the Internet user to find practically any piece of information he may be looking for.
Google periodically scans the entire Internet content and, through technologically advanced algorithms, complements and updates its database adding each new item of information found to its result indexes.Figure 3 shows this process.Joel Yutaka Sugano, Eduardo Jardel Veiga Gonçalves e Mariane Figueira _______________________________ RAI -Revista de Administração e Inovação, São Paulo, v. 6, n. 3, p. 46-62, set./dez.2009.
For instance, if at a certain period N in time, there existed an X number of sites on the Internet, Google's search tool would scan those sites and would create a database containing a Y index of results by means of relevance ranking.
However, in the N+1 period, new Web pages would be created, increasing the volume of Internet content.In the new scanning, in the N + 1 period, an X + n number of sites will be found, and the Y index will be complemented and updated, and that will create a new Y" index of results through relevance ranking, making the Y" index better than the previous Y index.
Later, in the N + 2 period, a new scanning will find an X"+ n number of pages (that is the same of "X + n" from the N + 1 period plus a new n number of sites), then the formation of an Y"" index is originated, which is better than the Y" index.
As the periodic scanning of the Internet is carried out, the Google database tends to grow and to get better.Continuing as in the example above, it can be said that the index generated in the N + 3 period will be larger and better than the Y"" index generated in the N + 2 period.The Google database tends to be continually refined and to accompany the growth of the Internet content.
What could be considered a 'chaos' resulting from the explosive increase in Internet content becomes, for Google, a continuous process of improvement of its search tool.
Therefore, the refinement of Google"s core competency (its search tool) takes place mainly through co-creation of value by the editors of Internet pages (that is, by the increase in the number of Internet pages).In that case, the editors that create and update the pages constantly add value to the Internet content, which ends up contributing to the enrichment of Google"s database.Consequently, one could assume that Google"s core competency refinement results from the following network effect: the larger the increase in Internet content, the more complete Google"s database will be and the better the results offered to the users of the search tool.As a consequence, if the search results are better, more users will be attracted by Google"s service, which in turn will attract even more announcers.
Figure 4 shows the process of traffic increase and revenues generated by Google"s core competency refinement.
In fact, the dynamics of Google"s core competency refinement through network effects is explained by Alecrim (2005), on the InfoWester site: The amount of information in the Internet is so large and so diversified that it is practically impossible to find everything that is necessary without the use of a search mechanism.There are very good search tools in the Internet, like Altavista, AlltheWeb, Yahoo and MSN.However, none of those sites is so wide ranging as Google.There are good reasons for that.To begin with, Google updates its information base daily.Here in InfoWester, for instance, every day we noticed the presence of the crawler Googlebot, a Google 'robot' that looks for new information in every site.That is really interesting because about 3 days after an article is published in InfoWester it is already possible to find it at Google.Other search mechanisms also possess crawlers, but they are less efficient in updating terms and classifying information (ALECRIM, 2005, p. 1)
FINAL CONSIDERATIONS
Within the new economy of Web-based businesses, it is crucial that new structures for analyzing companies" strategies be created.Therefore, this study aimed at offering a new contribution, based on the conceptual frameworks of business model and core competency refinement.Nevertheless, as demonstrated by the Google case study, it should be pointed out that an innovative technology alone does not guarantee the translation of a good business idea into sustainable competitive advantages.
Two elements are relevant for a company"s development and evolution.First of all, it is necessary to build the accurate architecture of the company"s business model.Secondly, it is of extreme relevance to consolidate the firm"s core competency.
In the case study analyzed in this work, the evolution of Google"s business model was leveraged by a more sophisticated search technology, which distinguished the company from the GoTo business model.Google"s first strategic move was guided by the assumption that Internet users were more interested in natural results than in advertisement results.Such a clue allowed the company to create new value for its customers: Internet users and companies interested in online advertising.Moreover, Google"s business model also contributed to the company appropriating value at a first moment through AdWords (inside Google"s Web page) and at a second moment through AdSense distribution channels (AdWords service inside third parties" Web pages).In terms of the architecture of a firm"s business model, Google surpassed GoTo at offering greater value at the same time it found a way to increase appropriability.
On the other hand, considering that Google"s core competency is based on the technology used in the search service, capable of offering benefits previously unknown, it can be said that the refinement of such a competency also contributed to the company"s business success, since the more refined it becomes, the more attractive Google"s search tool is, since Internet users will be more confident that they will find almost any item of information they may be looking for.
Google"s core competency refinement results from the following network effect: the larger the increase in Internet content, the more complete Google"s database will be, and so will the results offered to users.
In conclusion, this paper demonstrates that the refinement of the company"s core competency and its business model act synergistically because if the search results are better (refinement of the core competency), more users will be attracted by Google"s service, and therefore, more announcers will be interested in online advertising, generating more revenues (the improvement of business model).
Figure 2 -
Figure 2 -Google"s business model X GoTo"s business model Source: Developed by the authors
Figure 3 -
Figure 3 -Google core competence refinement through network effects Source: Developed by the authors
Figure 4 .
Figure 4.The process of traffic increase and revenues generated by the Google"s core competence refinement Source: Developed by the authors | 7,638.4 | 2009-12-28T00:00:00.000 | [
"Business",
"Computer Science"
] |
Latency-Aware Power Management in Software-Defined Radios
Cloud computing provides benefits in terms of equipment consolidation and power savings from higher utilization for virtualizable software. Cellular communication software faces challenges in cloud computing platforms. BSs create a specific load profile that differs from traditional cloud service loads. Cellular communication system implementations have real-time deadlines with fixed, periodic latency requirements. In this paper, we assess the suitability of an unmodified Ubuntu Linux OS running on a commodity server to operate latency-critical software using a 4G LTE BS software-defined radio implementation. Scaling of the CPU clock frequency is shown to be feasible without excessive impact on the platform’s ability to meet the 4 ms processing delay requirement imposed by the LTE standard. Measurements show the relationship between the processor’s operating frequency and the number of missed subframe processing deadlines to be nonlinear. The results obtained also indicate that a high computational capacity does not suffice to ensure satisfactory operation since fronthaul processing overhead can limit achievable performance. Use of offload-capable network interface cards is studied as a potential remedy.
Introduction
Evolution of telecommunication systems is directed by the intersection of demand and available technical solutions. BS design evolution reflects how Moore's law has enabled increased platform flexibility. In early BSs, specialized functions were implemented by discrete elements. Over time, discrete solutions were replaced by specialized ASICs. More recently, the rigidity of ASICs was eschewed in favor of FPGA-and DSP-based platforms. Nowadays, BS processing is within the reach of general purpose processors (GPPs) [1][2][3].
Increased use of software has enabled greater consolidation of logical functions into physical devices through the use of network function virtualization (NFV), software-defined networking (SDN), and software-defined radio (SDR). Consequently, this trend has lead to investigation of the feasibility of replacing specialized hardware by commodity servers with general purpose processors (GPPs) and even PCs. In this paper, the suitability of cloud servers to provide cellular radio access processing, known as cloud radio access network (C-RAN), is assessed.
General purpose servers aim to provide reasonable throughput for a wide range of tasks and by definition are not optimized for any particular one of them. In order to serve the needs of cellular systems, general purpose computing platforms must be adapted to satisfactorily run latency-sensitive cellular communication applications while still retaining the flexibility inherent in a software-based design.
By porting radio access functionality to a cloud platform, cellular system development can be set onto the same trajectory as other cloud-based services. Virtualization enables consolidation of computing hardware, reduces system cost, provides power savings, and increases flexibility [4]. However, it comes at the expense of process isolation and reduced predictability. Very stringent processing delay requirements in cellular base stations (BSs) may make centralization impractical. In order to remedy this problem, the trend is to migrate the C-RAN computation towards the edge of the network into edge clouds [5,6].
For C-RAN to realise effective coexistence of multiple BSs, the implementation must cope with the unpredictable delays and variable processing power availability of general purpose server environments. Achieving this aim calls for the creation of SDR BS implementations and system tests to outline the limits of current server platforms in order to guide their evolution.
In addition to tight latency and timing requirements, energy efficiency has gained importance as a cellular system metric. Global energy expenditure of the ICT industry represents 2% of global consumption and is projected to reach 3% by 2020 [7]. Meeting both the ever growing and more varied needs for wireless communication, along with acceptable levels of energy consumption, requires solutions enabling power management to take into account the latency bounds inherent to real-time cellular systems. In particular, this study focuses on improving power management in a C-RAN type shared computational environment with latency constraints.
In this paper, we describe the specific computational requirements of a cellular BS and what constraints it imposes on a cloud platform. To serve this computational load takes not only software adaptation but also suitable hardware. e suitability of current commodity server platforms is investigated using a 4G cellular system BS running on an Intel server platform. Assessing the suitability of a general purpose Linux-based operating system (OS) constitutes a prerequisite to creating a suitable C-RAN to exploit the consolidation benefits of cloud technologies. Improvement opportunities are outlined based on the results obtained.
is article is organized into nine parts. e structure and functionality of a typical BS are presented in Section 2. Related work is surveyed in Section 3. Sections 4 and 5 describe the pertinent BS features and their implementation in the agile radio framework (ARF) SDR platform. In Sections 6, 7, and 8, the performance model, experimental setup, and the results obtained therewith are presented. Section 9 concludes this article.
Base Station Evolution into C-RAN
A cellular BS generates load that is characterized by high computational requirements along with stringent periodic completion deadlines. Because of these requirements, BSs are usually implemented in dedicated hardware with a realtime OS.
Each evolutionary stage provides more run-time configurability than the previous.
In a cloud environment, it is desirable to use general purpose hardware and virtual machines executing non-realtime OSs. Cloud-based SDRs would be implemented as an application process that can be created with libraries, toolsets, and frameworks employed in general software development. Implementation of BSs in centralized servers is called cloud radio access network (C-RAN). C-RAN systems are usually split up into remote radio head (RRH) and baseband unit (BBU). ese units are connected over a fronthaul link. e most efficient way to split functionality between BBU and RRH remains an open question. One of the issues is in which system component to place physical and MAC layer processing. is paper describes a centralized approach to C-RAN. RRHs receive modulated samples and perform baseband signal up and down conversion. e BBU then handles the computationally heavy baseband processing.
Softwarization of implementation combined with the physical decoupling of the BBU from the RRH introduces the possibility of virtualization and centralization. A single server may operate multiple BSs serving multiple cell sites. ese sites only require RRHs and a communication link to the centralized server. By eliminating computational resources from access points, a more efficient architecture can be realised, in which processing resources are allocated from the pool based on demand. Enabling demand-based resource provisioning, in turn, allows for many low-cost, lowenergy RRHs to be built to enhance coverage uniformity.
In the coverage area of a small cell, the number of active users can vary significantly. is, in turn, wastes energy with current peak-dimensioned designs due to a high probability of transmitters being idle [11]. Turning off idling base stations is one potential solution [12][13][14] but becomes problematic if one aims towards low-latency and high reliability communication. In such cases, when having a wake-up delay is unacceptable, energy reduction techniques constitute a preferable alternative.
Cellular networks exhibit spatial and temporal patterns in the load they experience [15,16]. Daytime load is higher than during the night, when many users are asleep. Furthermore, due to diurnal variations between areas, load varies spatially by C-RAN instance as well as users move from residential areas to workplaces and back.
While RTOSs exist to solve latency and jitter challenges, they cannot be used in a virtualized environment since they cannot offer any guarantees when running on top of a nonreal-time hypervisor controlling access to the actual hardware. Indirect access to hardware through the hypervisor further complicates management of timers and interrupts. Additionally, a real-time hypervisor's strict division of time between guests restricts opportunities for exploiting variable loads in guests.
Alternatively to RTOS, overprovisioning can be used to meet requirements.
is method wastes both capital and energy. e predicted increase in the number of cell sites in 5G only compounds this problem.
In light of the above, it becomes necessary to investigate the ability of virtualizable, general purpose OSs and hardware to meet the timing requirements of BSs. In a non-realtime OS, packets can be lost due to missing the packet preparation deadline, denoted as late packets. In this work, soft-real-time is defined as a task that must meet its deadline on average but can tolerate occasional overruns [17,18]. Conjointly, the relationship between energy efficiency and performance must also be investigated to determine design parameter trade-offs. Slowing down computing helps to run processors at more power efficient clock speeds.
By exploiting the diurnal variation, operators can save energy by reducing the processing power and thus energy consumption during off-peak hours and in lightly loaded cells. is could be realised, for example, by grouping the processing of geographically close cells in the same C-RAN server. e power-performance profile of each server (and therefore cell group) can then be adjusted according its specific needs. Further refinement of the configuration granularity becomes possible on hardware support per-core adjustment of frequency and voltage.
Determining parameters with highest impact allows for the design of cloud systems better suited to the needs of virtualized BSs. e BS can reduce the amount of late packets by adjusting the radio link throughput and thereby the computational load.
is opens up the possibility of leveraging a C-RAN platform to allocate computing resources intelligently. e following sections review research that has been conducted into latency-sensitive and energyefficiency conscious software.
Server Platforms for Time-Critical
Systems. Management of system power consumption through online variation of processor voltage and frequency is known as dynamic voltage and frequency scaling (DVFS). Work presented in [19] proposes a statistical scheme to estimate and adapt to variation in load for latency-critical tasks. e authors consider variable arrival and processing times. ey determine that queuing delays often dominate total latency. While similar in aim, the characteristics of the offered load in the present article are different. Due to the periodic nature of the LTE frame structure, arrival times are well determined and required completion times are known. Consequently, stale work items in queues can be discarded based on this known deadline. e BS also partially knows future load due to its control over resource allocations for connected devices it serves (see Section 2). e authors in [20] similarly focus on queuing. ey however propose extending the time a task spends in the queue in order to obtain longer periods during which the processor resides in a low power state. Such a solution can be problematic in cellular systems, where communicating nodes must uphold strict timing in order to preserve synchronization. DVFS use in an embedded computer has been investigated in [21]. e authors studied the impact of voltage scaling on the worst-case execution cycle counts of their test programs. Unlike the present article, none of their test cases involved external interrupts caused by fronthaul data arriving at the network interface card (NIC) or other peripherals. Problems involved in operating low-latency systems involving substantial network communication are discussed in [22]. e authors of [22] discuss the general characteristics and broad outlines of potential solutions but no concrete solutions are offered. e aforementioned work demonstrates that power savings are possible but the case of interrupt-heavy periodic loads has received little attention.
3.2.
Software-Based BS Implementations. Implementation of tightly latency constrained wireless communication systems on server hardware has been investigated before. In [1], the authors present their approach to running the LTE physical layer on Linux. In contrast to the approach used in this paper, they do not implement protocol layers above the physical. It is also unclear whether time-division duplexing (TDD) or frequency-division duplexing (FDD) is employed. In order to obtain satisfactory performance, the authors pin execution threads to specific CPU cores according to a handtuned pattern. In [23,24], communication with the radio frontend occurred over a Peripheral Component Interconnect Express (PCIe) bus instead of an Ethernet connection as in the present work. Furthermore, in the latter case, the authors used the real-time framework Xenomai to introduce timing guarantees to the OS. Work presented in [25] reports on the methodology used to implement TD-SCDMA. e authors modified the Linux kernel's scheduling interrupt timer's frequency.
is technique is no longer applicable to modern tickless versions of the kernel. Techniques applicable to real-time approaches, such as Xenomai, are more cumbersome since they attempt to enforce timing constraints on the entire BS software stack instead of only network packet processing. Interrupt patterns of IP-based traffic differ from those of PCIe. Studies into the performance of IP-based soft-real-time SDR are therefore needed.
Contribution.
e above-presented related works considered either the problem of implementing latency-constrained communication systems or the reduction of energy consumption in processing local tasks. is article aims to combine both aspects and provide a scheme for reducing power usage while maintaining processing delays acceptably low. Energy savings are accomplished through CPU clock frequency scaling. Measurements quantify the dependence between the operating frequency and the BS's ability to complete tasks in a timely fashion. Factors taken into account include processing in the BBU, the radio frontend, and the network communication between them. e present work explores the feasibility of implementing BSs on GPPs with a standard Linux OS kernel through tuning of hardware and OS parameters. e aim is to assess the suitability of a soft-real-time latency-critical cellular software to operate on cloud infrastructure. e techniques used do not require any modifications to the standard OS kernel or the hardware. is helps to ensure applicability in C-RAN execution environments.
Logical Functions in a Base Station
All BSs present the same functional interface to user equipment (UE) to allow interoperability. From the network's point-of-view however, they are not identical nor do they serve the same purpose. Some BSs, known as macro BSs, target a large coverage area called a macrocell. Complementing these are micro-and picocells serving demand in small hotspots. Large macrocells are suitable for serving fast moving users, since their large coverage area will result in less frequent handovers than if the user was served by more spatially limited access points.
While all the BSs are equipped with the same specification-mandated functions, they might be called at different rates and with different target parameters. As such, BSs can generate different computational loads. ese differences provide opportunities for intelligent resource adaptation.
BS radio interface supports two-way communication. e BS receives data from the core network and prepares it for transmission over the air interface and conversely it takes the signal from the radio interface and converts it to bits to be transmitted to the core network. In order to compensate for channel errors, signals have to be acknowledged positively or negatively. e specification-mandated period [26] within which this must be accomplished sets a constraint on computing speed for decoding received data and sending out the acknowledgments. e processing in BS can be split into physical layer processing and higher layer processing. e physical layer related processing is mainly execution of data flow type computationally heavy algorithms. Higher layers deal dominantly with users and protocol states. Figure 1 depicts the processing flow for data to and from the air interface. e BS's external connection to the mobile core network is beyond the scope of this work.
Functions dealing with digitized samples of the signal received at the antennas are collectively known as Layer 1 (L1). In 3GPP-specified cellular systems, L1 operates on groups of samples contiguous in time known as subframes or transmission time intervals (TTIs). In modern cellular systems, the TTI is the basic time unit for processing. e samples to be transmitted have to be prepared for each TTI and received samples have to be analyzed during certain TTIs.
e main functions in L1 are modulation, equalization, channel coding, and waveform processing. Processing load depends on the modulation and coding scheme (MCS) which the BS selects based on a mapping from the observed radio link quality. e MCS value selects operating parameters, such as constellation size and coding rate, for the modulator, demodulator, encoder, and decoder. In traditional systems, the choice of modulation accounts only for the quality of the channel between communicating nodes. In cloud-based systems, there exists an additional trade-off based on processing requirements. A higher MCS value allows for more bits to be transmitted but requires more processing for receiving those bits. e server can trade off lower data rates for reduced processing power requirements.
Above the physical layer reside the medium access control (MAC) functions. ese primarily handle resource allocation, scheduling, and channel multiplexing. e MAC also carries the responsibility of generating acknowledgments and negative acknowledgments as well as responding to those received from the UE. In the LTE standard, the available response generation time is never shorter than four milliseconds. Resource allocation relies on these acknowledgments and on channel quality reports to inform the BS as to which transmission parameters are appropriate for the conditions experienced by each UE. Since the computational load is a function of user resource allocation, the scheduler can directly impact the BS's processing burden.
Connected to the core network are the BS functions dealing with IP packets. ese provide header compression, encryption, integrity protection, and segmentation. Encryption and integrity protection provide security. Segmentation and concatenation functions are necessary to enable IP packets to fit the available radio resources. Header compression helps in this regard by eliminating needlessly redundant information from transmitted packets.
BS Implementation Using the ARF Platform
e agile radio framework (ARF) is a soft-real-time SDR platform designed to run on commodity computer hardware using a GNU/Linux OS as shown in Figure 2. In this work, it is used to implement an LTE BS in order to evaluate C-RAN latency and computation load issues. e ARF is designed to be compatible with a wide variety of different server platforms. As such, the ARF does not require special drivers, beyond those for the radio frontend in use, or modifications to the kernel of the OS. is entails that no hard-real-time extensions need be applied. While RTOSs provide tools to solve latency and jitter-related issues, they cannot do so when operating virtualized on top of a hypervisor. Additionally, compatibility of the ARF with standard software tools and libraries leads to wide portability. e same applies to online migration of virtual machines. Apart from the radio frontend, the ARF does not need any special hardware. However, use of such is not precluded by the design. For instance, one could use a graphics processing unit (GPU) to accelerate computations [27].
Architecturally, the ARF platform is divided into three main components as depicted by Figure 3. e lowest layer is the Virtual Hardware Enhancement Layer (VHEL) [28]. Its purpose is to serve as an abstraction layer for hardware nonidealities. Radio frontend hardware interfacing is done through the Universal Software Radio Peripheral Hardware Driver (UHD) [29]. Since the ARF does not assume hardreal-time guarantees from the OS, protocol processing may be late in the upper or lower layers. As explained in Section 2, cellular systems require transmitted and received samples to be ready for a specific TTI. In a non-real-time system, the processing could exceed its allotted time or be delayed past its deadline. In this paper, such events are termed lates. Upon occurrence of a late, the VHEL sends a preconfigured contingency subframe to the radio frontend to help maintain timing alignment. is could, for example, be a zero-filled subframe or a pregenerated subframe containing only pilots and synchronization signals if appropriate. In the receive direction, the VHEL will similarly mask lates and overflows by handing the protocol's physical layer a subframe containing the correct number of samples even if some were lost. e VHEL hides lates and therefore the soft-real-time nature of the platform from upper layers. ese are written as if the samples would always arrive on time. Upper layers can therefore apply block-based processing while ignoring timing related issues. e communication protocol's retransmission mechanisms can take care of performing a new transmission of data lost due to lateness of processing in the transmitter part 4 Journal of Electrical and Computer Engineering of the ARF platform. From the communication protocol's point-of-view, this is no different than experiencing poor channel conditions, provided late processing occurs seldom enough. While this approach does not provide the same level of timing determinism as RTOS-based designs, it simplifies development. Code related to handling TTI timing and meeting deadlines resides only in the VHEL. Other code may be written as non-latency-critical software. In case performance proves insufficient, traditional software optimization techniques can be applied until deadlines can be met with some probability. Furthermore, an intelligent cloud platform could take advantage of the difference in processing load between different BSs as described in Section 2 to adapt its resources optimally.
C-RAN Processing Performance Model
e main challenge in C-RAN implementation is reduction of late packets. Whether a packet is late depends on the total packet processing time. is time is a function of the packet processing time within the BS stack T BS , delays related to operating system functionality T OS , and delays related to data transmission over the fronthaul link T f . Knowledge of the latter is required in order to estimate how far ahead of the deadline a packet must be sent to arrive in time at the frontend.
Accurate total processing time information might not be available to the C-RAN. In practical systems, it is easier to measure the number of late packets as a function of these various delays F P (T BS , T OS , T f ). e function F P provides a tool for adapting BS processing. To achieve a given packet outage target P out , the C-RAN should manage delays such that While allocating its resources, the C-RAN can track F P in real time. Optimal allocation raises the question of whether F P captures the system's characteristics sufficiently well and which parameters are the most significant for system performance. Function F P is implementation dependent. However, system-specific dependencies can be measured and learned for each particular platform at run time. Journal of Electrical and Computer Engineering e ARF platform is used as a measurement tool for identifying cloud processing bottlenecks while executing an SDR BS load. Execution time is subdivided into two parts: cellular BS-related functionality and operating system housekeeping activities. e former constitutes the lion's share of the load. In turn, it is composed to two components. e first is air interface processing, comprised of relatively computationally heavy physical layer algorithms executed each in TTI (1 ms interval in LTE). Higher layer communication protocol processing executes separately from the physical layer and presents a comparatively much lighter processing burden. e second component includes all noncore-functionality processing, termed management processing, such as data copying, OS function calls, and fronthaul data transmission. Contention for these resource as well as OS kernel scheduling decision can influence whether processing completes on time. Overall C-RAN behavior is characterized by how the system management and BS processing work together.
is was investigated through the insertion of measurement points into the BS and management parts of the ARF code.
e results presented in this article were obtained by running a partial LTE Release 8 payload in TDD mode on the ARF. Consequently, the TTI duration is 1 ms. e measurements were done while sending data over the air. Performance of the TX processing impacts the RX processing and vice versa. Processing-time overruns in one will reduce the CPU time available for the other. is stems from the need to know whether to send a positive or negative acknowledgment and, on the transmit side, whether the retransmission buffer can be cleared after a successful reception by the remote node. UEs must first receive grants from the BS before they know when and with what parameters they may transmit. is limits the available time to prepare data to the time between receipt of the grant and the transmission time.
Packet processing time (including transmission to RRH) should be less than the TTI duration. Each component of the packet late function F P contributes to overall processing time differently. e delay T BS , related to user load, is a linear function of the computational demands on the CPU. e more data the UEs want to receive, the more work the BS must perform to transmit it to them. In order to fit a greater quantity of data into the same, fixed, amount of spectrum, more complex modulation, equalization, and channel coding schemes must be employed. Doing so increases computational complexity. Increased load can be managed by adding more processing capacity. is could, for example, be more or faster CPUs as well as accelerators.
Fronthaul transmission-related delays are composed of data transmission and endpoint processing. For dedicated fronthaul links, the data transmission delay T f is largely fixed and adds latency without any means for the BBU to compensate. Endpoint processing, on the other hand, can be sped up in the BBU. Typically, it is the OS that handles network-related tasks. It is therefore possible to obtain improved performance by switching to more capable network hardware, a newer kernel, or different OS. e main contributor to OS-related delays T OS is interrupt processing. It causes delay and jitter due to context switches to interrupt service routines and handlers [35]. Context switches degrade performance even if they are not computationally expensive as they might cause data to be evicted from cache, new processor state information to be loaded, and virtual memory translation lookaside buffers to be flushed [36]. Since context switches can be caused by aperiodic background processes and hardware interrupts, their effect on an SDR platform-or any other software-is not easily predicted or quantified by said software itself. Mitigation strategies must therefore extend beyond the SDR code base into the operating system, hardware, and load management.
Experimental Setup
Measurements to quantify the contribution of each factor of F P (equation (1)) were carried out using two different systems. ese measurements serve to quantify the impact of general purpose hardware and operating systems on cellular BS implementation performance. Table 1 presents the test systems' main components while Table 2 lists the Linux kernel boot arguments. Both systems were directly connected to their respective frontends using Gigabit Ethernet. e ARF SDR platform was configured as an LTE Release 8 BS with one transmitter and one receiver antenna. Assessing the impact of protocol processing was done through the use of the data plane. Turbo Code decoding was used to create a uniform and constant load. Five iterations of the decoder were applied to 25 resource blocks (RB) in the LTE subframe structure. Modulation and coding scheme (MCS) 9 was used as defined in LTE Release 8 for uplink data transmissions.
e operating system used was Ubuntu 16.04 LTS. In an effort to reduce interrupt and CPU contention for the BS code, OS boot-time parameters were modified from their defaults. e aim of the changes is to improve the performance of the ARF platform by dedicating resources. Listing 1 gives the parameters applied to the first system's Linux kernel on boot and Listing 2 presents the same for the second system. e "intel_pstate � disable" parameter was used to prevent dynamic control of the operating frequency in order to enable consistent measurement runs. e OS's scheduler was instructed to avoid CPU cores 2-7 and 10-15. Doing so reserves them for use by the BS code. e parameters in Listing 1 and Listing 2 were in addition to the "root�" parameter as well as the default values of Ubuntu 16.04 for each system, given in Listings 3 and 4, respectively. No additional kernel boot settings were applied to System 3.
In addition to boot-time parameters, measures were taken after system start-up to further improve performance on System 1 and System 2. e governor for all processor cores was set to the "performance" setting. e energyperformance bias parameter was also changed. It was set to indicate to the CPU to prefer higher performance over lower energy consumption. is was done in an effort to minimize latency and increase the repeatability of the data since the decisions of the CPU are opaque to the user. e SDR platform process was also executed with a high priority. is 6 Journal of Electrical and Computer Engineering helps to ensure that the OS's scheduler tries to minimize interruptions caused by other tasks requesting processor time. Ensuring constant operating parameters reduces jitter from transitions between them and helps avoid unnecessary delays. Such transitions were observed to occur frequently. One possible reason for this is that relatively low CPU utilization rate led the OS to reduce clock frequency in order to save power as it believed the system to be relatively unloaded. In fact, the system was likely busy moving data or waiting for it. Waking up from a low power state when the data does arrive takes more time than resuming processing from a fully on state. e cset application [37] was used to set the ARF code to run on the isolated CPUs. On System 1, two cores and their adjoining Hyperthread cores were kept for other processes while on System 2, the corresponding number was one. On System 3, the CPU governor was set to "performance" and the interrupt coalescing value to 10 μs.
Although the measurements presented in this work were obtained on a physical host without virtualization, we argue that the results provide meaningful insights into C-RAN implementation for three reasons. Firstly, a C-RAN differs from a public cloud service in that the platform is purposebuilt to host cellular BBUs under the control of the same administrative entity, i.e., the network operator. As such, fewer abstraction layers are required than in a public cloud. For the same reasons, direct access to hardware resources can be granted to guests. Furthermore, hardware-assisted virtualization technology, such as single root input/output virtualization (SR-IOV), enables a single device to be shared amongst the guests at a hardware level with low overhead [38]. Secondly, being a purpose-build platform also makes it feasible to provide an interface (i.e., paravirtualization) for the guests to communicate their load status to the hypervisor. e latter can then utilize the similarity of the diurnal cycle induced load (see Section 2) across neighboring BBUs to scale down the CPU frequency of the whole system.
irdly, an operator's business model differs from a public cloud provider. e latter might oversubscribe resources to increase revenue [39]. Another difference is that public clouds do not know a priori what load type their customers will run. Infrastructure must therefore be designed to be generic. A C-RAN platform, on the other hand, knows the load type to be executed and places meeting latency requirements first. Consequently, resource allocations can be tailored to the task at hand. Furthermore, since payloads in a C-RAN platform originate from trusted users, less need for hardware abstractions and security isolation overhead exists. Performance, therefore, behaves more akin to a physical host, yet still provides the benefits of consolidation by enabling multiple BSs to be hosted on a single server.
Measurements were performed to determine the impact of two different system parameters on the performance of the ARF. e first one was the clock frequency of the CPU. It was varied from highest to lowest supported by the CPU (see Table 3). CPU clock frequency measurements were done to study the feasibility of reducing power consumption without compromising performance. A lower clock frequency enables operating voltage to be dropped, which in turn leads to power savings. e CPU's operating speed impacts the T BS parameter of F P . e second type of measurement involved varying the interrupt coalescing behavior of the NIC (see Section 3.3). Table 3 shows the parameters used for interrupt coalescing. e value labeled "rx-usecs" indicates the amount of time in microseconds that the NIC was configured to wait for further network packets to arrive before notifying the CPU in an effort to improve the interrupt-to-payload ration. Interrupt coalescing was selected as test parameter to assess the impact of OS processing (T OS in F P ) on BS performance. A greater number of NIC interrupts result in more processing time spent in kernel space. is does not significantly change the computational load as each network packet still needs to be processed but does reduce the number of context switches required.
Results and Analysis
Results from the measurements are reported as the probability of the subframe processing being late. It is computed by normalizing the number of late subframes by the total number of subframes. is metric was chosen instead of the more conventional CPU usage as it better reflects the objective: to process received subframes and prepare new ones to transmit within the alloted time. It would indeed be possible for the processor to be relatively unoccupied but to have data be delayed by other factors (for example, network stack processing or interrupt moderation by NICs). CPU clock frequency and interrupt coalescing measurements were carried out using System 1 and System 2 while the NIC offload measurements were performed using System 3. Figures 4 and 5, performance can be seen improving from the lighter processing load to the more demanding one. Since the ARF platform can handle higher data rate (load) better, improved performance at a higher load suggests computational capacity is not the sole factor influencing performance. To confirm that delays outside of the SDR platform impact performance, measurements were carried out to determine the effect of additional system delay in processing incoming network traffic. e NIC's interrupt coalescing timeout was varied to introduce extra delay. Despite load, bandwidth, and CPU clock frequency remaining constant, Figure 8 shows an increase in the ratio of dropped TTIs. Journal of Electrical and Computer Engineering
Performance per MHz. Comparing
Even though a subframe may be ready in time in the BBU, it still needs to be transported to the RRH. When setting the frequency of the CPU, frontend transmission delays must also be taken into account. For receiver-side data processing, the same principle applies in reverse; not all of the TTI duration is available for baseband processing. is reduction in available processing time must be taken into account in the design of the SDR platform and the configuration of the OS it runs on. Unlike RTOS running on ASIC-based designs, a margin should also be included to protect against jitter in network processing caused by competing processes running on the same machine. e measurement with heavy protocol processing load leads to the situation depicted in Figure 6. e shape of the curve remains the same but the ratio of dropped TTIs below the threshold frequency rises. Performance above this threshold point remains essentially unchanged. Operating the CPU at full frequency therefore needlessly increases energy expenditure without providing a corresponding improvement in the timeliness of computations or the performance of the platform in general. It is already operating at effectively the same performance as a dedicated design with preset timing and scheduling.
A potential alternative would be to execute the job as quickly as possible using the highest performance setting and then enter a low-power state. Such an approach may not be suitable in all cases. Resuming normal execution from a low-power state incurs a delay and consumes full power [40]. erefore, in order to be beneficial, the length of the idle period must be long enough that the energy and performance penalty [41] of transition into a power saving state is recouped. e latency is of particular concern in cellular systems. Processing a subframe requires obtaining all its constituent samples from the radio frontend. ese do not arrive at the same time in one transaction but are instead sent in chunks, the size of which is determined by the Ethernet maximum transmission unit (MTU) size. Frames are sent as soon as they are filled with samples. is means the C-RAN platform must continuously process incoming data from the network and thus requiring CPU involvement. Delaying processing of arriving data means accumulating work to be done once the last sample is received. is backlog of work then creates extra delay in the handling of the subframe as pending data frames must be handled first. Similarly, if TTIs get shorter or subframes are processed in smaller parts to reduce latency, the intervals available for power states decrease even further. However, the frequency-scaling method presented in this work is not mutually exclusive with other power management techniques but rather a complementary approach. For example, it may be possible to hand over users from several lightly loaded BBUs to one. en, the all but one could be put into power saving mode while the active one executes with the lowest power state providing the required performance. How to combine these techniques as part of an overall solution is left up to future work. Figure 7 indicates that the existence of the energy-saving frequency threshold is not specific to System 1. System 2 exhibits the same type of behavior but with a greater potential energy saving due to a higher maximum CPU operating frequency. Journal of Electrical and Computer Engineering
Performance
Modeling. C-RAN server run-time adaptation requires learning the BS's performance vis-à-vis its load and to be able to predict the impact of changes in operating parameters. One way to accomplish this is to extract a dependency function, the parameters of which can be learned in real-time. Such a function was sought using collected performance data. Analysis of the data (see Figures 4-7) suggested that the impact of CPU frequency can be divided into two distinct regimes: one in which it majorly affects the late rate and one in which it does not. Due to this shape, two function families were selected: (2) e criteria for the selection of the equations' form were being a function of CPU frequency and sampling rate, possessing two regions (steep and shallow), and having a suitably rapid transition from one region to the other. Parameterwise, CPU frequency was selected since it is user tunable and significantly affects both performance and energy consumption. Sampling rate similarly heavily impacts the amount of data needed to be processed. rough preliminary analysis of early measurements, these two factors were picked as being the most significant.
Studying the effect of sampling rate provides one of the defining characteristics of C-RAN, namely, a steady and constant inflow of samples to process. e analysis could, however, be made more general by considering a generalized load factor. Such a load factor would be constituted of the traffic-independent part (i.e., sampling rate) and the trafficdependent part (i.e., per-resource block processing). e latter would be subject to the diurnal patterns discussed in Section 2. e analysis of such a generalized model is left up to future work.
While the general form of the function could be determined by inspection of the collected data plots, parameter combinations are too numerous for manual determination to be practicable. Instead, an exhaustive search through all the parameter combinations determines the best selection, as well as their coefficients as presented in [42]. Functions g 1 , g 2 , and g 3 (equations (4)-(6)) contain these coefficients: Fitting of the model was done using the least squares method in MATLAB [43]. Mean-squared error (MSE) was used as the goodness-of-fit metric. e least squares method exhibits sensitivity to its starting point. Multiple initial values were therefore employed. Initial values were obtained as two-step process. First, random values were obtained by multiplying a random number uniformly distributed in [0, 1] with a multiplier. Table 4 lists the multipliers used. Each parameter of the model received an independently selected value. An initial fitting was then conducted. A subset of the lowest MSE coefficients was retained to serve as initial values for subsequent fittings.
Iterations of the search potentially yield unsuitable results. is may occur due to ill-conditioned Jacobians or rank deficiency. Any set of coefficients producing issues of the aforementioned type, as reported by MATLAB, was rejected. Additionally, significance of each parameter to the overall model formed an additional criterion. Parameters more likely than α � 0.05 to result from the null hypothesis resulted in rejection of the generated model.
5526e + 04 -1.0976e + 13 9.3501e + 07 9.9289e + 05 - e corresponding values for f 1 are given in Tables 7 and 8. Similar results for System 2 are omitted for brevity. ey followed a similar pattern to the results for System 1.
After an initial sharp drop in MSE between one and six parameters, performance remains mostly stagnant from seven parameters upwards. For f 0 , the lowest MSE occurs for 14 parameters and for f 1 , at 13. Lower parameter count models are preferable as they are less likely to overfit, which degrades predictive accuracy, and since they are less costly to fit parameters for processingwise. erefore, we select f 0 at seven parameters as the most suitable model (its MSE being lower than f 1 at the same number of parameters). Equation Figure 9 illustrates the selected model's fit for System 1 data. To assess the impact of specific system characteristics on performance, Figure 10 presents the fit f m with the data recorded for System 2. It can be observed that while the general shape of the curve remains similar, there is more divergence between modelled and recorded than in Figure 9. Residual plots (Figures 12 and 13) for the selected model indicate a different pattern on both systems. e quality of the fit improves when the model is retrained based on System 2 data as shown in Figure 11. is indicates that the general form of the function applies to multiple platforms. Machine-specific variations are expected since hardware, OS, driver, and load differences impact behavior. Completely accounting for all such variations in practice presents an almost infeasible task.
Determining when diminishing returns set in as a function of f m accomplished by analysing the relationship between the dropped TTI ratio and the CPU clock rate. Beyond the threshold frequency, performance stops increasing. A practical SDR platform implementation may track this information and use it to build time averaged statistics. ese in turn can be utilized in online computations of the predictive equation's parameter values reflecting the current state of the execution environment. Shorter averaging times lead to a more responsive estimation of the required CPU frequency while longer ones reject transients better.
In addition to the statistics collection above, SDR systems may also utilize communication protocol scheduler data for performance-energy optimizations. Since in an LTE system UEs may only transmit when given a grant by the BS, the latter knows to a large degree its receiver-side processing load some period of time into the future. It is not possible to account for all incoming traffic (e.g., random access bursts), so a margin should be left to avoid underestimating the required computational resources. No fluctuation margin was included in the values computed in this section as that is a system design issue and therefore dependent on the use-case.
Network Processing Impact.
Cloud infrastructure exhibits not only a non-real-time computational - environment but also non-real-time data transfers. Samples must be moved to and from the radio frontends to the virtualized BBU. Network traffic interrupts were observed to have a significant impact on platform performance. Network traffic originated interrupts can disrupt the dataflow processing of the physical layer. is will not be visible in the CPU usage of the baseband task but can still cause processing to be late. CPU clock frequency adjustment algorithms may therefore make incorrect predictions. A smaller standard deviation provides a more predictable environment for the SDR platform to adapt to, thus making it possible to scale CPU frequency down more aggressively.
Measurements were carried out to quantify the proportion of time spent handling network related functions. In an effort to isolate variance to that caused by network processing itself, no LTE processing was executed concurrently. Tables 9 and 10 show round-trip time (RTT) obtained for 50 megasamples per second with 368 samples per TTI at two different MTU sizes.
One method to relieve the CPU is the use of offloadcapable NICs. ese take on the task of processing incoming network packets instead of the OS. As such, they only deliver ready-to-use payload data straight to the application as there is no need to invoke any OS kernel functionality. Offloading network processing presents gains orthogonal and independent of baseband processing capacity.
In both the small and large MTU cases, offloaded network processing provided the best performance. e much lower standard deviation improves reliability of the BS software when the CPU clock frequency is adjusted close to the minimum required as described in Section 8.1. ese latencies measured represent a lower bound on TTI preparation time that is independent of computing capacity. It should also be noted that the offloading results in less CPU usage and context switches.
While LTE requirements can be met, the impact of network processing on SDR performance becomes more severe as TTI durations decrease. In 5G, TTI duration is expected to shrink to provide lower latency communication.
e ratio of TTI duration to interrupt handling latency will worsen the risk becoming the limiting factor for 5G SDR implementations. Additionally, larger bandwidth will require more samples to be transferred between RRHs and BBU. e resultant increase in network traffic increases the number of packets to process and thus network processing load on the OS.
Conclusion
Cellular BS execution on general purpose hardware and OSs is feasible. e SDR aim of increasing the flexibility of communication protocol implementations can be met if system parameters are appropriately taken into account to achieve optimal performance. It was demonstrated that acceptable performance can be obtained without resorting to a hard-real-time OS or dedicated ASIC-based designs. is opens up the possibility of consolidating BS processing into C-RAN data centers. is could further increase the flexibility of SDR system deployment by enabling on-demand allocation of resources to those cells experiencing load while activating power saving measures on unloaded ones. Concentration of computations produces savings in the hardware investments required to build the network. In addition, energy savings can be realised through CPU frequency scaling. Measurements showed that the relationship between operating frequency and the probability of late subframe processing is nonlinear. By operating at, or slight above, the threshold point, performance can be kept at virtually the same level as fully on but with a significantly lower energy consumption. It was shown that optimising for computations-persecond is not sufficient-latencies and jitter caused by competing processes must be taken into account. On the other hand, energy-efficient use of computing resources demands that CPU clock frequencies be kept low and idle periods extended as much possible. In order to combine these two objectives-few missed TTI deadlines and high power savings-parameter tuning should take into account not only the processing needs of the application itself but also delays external to the platform. In particular, latency from passing data from the NIC through the network stack to the user process was studied. It was found that network traffic generated interrupts impact processing time and must therefore also be taken into consideration. Especially for shorter TTI durations, network processing delay can constitute a substantial portion of the total computation time budget. Accounting for this is of particular relevance in C-RAN environments, where RRHs are physically separate from the servers executing the baseband processing. Mitigating the impact of moving data to-and-from BBU constitutes an important avenue of research to improve the performance of virtualized cellular software platforms. NICs offering full network stack offload constitute one possible solution.
Several metrics along with a performance model were also proposed to help in estimating suitable operating points for the CPU clock frequency. Such a model may be used to determine appropriate resource allocation levels for software-based BSs according to load. Design of a self-tuning platform is left up to future work.
Data Availability
e latency measurement data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper. | 11,179 | 2020-02-11T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
MgO nanocube hydroxylation by nanometric water fi lms †
Hydrophilic nanosized minerals exposed to air moisture host thin water fi lms that are key drivers of reactions of interest in nature and technology. Water fi lms can trigger irreversible mineralogical transformations, and control chemical fl uxes across networks of aggregated nanomaterials. Using X-ray di ff raction, vibrational spectroscopy, electron microscopy, and (micro)gravimetry, we tracked water fi lm-driven transformations of periclase (MgO) nanocubes to brucite (Mg(OH) 2 ) nanosheets. We show that three mono-layer-thick water fi lms fi rst triggered the nucleation-limited growth of brucite, and that water fi lm loadings continuously increased as newly-formed brucite nanosheets captured air moisture. Small (8 nm-wide) nanocubes were completely converted to brucite under this regime while growth on larger (32 nm-wide) nanocubes transitioned to a di ff usion-limited regime when ( ∼ 0.9 nm-thick) brucite nanocoatings began hampering the fl ux of reactive species. We also show that intra-and inter-particle microporosity hosted a hydration network that sustained GPa-level crystallization pressures, compressing interlayer brucite spacing during growth. This was prevalent in aggregated 8 nm wide nanocubes, which formed a maze-like network of slit-shaped pores. By resolving the impact of nanocube size and microporosity on reaction yields and crystallization pressures, this work provides new insight into the study of mineralogical transformations induced by nanometric water fi lms. Our fi ndings can be applied to structurally related minerals important to nature and technology, as well as to advance ideas on crystal growth under nanocon fi nement
Introduction
[10][11][12] Periclase (MgO; magnesia) is an ideal hydrophilic mineral 13,14 for tracking water film-driven transformations, 6,15 as its rock salt structure can readily transform to brucite nanosheets (MgO + H 2 O → Mg(OH) 2 ) (Fig. 1).Transformations can be topotactic 16 when water diffuses through the (111) plane of MgO, forming OH groups along the (001) plane of brucite (Fig. 1a).Because these transformations can be shortrange, they can even produce intralaminar spacings intermediate to those of both minerals. 16,17][24] Hydroxylated surfaces produce reactive soluble (e.g.Mg 2+ , MgOH + ) species leading to Mg(OH) 2 nanosheet nucleation and stacking (Fig. 1b).Brucite growth then expands the volume of the reactive solid materials by ∼150%.Under confinement, this volumetric expansion has the thermodynamic potential of generating GPa-level crystallization pressures. 25Expansion can crack MgO-based cements 26 and refractory castables, 27 and is of great interest in the study of reaction-induced fracturing in Earth's crust. 12,25n water-unsaturated environments, water films formed by exposure to atmospheric moisture can be sufficiently thick to mediate brucite growth via dissolution, hydroxylation, nucleation, and crystal growth (Fig. 1b).Reactions can therefore be comparable to those occurring in aqueous solutions, except that they proceed in the nearly two-dimensional environment of water films. 20,280][31][32][33][34] Exploring these variations in the low waterto-solid environment of water films is strongly needed, especially considering the widespread importance of periclase in industry, 26,27,35,36 and emerging technologies planning to use MgO-bearing wastes for direct atmospheric CO 2 capture from moist air. 37dvancing knowledge about these water film-mediated reactions can be achieved by working with synthetic periclase nanocubes with contrasting properties.In particular, synthetic periclase nanocubes tailored by controlled thermal dehydroxylation (Mg(OH) 2 → MgO + H 2 O) are of great utility.When produced below ∼600-650 °C, synthetic periclase nanocubes are more reactive towards hydroxylation compared than those produced above this value. 30,31Nobel prize laureate William Giauque, who in the late 1940s studied MgO hydroxylation to investigate the third law of thermodynamics, explained enhanced MgO nanoparticle reactivity below this threshold temperature in terms of favorable surface energetics, 29 and these were finally measured experimentally over 70 years later by Hayun et al. 15 In the 1960s, Feitknecht and Braun 32 suggested that microporosity favored reactivity, and that it was even responsible for generating high crystallization pressures.
In the 1980s, Naono 31 validated this link by revealing a systematic hike in microporosity with synthesis temperature, and a near-complete loss above this threshold temperature.At the same time, experimental and theoretical studies detailed the topotactic interconversion of periclase and brucite in near in vacuo conditions, 16,17,38,39 as well as morphological transformations and thermodynamics in aqueous solutions. 33,40,41More recently, water films were even shown to drive aggregation of periclase nanocubes into nanobars, 3,42,43 a discovery that contributed greatly to ideas on crystal growth by (oriented) aggregation.Less remains, however, understood about mechanisms in nanometrically thin water films that can drive solution-like brucite formation, yet that are insufficiently thick to host vast pools of reactive species as in bulk water.Under these conditions, growth may be at first nucleation-controlled 44 while Mg 2+ /MgOH + species precipitate to brucite in water films (Fig. 1b).Growth may, however, become later diffusion-controlled 45 as brucite nanocoatings hamper the flux of reactive species to growth fronts 46 (Fig. 1c).
In this study, we offer new insight into the conversion of periclase by nanometrically thick water films, which were formed under environmental-relevant conditions of high humidity.This work fills a gap between previous efforts focused on low pressure/vacuum 16,17,20,38,39,47 and aqueous systems, 33,40,41 and by contrasting the reactivity of periclase nanocubes produced below and above the ∼600-650 °C threshold.We show that differences in nanocube size and microporosity have a direct impact on reaction yields and crystallization pressures during brucite growth.Our findings have direct implications in understanding water film-driven transformations of chemically and structurally related nanominerals (e.g.CaO, FeO).They also have broader implications for understanding mineral growth mechanisms under nanoconfinement.
In this study, Pe5 and Pe10 nanocubes were exposed to a flow of 90% Relative Humidity (RH) in N 2 (g) at 25 °C.This gas composition was generated using a proUmid MHG32 instrument.Reactions were monitored in situ by X-ray diffraction (XRD), vibrational spectroscopy and microgravimetry, and ex situ by electron microscopy, thermal gravimetry and X-ray photoelectron spectroscopy (ESI †).
X-ray diffraction
Crystalline phase transformations were monitored by powder XRD on Pe5 and Pe10 samples exposed to a 250 mL min −1 flow of 90%RH.X-ray diffractograms were acquired with a PANalytical X'Pert 3 powder diffractometer using an Anton Paar MHC-trans humidity chamber working in transmission.All diffractograms were collected within the 10-55°2θ range because of the inherent limitations of working in transmission geometry.The sample stage was aligned along the vertical using corundum powder as a standard.This procedure was conducted prior all experiments to ensure that diffraction peaks did not shift from a misplaced sample stage.Periclase samples were thereafter placed on small cups assembled with a thin Kapton® film at the bottom for incoming X-rays.These cups were then placed on the rotatable sample stage of the transmission chamber.The samples were first dried with N 2 (g) for 1 h, and their XRD profile acquired.The samples were then exposed to 90%RH over 40 h period while XRD profiles were recorded every 2 h.
Simulations of XRD profiles were performed using the Rietveld program BGMN® 48 with the GUI software of Profex v4.1.Structure control files were converted from reference structure files from the American Mineralogist Crystal Structure database 49 (0000501 for periclase 50 and 0007912 for brucite 51 ).Phase quantification by Rietveld refinement using the complete XRD profiles (10-55°2θ) revealed considerable variations from an abnormal (001) reflection of brucite.Because attempts at using a brucite model with a broken symmetry did not extract meaningful phase quantification results, we limited our Rietveld refinement to the 30-46°2θ range.This model converged to a stable solution with acceptable deviations (χ 2 ≤ 1.5) to the data.
The resulting time-resolved Rietveld refinement results were modeled using kinetic growth models 44 described in the ESI.† Briefly, an Avrami-type 52,53 model was used to predict nucleation-limited growth in water films, and a Shrinking Core Model 54 was used to predict diffusion-limited transport of reactive species to brucite growth fronts.These calculations were carried out using Matlab 2021b (The Mathworks).
Vibrational spectroscopy
Fourier transform infrared (FTIR) spectroscopy was used to monitor the surface hydration and hydroxylation of periclase to brucite.Thin dry periclase films were first formed by depositing, then drying, a centrifuged MgO-ethanol paste on the diamond window of an Attenuated Total Reflectance (ATR) cell (Golden Gate, a single bound diamond window).The resulting sample was then covered with a flow-through lid pressed on the ATR plate using an anvil.Liquid ethanol was thereafter removed from the paste using a stream of dry N 2 (g).Complete removal of ethanol was confirmed by tracking the loss of characteristic C-H stretching modes during drying.This procedure resulted in a packed solid-state film of periclase nanocubes on the ATR cell.Hydration and hydroxylation reactions were thereafter initiated by exposing the sample to 500 mL min −1 stream of 90%RH mixed with N 2 (g) for a period of up to 5 d.
All spectra were acquired at a resolution of 4 cm −1 over the 600-4500 cm −1 range at a forward/reverse scanning rate of 10 kHz.These were obtained by coadding 500 spectra for Pe5 (7.5 min acquisition time) and 1000 spectra for Pe10 (15 min acquisition time) using a Bruker Vertex 70/V instrument.This instrument was equipped with a deuterated L-alanine doped triglycine sulfate (DLaTGS) detector.
Imaging
To image reaction products, periclase powder was reacted in a flow-through reaction vessel to a stream of 90% RH mixed with N 2 (g) for a period of up to 48 h.Samples were imaged by Scanning Electron Microscopy (SEM) and bright-field Transmission Electron Microscopy (TEM).SEM images were taken on a Carl Zeiss Merlin microscope while a FEI Talos L120 microscope (120 kV) was used for low-resolution TEM images.High-resolution transmission electron microscopy (HRTEM) images were taken under cryogenic conditions (−90 °C) to minimize well-known effects of electron beam damage on magnesium hydroxides. 55,56These images were acquired with a FEI Titan Krios electron microscope equipped with a field emission gun operated at 300 kV and a K2 detector.
(Micro)Gravimetry
Water loadings acquired by Pe5 and Pe10 were determined by microgravimetry, using a DVS Advantage ET 2 instrument (Surface Measurement Systems).An aliquot of ∼10-20 mg periclase was first dried with N 2 (g) at 25 °C for 5 h.The weight of the resulting sample was then monitored in an 11-point adsorption isotherm from 0 to 95% RH, using an equilibrium period of 1 h at each preselected RH.In an additional experiment, Pe5 and Pe10 were exposed to 90% RH over a 40 h period.The reacted samples were then dried under N 2 (g) to determine the mass of the water film.The mass of Mg(OH) 2 produced by these reactions was also determined by Thermal Gravimetry Analysis (TGA) on samples reacted under the same conditions.Samples were thermally decomposed using a Metter-Toledo TGA instrument under a stream of 20 mL min −1 N 2 (g) from 30-700 °C, and at a heating rate of 10 °C min −1 .
Pe5 and Pe10 hydroxylation reactions were triggered by exposing the particles to a stream of 90% RH in N 2 (g) at 25 °C.Reactions were monitored in situ by XRD (Fig. 3a-c), vibrational spectroscopy (Fig. 3d-f ) and microgravimetry (Fig. 4).Particle morphological changes were then resolved ex situ by electron microscopy (Fig. 5).Finally, XRD provided insight into variable nanosheet stacking as brucite nanosheets grew in water films (Fig. 6).
Brucite growth triggered by three monolayer-thick water films
XRD captured hydroxylation reactions through the progressive loss of the primary (200) and (111) reflections of periclase, and by the appearance of the (011) and of brucite (Fig. 3a-c).To quantify the progress of the conversion reactions, we analyzed these main reflections by Rietveld refinement 57,58 (Fig. 3c).This analysis showed that the crystalline fractions of Pe5 and Pe10 reacted at identical rates in the first ∼8 h.Reactions in Pe10 however continued to progress at a slower rate than Pe5, reaching ∼85% conversion after 40 h.Pe5 was, on the other hand, fully converted only after ∼12 h of exposure to 90% RH.
Vibrational spectroscopy captured the formation of bulk brucite OH groups through the growth of a O-H stretching band, first appearing at ∼3701 cm −1 (Fig. 3d and e).Timeresolved band intensities, obtained by Lorentzian fitting (Fig. 3f ), showed that growth curves had comparable shapes to those obtained by XRD (Fig. 3c).The reactions were, however, slower because these measurements required MgO nanocubes in the form of packed thin solid-state films, rather than loose powders as in all other methods used for this work.From the progressive shift of this band to ∼3697 cm −1 , we infer that brucite OH groups formed stronger intersheet hydrogen bonds over time.These bonds were, however, not fully established, because only thermal treatment (Fig. S4 †) could shift the band to the characteristic vibrational frequency of crystalline brucite (3694 cm −1 ).This consequently indicated that brucite contained defects which, in the following sections, will be chiefly attributed to nanosheet dislocation. 16,17icrogravimetry (Fig. 4a) showed that periclase nanocubes exposed to 10-60%RH formed water films with steady coverages of up to 2 monolayers (MLs), at least within the first hour of reaction.Exposure to greater levels of humidity triggered, in contrast, an immediate and continuous uptake of water which signaled a rapid onset of the hydroxylation reactions.At 90%RH, reactions were triggered by ∼3 ML-thick films (Fig. 4b) and continued for up to 15 h for Pe5 and up to at least 40 h for Pe10 (Fig. 4b), in alignment with our Rietveld refinement results of the XRD data (Fig. 3c).We additionally find evidence that newly-formed brucite particles increased water film loadings over the course of the reaction.This was seen by microgravimetry through H 2 O : MgO ratios exceeding the expected (1 : 1) reaction stoichiometry (Fig. 3b), and by vibrational spectroscopy (Fig. 3d and S4 †) through the rise of the main water band (∼3300 cm −1 ).
Drying the films off the reacted particles showed that H 2 O : MgO reaction ratios were of only ∼0.85 for Pe5 and ∼0.75 for Pe10 (Fig. 4b).These results thus contrasted with reaction yields obtained by XRD (Fig. 3c).To understand the implications of these results, we thermally decomposed the reaction products back to MgO using TGA (Fig. 4c).These experiments showed that dehydroxylation recovered 100% of the weight of Pe5 and ∼80% of the weight of Pe10.Because these results matched reaction yields obtained by Rietveld refinement (Fig. 3c), we conclude that unreacted Pe5 and Pe10 contained non-stoichiometric OH groups.This conclusion was supported further by vibrational (Fig. S4 †) and X-ray photoelectron (Fig. S5 †) spectroscopic measurements of the unreacted materials.
Nucleation-vs. diffusion-controlled brucite growth
To explain the contrasting time-dependent reaction yields of Pe5 and Pe10 (Fig. 3c and 4b, c), we modeled our Rietveld refinement results (Fig. 3c) with a hybrid kinetic growth model taken from the solid-state catalysis literature (cf.ESI † for full details on the model). 44We predicted the early stages of growth using a nucleation-limited model to account for competing ingestion and merging of nucleation sites in the water films.Later stages of growth were, on the other hand, predicted using a Shrinking Core Model 54 to account for a diffusion-limited growth caused by the passivation of the reactive MgO core by brucite nanocoatings.Evidence for this passivating layer can also be appreciated by X-ray photoelectron spectroscopy (Table S2 †).These results showed that Pe10 surfaces were entirely hydroxylated although XRD (Fig. 3a-c) indicated that the reactions were not completed.As such, we liken these assemblages to a biphasic MgO@Mg(OH) 2 core-shell structure.
The sinusoidal portions of Pe5 and Pe10 at the onset of the reactions were best described using a Avrami-Erofeyev 52,53 model.This model ([−ln(1 − α)] 1/3 = k AE t; where α = [0,1] is reaction progress and t reaction time) described in terms of the competing ingestion nucleation sites and merging nuclei. 44It described the complete conversion (α = 0 → 1) for Pe5 and the partial conversion (α = 0 → 0.5) for Pe10 using a single growth constant (k AE = 6.6 h −1 ).To give additional perspective on this growth term in the context of water films, we note that a single Pe5 nanocube cannot completely dissolve into three monolayer-thick films (2.1 Mg 2+ per H 2 O).The sustained rates of conversion must have therefore relied on the continual capture of water vapor by newly formed brucite nanoparticles.Again, evidence for this capture was detected by microgravimetry (Fig. 4b) and by vibrational spectroscopy (Fig. 3d and S4 †).
The slower reactions in Pe10 after ∼4 h were predicted using a 3D Shrinking Core Model 54 (Fig. 1).To this end, we used the Carter-Valensi 59 adaptation of the Ginstling-Brounshtein model 60 v is molar volume) on the reaction rates (k VC ).The model predicts that diffusion-limited growth ( k VC R 2 = 230 h −1 nm 2 ) began after ∼4 h of reaction where ∼15% (α = 0.15) of the Pe10 transformed to brucite by nucleation-limited growth.We note that this level of conversion amounts to the consumption of the topmost ∼0.9 nm of the Pe10 surface, namely the equivalent of ∼5000 nm 3 of MgO.As this volume corresponds to about ten Pe5 nanocubes, we conclude that Pe5 was completely converted to brucite under the nucleationlimited regime.This also implies that brucite nanocoatings formed on Pe5 were insufficiently thick to hamper the flux of reactive species to brucite growth fronts.
Morphological changes and co-existing phases
To identify morphological changes undergone by the nanoparticles, we imaged reacted samples using electron microscopy (Fig. 5a-l).Inspection of the larger Pe10 nanocubes provided insight into the earliest stages of the dissolution reactions (Fig. 5g-i).These images revealed a progressive increase in nanocube roundness.This aligns with previous work 33,46,61 underscoring the thermodynamic drive for the conversion of the dominant (100) face to the (110) and (111) faces under hydration. 18,21,62,63These results thus support the idea that a preferential dissolution of the most reactive sites (e.g.nanocube corners and edges) triggered fluxes of Mg 2+ ions in the water film, inducing the first events of brucite nucleation and growth.It is even possible that these new faces, alongside related defects, became nucleation sites for hydroxylation reactions, or even entry zones for water diffusion into the periclase bulk.
Imaging of samples reacted over a period of 48 h revealed a progressive conversion of periclase nanocubes to brucite nanoflakes (Fig. 5f and l).Brucite growth from Pe5 nanocubes (Fig. 5a-f ) was chiefly limited to the confines of the embedding hexagonal particles.Growth thereby occurred within the microporous interstices of aggregated Pe5 nanocubes/nano-bars, as illustrated in Fig. 5m.In contrast, growth from Pe10 extended well beyond the sizes of the original nanocubes (Fig. 5g-l).This implies that a network of water films secured the flux of soluble Mg 2+ species from different periclase particles to brucite growth fronts, such as represented in Fig. 5n.
Finally, to directly identify mineralogical phases by imaging, we turned to High-Resolution TEM (HRTEM).Cryogenic conditions minimized risks for electron beam damage. 55Imaging of reacted Pe10 (Fig. 5o) revealed spatially resolved lattice fringes from co-existing periclase (Region 2) and brucite (Regions 1) particles.Both Regions 1 and 3 contained a range of lattice fringes (4.5-6.0Å) with the lowest value close to the expected d 001 -spacing value of brucite.In contrast, the larger values indicated that brucite contained various configurations of interstratified nanosheets.These findings consequently align with our vibrational spectra (Fig. 3e, f and S4 †), and with previous imaging work, 16,17 revealing weak intralayer bonding in dislocated brucite nanosheets.In the following section, we establish a link between these lattice fringes and our XRD measurements.
These two peaks also grew in parallel with another set of reflections at 14-15°2θ (Fig. 6e and f).These reflections indicate d 001 -spacing values in the 5.91-6.33Å range, and therefore correspond with lattice fringes seen by cryogenic HRTEM (Fig. 5o).Shifts in peak position over reaction time also revealed that these spacing values shrank (6.27 → 5.82 Å) as spacing values from the main (001) reflection expanded (4.48 → 4.53 Å).As these spacings were not sufficiently large to accommodate intercalated water (d 001 + 2r H 2 O = 4.82 Å + 2.80 Å = 7.62 Å; where r H 2 O is the radius of a water molecule), we conclude that the 14-15°2θ reflections arose from unresolved interstratified layers, and that these dynamically changed during the course of the reactions.Transient mixed oxyhydroxide (Mg x+y O x (OH) 2y ) intermediates, formed by water diffusion into the periclase bulk, 17 could have also partially contributed to these results.
We can explain the uncharacteristically low d 001 -spacing values if high crystallization pressures were achieved during the reactions.This idea was already conveyed and Braun 32 who, in the 1960s, assigned a similar value (4.578 Å) to brucite grown under comparable conditions.Referring to pressure-resolved d 001 -spacing values 64,65 published decades after that study, we infer crystallization pressures of ∼4 GPa could have been achieved during brucite growth.
This interpretation aligns with thermodynamic predictions 12,25 for GPa-level crystallization pressures, and with our observation that removing the water film (Fig. S8 †) shifted d 001 -spacings of reacted materials to low-pressure values.Whereas previous studies 12,25 did show that reactions in compacted materials can stop at MPa-level pressures because water films are squeezed from the intergrain boundary, we can explain our findings the inherently large (26 μL g −1 ) microporosity of Pe5 nanocubes (Fig. 2b and c) sustained GPa-level pressures by retaining the network of water films.This was also the case for a minor portion of Pe10, which could be explained in terms of surface microporosity.These results consequently highlight the singular ability of synthetic periclase nanocubes, especially those of Pe5 aggregated in a 2D mazelike microporous network, to host high pressure reactions.
Conclusions
Two types of partially hydroxylated periclase nanocubes of contrasting size and microporosity provided an opportunity to explore the water film-driven nucleation-and diffusion-limited transformations to brucite nanosheets.Growth was triggered by three monolayer-thick water films, and autocatalyzed as water films grew onto newly formed brucite nanosheets.Nucleation-limited reactions initiated brucite growth, and completely converted (8 nm-wide) Pe5 nanocubes.Reactions however transitioned to a diffusion-limited growth regime in the larger (32 nm-wide) Pe10 nanocubes.Establishement of a biphasic MgO@Mg(OH) 2 core-shell structure hampered the flux of species to growth fronts.Additionally, the microporous network between aggregated Pe5 nanocubes and pores at Pe10 surfaces hosted GPa-level crystallization pressures that compressed brucite interlayer spacings during growth.These interlayer spacings however expanded back to ambient pressure values once water films were removed.
By resolving brucite growth in terms of concurrent nucleation-and diffusion-limited regimes, our work unveiled important differences caused by nanoparticle formation history on the composition and structure of reaction products.Because water films are important drivers of mineral alteration in nature and technology, consideration of these findings will be needed in studying nanomineral transformations in areas including atmospheric chemistry, catalysis, electrochemistry, geochemistry, and surface science.Considerations of these findings can even apply to broader aspects of material alteration and crystal growth by nanometric water films.This includes structurally-related materials (e.g., CaO, FeO) as well as, more generally, transformations under nanoconfinement (e.g., nanopores) in minerals (e.g., clays, zeolites) or other materials of technological interest (e.g., metal-organic frameworks, carbon nanotubes).
Fig. 2
Fig. 2 Periclase nanocube morphology and size.Electron microscopy images of (a-d) Pe5 and (f-i) Pe10, alongside (e and j) corresponding schematic representations of typical particles.Scanning Electron Microscopy (a and f ) and Transmission Electron Microscopy revealed (b and c) Pe5 nanocubes clustered as nanobars in hexagonal casings, which are relicts of the synthetic brucite from which they were produced.Arrows in (c) highlight preferential arrangement of the ∼8 nm wide Pe5 nanocubes into nanobars in a fashion aligning with previous work. 42,43(g and h) Pe10 nanocubes were monodispersed.(d and i) High Resolution Transmission Electron Microscopy revealed lattice fringes expected from the crystallographic structure of periclase.See Fig. S3 † for information on area and microporosity.
Fig. 3
Fig. 3 XRD and vibrational spectroscopic evidence for brucite growth from periclase in nanometric water films.Pe5 and Pe10 samples were exposed to a flow of N 2 (g) with 90% RH at 25 °C over time.(a and b) Time-resolved X-ray diffractograms of (a) Pe5 and (b) Pe10 revealing the transformation of periclase (Fm3 ¯m space group) to brucite (P3 ¯m1 space group).(c) Converted fraction (α) of Pe5 and Pe10 resolved by Rietveld refinement of data in (a) and (b) over a 40 h reaction period.Curves were generated with the Avrami (nucleation-controlled) and Ginstling-Brounshtein (diffusion-controlled) models (ESI †).(d and e) Vibrational spectra of Pe5 during the reactions, revealing concomitant growth of brucite (two bands >3600 cm −1 ) and water films (∼3300 cm −1 ).(e) Background-corrected main band of brucite showing a progressive shift of the bulk O-H stretch from 3701 to 3697 cm −1 .The black full line denotes spectrum synthetic brucite used to produce Pe5.The dashed line shows the spectrum of crystalline brucite.(f ) Lorentzian fitting of the 3680-3720 cm −1 region of (e) for Pe5 (cf.Fig. S4d † for Pe10) showing comparable shapes of growth curves (intensity) as in (c) XRD as well as shifts in band position.Note that differences in sample preparation (loose MgO powders by XRD and solid MgO state films by vibrational spectroscopy) explain the contrasting reaction times between the two techniques.
Fig. 4 Fig. 5
Fig. 4 Gravimetric tracking of periclase hydroxylation dehydroxylation.(a) Microgravimetrically-measured water loadings by water vapor from 0.9 to 92% RH at 10% RH intervals, each with a reaction time of 1 h.The right-hand side of (a) is a size-scaled schematic representation of the total equivalent water films thickness in relation periclase nanocube size.One water monolayer (ML) corresponds to 12 H 2 O per nm 2 .(b) Time-resolved water uptake at 95% RH by microgravimetry.Periclase was covered by a 3 ML-thick water film at the onset of the reaction.Water mass increases were driven by hydroxylation reactions and water film growth on newly formed brucite nanoparticles.Removal of water films by drying after 40 h revealed the reaction of 85% of Pe5 O groups and 75% of Pe10 O groups.(c) Thermogravimetric analysis (TGA) of brucite dehydroxylation after exposing Pe5 and Pe10 under 95% RH for 40 h.The full reconversion of Pe5-derived brucite (100% by XRD, Fig.3c) showed that 15% of Pe5 was originally hydroxylated because (b) microgravimetry revealed 85% conversion.The 80% reconversion of Pe10-derived brucite (80% by XRD) (Fig.3c) showed that 5% of Pe10 was originally hydroxylated because microgravimetry (b) revealed 75% conversion.Spectroscopic evidence for OH groups on Pe5 and Pe10 is provided in Fig.S5and S6. †
Fig. 6
Fig. 6 XRD (001) reflections of brucite over time (a and b) Brucite (001) reflections from time-resolved X-ray diffractograms of Fig. 3 for (a) Pe5 (orange) and (b) Pe10 (blue), highlighting dominant reflections appearing as periclase is exposed to 90% RH for 40 h.Lorentzian fitting parameters of all reflections (Fig. S7 †) are shown as (c and e) peak position (2θ) and corresponding d 001 -spacing and (d and f ) peak intensity. | 6,178.2 | 2023-05-16T00:00:00.000 | [
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Production of Kudzu Starch Gels with Superior Mechanical and Rheological Properties through Submerged Ethanol Exposure and Implications for In Vitro Digestion
Producing starch gels with superior mechanical attributes remains a challenging pursuit. This research sought to develop a simple method using ethanol exposure to produce robust starch gels. The gels’ mechanical properties, rheology, structural characteristics, and digestion were assessed through textural, rheological, structural, and in vitro digestion analyses. Our investigation revealed an improvement in the gel’s strength from 62.22 to178.82 g. The thermal transitions were accelerated when ethanol was elevated. The exposure to ethanol resulted in a reduction in syneresis from 11% to 9.5% over a period of 6 h, with noticeable changes in size and color. Rheologically, the dominating storage modulus and tan delta (<0.55) emphasized the gel’s improved elasticity. X-ray analysis showed stable B- and V-type patterns after ethanol exposure, with relative crystallinity increasing to 7.9%. Digestibility revealed an ethanol-induced resistance, with resistant starch increasing from 1.87 to 8.73%. In general, the exposure to ethanol played a crucial role in enhancing the mechanical characteristics of kudzu starch gels while simultaneously preserving higher levels of resistant starch fractions. These findings have wide-ranging implications in the fields of confectioneries, desserts, beverages, and pharmaceuticals, underscoring the extensive academic and industrial importance of this study.
Introduction
Hydrogels are characterized as polymer networks that are hydrophilic and threedimensional in nature.They possess a notable capacity to absorb and retain significant amounts of water or biological fluids.Their high water retention capacity, coupled with their inherent softness and flexibility, opens up numerous potential applications across various fields [1,2].Within the food industry, hydrogels encompass a wide range of substances that span from fully developed products to unprocessed components utilized in the production of novel food derivatives [1].In the specific context of confectioneries (gummy candies), beverages (bubble teas), and gel-based desserts (panna cottas), the pressing need for hydrogels with consistent rheological and textural properties has become paramount to ensure optimal product quality and consumer satisfaction.Moreover, such hydrogels effectively encapsulate active ingredients, including antimicrobials and antioxidants, further elevating the general quality of the products [3,4].
Despite their promise, hydrogels' poor mechanical and rheological properties frequently hinder their widespread industrial application.This shortcoming is generally Foods 2023, 12, 3992 2 of 17 linked to imperfections in the cross-linking process, leading to an inconsistent structural network.Moreover, inadequate energy dissipation mechanisms contribute to their poor resistance to mechanical stress and strain [5,6].Thus, the need for the development of hydrogels with enhanced mechanical properties for diverse applications, including food and non-food products, is evident.
Scientists have been innovative in addressing these challenges, exploring structural designs and energy dissipation systems and incorporating techniques such as post-gelation treatments [7,8].Post-gelation exposure to solutions containing ions or cross-linking agents has emerged as a relatively simple and efficient approach.The application of this treatment results in the initiation of dehydration, reorganization of the structure, and transfer of constituents within the hydrogel, ultimately resulting in the formation of a resilient network.
The aforementioned procedure has the potential to increase the crosslinking density, thereby resulting in enhanced mechanical and rheological properties [2,8].
Ethanol, a solvent that is semi-polar, water-miscible, and innocuous, presents an intriguing solution following the process of gelation.The dehydration and structural reconfiguration capabilities have the potential to enhance the internal molecular strength of the hydrogel [2,9].Nevertheless, the effectiveness of this procedure relies on specific factors including the concentration of ethanol, duration of exposure, and the specific natural biomolecules being targeted.Notably, higher ethanol concentrations induce changes in solubility and increase tensile strength in hydrogels.It is suggested that the molecular exchange in gels in the presence of ethanol can enhance the internal network chains, inducing retrogradation and thus improving the mechanical and rheological properties of hydrogels [9,10].
There has been a recent focus on starch, an essential polysaccharide found in biopolymerbased hydrogels, due to its biocompatibility, biodegradability, and significant biological functionality [3,11].In particular, kudzu (Pueraria lobata) starch [12], with its distinctive characteristics, shows promising gel properties [13].However, like many physically synthesized gels, kudzu starch gels commonly lack the desired mechanical strength and exhibit suboptimal rheological performance.The aforementioned properties could be greatly improved through the utilization of the innovative and expeditious post-gelation ethanol-exposure technique [1,8].
Nonetheless, the effects of alcohol-exposure techniques go beyond the mere physical characteristics of the gel.Potential health implications may arise from alterations in starch digestibility, specifically in relation to blood glucose levels, glycemic response, gut health, and weight management [14].Therefore, the implications of ethanol exposure on the in vitro digestion characteristics of kudzu starch gels are also worth investigation.Currently, there is a lack of documented research examining the effects of ethanol exposure as a gelimproving approach on the mechanical, rheological, and in vitro digestion characteristics of kudzu starch gels.The objective of this study is, therefore, to evaluate the effects of post-gelation ethanol treatment on the mechanical properties, rheology, and the in vitro digestibility of kudzu starch gels.The findings from this research could enhance the value of kudzu starch gel and facilitate its broader application within the food industry specifically, in confectioneries, gel-based desserts, beverages, and edible nutritional pharmaceuticals.
Kudzu Starch Gel Formation
Kudzu starch was extracted from the roots following a conventional starch extraction method [14].A 25% (w/v) starch suspension was prepared from the extracted starch and gelatinized at 90 • C for 30 min, with regular stirring.The resultant gel was poured into a 10.0 mL cylindrical mold and allowed to set at room temperature.Subsequently, the gels were immersed in ethanol solutions of varying concentrations (30%, 60%, 80%, and 100%).The set-up of gel immersed in alcohol solution was allowed to stand at room temperature over varying periods of 2, 4, and 6 h for each concentration.For comparison, a control sample was prepared with the same gelling approach without ethanol exposure but kept at 4 • C for 12 h.After the designated periods, samples were appropriately removed and kept for further analysis.
Gel Syneresis, Size, and Color Characteristics
Sample gels after ethanol exposure were stored at 4 • C for 24 h, thawed, and centrifuged at 5000× g for 15 min.The amount of water released from the gel was weighed and used to calculate syneresis degree, expressed as a percentage of the initial gel weight [15].The size of the gels exposed to ethanol were measured and reported as volume (cm 3 ) using Equation (1).The color of gels was also assessed following the method used by Ekumah et al. [16].The C.I.E.LAB color parameters (lightness (L*), redness (a*) and yellowness (b*) of the samples) were measured using the HunterLab ColorQuest XE Spectrophotometer (Hunter Associates Laboratory, Reston, VA, USA).
Mechanical Properties
The determination of the mechanical properties of the gels were achieved using a texture profile analyzer (TA.XT plus, StableMicro Systems, Surrey, UK) equipped with a 0.5 inch probe (p 0.5) after calibrating it with a 1 kg load.The test speed and compression strain were set at 1 mm/s and 75%, respectively.The hardness (g), springiness, chewiness, and resilience data were then recorded [9].
Rheological Properties
The starch gel's rheological characteristics were evaluated using a DHR-1 rotation rheometer (TA instruments-Waters, Shanghai, China), equipped with a 40 mm diameter parallel plate and a gap of 1.0 mm.The apparent viscosity was studied across a shear rate ranging from 0 to 300 s −1 .Measurements were taken for the elastic modulus (G ), viscous modulus (G ), and loss tangent (Tan δ) based on the angular frequency (ω) spanning from 0.1 to 100 rad/s, ensuring a 2% strain within the linear viscoelastic domain.Modeling of the rheological properties was achieved by fitting the curve to the power model, Equation (2) [17].
Scanning Electron Microscopy (SEM)
The morphological characteristics and microstructure of starch gels were evaluated using scanning electron microscopy (SEM) according to Ahmad et al. [18].Freeze-dried starch gel samples were loaded into an aluminum stub using double-sided adhesive carbon tape.The sample photographs were taken using a JSM-7001F SEM apparatus (JEOL USA Inc., Peabody, MA, USA) at an accelerating potential of 15 kV.
X-ray Diffraction (XRD)
The X-ray diffractometer (D2 PHASER, Bruker, Germany) at 40 kV and 30 mA with Cu-Ka radiations was used to determine the crystallographic structural characteristics of the starch gel samples.The X-ray diffraction profile was obtained for 2θ from 5 • to 40 • with a step size of 0.02/min.The Origin software (Version 19.0, Microcal Inc., Northampton, MA, USA) integrated the amorphous and crystalline areas, while the relative crystallinity was estimated from Equation (3) as described by Zhang et al. [19].
Fourier Transform Infrared Spectroscopy (FTIR) Analysis
The chemical and structural configuration of sample starch gels was evaluated using attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR) (Nicolet iS10, Thermo Electron Inc., Waltham, MA, USA) following procedures reported by Wu et al. [20].In summary, the freeze-dried powdered starch gel samples were directly loaded onto the detection platform and scanned at a resolution of 4 cm −1 .The spectra ranging from 4000 to 400 cm −1 were recorded three times for each sample in transmission mode and evaluated by Origin software (Version 19.0, Microcal Inc., Northampton, MA, USA).
Differential Scanning Calorimetry (DSC)
The thermal properties of the starch gels were determined by differential scanning calorimetry (DSC) using a differential scanning calorimeter (DSC-60, Shimadzu, Singapore) as per the method described by Ahmad et al. [18].A sample of dried starch gel (3 mg) was weighed in the aluminum pans and mixed with water in a ratio of 1:3.The pans were sealed and allowed to stand for 12 h at 4 • C for moisture equilibration.The samples were then scanned from 25 to 120 • C at 10 • C/min.The equipment was calibrated with indium, and an empty sealed pan was used as a reference for all experiments.The onset temperature (To), peak temperature (Tp), conclusion temperature (Tc), and gelatinization temperature range (Tc-To) were noted from the graphs.The enthalpy of gelatinization (∆H) was estimated by integrating the area between the thermograms and a baseline under the peak and reported as joules per gram of dry starch gels.
In Vitro Digestibility
The in vitro digestion of starch gels was achieved following the INFOGEST static in vitro simulated gastrointestinal digestion method [21].Briefly, a 5 g starch gel was mixed with 5 g Simulated Salivary Fluid (SSF), Table 1; 75 U/mL salivary amylase was achieved by adding 3 mL of the enzyme and pH was adjusted to 7 with NaOH (1.0 M).The mixture was then incubated at 37 • C for 2 min amidst agitation.The resultant oral bolus was subsequently mixed with an equal volume of Simulated Gastric Fluid (SGF) (Table 1) to attain a final ratio of 1:1 (v/v).The pH was adjusted to 3.0 with HCl (1.0 M) and incubated at 37 • C for 2 h with agitation.Furthermore, the chyme from the gastric digestion was mixed with an equal volume (1:1 v/v) of SIF preheated at 37 • C. The pH was adjusted to 7.0 by adding NaOH (1.0 M).Bile salt (10 mM) was added, followed by pancreatic alpha-amylase (200 U/mL).The set-up was incubated for 2 h at 37 • C in a shaking incubator.Finally, the digested product was centrifuged at 14,000× g for 15 min to collect the transparent supernatant for DNS analysis, to determine the digestible, as well as the pellet for the determination of resistant starch proportion of the gels.
Statistical Analysis
All samples were analyzed in triplicate, and the results were presented as means and standard deviations.A one-way analysis of variance (ANOVA) was used to compare means while Tukey test was used to study the significant differences between the mean values at p < 0.05.Pearson's correlation analysis was also used to find the correlation between the factors evaluated.All the analyses and graphs were achieved using Origin (Version 2019, Microcal Inc., Northampton, MA, USA).
The Textural Characteristics of Kudzu Starch Gels
The control exhibited the lowest values for all measured parameters, as shown in Table 2.The study additionally demonstrated that exposure to ethanol, even at low concentrations, resulted in a statistically significant increase in the hardness of the gels, regardless of the duration of exposure [2].However, as the concentration of ethanol increased, the hardness of the gels increased across all exposure durations, with the 100% ethanol at 6 h marking the highest at 178.82 g.This implies that ethanol-induced changes in the structure of starch resulted in increased resistance, likely due to a mechanism involving the removal of water through ethanol dehydration [7,8].Similarly, with an increase in ethanol concentrations, there was a corresponding increase in springiness across all parameters.The sample subjected to 100% ethanol concentration over a 6 h interval reached a springiness of 1.01.This data suggests an augmentation in the molecular elasticity of the starch gel matrix post ethanol treatment, enhancing its ability to recover after deformation.Such enhanced recovery properties can have a profound advantage in foods, especially in gummy confectioneries and food nutrient delivery agents, driving innovation in texture, consistency, and functional benefits.Furthermore, the resilience exhibited similar trends as those observed in springiness.The observation indicates that kudzu starch gels treated with ethanol exhibit enhanced energy dissipation properties, thereby reducing the occurrence of permanent deformation when subjected to external forces.This characteristic is lacking in numerous natural biopolymer hydrogels [5,8,10].Furthermore, the patterns displayed in resilience closely mirrored those seen in springiness, possibly due to their interconnectivity supported by a positive correlation (r = 0.795).From the control (61.31), the value peaked at 91.15 with 100% ethanol for 6 h, indicating superior energy dissipation in ethanol-treated gels as observed in a similar study by Sun et al. [2].With the enhancement in the ethanol-treated kudzu starch gel's energy dissipation, they appear to be more durable and will resist degradation when packaged and stored, which could extend shelf life due to enhanced structural stability.The chewiness exhibited a rise in value with ethanol concentration, especially over extended durations.The 6 h, 100% ethanol sample reached 79.89, corroborating the report by Lin et al. [6].Utilizing these gels as kudzu gel cubes and pearls in beverages like bubble tea and whole milk becomes notably ideal, delivering a conspicuously chewy mouthfeel.The substantial implication here is the possible increase in resistance to masticatory forces.The evident increase in chewiness and resultant resistance to forces imply that the mouth-feel experience in beverages and snacks will remain consistent throughout consumption.This uniformity from the first to the last bite can elevate the overall eating and drinking experience, making it particularly pertinent for the food and beverage industry.Consequently, the data presented in Table 2 clearly demonstrated that kudzu starch gel properties were influenced by both ethanol concentration and exposure time in a synergistic manner.Specifically, longer durations of exposure amplified the impact of ethanol on the kudzu starch gels.
Thermal Properties of the Kudzu Gels
Table 3 shows the effects of the ethanol concentrations and exposure time on the thermal properties of the starch gels.The data in the table reflects significant variances in thermal properties with changing ethanol concentrations and exposure time.A clear trend observed is the fluctuation of onset, peak, and conclusion temperatures (T o , T p , T c ) and gelatinization enthalpy (∆Hg) as ethanol concentration and exposure time changed.This implies that the interaction of intrinsic factors, such as slight variations in crystallinity (Table 3) and the reconfiguration of the gel network, played a role in the transition, in addition to the concentration of ethanol and the duration of exposure [22].For control samples (0% ethanol), the onset temperature (T o ) was 45.32 • C, peak temperature (T p ) was 53.92 • C, and conclusion temperature (T c ) was 66.92 • C.This finding corroborates the findings of Sun et al. [2], which propose that untreated physically crosslinked gels possess advantageous properties for the delivery of heat-sensitive bioactive compounds [23].Moreover, with an increase in ethanol concentration, the treated samples exhibited fluctuating onset, peak, and conclusion temperatures, without a discernible trend towards an increase.The T c -T o narrowed; notably, the 100% ethanol sample at 6 h (16.53-53.53• C) was 6.52 • C, the smallest value recorded, indicating that the thermal transition became quicker as ethanol concentration increased.This observation may indicate a heightened rate of thermal transition at elevated ethanol concentrations.The aforementioned attribute is highly sought after in the industrial sector, as it serves as a crucial factor in determining the level of energy utilized during the ethanol-based kudzu gel processing [2,10,12].
Furthermore, the gelatinization enthalpy (∆Hg) varied with changes in ethanol concentration and exposure time.The highest ∆Hg was observed for 100% ethanol concentration at 2 h (2.97 J/g).This could be attributed to the improved cohesion and internal strength conferred on the gel with ethanol exposure irrespective of the exposure time [5,6].This high ∆Hg compared to the control signifies a robust matrix directly influencing gel's reactions to external stimuli.Essentially, a starch gel of this nature demonstrates enhanced stability against challenges such as thermal fluctuations, applied pressure, and the presence of chemical additives [3].The results of the study indicate that the thermal properties of starch gels are notably affected by both the concentration of ethanol and the duration of exposure.These findings have important implications for the stability and texture of the gel.
Gel Syneresis, Size, and Colorimetric Properties
Gel production that deviates from the traditional production route towards improving its quality characteristics has the potential to affect the syneresis, gel size, color, and general appearance.As presented in Table 3, the analysis of syneresis in starch gels exposed to varying concentrations of ethanol over different time intervals provides an understanding of ethanol's role as a modulating agent in starch-based systems [15,24].Starting with the control group, a natural decline in syneresis from 11% to 9.5% over 6 h suggests that the gel matrix undergoes dehydration and maturation, leading to better matrix stability [24,25].The observed decrease in gel properties was found to be more pronounced as the ethanol concentration increased, providing further evidence for the influence of soaking duration on the enhancement of cross-linking properties in the gel [26].Moreover, the data demonstrates a consistent reduc-tion in syneresis with increasing ethanol concentration.This suggests that ethanol may act as a plasticizer, enhancing the mobility of polymer chains and consequently improving the capacity to dissipate energy when subjected to stress [15,27].This observation is in line with previous studies which indicate that solvents can alter the swelling behavior of biopolymer networks, although the specifics of rate and degree of syneresis reduction appear to be novel and warrant further investigation [2,8].These findings may hold substantial significance for industries that require gel matrixes with a stable texture and low moisture content.This is particularly relevant for confectioneries and certain pharmaceutical applications designed for the delivery of essential minerals and nutrients [1,24].
In Figure 1, a pictorial representation of gel size (A), the measured gel sizes in volume (B), and the mean color values of the CIELAB color parameters were presented.According to Figure 1A,B, gel size in volume (cm 3 ) decreased as ethanol concentration increased.Within 2 h, gel size shrank from 8.0 cm 3 in controls to 6.3 cm 3 at 100% ethanol.By 6 h, it compressed further to 6.2 cm 3 .Ethanol's solvent nature possibly reconfigured the gel network, causing this shrinkage.This aligns with prior research demonstrating solvents' effects on gel structures [28][29][30].In addition, it has been shown that ethanol has the potential to initiate syneresis, a phenomenon that is supported by a significant connection (r = 0.746; Table 4) between the occurrence of syneresis and the size of the gel.In terms of color (Figure 1C), the 'L*' value decreased with rising ethanol levels, suggesting darkening gels.For instance, the control had 'L*' value of 65.4 drops to 53.1 at 100% ethanol.Both 'a' and 'b' values fluctuated: the 'a*' value increased to 5.6, and 'b*' peaked at 7.3 at 80% ethanol, denoting shifts in color.Such color variations could be due to ethanol's interaction with the gel matrix, a phenomenon seen in food gels [30,31].Correlations between 'b*' and syneresis (r = 0.653) and between gel size and 'a*' (r = 0.545) highlight the intertwined nature of these attributes.The manipulation of ethanol concentration and exposure time has a significant impact on the structural and aesthetic characteristics of gels, thereby offering a promising opportunity for optimizing gels in industrial applications.
Rheological Properties
The rheological data presented in Figure 2 showcased variations in rheological parameters, with a clear decline in viscosity as shear rate increases, highlighting the starch gel's shear-thinning behavior (Figure 2D-F).Roux et al. [29] attribute this to starch molecule realignment under shearing.It could be inferred that ethanol enhances the gel matrix's fluidity, promoting starch realignment.Over time, ethanol interactions may concentrate the gel, increasing resistance at low shear rates and accentuating shear-thinning at higher rates due to matrix disruption.Furthermore, the power law model was employed to characterize the shear thinning behavior, and the results are detailed in Table 2 with R 2 > 0.95 for all samples.This could suggest that models could be use in the process optimization and consistent production of mechanically stable kudzu starch gels.Furthermore, the rheological characteristics, particularly related to the viscoelasticity of the kudzu starch gels, Foods 2023, 12, 3992 9 of 17 reveal their structural and functional dynamics under varied ethanol conditions [2].Our study's Tan δ values, consistently below 0.55, signify a predominantly elastic nature.The control's Tan δ values, which ranged from 0.26 to 0.44, further corroborate this observation.Such low values emphasize and affirm a sturdy and robust gel network.The exposure to ethanol over time, however, introduced a slight plasticizing effect that increased the Tan δ values.Nonetheless, values were still within an appreciable elastic domain [2].This trend is reminiscent of findings in earlier research, where low Tan δ values have been frequently associated with a robust gel network [8,28].Nevertheless, the increasing Tan δ values with prolonged ethanol exposure underscore a diminishing elasticity, likely due to ethanol's interference with the intricate network of the starch gel, reducing its size and elastic nature.ethanol, denoting shifts in color.Such color variations could be due to ethanol's interaction with the gel matrix, a phenomenon seen in food gels [30,31].Correlations between 'b*' and syneresis (r = 0.653) and between gel size and 'a*' (r = 0.545) highlight the intertwined nature of these attributes.The manipulation of ethanol concentration and exposure time has a significant impact on the structural and aesthetic characteristics of gels, thereby offering a promising opportunity for optimizing gels in industrial applications.Examining the relationship between the storage modulus (G ) and the loss modulus (G ) reveals their crucial distinction.A consistent G greater than G throughout the experimental angular frequency indicates the gel's dominant elastic behavior.Interestingly, the elevation of G with increasing ethanol concentration and exposure time suggests that, while ethanol disrupts the gel network (as inferred from Tan δ values), it might simultaneously be inducing a structural reorganization or densification in the gel matrix.This behavior, where G rises with solvent concentration or exposure time, has been observed in other polysaccharide systems exposed to different solvents [9,28].For industries, understanding these subtle changes is crucial since modulating ethanol concentration offers a tool to modify the textural properties of starch-based hydrogels.Enhanced gel strength can elevate food texture and appeal while affecting product delivery in pharmaceuticals or cosmetics; thus, our results hold both academic and industrial significance.
Scanning Electron Microscopy
The Scanning Electron Microscope (SEM) offers an in-depth visualization of the microstructural changes in materials, including starch gels.When kudzu starch gels were exposed to varying concentrations of ethanol and for increasing time duration, several microstructural alterations were observed.Figure 3 shows the SEM images of the internal morphology of the freeze-dried starch gels.All samples exhibited typical porous three-dimensional network structures, with the control gel having the largest and open microstructures, while that of the ethanol-exposed gels reduced with increasing ethanol concentration.The flaky surface of the control gel (Figure 3A) exhibited a loose microstructure with comparably larger air spaces.Post ethanol exposure, however, the pore wall structure of the starch gels became densified with an apparent reduction is pore space (Figure 3B-E).This corresponded with the gel size reduction with ethanol and increasing exposure time.The phenomenon might have been caused by the osmotic pressure of the alcohol, and this might have increased the packing density of the starch polymer chains [8,30,31].The starch gel pore walls in Figure 3B-D were relatively flat and smooth with decreasing holes as the concentration of ethanol increased.The 100% ethanol exposure (Figure 3E) typically revealed a highly reduced microstructure with smooth surfaces.According to Zheng et al. [8], ethanol dehydrates the gel at high concentration by removing bound and free water, compacting its microstructure and causing it to partially collapse, resulting in smoother surfaces.Additionally, ethanol being polar in nature interacts with starch gel's network, disrupting and reorganizing the gel matrix, leading to a denser, smoother structure [2,8].Examining the relationship between the storage modulus (G′) and the loss modulus (G′′) reveals their crucial distinction.A consistent G′ greater than G′′ throughout the
X-ray Diffraction Analysis
The diffractive peak values are significant for understanding the structural changes in materials when exposed to various conditions relying on their A-, B-, or C-type crystallinity pattern [32].Here, Fig. 4 presents the diffractive peak values of kudzu starch gel with and without ethanol exposure over different time intervals.The gels without ethanol exposure exhibited peaks at 15.33°, 16.75°, and 17.82°, showing the typical diffraction pattern of a B-type structure [9,33,34], with a more hydrophilic configuration typical of root and tuber polysaccharides.In addition, the starch gel had an apparent peak at 23.00°, which exemplifies a typical V-type structure exhibited by macromolecules that has undergone heating and subsequent retrogradation.Therefore, the control starch gel was characterized by a B-and V-type structure.Comparably, the gel samples exposed to ethanol had characteristic peaks like the control at 15.33°, 16.75°, 17.89°, and 23°, thus indicating a typical B-and V-type structure, suggesting both the regular B-type crystallinity and a heat-and water-interaction-driven V-type configuration.Therefore, with the subtle change in peak values, the crystalline type of starch gel did not change after ethanol exposure.This observation in kudzu starch gel aligns with finding in similar solvent-exposed polysaccharide studies [35,36].
The relative crystallinity (Table 3) of the starch gels with and without ethanol exposure was calculated with diffractograms.The crystallinity value of the control kudzu starch gel remained stable at 4.7 across all time points (2, 4, and 6 h), highlighting the consistent crystalline nature of the starch gel in the absence of ethanol.Concurrently, as the ethanol concentration rises, a distinct trend of increasing crystallinity values emerged, with each time frame showing a progressive increase in crystallinity from 30% to 100% ethanol concentration.Additionally, each ethanol concentration demonstrates a timedependent augmentation in crystallinity from 2 to 6 h.The crystallinity of the non-ethanolexposed starch gel was the lowest at 4.7%.Starch gels exposed to ethanol showed an
X-ray Diffraction Analysis
The diffractive peak values are significant for understanding the structural changes in materials when exposed to various conditions relying on their A-, B-, or C-type crystallinity pattern [32].Here, Fig. 4 presents the diffractive peak values of kudzu starch gel with and without ethanol exposure over different time intervals.The gels without ethanol exposure exhibited peaks at 15.33 • , 16.75 • , and 17.82 • , showing the typical diffraction pattern of a B-type structure [9,33,34], with a more hydrophilic configuration typical of root and tuber polysaccharides.In addition, the starch gel had an apparent peak at 23.00 • , which exemplifies a typical V-type structure exhibited by macromolecules that has undergone heating and subsequent retrogradation.Therefore, the control starch gel was characterized by a B-and V-type structure.Comparably, the gel samples exposed to ethanol had characteristic peaks like the control at 15.33 • , 16.75 • , 17.89 • , and 23 • , thus indicating a typical B-and V-type structure, suggesting both the regular B-type crystallinity and a heat-and water-interaction-driven V-type configuration.Therefore, with the subtle change in peak values, the crystalline type of starch gel did not change after ethanol exposure.This observation in kudzu starch gel aligns with finding in similar solventexposed polysaccharide studies [35,36].
The relative crystallinity (Table 3) of the starch gels with and without ethanol exposure was calculated with diffractograms.The crystallinity value of the control kudzu starch gel remained stable at 4.7 across all time points (2, 4, and 6 h), highlighting the consistent crystalline nature of the starch gel in the absence of ethanol.Concurrently, as the ethanol concentration rises, a distinct trend of increasing crystallinity values emerged, with each time frame showing a progressive increase in crystallinity from 30% to 100% ethanol concentration.Additionally, each ethanol concentration demonstrates a time-dependent augmentation in crystallinity from 2 to 6 h.The crystallinity of the non-ethanol-exposed starch gel was the lowest at 4.7%.Starch gels exposed to ethanol showed an increase in crystallinity, rising from 5.2% at 30% ethanol concentration for 2 h to 7.9% at 100% concentration for 6 h, highlighting ethanol's effectiveness in enhancing starch gel crystallinity.Ethanol tends to disrupt the organized structure of starch molecules, changing their crystalline attributes.The data presented reveals an uptick in crystallinity as ethanol concentration rises, insinuating ethanol's role in fostering a more regimented starch molecule arrangement in the gel [2,29].This observation can be potentially attributed to ethanol, as a solvent, initiating partial perturbation of the starch gel's amorphous sections, thereby amplifying the relative crystalline area.This aligns with several studies illustrating the solvent-induced enhancement of starch crystallinity through amorphous region disruption [30,37,38].Moreover, the increasing crystallinity with ethanol concentration underscores a pronounced ethanol-starch interaction, possibly due to amplified solvent infiltration disrupting the less-ordered regions [10].This crystalline transition was not immediate but evolves and stabilizes over time upon sustained ethanol contact.
FTIR Spectra Analysis
The structural configuration of kudzu starch gels after timed ethanol exposure was characterized by FTIR as presented in Figure 4.The figure revealed a high similarity between the timed-ethanol-exposed gels and that of the control.The findings indicate that, while there may be potential changes in the structure of the ethanol-exposed gels, no new compounds were introduced from the ethanol solutions during the specified exposure period [12,39].This observation corresponds with the results reported by Sun et al. [2] in their study on the enhancement of maize starch gel properties through cross-linking.The consistent spectra provide assurance that any variations in the properties of the gels are not due to the introduction of new chemical entities but a potential reconfiguration of existing bonds or subtle alterations in molecular environments.In this regard, with an increase in exposure time there were negligible subtle changes in the band of relevance to the properties of the gels.The spectra of the gels exhibited broad bands at 3330 cm −1 for 2 and 6 h (Figure 4A,C) and at 3354 cm −1 for 4 h (Figure 4B).This is indicative of the presence of hydrogen bonding interactions of the hydroxyl (O-H) groups typical of natural polymers composed of amylose and amylopectin (starches).The variability, however, suggests the extent and strength of hydrogen bonds which were largely maintained even after ethanol exposure [40].This property is significant when considering the gel's utility in controlled-release systems or encapsulation applications, where the maintenance of the gel structure is imperative.The band within the range of 2920 to 2940 cm −1 was ascribed to the stretching of CH 2 groups associated with starch monomers including glucose.The observed variability may be associated with variations in the duration of exposure.Ethanol, being a polar molecule, has the ability to engage in interactions with starch molecules, leading to alterations in their structure.This is achieved by modifying the surrounding environment of the C-H bonds present in the glucose units, thereby inducing subtle changes over time [35,41].Again, exhibiting of bands at 1660, 1649, and 1630 cm −1 for the 2, 4, and 6 h samples is indicative of the presence of bound water in the gel (water-bending vibration).The phenomenon of time dependence was observed in the fluctuation of wavenumber over time.Specifically, shorter durations were found to be associated with higher wavenumbers, indicating an increase in the amount of bound water present in the starch gels.This increase in bound water content can be attributed to the marginal dehydrating effect caused by prolonged exposure to ethanol.This supports the conclusion drawn by Zhao et al. [14], buttressed by the physical gel appearance (Figure 1A).C-O-C glycosidic linkage stretching typical of polysaccharides was shown at 1180 cm −1 while the C-O stretching vibration was shown between 992 and 857 cm −1 of the 4 and 6 h ethanol-exposed gel.These FTIR findings not only reaffirmed the molecular intricacies of kudzu starch gels but also emphasized their robustness post ethanol exposure.The subtle distinction observed in the spectra highlights the need for considering such when designing systems that leverage the unique properties of these gels, especially in food, beverages, and edible nutrient delivery agents.
designing systems that leverage the unique properties of these gels, especially in food, beverages, and edible nutrient delivery agents.
In Vitro Digestion Characteristics
The data presented in Table 3 offers insights into the proportion of digestible and resistant starch in kudzu starch gel when exposed to different ethanol concentrations and durations of exposure.The data reveals a consistent pattern: as the concentration of ethanol increases, there was a commensurate decrease in the percentage of digestible starch for every time interval.Predictably, control samples consistently exhibited the highest digestibility percentages (97.11-98.15%).Moreover, there was a time-dependent decrease in digestibility within each ethanol concentration, suggesting that both ethanol's presence and exposure duration critically influence the gel's digestibility [35].At a 2 h exposure, the control had a digestibility of 98.15%.In contrast, gels exposed to 100% ethanol offered a digestibility of 92.19%.This marked difference (p < 0.05) underscores ethanol's potency in curbing starch gel digestibility, potentially due to ethanol's interference with starch molecular structures [8,31].
The analysis of the residual undigested fraction (resistant starch) results revealed that with rising ethanol concentration comes an increase in the resistant starch.This trend holds true across all time intervals.Typically, the control for a 2 h exposure had a resistant starch level of 1.87%, while the sample at 80% ethanol records 7.92%.The data ranges from the control's 1.87% at 2 h to a peak of 8.73% with 100% ethanol at 6 h.Drawing parallels with the digestible starch data, it is clear there was an inverse correlation (r = −0.845).The elevated resistant starch in the presence of ethanol might be a result of the immediate recrystallization of amylose, forming structures less accessible to enzymatic action [8,26,32,40].Furthermore, the impediments caused by disruptions and subsequent rearrangements occurring within the starch matrix can hinder the penetration of enzymes.This phenomenon has been observed in other polysaccharides treated with ethanol, particularly after the drying process, as discussed by Sun et al. [2].
In Vitro Digestion Characteristics
The data presented in Table 3 offers insights into the proportion of digestible and resistant starch in kudzu starch gel when exposed to different ethanol concentrations and durations of exposure.The data reveals a consistent pattern: as the concentration of ethanol increases, there was a commensurate decrease in the percentage of digestible starch for every time interval.Predictably, control samples consistently exhibited the highest digestibility percentages (97.11-98.15%).Moreover, there was a time-dependent decrease in digestibility within each ethanol concentration, suggesting that both ethanol's presence and exposure duration critically influence the gel's digestibility [35].At a 2 h exposure, the control had a digestibility of 98.15%.In contrast, gels exposed to 100% ethanol offered a digestibility of 92.19%.This marked difference (p < 0.05) underscores ethanol's potency in curbing starch gel digestibility, potentially due to ethanol's interference with starch molecular structures [8,31].
The analysis of the residual undigested fraction (resistant starch) results revealed that with rising ethanol concentration comes an increase in the resistant starch.This trend holds true across all time intervals.Typically, the control for a 2 h exposure had a resistant starch level of 1.87%, while the sample at 80% ethanol records 7.92%.The data ranges from the control's 1.87% at 2 h to a peak of 8.73% with 100% ethanol at 6 h.Drawing parallels with the digestible starch data, it is clear there was an inverse correlation (r = −0.845).The elevated resistant starch in the presence of ethanol might be a result of the immediate recrystallization of amylose, forming structures less accessible to enzymatic action [8,26,32,40].Furthermore, the impediments caused by disruptions and subsequent rearrangements occurring within the starch matrix can hinder the penetration of enzymes.This phenomenon has been observed in other polysaccharides treated with ethanol, particularly after the drying process, as discussed by Sun et al. [2].
The residual resistant starch after 242 min. of oral, gastric, and intestinal digestion suggests relics of nondigestible portions of kudzu starch gels [42].The proportion, however, improved with ethanol exposure over time.This finding reflects studies [28,35] positing that solvents, including ethanol, can alter starch structures, rendering them more resistant to enzymatic degradation.This observed ethanol modulating effect is desirable due to the established beneficial health significance of resistant starches including improved gut health, blood sugar regulation, satiety, and potential disease risk reduction [43][44][45].Based on the findings, the increased concentration of resistant starch in the kudzu starch gel exposed to ethanol indicates a potential enhancement in its health-promoting properties when compared to the untreated kudzu starch gel.In line with the health implications, ethanol is volatile and rapidly evaporates after treatment, rendering its residue in the final product negligible [46].The potential ethanol remnant in our kudzu starch is therefore innocuous, comparable to what is found in everyday foods, and would not result in any detrimental health effects upon consumption or as a component of food.In essence, we opine that our study resonates with the existing literature regarding the nuanced interplay between ethanol, starch gel mechanical properties, crystallinity, and digestibility.
Conclusions
Our research highlighted the profound influence of ethanol concentration and exposure time on kudzu starch gels.At the lowest ethanol concentrations, gel strength was still enhanced, attributed to a water-ethanol dehydration mechanism.The decreased T c -T o with increased ethanol suggests faster thermal transitions.Ethanol reduced syneresis, which corresponded with changes in gel size and color.The starch gels displayed a shear-thinning behavior validated by the power law model, with R 2 > 0.95.Furthermore, the higher G over G coupled with Tan δ values emphasized the gels' elasticity, modified slightly by ethanol.
SEM images reveal matrix densification upon ethanol treatment, an essential characteristic for efficient absorption and encapsulation of bioactive constituents.Furthermore, the gels' crystalline characteristics and FTIR spectra remained largely unchanged post ethanol exposure, indicating the absence of detrimental chemical changes due to ethanol.Digestibility tests revealed a shift from digestible starch to resistant starch, providing potential benefits for gut health, diabetes management, and metabolic syndrome prevention.In conclusion, our results emphasize ethanol's transformative impact on kudzu starch gel's mechanical, rheological, and digestibility properties, suggesting opportunities to optimize starch-based products.The enhanced robustness of the ethanol-treated kudzu starch gels aligns well with gel-based desserts, confectionery needs, beverages, and nutritional pharmaceuticals, where a consistent texture is essential.
Foods 2023 ,
12, x FOR PEER REVIEW 9 of 18 gels.For instance, the control had 'L*' value of 65.4 drops to 53.1 at 100% ethanol.Both 'a' and 'b' values fluctuated: the 'a*' value increased to 5.6, and 'b*' peaked at 7.3 at 80%
Figure 1 .Figure 1 .
Figure 1.(A) Physical appearance of kudzu starch gel exposed to varying concentrations of ethanol and exposure time.(B) Gel size of kudzu starch gel exposed to varying concentrations of ethanol for 2, 4, and 6 h.(C) CIELAB color parameter of kudzu starch gels at different concentrations at the end of the exposure time.Lowercase alphabets (a, b, c) denote statistical differences.Bars with different alphabets within a cluster are significantly different (p < 0.05) Figure 1.(A) Physical appearance of kudzu starch gel exposed to varying concentrations of ethanol and exposure time.(B) Gel size of kudzu starch gel exposed to varying concentrations of ethanol for 2, 4, and 6 h.(C) CIELAB color parameter of kudzu starch gels at different concentrations at the end of the exposure time.Lowercase alphabets (a, b, c) denote statistical differences.Bars with different alphabets within a cluster are significantly different (p < 0.05).
Figure 2 .
Figure 2. Rheological parameters of ethanol-exposed kudzu starch gel.Tan delta of kudzu starch gel exposed to varying concentrations of ethanol for (A) 2 h, (B) 4 h, and (C) 6 h.Change in viscosity with shear rate of kudzu starch gel exposed to varying concentrations of ethanol for (D) 2 h, (E) 4 h, and (F) 6 h.Storage modulus (G') and loss modulus (G") of kudzu starch gel exposed to varying concentrations of ethanol for (G) 2 h, (H) 4 h, and (I) 6 h.
Figure 2 .
Figure 2. Rheological parameters of ethanol-exposed kudzu starch gel.Tan delta of kudzu starch gel exposed to varying concentrations of ethanol for (A) 2 h, (B) 4 h, and (C) 6 h.Change in viscosity with shear rate of kudzu starch gel exposed to varying concentrations of ethanol for (D) 2 h, (E) 4 h, and (F) 6 h.Storage modulus (G ) and loss modulus (G ) of kudzu starch gel exposed to varying concentrations of ethanol for (G) 2 h, (H) 4 h, and (I) 6 h.
Figure 4 .
Figure 4. FTIR spectra of kudzu starch gel exposed to varying concentrations of ethanol for (A) 2 h, (B) 4 h, and (C) 6 h.X-ray diffraction pattern of kudzu starch gel exposed to varying concentrations of ethanol for (D) 2 h, (E) 4 h, and (F) 6 h.
Figure 4 .
Figure 4. FTIR spectra of kudzu starch gel exposed to varying concentrations of ethanol for (A) 2 h, (B) 4 h, and (C) 6 h.X-ray diffraction pattern of kudzu starch gel exposed to varying concentrations of ethanol for (D) 2 h, (E) 4 h, and (F) 6 h.
Table 1 .
Constituent and volume of simulated digestion stock solutions.
Table 2 .
The mechanical characteristics and fitted rheological parameter of kudzu starch gel exposed to different ethanol concentrations and time.
Table 2 .
Cont.Data are presented as mean ± standard deviation.EC-Ethanol Concentration, ET-Exposure Time, k-consistency index, n-flow behavior index.Results along the same column with different superscript letters are significantly different at p < 0.05 (n = 3).
Table 3 .
Thermal transition, digestibility, syneresis, and relative crystallinity of kudzu starch gel exposed to ethanol at different concentrations and time.
a Data are presented as mean ± standard deviation.Results along the same column with different superscript letters are significantly different at p < 0.05 (n = 3).EC = Ethanol Concentration, ET = Exposure Time, S = Syneresis, RC = Relative Crystallinity, DS = Digestible Starch, RS = Resistant Starch, Others (S and RC) = characteristics that had only one parameter evaluated.
Table 4 .
Pearson correlation analysis of gel mechanical properties, syneresis, relative crystallinity, size, digestibility, and color parameters. | 9,825.2 | 2023-10-31T00:00:00.000 | [
"Materials Science"
] |
Spin Measurements of NV Centers Coupled to a Photonic Crystal Cavity
T. Jung,1 J. Görlitz,1 B. Kambs,1 C. Pauly,2 N. Raatz,3 R. Nelz,1 E. Neu,1 A. M. Edmonds,4 M. Markham,4 F. Mücklich,2 J. Meijer,3 and C. Becher1, ∗ 1Universität des Saarlandes, Fachrichtung Physik, Campus E 2.6, 66123 Saarbrücken, Germany. 2Universität des Saarlandes, Fachrichtung Materialwissenschaft und Werkstofftechnik, Campus D 3.3, 66123 Saarbrücken, Germany. 3Universität Leipzig, Angewandte Quantensysteme, Linnéstraße 5, 04103 Leipzig, Germany. 4Element Six Global Innovation Centre, Fermi Avenue, Harwell Oxford, Didcot, Oxfordshire OX11 0QR, United Kingdom. (Dated: July 18, 2019)
I. INTRODUCTION
The nitrogen-vacancy (NV) center, a point defect in diamond consisting of a lattice vacancy and an adjacent nitrogen substitution, has attracted a lot of interest during the past years owing to its outstanding optical and spin properties. [1] The triplet ground state exhibits two sublevels attributed to two spin projections m s = 0 and m s = ±1 of the NV electron spin. [2] In addition to an ultralong spin coherence time of more than one second at liquid helium temperatures, [3,4] the NV center features spin-conserving optical transitions. [5] Furthermore, the electron spin may be coherently manipulated by microwave signals [6] and purely optically initialized as well as read-out. [7] Spin initialization and read-out are enabled by a spin-selective intersystem crossing (ISC) towards the singlet system: the long lifetime in the singlet system facilitates a spin-dependent fluorescence and a preferred decay towards the m s = 0 ground state, [8,9] allowing for fast spin initialization. Spin polarizations of about 80 % at room temperature [10,11] and over 99 % at liquid helium temperature [5] may be reached, as well as spin-dependent fluorescence contrasts of up to 30 % for an optical spin read-out under non-resonant laser excitation. [12] Besides the spin-dependent fluorescence contrast, the reliability of an optical spin read-out, designated as the signal-tonoise ratio (SNR), also depends on the detected photon count rate. The SNR for an optical measurement distinguishing between the two possible spin projections m s = 0 and m s = ±1 *<EMAIL_ADDRESS>of a NV center is defined as [13] Here N 0 (N 1 ) is the expectation value for the detected photon count rate when preparing the NV center in the spin projection m s = 0 (m s = ±1). Due to the Poisson-distribution of the photon count rate we expect that the random variables N 0 and N 1 are also Poisson-distributed, [14] hence their difference is Skellam-distributed with variance σ 2 = N 0 + N 1 . [15] As apparent in equation (1), the SNR is mainly determined by the difference N 0 − N 1 . Normalized by N 0 , we obtain the already mentioned spin-dependent fluorescence contrast C = (N 0 − N 1 )/N 0 . With this measure we get the relation As visible from equation (2), a large SNR of optical spin readout requires both a large collected photon rate and a large contrast of spin-dependent fluorescence. [16] In view of applications, a sufficiently large SNR facilitates the use of NV centers as quantum sensors for temperature, [17] pressure [18] as well as magnetic fields on the nanoscale [19][20][21][22] or the verification of fundamental principles of quantum mechanics as for example demonstrated by a loophole free Bell test. [23] Furthermore, a high enough SNR in combination with the long spin coherence time enables the coupling of NV centers to nearby nuclear spins used as quantum bits [24][25][26][27] or as building blocks of quantum repeaters. [28,29] In particular, for an aspired scaling of quantum systems towards quantum networks, [30] a speed-up of the entanglement generation is a central requirement and hence a preferably large SNR desirable.
arXiv:1907.07602v1 [quant-ph] 17 Jul 2019
The photon detection rate is usually limited by a non-perfect photon collection. Consequently, several approaches to enhance the collection efficiency have been followed by modifying the directivity of emission such as using an optimal crystal orientation, [31] fabricating solid immersion lenses around NV centers [5,32] or incorporating NV centers in nanopillars, [33,34] nanowires, [35] waveguides [36,37] or metalenses. [38] Furthermore, the collection efficiency can be modified by coupling NV centers to whispering gallery [36,39] or photonic crystal (PhC) cavities [40][41][42][43][44] as well as to plasmonic structures. [45,46] In addition, by such a coupling the local density of states at the emitter's position and hence its spontaneous emission rate may be enhanced or, correspondingly, the spontaneous emission lifetime reduced by the Purcell-factor F. [47] In addition to a reduced lifetime, the coupling of NV centers to a cavity has the advantage that more than the usual 3 % of the photons are emitted into the zero phonon line (ZPL). Hence, entanglement generation by interference of ZPL photons at a beam splitter [23,[48][49][50] may be further sped up by coupling to a cavity featuring a mode in resonance with the NV-ZPL. However, a modification of the population dynamics, such as Purcell enhancement of emission, also influences the spin-dependent fluorescence contrast C. Bogdanov et al. showed for NV ensembles in nanodiamonds, that the contrast decreases when reducing the emitter's lifetime by coupling to plasmonic islands. [46] Furthermore, Babinec et al. in a theoretical study found that the spin read-out SNR achieves a maximum value for Purcell-factors on the order of 1. [51] In this article, we report on the SNR enhancement achieved by coupling NV centers to a two-dimensional PhC cavity. Starting from ultrapure single crystal diamond membranes bonded on a sacrificial silicon substrate and thinned by reactive ion etching (RIE), two-dimensional PhC cavities are fabricated by focused ion beam (FIB) milling at thoroughly characterized and carefully selected membrane positions. [52] NV centers are subsequently incorporated into the PhC cavities by a high resolution AFM implantation technique. [53] A FIBmilled hole in the AFM-tip serves as an aperture, which enables the accurate implantation of nitrogen into the cavities. We activate the NV centers by extensive post processing, i. e. annealing and cleaning procedures. We here also report on the deterministic spectral tuning of a cavity mode in resonance with the NV-ZPL using thermal oxidation of diamond as well as condensation of residual gas in the cryostat. We finally experimentally measure and theoretically simulate the change in spin-dependent fluorescence contrast C and SNR on resonance.
A. Sample system with FIB-milled cavities
The Purcell-factor F, quantifying the lifetime reduction achieved by the emitter-cavity-coupling is directly proportional to the ratio of quality factor Q and modal volume V of a PhC cavity mode. The Q-factor is strongly dependent A CVD-grown, ultrapure, single crystal diamond film is positioned on the HSQ layer generating an air suspended diamond membrane. After RIE thinning from the topside the diamond has a final thickness of a few hundred nanometers. PhC cavities are produced by FIB milling at pre-selected defect-free spots with a suitable thickness. (b) Scheme of a M0-cavity generated by a slight shift of two adjacent holes. (c) Photoluminescence (PL) spectroscopy of a M0cavity at room-temperature. The cavity mode at 644.8 nm features a FWHM of 0.078 nm, corresponding to a Q-factor of 8250. The spectra were taken with an integration time of 30 s under non-resonant laser excitation at 532 nm and a laser power of 1 mW.
on the precision of fabrication and deviations from the design parameters. In order to produce PhC cavities with modes featuring a high Q-factor and a spectral position close to the NV-ZPL, diamond membranes with a precise thickness are required. However, due to polishing wedges as well as local deviations in the etching rate during RIE-thinning the thickness typically varies over the diamond film by several hundred nanometers. [52] Therefore, the thinned membranes need to be characterized carefully in order to select suitable spots for the subsequent cavity production. The challenge in FIB milling of the PhC array is the fabrication of regularly hole patterns with vertical hole sidewalls. Conical shapes with typically observed inclination angles of as large as 9 • may degrade the Q-factor by one order of magnitude. [52,54] The fabrication process and characterization methods are described in detail in our previous publication [52].
The sample system is depicted in Fig. 1a. As starting material we use 30 µm thick, chemical vapor deposition (CVD) grown, (001)-oriented, ultrapure, single crystal diamond membranes (electronic grade quality, ElementSix) with a nitrogen concentration below 5 ppb. At first, the diamond film is etched by RIE in an Ar/O 2 -plasma to remove 5 µm of the surface material as its quality is degraded due to the polishing process. [55] After acid-cleaning, the remaining 20 µm thick diamond film is, mediated by a spin-coated 50 nm thick layer of hydrogen silsesquioxane (HSQ XR-1541-002, DowCorning), bonded to a silicon substrate containing pre-fabricated windows. Curing the sample system at 600 • C renders the bond persistent during the post-processing and cleaning procedure required after FIB milling as well as for removing damages in the diamond crystal lattice after nitrogen implantation (see section II B). Furthermore, the stable bond allows measurements at liquid helium temperatures. The final membrane thickness of a few hundred nanometers is finally reached by further RIE thinning from topside. The membranes are subsequently characterized by laserscanning microscopy, cross-section measurements, and quantitative dispersive X-ray spectroscopy. The combination of these methods allows us to map the thickness of the diamond films as well as the surface structure with high resolution, enabling the selection of defect-free spots featuring a suitable thickness for the fabrication of PhC cavities. M0-cavities generated by a shift of two adjacent holes ( Fig. 1b) are fabricated by FIB milling. The hole radii of R = 68 nm and the lattice constant of a = 250 nm of the photonic crystal array are chosen such, that the cavity modes match the NV-ZPL position at 637 nm. In addition, the M0-cavity is optimized by slight changes in position and/or radii of holes close by the point-defect. [56] The simulated Q-factor of the cavity mode is 320 000 at a mode volume of 0.35 (λ /n) 3 . Optimizations in the FIB milling process as for instance the use of overmilling and drift control programs, realizing a chamber pressure below 5 · 10 −6 mbar and a temperature stabilization of the ion-column as well as the deposition of a metal protection layer prior to FIB milling reduce the conical hole shape to below 4 • , optimize the hole positions within the pattern and lead to sharp and well-defined hole edges. After an extended post-processing, consisting of annealing steps in vacuum at 1000 • C and acid-cleaning, the fabricated cavities are analyzed in a home build confocal setup. The PhC cavities feature modes with Q-factors up to 8250, as depicted in Fig. 1c. Hence, the obtained Q-factors reach the same order of Q-factors of two-dimensional PhC cavities with small modal volumes (around one cubic wavelength) and a spectral mode position close to the NV-ZPL as currently observed from RIE fabrication methods. [40,44,57]
B. NV incorporation by AFM implantation
This section summarizes how we generate NV centers located at the field maximum of the PhC cavity. As we used ultrapure diamond as starting material, at first nitrogen has to be implanted. In the past few years several high resolution implantation techniques were developed, most of them masking the sample surface by spin-coated photoresist films, [58,59] Mica layers, [60] transferred silicon hard masks [61] as well as structured AFM-tips, [53] each featuring small holes as apertures. Also a maskless FIB-implanter was realized. [62] The last two techniques have the outstanding advantage, that the implantation spot can be positioned relative to previously produced nanostructures with an accuracy at the nanoscale. Whereas the lateral resolution of a nitrogen FIB implantation is about 100 nm at a typical acceleration voltage of 30 kV, nitrogen may be implanted through an AFM-tip with a lateral resolution of up to 20 nm at a typical implantation energy of 5 keV. [63] As precise positioning is crucial for efficient cavity coupling, we here use the AFM-tip technique.
The home built AFM-setup combines a conventional lowenergy ion source for generation and acceleration of nitrogen ions with an AFM-unit. A small hole is FIB-milled close to the apex of the pyramidal AFM-tip which is positioned over the implantation spot (Fig. 2a). To align the AFM-tip relative to the sample, AFM-scans are performed prior to every implantation (Fig. 2b). The lateral implantation resolution with regard to the diameter of the AFM-aperture of 70 nm, the alignment accuracy of the tip to the sample of about 1 nm, and the ion straggle in diamond of 3 nm at the chosen implantation energy of 5 keV yields a total accuracy of 74 nm. Note that small straggling effects of ions at the edges of the 70 nm aperture are not included in the analysis above and are under present investigation. The expected implantation depth of the nitrogen ions in (001)-oriented diamond samples is 13 nm on average [64] and the expected yield about 0.8 %. [65] The implantation dose aiming at one NV center per cavity is calculated to 2.7 · 10 12 ions/cm 2 . As the generation of NV centers is a statistical process, the final implantation doses were varied between half and triple of the calculated value. After implantation, an extensive post-processing is required in order to restore a good diamond crystal quality and to activate NV centers. At first, the samples are therefore annealed in vacuum (p ≤ 10 −6 mbar) at 900 • C for 10 h. Subsequently, oxidation of the samples at 450 • C for 3 h in air atmosphere and acid cleaning (5 h in a tri-acid mixture of perchloric, sulfuric and nitric acid) removes graphitic residuals from the surface and provides an oxygen termination. Hence, the possibility to obtain negatively charged NV centers within the PhC cavity is enhanced. [66] In Fig. 2c a typical spatially resolved photoluminescence (PL) image after post-processing is shown. Generated NV centers are localized in the PhC cavities as well as outside the area masked by the AFM-cantilever. This observation is in agreement with the results of additionally performed optically detected magnetic resonance (ODMR) measurements, which reveal a dip at frequencies around 2.87 GHz, characteristic for NV centers, [7] inside the cavities and no hints of NV cen- ters within the surrounding PhC arrays. The cavities were further examined with PL spectroscopy at low temperatures. In Fig. 2d and 2e PL spectra of the M0-cavity with the lowest applied implantation dose are shown. Besides the cavity mode spectral lines around 638 nm are visible featuring Gaussian shapes with half widths (FWHM) of 200 GHz and 370 GHz, respectively. We performed photon correlation (g 2 ) measurements to estimate the number of generated NV centers. As the g 2 results did not show a dip but Poissonian photon statistics we have to assume that a few NV centers were created inside the cavity volume. The deviation from the expected implantation yield might be explained by a large number of defects in the material as a consequence of the PhC fabrication process, providing a high density of vacancies for NV center creation. In addition, the emission lines might be shifted by local strain and strongly broadened by spectral diffusion due to nearby charges. [67,68] III. RESONANCE TUNING In the past few years several techniques have been developed for the deterministic tuning of cavity modes into resonance with the ZPL of color centers. A well-established but irreversible method is the oxidation of diamond in an air or oxy-gen atmosphere. [41,69] At temperatures above 450 • C the diamond surface starts to oxidize, the thickness of the diamond membrane decreases with an accompanying enlargement of the hole diameters. Larger holes as well as thinner diamond films lead to a spectral blue shift of the cavity modes. Finite Difference Time Domain (FDTD) simulations predict a blue shift of 12 nm for our M0-cavity if 5 nm diamond are removed from the surface. On the other hand, cavity modes have been successfully redshifted by condensing inert gases like xenon or nitrogen on the sample's surface, [41,70,71] thereby increasing the sample thickness and reducing the hole radii. In contrast to the oxidation technique, a tuning by gas adsorption is a reversible process where heating the sample enables the residual-free removal of the condensed layers. [71] In the following we focus on the M0-cavity implanted with the lowest implantation dose of 1.35 · 10 12 ions/cm 2 , featuring a cavity mode with a Q-factor of 2060 (spectra in Fig. 2d and 2e). At first, the oxidation technique described above, using a temperature of 525 • C, is applied to tune the cavity mode to shorter wavelengths. After tuning and acid-cleaning the resulting mode position is 634 nm. In a second step, the residual gas present in the sample chamber of the cryostat (Attodry 2100, Attocube) is adsorbed to the sample, allowing a redshift of the cavity mode under continuous optical control: we observed that during PL measurements at room- temperature and a pressure of 10 −4 mbar cavity modes show a red shift under continuous laser excitation at 532 nm. Furthermore, only the modes of a cavity directly irradiated with laser light are affected and the observed shift rates scale with the power. All these observations may be explained as follows: as the vacuum pump is attached at the topside of the cryostat, pumping leads to an efficient removal of lightweight molecules, whereas heavy gas molecules, e. g. hydrocarbons, partly remain in the sample chamber. Based on the observations we assume a light-assisted adsorption of residual gas molecules onto the sample's surface. [71,72] Under illumination with 1.5 mW of laser light at 532 nm we observe a shift rate of the cavity modes of approximately 1.8 nm/h. The Qfactor remains almost unchanged with Q = 2021 after tuning. Importantly, after further pumping and cooling to liquid helium temperatures no further mode shifts are observable under laser illumination. We point out that the described tuning by gas adsorption is a reversible process. Heating the sample to 400 • C in air atmosphere resets the sample to the initial state before the gas adsorption. The PL spectra depicted in Fig. 3a show a strong enhancement of the ZPL intensity by tuning the cavity mode on resonance. We further observe an enhancement of the saturation count rate filtered in a 2.5 nm wide window by a factor of 2.8 from 13.6 kHz to 37.5 kHz (Fig. 3b). Furthermore, the emitter's lifetime decreases from 9.0 ns at a spectral mode position of 634 nm to 8.0 ns in resonance with the NV-ZPL. The recorded lifetime traces (Fig. 3c) feature a double exponential decay. The second time constant on the order of 1 ns may be attributed to fast decaying fluorescence in the diamond membrane (background). Moreover, PL spectra allow for the estimation of the fraction of emission into the cavity mode as well as the resulting Purcell-factor. The de-duced spontaneous emission coupling factor on resonance is β * = I mode /I total = 18.3 % (Fig. 3d). As the incorporated NV centers feature an off-resonant Debye-Waller factor of 2.1 %, we conclude that the emission fraction into the ZPL is strongly enhanced due to the cavity coupling. The β * -factor finally enables us to calculate the total Purcellfactor to be 1 + F * = 1.224. We modeled the total Purcellfactor 1 + F * on resonance by using a phonon assisted cavity coupling model presented in [73]. With the Q-factor and modal volume V of the cavity mode as well as the measured linewidths of the ZPL and the sideband transitions of the NV centers a Purcell-factor of 1 + F * = 4.9 is predicted. The experimentally determined value of 1 + F * = 1.224 is reduced due to a non-perfect lateral positioning of the implanted NV centers relative to the mode field, a shallow implantation depth as well as a non-perfect dipole orientation in the used (001)oriented diamond samples. The model further correctly predicts the experimentally observed lifetime reduction.
To analyze the NV-ZPL in detail despite the existing resonance with the cavity mode, a photoluminescence excitation (PLE) spectrum was recorded for wavelengths between 636.2 nm and 638.5 nm. In the spectrum depicted in Fig. 4 it is noticeable, that only one of the previously detected two emission lines (see Fig. 2e) remains. In the PLE spectrum this line at 637.4 nm has a half width of 360 GHz, in good agreement with the value of 370 GHz deduced from the PL spectra. The absence of the second line is most likely due to the removal of shallow implanted NV centers during the extended tuning steps by oxidation.
IV. SNR ENHANCEMENT
To estimate the SNR enhancement due to the emitter-cavitycoupling we at first have to consider the change in the photon count rate N 0 . For this, we have to take into account the shortening of the emitter's lifetime as well as the change in collection efficiency. Furthermore, for the SNR the change in spin-dependent fluorescence contrast C has to be considered. To this end, a reliable methodology is required to compare the contrast before and after tuning the cavity mode in resonance with the NV-ZPL.
A. Light extraction from a PhC cavity
We simulate the emission of the cavity-coupled NV centers using a finite element software (FDTD solutions, Lumerical) by modeling the emission of an electric dipole point source positioned in the mode field maximum. The simulated photonic nanostructure features the same number of holes as the produced M0-cavity where the holes have a conical shape with an inclination angle of 4 • (see section II). We calculate the emission fractions in the two half-spaces above and below the PhC as well as the collection efficiency for a microscope objective (NA = 0.8) positioned vertically above the diamond membrane. Each simulation is performed for a E z dipole oriented vertically to the diamond film as well as for the in-plane dipoles E x and E y . These dipoles are oriented such that the cavity mode is fed by the E y dipole whereas the E x dipole has orthogonal polarization. The orthogonality of the dipoles also allows us to calculate the emission for arbitrary dipole orientations as discussed below.
As an example we show in Fig. 5a a simulation for the E y dipole. We find that the collection efficiency drops to 3.4 % at the resonance wavelength of the cavity mode, whereas for other wavelengths within the photonic band gap collection efficiencies around 25 % are achieved. This minimum arises from a modified directional characteristic of the emitted light. Two factors play a role here: first, the fraction of photons emitted in the top half-space decreases at the mode's resonance wavelength from values over 50 % to values below 12 % (Fig. 5a). Second, a smaller part of the photons emitted in the top half-space (below 57 % instead of over 62 %) can be collected within the NA at the resonance wavelength of the mode (Fig. 5b). The NV emission dipoles are oriented in the (111)-plane of the diamond lattice. For the small NV ensemble in our experiment we average over all possible dipole orientations within the (111)-plane. As the used diamond material features a (001)-orientation, the 111 -axis exhibits an angle of 35.3 • to the xy-plane (membrane plane). The projection of the averaged NV dipoles onto the x or y-axis amounts to 24 % and 52 % onto the z-axis. To calculate the resulting collection efficiency for our NV ensemble, also the Purcell-factors for the three dipole orientations have to be considered. The emission directivity of photons emitted into the cavity mode is only determined by the mode emission directivity. Further, the emission directivity of off-resonant photons is defined by the photonic nanostructure. Considering this, we first calculated the spontaneous emission ratesγ i of the projections of the averaged NV dipoles onto the x, y and z-axis considering the corresponding Purcell-factors F i as follows: with the free-space spontaneous emission rate γ, k i = 0.24 for i = x, y and k i = 0.52 for i = z. Subsequently, the fraction of emission produced by the averaged NV dipole projected to the x, y or z-axis may be calculated by normalizing the spontaneous emission ratesγ i to the sum over all these rates. To finally calculate the collection efficiency at the given dipole orientation, the simulated collection efficiencies for a dipole oriented in x, y or z-direction are weighted with the respective fraction of emission and the resulting values summed up. For the optical read-out of the NV electron spin we can distinguish between two fundamental cases. In the first case only ZPL photons are considered. This is for instance the case, if indistinguishable photons are required. On the other hand, for projective spin read-out generally all the emitted photons are used, e. g. if NV centers are used as magnetic field sensors on the nanoscale. [19][20][21][22] The simulations predict a collection efficiency of 3.9 % for the off-resonant mode position at 634.0 nm, which is slightly reduced to 3.4 % in resonance with the NV-ZPL. Hence if for the spin read-out only ZPL photons are used, the collection efficiency drops by a factor of 0.87. If in the second case all emitted photons are used for the spin read-out, the collection efficiency drops only by a factor of 0.97. The reduction in the second case is smaller, as only a fraction of the emitted photons is affected by the dominant decrease of collection efficiency at the resonance wavelength of the cavity mode.
B. Fluorescence contrast measurements
We apply a protocol composed of three succeeding measurements for the reliable and reproducible determination of the time-resolved, spin-dependent fluorescence contrast of the cavity-coupled NV centers. For the considered offresonant spectral mode position at 634 nm at first a ODMRmeasurement under continuous laser and microwave excitation is performed. An external magnetic field of 2 mT is applied to split the two ground state sublevels m s = −1 and m s = +1. Hence, in the ODMR-spectrum in Fig. 6f, two dips are visible belonging to the resonance frequencies of the ground state transitions from m s = 0 to m s = −1 and m s = +1 respectively. In the following we only focus on the transition to the m s = +1 sublevel featuring a resonance frequency of ν +1 = 2.917 GHz. For all presented measurements the optical excitation of the NV centers coupled to the M0-cavity is carried out in the PL saturation regime.
To determine the population inversion time a Rabi measurement on the transition m s = 0 to m s = +1 is performed (Fig. 6a). From the observed damped Rabi oscillations a πtime of 550 ns and a spin coherence time of T * 2 = 1.5 µs is deduced. The value of T * 2 is in accordance with typical spin coherence times observed for shallow NV centers in nanophotonic structures based on single crystal diamond. [74] This indicates that our PhC fabrication process does not adversely influence the NV spin coherence properties.
In Fig. 6b we present the time-resolved, spin-dependent fluorescence. Here, after spin initialization a resonant microwave π-pulse is applied, resulting in a preparation of the NV centers in the m s = +1 state. During the spin read-out a 50 ns wide photon detection gate is temporally shifted. For each gate position the measurement is repeated for a NV preparation in the m s = 0 state and the difference of the two fluorescence curves, the time-resolved fluorescence contrast, calculated. As expected, the fluorescence curves at first rise for both spin states whereas the count rate for the m s = 0 state (bright state) is generally higher as for the m s = +1 state (dark state) with a maximum contrast of C = 4.2 %. With progressing laser excitation time both fluorescence curves converge towards a joint value, indicating an equilibrium, spin-mixed state. Whereas the fluorescence contrast measured on single NV centers under zero magnetic field can reach values of 20 % [75] to 30 % [12], for NV ensembles in a magnetic field contrasts of only a few percent are expected. [76] Possible reasons are lattice and surface defects introduced by FIB milling, impairing charge state stability and spin coherence of the shallow implanted emitters. [76,77] Furthermore, a strain gradient may locally alter the ground state splitting. Hence, different emitters of the considered small NV ensemble may feature slightly different resonance frequencies.
Subsequently, the cavity mode is tuned into resonance with the NV-ZPL (see section III). As for the tuning process the sample has to be dismounted from the cryostat, a repositioning of the microwave antenna, an air suspended gold wire loop mounted on a positioner, is required after remounting the sample. To establish comparable experimental conditions we position the antenna in such a way that a π-time of 570 ns is reached (Fig. 6d), in good agreement with the π-time of 550 ns (Fig. 6a) for the NV-ZPL off resonance with the cavity mode. We follow the same protocol as in the off-resonant case to measure Rabi oscillations (Fig. 6d) as well as fluorescence curves (Fig. 6e) on resonance. When comparing the resulting time-resolved fluorescence contrast on-and off-resonance (Fig. 6c), we find a small reduction of contrast of 1.5 % on resonance (integrated over the entire time interval in Fig. 6c).
C. Rate equation model
To analyze the measured spin-dependent fluorescence contrast we set up a rate equation model following Wolf et al. . [14] In this model a NV center is adopted as a five level system (Fig. 7a), consisting of the two ground states m s = 0 and m s = ±1, respectively, the corresponding excited states and a long-living singlet state. For the modeling we assume that the excitation rates out of the two ground states are identical for the non-resonant laser excitation. [78] Furthermore it is assumed that the emission rates from the excited to the ground states of the triplet system are spin independent. [79] In addition, the transition rate from the excited m s = 0 state to the singlet state is neglected as this rate is four orders of magnitude smaller than the corresponding transition rate for the m s = ±1 state. [8,79,80] As a further assumption the transition rate from the singlet state to the m s = ±1 ground state is neglected, because the rate to the m s = 0 ground state is about six times larger. [8,9] By reason of these assumptions a spinmixing, leading to a statistical mixture of m s = 0 and m s = ±1 states due to the spin-selective intersystem crossing is already included in the model. Such a spin-mixing was both theoretically predicted [9,14,46] and experimentally confirmed. [8] If, however, the only spin-mixing process was due to ISC, the modeled population would end up in the m s = 0 state for sufficient long-lasting laser excitation and the modeled fluorescence would thus be maximized. Instead, the spin-dependent fluorescence curves in our experiment ( Fig. 6b and 6e) as well as for other NV centers (see e. g. [11,13]) show a convergence of the fluorescence and hence the populations towards a steady state. Therefore a further spin-mixing has to be included in the model. Wolf et al. propose as additional spinmixing mechanisms on the one hand a radiative spin-mixing between the excited and ground states of the triplet system and on the other hand a purely non-radiative spin-mixing between the excited states. [14] As can be seen in Fig. 7b and 7c, respectively, the measured data may be fitted well under the assumption of a radiative spin-mixing and, in particular, better than under the assumption of a non-radiative spin-mixing in the excited state. However, Kalb et al. demonstrated that a radiative spin-mixing occurs only with a probability of well below 1 % and hence should not be the dominant spin-mixing mechanism in our experiments. [8] Instead, the reason for the additionally observed spin-mixing mechanism is that in our experiments we apply an external magnetic field to split the ground states of the NV centers (see section IV B). As the diamond sample features a (001)-surface and the magnetic field an orientation vertical to the diamond's surface, the magnetic field exhibits an angle of here 54.7 • to the magnetic dipole axis of the NV centers. As now both ground and excited states consist of superpositions of bare, zero-field spin states, optical transitions with spin flips become allowed resulting in an effective radiative spin mixing. [81] Furthermore, the rates of ISC transitions are modified. Therefore, in summary, the data are fitted appropriately under the assumption of a spin-mixing due to ISC and by radiative transitions in the triplet system. In the following we assume for simplicity that the spin-mixing induced by the off-axis magnetic field is the same for excitation and emission. With this, the following rate equations are set up, determining the internal dynamics of a NV center: The radiative triplet transitions (both spinconserving (green, red) and spin-mixing (blue)) are illustrated as colored and the ISC transitions as black arrows. The dashed arrow indicates a scenario where non-radiative spin-mixing happens in the excited state. (b and c) Measured timeresolved, spin-dependent fluorescence after preparing the NV centers in the m s = 0 state (red dots) and m s = ±1 state (black dots) for the NV centers off resonance with the cavity mode. The modeled curves (red and black lines) were adapted for the rates K e = K f = 111 MHz under the assumption of a radiative spin-mixing (b) and a nonradiative spin-mixing in the excited state (c), respectively. (d) Simulated fluorescence contrast of NV centers off (black curve) and on (blue curve) resonance with the cavity mode under the assumption of a spin-mixing due to ISC and by radiative transitions in the triplet system. K s the transition rate from the excited m s = ±1-state to the singlet state, K 0 the transition rate from the singlet state to the m s = 0 ground state and K m the rate of the radiative spinmixing induced by the off-axis magnetic field. As the measurements are performed in the PL saturation regime, the relation K e = K f holds in the following. According to the measured off-resonant lifetime value of 9.0 ns, a decay rate of K f = 111 MHz is set in the model. With the parameters K e and K f fixed, the rate equations are solved and the simulated time-resolved fluorescence is fitted to the measured curves by varying the free parameters K 0 , K s and K m (Fig. 7b). From this fit a spin-mixing rate of K m = 1.35 MHz, a transition rate to the singlet state of K s = 1.79 MHz and a transition rate to the m s = 0 ground state of K 0 = 5.80 MHz are determined. These rates allow us to theoretically predict the time-resolved, spin-dependent fluorescence contrast on resonance. Fig. 7d shows the fluorescence contrast simulated by the rate equation model for the cavity mode on and off resonance with the NV-ZPL. The theoretically predicted fluorescence contrast on resonance is slightly lower than for the off-resonant case. This is expected, as the emission rate K f scales with the Purcell-factor and the probability for spin-mixing is the larger the more fluorescence cycles occur per time unit. Depending on the position as well as the size of the temporal read-out window, a reduction of the fluorescence contrast by tuning the mode into resonance with the NV-ZPL of up to 5 % is theoretically predicted. For a realistic read-out photon gate of 250 ns, as for instance typically used for the acquisition of Rabi measurements, the fluorescence contrast would be reduced by 4.1 %. Such a reduction is conformable with the experimental results (see section IV B).
D. Implications for the SNR
We now discuss the modification of the spin measurement SNR induced by the modified photon collection and modified spin-dependent fluorescence contrast due to the cavity coupling. With equation (1) as well as the appropriate assumption of small contrasts, we arrive at: where variables with (without) a star indicate the on-(off-) resonant case. Based on the presented measurements as well as the theoretical modeling we assume in the following a reduction of the spin-dependent fluorescence contrast by 4.1 %, i. e. C * /C = 0.959. Due to the lifetime reduction the number of emitted photons is increased by a factor of 1.13, when the mode is tuned into resonance with the NV-ZPL. If we, in a first scenario, consider only ZPL photons for spin read-out, the collection efficiency is reduced by a factor of 0.87 (see section IV A). Furthermore, the fraction of photons emitted into the ZPL is modified from 2.1 % off resonance to 18.3 % on resonance (see Fig. 3d), resulting in an enhancement factor of 8.7. The total estimated enhancement of the collected photons by applying a narrow-band photon detection around the ZPL is hence N * 0 /N 0 = 1.13 · 0.87 · 8.7 = 8.5 and the SNR, also taking the contrast reduction of C * /C = 0.959 into account, thus enhanced by a factor of ζ = 2.8. As a result, the SNR is almost tripled by tuning the mode into resonance with the NV-ZPL. If we, in a second scenario, consider the collection of all photons for the spin read-out, we cannot benefit from the higher emission fraction into the ZPL any more, but the number of emitted photons is still enhanced by a factor of 1.13 due to the lifetime shortening on resonance. The collection efficiency is here reduced by a factor of 0.97 (see section IV A). Altogether the number of detected photons by applying a broad-band photon detection is enhanced by a factor of N * 0 /N 0 = 1.13 · 0.97 = 1.10, resulting in a very small SNR enhancement of about 0.5 %. In summary, the cavity coupling of NV centers as demonstrated here leads to a spin read-out SNR enhancement of up to a factor of ≈ 3. This factor is within the same order of magnitude as the SNR enhancement achieved by other methods for improving the photon collection efficiency. [5,13,31] V. CONCLUSIONS In summary, we reported on the SNR enhancement of the optical spin read-out achieved by tuning the mode of a twodimensional PhC cavity into resonance with the NV-ZPL. To achieve this, ultrapure (001)-oriented CVD-grown diamond films were used as starting material for the RIE fabrication of thin, air-suspended membranes. An extended characterization allowed us to select defect-free spots featuring a suitable thickness for the subsequent fabrication of PhC cavities by FIB milling. The analyzed cavity modes showed Qfactors of up to 8250 at mode volumes of less than one cubic wavelength. The application of a high-resolution implantation technique using a pierced AFM-tip allowed the subsequent generation of NV centers in the cavities. The combination of two spectral tuning methods, an oxidation technique for the blue shift and a gas adsorption technique for the red shift, facilitated the reliable and precise tuning of a cavity mode. For the considered cavity-coupled NV centers the SNR was almost tripled. A theoretical model, taking into account the measured shortening of the emitter's lifetime, the measured and theoretically predicted change in fluorescence contrast as well as the simulated modification of the collection efficiency reproduces the experimental findings very well. Whereas the reported SNR enhancement is on par with simpler methods for photon collection enhancement, [5,13,31] it could be still increased by a further optimized cavity coupling: a (111)-oriented diamond sample with an optimal dipole orientation may lead to a fourfold enhancement of the total Purcell-factor. For an optimal implantation depth in the center of the diamond film, instead of the shallow implantation, the Purcell-factor may be further increased by a factor of 3.2. In total, for an optimal cavity coupling our theoretical model predicts a SNR enhancement by a factor of more than 6. A possible method to reach this is a change of the fabrication order such that at first NV centers are implanted into the diamond film and subsequently a PhC cavity is fabricated around. This would allow a maskless implantation with higher energies resulting in deeper implanted NV centers. Subsequently, NV centers could be pre-characterized and suitable single emitters chosen, featuring an ideal dipole orientation. Alternatively, also improved nanoimplantation techniques such as a maskless FIB-implantation of ions with high lateral resolution are in reach. [82] Eventually, the here generated NV centers feature an optical linewidth of several hundred GHz, whereas narrow line widths below 100 MHz are accessible, [83] at least in µm-thin RIE-etched diamond membranes. Smaller linewidths would further increase the total Purcell-factor. Therefore, in conclusion, higher SNR enhancements are within reach with the method presented here.
ACKNOWLEDGMENTS
We thank B. Lägel and S. Wolff (Nano Structuring Center, University of Kaiserslautern) for helpful discussions on nano-fabrication and use of their facilities. We further thank Alexander Huck and Simeon Bogdanov for helpful discussions on fluorescence contrast measurements and modeling. This research has been partially funded by the European Quantum Technology Flagship Horizon 2020 (H2020-EU1. | 9,651.6 | 2019-07-17T00:00:00.000 | [
"Physics"
] |
Survival probability of stochastic processes beyond persistence exponents
For many stochastic processes, the probability \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S(t)$$\end{document}S(t) of not-having reached a target in unbounded space up to time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t$$\end{document}t follows a slow algebraic decay at long times, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S(t) \sim {S}_{0}/{t}^{\theta }$$\end{document}S(t)~S0∕tθ. This is typically the case of symmetric compact (i.e. recurrent) random walks. While the persistence exponent \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}θ has been studied at length, the prefactor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${S}_{0}$$\end{document}S0, which is quantitatively essential, remains poorly characterized, especially for non-Markovian processes. Here we derive explicit expressions for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${S}_{0}$$\end{document}S0 for a compact random walk in unbounded space by establishing an analytic relation with the mean first-passage time of the same random walk in a large confining volume. Our analytical results for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${S}_{0}$$\end{document}S0 are in good agreement with numerical simulations, even for strongly correlated processes such as Fractional Brownian Motion, and thus provide a refined understanding of the statistics of longest first-passage events in unbounded space.
I n order to determine the time it takes for a random walker to find a target, or the probability that a stochastic signal has not reached a threshold up to time t, it is required to analyse the first-passage time (FPT) statistics. This has attracted considerable attention from physicists and mathematicians in the last decades [1][2][3][4][5][6] notably because of the relevance of FPT related quantities in contexts as varied as diffusion controlled reactions, finance, search processes, or biophysics 7,8 .
A single-target first-passage problem is entirely characterized by the so-called "survival probability" SðtÞ (the probability that the target has not been reached up to time t), or equivalently by the FPT distribution FðtÞ ¼ À∂ t SðtÞ. For a symmetric random walk in a confined domain, the mean FPT is in general finite and has been studied at length. This led recently to explicit results for broad classes of stochastic processes 2,[9][10][11][12] . The opposite case of unconfined random walks is drastically different. In this case, either the walker has a finite probability of never finding the target (non-compact random walks), or it reaches it with probability one (compact random walk) and the survival probability decays algebraically with time, SðtÞ $ S 0 =t θ , with θ the persistence exponent that does not depend on the initial distance to the target. In this case the mean FPT is often infinite so that the relevant observable to quantify FPT statistics is the long-time algebraic decay of the probability SðtÞ that the target has not been reached up to t. This, additional to the fact that θ can be nontrivial for non-Markovian random walks, has triggered a considerable amount of work to characterize the persistence exponent θ in a wide number of models of non-equilibrium statistical mechanics. Indeed, SðtÞ is an essential observable to quantify the kinetics of transport controlled reactions and the dynamics of coarsening in phase transitions in general 13,14 .
However, if one aims to evaluate the time t to wait for observing a first-passage event with a given likelihood, or to determine the dependence of the survival probability on the initial distance to the target, one needs to know the prefactor S 0 , which turns out to be much less characterized than the persistence exponent θ. Even for Markovian random walks this problem is not trivial 15 , as exemplified by recent studies for onedimensional Levy flights 16 , while only scaling relations for S 0 (with the initial distance to the target) are known 17 in fractal domains. However, if the dynamics of the random walker results from interactions with other degrees of freedom, the process becomes non-Markovian and the determination of S 0 becomes much more involved 18 . In this case, the only explicit results are derived from perturbation expansion around Markovian processes 19,20 , or have been obtained for particular processes such as "run and tumble" motion (driven by telegraphic noise 21 ) or the random acceleration process 22 . For long-range correlated processes, such as fractional Brownian Motion, the existence of S 0 is not even established rigourously 15,23 , and it has been found that straightforward adaptation of Markovian methods can lead to order-of-magnitude overestimations of S 0 and even to erroneous scalings 24 .
In this article, we rely on a non-perturbative strategy to determine S 0 , which is of crucial interest to quantify the statistics of long FPT events. Our main result is a relation between the prefactor S 0 in the long-time survival probability in free space and the mean FPT for the same process in a large confining volume. Our formula thus shows how to make use of the wealth of explicit results obtained recently on first-passage properties in confinement 2,9,10,25 to determine the decay of the free-space survival probability. This formula is shown to be robust and holds for Markovian or non-Markovian processes with stationary increments, that are scale invariant at long times with diverging moments of the position, in one or higher spatial dimensions, and also for processes displaying transient aging (i.e., processes with finite memory time, whose initial state is not stationary, see below). This theory is confirmed by simulations for a variety of stochastic processes, including highly correlated ones such as Fractional Brownian Motion.
Results
Markovian case. We consider a symmetric random walker of position rðtÞ moving on an infinite discrete lattice (potentially fractal) of dimension d f (see Fig. 1a for the continuous space counterpart) in continuous time t, in absence of external field. The initial position is r 0 . We assume that the increments are stationary (no aging), which means in particular that σðt; τÞ hjrðt þ τÞ À rðtÞj 2 i is independent of the elapsed time t. Note that in the case of fractal spaces, we use the standard "chemical" distance defined as the minimal number of steps to link two points on the lattice. We define the walk dimension d w such that σðt; τÞ / τ 2=d w for τ ! 1. Note that (i) this scale invariance is a b Fig. 1 First-passage problem with or without confinement. Two first-passage problems in which a random walker starting from a given site (green square) reaches a target (red disk) at the end of a stochastic trajectory: a in free space, b in a confined reflecting domain. Sample trajectories for fractional Brownian motion (H ¼ 0:45) are shown assumed only at long times, and that (ii) it implies that all even moments of the position diverge with time. We assume d w >d f so that the process is compact 26,27 (and eventually reaches any point with probability one). We also introduce the Hurst exponent We first consider the case of Markovian (memoryless) random walks. One can then define a propagator pðr; tjr 0 Þ, which represents the probability to observe the walker at site r at time t given that it started at r 0 at initial time. Note that p is defined in absence of target. We now add an absorbing target at site r ¼ 0 (different from r 0 ). We start our analysis with the standard renewal equation 1,18,28 : which relates the propagator p to the FPT distribution F that depends on r 0 . This equation is obtained by partitioning over the FPT to the target, and can be rewritten in Laplace space as where e FðsÞ ¼ R 1 0 dtFðtÞe Àst stands for the Laplace transform of FðtÞ. Here, we only focus on the long-time behavior of FðtÞ, that can be obtained by expanding Eq. (2) for small s. Scale invariance at long times implies 27 that for any site r where the notation "$" represents asymptotic equivalence, and K is a positive coefficient. Note that K is known to be position independent and is well characterized (at least numerically) for a large class of stochastic processes, including diffusion in a wide class of fractals 17 , [29][30][31] . We find that the small-s behavior of the propagator is where ΓðÁÞ is the Gamma function. Eqs. (2) and (4) (written for r ¼ 0 and r ¼ r 0 ) lead to Taking the inverse Laplace transform (and using FðtÞ ¼ À _ S) leads to SðtÞ $ S 0 =t θ with θ ¼ 1 À d f =d w (as found in ref. 17 ), and to This expression is exact and characterizes the decay of the survival probability of unconfined scale invariant Markovian random walks. We now consider the target search problem for the same random walk, with the only difference that it takes place in a confining volume V (that is equal to the number of sites N in our discrete formulation) (see Fig. 1b). For this problem, the mean FPT hTi is in general finite and it is known that it scales linearly with the volume and reads 2,9 hTi We recognize in the above expression the time integral of propagators appearing in Eq. (6), leading to Hence, for compact Markovian random walks, we have identified a proportionality relation between the prefactor S 0 that characterizes the long-time survival probability in free space and the rescaled mean FPT to the target in unconfined space. The proportionality coefficient involves the walk dimension d w and the coefficient K which characterizes the long-time decay of the propagator (see Eq. (3)). Formula (8) is the key result of this paper. As we proceed to show, it is very robust and is not limited to Markovian walks. As a first application, consider the case of scale invariant Markovian random walks (such as diffusion on fractals), for which it was shown 32 that T ' r d w Àd f 0 , where the mean waiting time on a given site is taken as unity, and r 0 is the initial source-target (chemical) distance. Inserting this formula into Eq. (8) thus leads to In this case, we thus recover the scaling result of ref. 17 but in addition obtain the value of the prefactor. We have checked this relation for the Sierpinski gasket: simulation results are shown in Fig. 2a. The long-time persistence is perfectly described by our formula without any fitting parameter for different source-target distances, confirming the validity of our approach (see SI for other examples).
As a second application, we can consider the one-dimensional Lévy stable process of index α, which is defined as the only Markovian process whose jump distribution is given by pðΔx; tÞ ¼ 1=ð2πÞ R 1 À1 e iΔx:kÀtjkj α dk. This process, defined in continuous space, is the continuous time limit of the Lévy Flight with same index α. Its walk dimension is d w ¼ α and it is compact for α>1, so that the first passage to a point target is well defined (note that we consider here the first arrival at the target, and not the first crossing event 33,34 ). For such a process, the prefactor S 0 for an unconfined random walk starting at a distance r 0 from the target has been shown to be S 0 ¼ α sinðπα=2Þ sinðπ=αÞΓð2 À αÞr αÀ1 0 =ðπΓð1=αÞðα À 1ÞÞ 35 . By computing the rescaled MFPT in confinement with Eq. (7), one can check that the relation (8), which can be readily generalized to continuous space, is still verified for this process.
Extension to non-Markovian processes. We now relax the Markov property and generalize our theory to the case of non-Markovian processes, i.e., displaying memory. In the following, we argue that the relation (8) yields much more accurate results for S 0 than Markov approximations; it is exact for processes with finite memory time, and is very precise (even though not exact) for strongly correlated processes such as the Fractional Brownian Motion. As the mean FPT in confinement has recently been characterized for non-Markovian Gaussian processes 25 , this equation (8) provides a means to estimate SðtÞ at long times, beyond persistence exponents, for a wide class of random walks with memory.
For simplicity, we consider one-dimensional processes and we switch to continuous space description. The stochastic trajectories xðtÞ are assumed to be continuous but non-smooth (the method in fact also applies to compact and not continuous processes, such as 1d Levy stable processes of index α>1 as discussed above), mathematically meaning that h _ x 2 i ¼ 1 and physically corresponding to very rough trajectories, similar to those of Brownian motion. We assume that the increments of the walk are stationary (meaning that there is no aging, even transient (In particular, the case of continuous time random walks (CTRWs) is not directly covered by our analysis; persistence exponents and prefactors for CTRWs can be obtained from the subordination principle)). This hypothesis is known to have two consequences: (i) the persistence exponent for the unconfined problem is exactly given by θ ¼ 1 À 1=d w 14,15,23,36-38 ; (ii) the mean FPT for the confined problem varies linearly with the confinement volume V, so that T is finite and has been identified as 25 : Here, pð0; tÞ is the probability density of x ¼ 0 at a time t after the initial state (where xð0Þ ¼ r 0 ), and p π ð0; tÞ denotes the probability density of finding the walker on the target at a time t after the first-passage: where pð0; t þ τjFPT ¼ τÞ is the probability density of x ¼ 0 at time t þ τ, given that the FPT is τ.
The starting point to relate T to S 0 consists in writing the generalization of Eq. (1) to non-smooth non-Markovian Non-stat. initial cond. Fig. 2 Survival probability SðtÞ for various stochastic processes. In all graphs, symbols are the results of stochastic simulations (detailed in SI), continuous lines give the theoretical predictions (Eq. (18)), and dashed line represent the predictions of the pseudo-Markovian approximation (The pseudo-Markovian approximation, which is similar to the Wilemski-Fixman approximation for the polymer cyclization kinetics problem, consists in using effective propagators in Eq. (18), i.e pðx; tjx 0 Þ ¼ e ÀðxÀx 0 Þ 2 =2ψðtÞ =ð2πψðtÞÞ d=2 .). a SðtÞ for a random walk on the Sierpinski gasket for two values of the initial (chemical) sourcetarget distance. Here, d f ¼ ln3=ln2, d w ¼ ln5=ln2, and K ' 0:30 31 . Simulations are shown for a fractal of generation 11. Continuous lines are the predictions of Eq. (9). b SðtÞ for a one-dimensional "bidiffusive" Gaussian process of MSD ψðtÞ ¼ t þ 30ð1 À e Àt Þ. c SðtÞ for a one-dimensional Rouse chain with N ¼ 20 monomers, for various source-to-target distance r 0 (indicated in the legend in units of the monomer length). d SðtÞ for the same system with N ¼ 15 and r 0 ¼ 3, comparing stationary initial conditions (the other monomers being initially at equilibrium) or non-stationary ones (for which all monomers start at the same position r 0 ). e SðtÞ for a one-dimensional FBM of MSD ψðtÞ ¼ t 2H with Hurst exponent H ¼ 0:34. f Two-dimensional FBM of MSD ψðtÞ ¼ t 2H in each spatial direction with H ¼ 0:35. The target is a disk of radius a ¼ 1 and r 0 is the distance to the target center. For (b), (c), (d), (e), and (f), the continuous lines represent our predictions (Eq. (18)), in which T is calculated by using the theories of refs. 12,25,48 ; in (b) and (c) the only hypothesis to predict T is that the distribution of supplementary degrees of freedoms at the FPT is Gaussian, in (e) and (f) we use the additional "stationary covariance" approximation. In (d), for non-stationary initial conditions, T is measured in simulations in confined space. A table that compares the values of S 0 in the theory and in the simulations is given in SI ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-10841-6 processes: To proceed further, we insert into Eq. (10) the expressions (11) and (12) of p π ð0; tÞ and pð0; tÞ: To avoid diverging integrals in the change of variables t ¼ u þ τ, we replace R 1 0 dtð:::Þ by lim A!1 R A 0 dtð:::Þ, so that Setting t ¼ uA and τ ¼ vA, we note that when A ! 1, only the large time behavior are involved in these integrals, where one can use the asymptotics FðAv; r 0 Þ $ S 0 θ=ðAvÞ 1þθ and which is a form imposed by dimensional analysis. As previously, K is the constant which characterizes the long-time behavior of the one point probability distribution function (i.e., pðx; tÞ $ t!1 K=t 1=d w ), G is a scaling function, with Gð1Þ ¼ 1, that does not depend on the geometrical parameters of the problem. Inserting these asymptotic behaviors into Eq. (14), we get: The fact that the above integral exists and is finite leads to the (known) relation θ ¼ 1 À 1=d w . This finally leads to the exact relation: We stress that the dependency of S 0 on the source-to-target distance, even when not trivial, is entirely contained in the term T. Indeed, the scaling function G depends only on the large scale properties of the random walk and not on the geometrical parameters.
While the exact determination of G is a challenging task, the following decoupling approximation turns out to be very accurate. In this approximation, the return probability to the target at a time t after the first-passage time is independent of the actual value of the FPT, which leads to pð0; t þ τjFPT ¼ τÞ ' p π ðtÞ for self-consistence reason. Within this decoupling approximation, G ' 1 and we obtain which generalizes Eq. (8) to non-Markovian processes. We now comment on the validity of this key relation. First, we stress that Eq. (18) is exact for processes with finite memory time (i.e. for which the correlation function of increments decays exponentially at long times). This comes from the very definition of the function G, which involves only large time scales in Eq. (15), over which this finite memory time becomes irrelevant. This case is illustrated here by considering a Gaussian process whose Mean Square Displacement function ψðtÞ ¼ h½xðt þ τÞ À xðτÞ 2 i is given by ψðtÞ ¼ Dt þ Bð1 À e Àλt Þ. This "bidiffusive" process involves two diffusive behaviors at long and short time scales, and presents only one relaxation time λ À1 . This is typically relevant to tracers moving in viscoelastic Maxwell fluids 39 , nematics 40 , or solutions of non-adsorbing polymers 41 . We also consider the effect of multiple relaxation times with the case that xðtÞ is the position of the first monomer of a flexible polymer chain with N monomers, in the most simple (Rouse, bead-spring) polymer model. We use recently obtained estimates of T in ref. 25 to obtain estimates of S 0 through Eq. (18) and compare with numerical simulations in Fig. 2b, c. We also compare with a pseudo-Markovian approximation (using Eq. (6) with effective "propagators" (The pseudo-Markovian approximation, which is similar to the Wilemski-Fixman approximation for the polymer cyclization kinetics problem, consists in using effective propagators in Eq. (18), i.e., pðx; tjx 0 Þ ¼ e ÀðxÀx 0 Þ 2 =2ψðtÞ =ð2πψðtÞÞ d=2 .)). Our prediction for S 0 is in good agreement with numerical simulations, and shows that even if the memory time is finite, memory effects are strong.
Second, it is showed in SI that Eq. (18) is also exact at first order in ε ¼ H À 1=2 for the fractional Brownian motion (FBM), which is an emblematic example of processes with infinite memory time. The FBM is used in fields as varied as hydrology 42 , finance 43 , and biophysics 44,45 . This Gaussian process is characterized by ½xðt þ τÞ À xðtÞ 2 ¼ κτ 2H , with 0<H<1. Third, in the strongly non-Markovian regime, where ε cannot be considered as small, it turns out that Eq. (18) provides a very accurate approximation (Fig. 2e) of S 0 , which takes the explicit form where β H is a function of H analyzed in ref. 25 . It can indeed be seen in Fig. 2e that Eq. (18) correctly predicts the long-time behavior of SðtÞ when H ¼ 0:34. For this value, non-Markovian effects are strong, as can be seen by comparing with the prediction of the pseudo-Markovian approximation, which is wrong by more than one order of magnitude (Fig. 2e, dashed line). The value of S 0 is slightly underestimated in the decoupling approximation, but can be made more precise by evaluating the scaling function G (see SI). Furthermore, our approach also holds in dimension higher than one, even for strongly correlated non-Markovian processes. Indeed, the dÀdimensional version of Eq. (18) (i.e., Eq. (8)) correctly predicts (but slightly underestimates) the value of S 0 for an example of two-dimensional FBM (Fig. 2f). In this example, the target radius a is not zero even if the a ! 0 limit is well defined for compact processes; the dependence of S 0 on the target radius is predicted to be the same as that of T, which is available in the non-Markovian theory of ref. 25 . Finally, in the case of processes with finite memory, we find that Eq. (18) also holds for non-stationary initial conditions. This is illustrated by considering the case of a flexible phantom polymer for which all monomers are placed initially at r 0 (instead of having the shape of a random equilibrium coil for stationary initial conditions). This non-stationary initial condition induces transiently aging dynamics, and S 0 is changed with respect to the case of stationary initial conditions, but is still predicted correctly by Eq. (18) (see Fig. 2d).
Finally, let us mention the case of the one-dimensional run and tumble process, where a particle switches between phases of constant velocities ± v with rate α. This process is smooth and is a priori not covered by our analysis. However, our relation (18) between S 0 and T=V is still exact, as is made clear by comparing the results for the mean FPT in confinement 21 and in semi-infinite space 46 . This agreement holds even for nonstationary initial conditions, where the probability p that the initial velocity is positive differs from 1=2: in this case, one can obtain S 0 ¼ ðr 0 þ pv=αÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2α=ðπv 2 Þ p ¼ T=ðKπÞ, with K ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi α=ð2πv 2 Þ p , and we can check that our relation still holds 21,46 . Furthermore, it also holds in the case of partially reflecting targets, as can be deduced from the results of ref. 47 . This suggests that our analysis can be extended to smooth non-Markovian processes with partial absorption as well.
Discussion
The determination of the survival probability SðtÞ, and in particular its dependence on the initial distance to the target, requires the knowledge of its prefactor S 0 , which has remained an elusive quantity up to now. In this article, we have bridged this gap by identifying a general relation between the long-time persistence and the mean FPT in confinement. The latter can be calculated with various recently introduced methods, for a large class of Markovian 2,10,11 and non-Markovian random walks 25 . Our theory holds for compact, unbiased walks with stationary increments that are scale invariant at long times (without confinement), with moments of the position that diverge with time. Our main result is Eq. (8), which is exact for both Markovian processes (such as diffusion in fractals) and for non-Markovian processes with finite memory time (for which memory effects are nevertheless quantitatively non-negligible). For long-ranged correlated processes such as FBM our formula provides a good approximation of S 0 in one or higher dimensions, and is found to be exact at first order in a perturbation expansion around Brownian motion. Together, our results thus improve our understanding of the impact of memory on the statistics of long first-passage events.
Data availability
The numerical data presented in Fig. 2 are available from the corresponding author on reasonable request.
Code availability
The code that generated these data are available from the corresponding author on reasonable request. | 5,733 | 2019-07-05T00:00:00.000 | [
"Mathematics"
] |