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image reconstruction based on an edge - sparsity assumption has become popular in recent years. many methods of this type are capable of reconstructing nearly perfect edge - sparse images using limited data. in this paper, we present a method to improve the accuracy of a suboptimal image resulting from an edge - sparsity image reconstruction method when compressed sensing or empirical data requirements are not met. the method begins with an edge detection from an initial edge - sparsity based reconstruction. from this edge map, a mask matrix is created which allows us to regularize exclusively in regions away from edges. by accounting for the spatial distribution of the sparsity, our method preserves edge information and and furthermore enhances suboptimal reconstructions to be nearly perfect from fewer data than needed by the initial method. we present results for two phantom images using a variety of initial reconstruction methods. | arxiv:1902.00092 |
this paper discusses the design and implementation of a python - based toolset to aid in assessing the response of the uk ' s advanced gas reactor nuclear power stations to earthquakes. the seismic analyses themselves are carried out with a commercial finite element solver, but understanding the raw model output this produces requires customised post - processing and visualisation tools. extending the existing tools had become increasingly difficult and a decision was made to develop a new, python - based toolset. this comprises of a post - processing framework ( aftershock ) which includes an embedded python interpreter, and a plotting package ( afterplot ) based on numpy and matplotlib. the new toolset had to be significantly more flexible and easier to maintain than the existing code - base, while allowing the majority of development to be carried out by engineers with little training in software development. the resulting architecture will be described with a focus on exploring how the design drivers were met and the successes and challenges arising from the choices made. | arxiv:1412.6410 |
the iot market is diverse and characterized by a multitude of vendors that support different device functions ( e. g., speaker, camera, vacuum cleaner, etc. ). within this market, iot security and observability systems use real - time identification techniques to manage these devices effectively. most existing iot identification solutions employ machine learning techniques that assume the iot device, labeled by both its vendor and function, was observed during their training phase. we tackle a key challenge in iot labeling : how can an ai solution label an iot device that has never been seen before and whose label is unknown? our solution extracts textual features such as domain names and hostnames from network traffic, and then enriches these features using google search data alongside catalog of vendors and device functions. the solution also integrates an auto - update mechanism that uses large language models ( llms ) to update these catalogs with emerging device types. based on the information gathered, the device ' s vendor is identified through string matching with the enriched features. the function is then deduced by llms and zero - shot classification from a predefined catalog of iot functions. in an evaluation of our solution on 97 unique iot devices, our function labeling approach achieved hit1 and hit2 scores of 0. 7 and 0. 77, respectively. as far as we know, this is the first research to tackle ai - automated iot labeling. | arxiv:2403.01586 |
building robust recognizers for arabic has always been challenging. we demonstrate the effectiveness of an end - to - end trainable cnn - rnn hybrid architecture in recognizing arabic text in videos and natural scenes. we outperform previous state - of - the - art on two publicly available video text datasets - alif and activ. for the scene text recognition task, we introduce a new arabic scene text dataset and establish baseline results. for scripts like arabic, a major challenge in developing robust recognizers is the lack of large quantity of annotated data. we overcome this by synthesising millions of arabic text images from a large vocabulary of arabic words and phrases. our implementation is built on top of the model introduced here [ 37 ] which is proven quite effective for english scene text recognition. the model follows a segmentation - free, sequence to sequence transcription approach. the network transcribes a sequence of convolutional features from the input image to a sequence of target labels. this does away with the need for segmenting input image into constituent characters / glyphs, which is often difficult for arabic script. further, the ability of rnns to model contextual dependencies yields superior recognition results. | arxiv:1711.02396 |
the conventional approach for analyzing gene expression data involves clustering algorithms. cluster analyses provide partitioning of the set of genes that can predict biological classification based on its similarity in n - dimensional space. in this study, we investigate whether network analysis will provide an advantage over the traditional approach. we identify the advantages and disadvantages of using the value - based and the rank - based construction in creating a graph representation of the original gene - expression data in a time - series format. we tested four community detection algorithms, namely, the clauset - newman - moore ( greedy ), louvain, leiden, and girvan - newman algorithms in predicting the 5 functional groups of genes. we used the adjusted rand index to assess the quality of the predicted communities with respect to the biological classifications. we showed that girvan - newman outperforms the 3 modularity - based algorithms in both value - based and ranked - based constructed graphs. moreover, we also show that when compared to the conventional clustering algorithms such as k - means, spectral, birch, and agglomerative algorithms, we obtained a higher ari with girvan - newman. this study also provides a tool for graph construction, visualization, and community detection for further analysis of gene expression data. | arxiv:2208.10119 |
i present a new model for the quark mass matrices, which uses four scalar doublets together with a horizontal symmetry s3 x z3. the model is inspired on a suggestion made a few years ago by ma, but it is different. the predictions | vts | \ approx ms / mb and | vub / vcb | > 0. 085 are obtained. flavour - changing neutral yukawa interactions do not exist in the down - type - quark sector. | arxiv:hep-ph/9907538 |
safeguarding privacy in sensitive training data is paramount, particularly in the context of generative modeling. this can be achieved through either differentially private stochastic gradient descent or a differentially private metric for training models or generators. in this paper, we introduce a novel differentially private generative modeling approach based on a gradient flow in the space of probability measures. to this end, we define the gradient flow of the gaussian - smoothed sliced wasserstein distance, including the associated stochastic differential equation ( sde ). by discretizing and defining a numerical scheme for solving this sde, we demonstrate the link between smoothing and differential privacy based on a gaussian mechanism, due to a specific form of the sde ' s drift term. we then analyze the differential privacy guarantee of our gradient flow, which accounts for both the smoothing and the wiener process introduced by the sde itself. experiments show that our proposed model can generate higher - fidelity data at a low privacy budget compared to a generator - based model, offering a promising alternative. | arxiv:2312.08227 |
the well - posedness is established for mckean - vlasov sdes driven by $ \ alpha $ - stable noises ( $ 1 < \ alpha < 2 $ ). in this model, the drift is h \ " { o } lder continuous in space variable and lipschitz continuous in distribution variable with respect to the sum of wasserstein and weighted variation distances, while the noise coefficient satisfies the lipschitz condition in distribution variable with respect to the sum of two wasserstein distances. the main tool relies on zvonkin ' s transform, a time - change technique and a two - step fixed point argument. | arxiv:2306.10970 |
we consider dirichlet exterior value problems related to a class of non - local schr \ " odinger operators, whose kinetic terms are given in terms of bernstein functions of the laplacian. we prove elliptic and parabolic aleksandrov - bakelman - pucci type estimates, and as an application obtain existence and uniqueness of weak solutions. next we prove a refined maximum principle in the sense of berestycki - nirenberg - varadhan, and a converse. also, we prove a weak anti - maximum principle in the sense of cl \ ' ement - peletier, valid on compact subsets of the domain, and a full anti - maximum principle by restricting to fractional schr \ " odinger operators. furthermore, we show a maximum principle for narrow domains, and a refined elliptic abp - type estimate. finally, we obtain liouville - type theorems for harmonic solutions and for a class of semi - linear equations. our approach is probabilistic, making use of the properties of subordinate brownian motion. | arxiv:1711.09267 |
two - point correlators and self - correlators of primordial perturbations in quasi - de sitter spacetime backgrounds are considered. for large separations two - point correlators exhibit nearly scale invariance, while for short distances self - correlators need standard renormalization. we study the deformation of two - point correlators to smoothly match the self - correlators at coincidence. the corresponding angular power spectrum is evaluated in the sachs - wolfe regime of low multipoles. scale invariance is maintained, but the amplitude of $ c _ { \ ell } $ could change in a non - trivial way. | arxiv:1401.6912 |
we demonstrate a " bottom up " approach to the computational design of a multifunctional chemical sensor. general techniques are employed for describing the adsorption coverage and resistance properties of the sensor based on density functional theory ( dft ) and non - equilibrium green ' s function methodologies ( negf ), respectively. specifically, we show how ni and cu doped metallic ( 6, 6 ) single - walled carbon nanotubes ( swnts ) may work as effective multifunctional sensors for both co and nh3. | arxiv:1004.5334 |
a representative but not exhaustive review of the schwinger - dyson equation ( sde ) approach to the nonperturbative study of qcd is presented. the main focus is the sde for the quark self energy but studies of the gluon propagator and quark - gluon vertex are also discussed insofar as they are important to the quark sde. the scope of this article is the application of these equations to the study of dynamical chiral symmetry breaking, quark confinement and the phenomenology of the spectrum and dynamics of qcd. | arxiv:hep-ph/9303278 |
in this paper, we present our numerical simulation results on the stimulated brillouin scattering ( sbs ) with injection of an ordinary mode ( o - mode ) electromagnetic wave ( our pump wave ) with frequencies 70 ghz and 110 ghz. solving the fourier transformed vlasov equation in the velocity space, creates a profile for distribution function. time evolution of the distribution function is investigated as well. considering an average density for plasma fusion ( n _ { 0 } ~ 10 ^ { 19 } m ^ { - 3 } ), we gain a profile for density. then two - dimensional instability rate for sbs is obtained. so, the fluctuation of distribution function affects density and again density affects instability rate. increasing the incident light wave frequency causes the instability growth rate to decrease. time evolution shows a clear damping for instability rate since the pump wave ' s energy is absorbed in plasma ( plasma heating ). furthermore, changing landau damping for ion acoustic waves ( iaw ) by changing ion - to - electron temperature ratio is presented as well, because this damping is more dominant in high temperatures. | arxiv:1612.02214 |
this paper considers two point boundary value problems for conservative systems defined in multiple coordinate systems, and develops a flexible a - posteriori framework for computer assisted existence proofs. our framework is applied to the study collision and near collision orbits in the circular restricted three body problem. in this case the coordinate systems are the standard rotating coordinates, and the two levi - civita coordinate systems regularizing collisions with each of the massive primaries. the proposed framework is used to prove the existence of a number of orbits which have long been studied numerically in the celestial mechanics literature, but for which there are no existing analytical proofs at the mass and energy values considered here. these include transverse ejection / collisions from one primary body to the other, str \ " { o } mgren ' s assymptotic periodic orbits ( transverse homoclinics for $ l _ { 4, 5 } $ ), families of periodic orbits passing through collision, and orbits connecting $ l _ 4 $ to ejection or collision. | arxiv:2205.03922 |
in this work we calculate neutron and proton energy gaps in neutron star matter, using the bonn meson - - exchange interactions and a model - - space approach to the gap equation. this approach allows a consistent calculation of energy gaps and single particle energies with the model - - space brueckner - - hartree - - fock ( mbhf ) method, without double counting of two - - particle correlations. neutron energy gaps are calculated at zero and finite temperature. proton energy gaps are calculated at beta equilibrium, and it is shown that the inclusion of muons has a significant effect. the results are compared with those of other works, and the implications for neutron star physics are briefly discussed. | arxiv:nucl-th/9602020 |
the coincidence cross - section and the interference structure function, r _ lt, were measured for the 12c ( e, e ' p ) 11b reaction at quasielastic kinematics and central momentum transfer of q = 400 mev / c. the measurement was at an opening angle of theta _ pq = 11 degrees, covering a range in missing energy of e _ m = 0 to 65 mev. the r _ lt structure function is found to be consistent with zero for e _ m > 50 mev, confirming an earlier study which indicated that r _ l vanishes in this region. the integrated strengths of the p - and s - shell are compared with a distorted wave impulse approximation calculation. the s - shell strength and shape are compared with a hartree fock - random phase approximation calculation. the dwia calculation overestimates the cross sections for p - and s - shell proton knockout as expected, but surprisingly agrees with the extracted r _ lt value for both shells. the hf - rpa calculation describes the data more consistently, which may be due to the inclusion of 2 - body currents in this calculation. | arxiv:nucl-ex/9709003 |
datasets are critical for scientific research, playing an important role in replication, reproducibility, and efficiency. researchers have recently shown that datasets are becoming more important for science to function properly, even serving as artifacts of study themselves. however, citing datasets is not a common or standard practice in spite of recent efforts by data repositories and funding agencies. this greatly affects our ability to track their usage and importance. a potential solution to this problem is to automatically extract dataset mentions from scientific articles. in this work, we propose to achieve such extraction by using a neural network based on a bi - lstm - crf architecture. our method achieves f1 = 0. 885 in social science articles released as part of the rich context dataset. we discuss the limitations of the current datasets and propose modifications to the model to be done in the future. | arxiv:2405.13135 |
we study central simple algebras in various ways, focusing on the role of $ p $ - central subspaces. the first part of my thesis is dedicated to the study of clifford algebras. the standard clifford algebra of a given form is the generic associative algebra containing a $ p $ - central subspace whose exponentiation form is equal to the given form. there is an old question as for whether these algebras have representations of finite rank over the center, and jointly with daniel krashen and max lieblich we managed to provide a positive answer. different generalizations of the structure of the clifford algebra are presented and studied in that part too. the second part is dedicated to the study of $ p $ - central subspaces of given central simple algebras, mainly tensor products of cyclic algebras of degree $ p $. among the results, we prove that $ 5 $ is the upper bound for the dimension of 4 - central subspaces of cyclic algebras of degree 4 containing pairs of standard generators. the third part is dedicated to chain lemmas. chain lemmas are of importance in the theory of central simple algebras, because they form one approach to solving the word problem for the brauer group. we prove the chain lemma for biquaternion algebras, both in characteristic 2 and characteristic not 2, and prove some partial results on the chain lemmas for cyclic algebras of degree $ p $. the fourth part is dedicated to the more computational aspects of the theory. it contains results on quaternion polynomial equations and on left eigenvalues of quaternion matrices. | arxiv:1406.0069 |
we use the ( m, n ) phase diagram recently introduced in hep - th / 0309116 to investigate the phase structure of black holes and strings on cylinders. we first prove that any static neutral black object on a cylinder can be put into an ansatz for the metric originally proposed in hep - th / 0204047, generalizing a result of wiseman. using the ansatz, we then show that all branches of solutions obey the first law of thermodynamics and that any solution has an infinite number of copies. the consequences of these two results are analyzed. based on the new insights and the known branches of solutions, we finally present an extensive discussion of the possible scenarios for the gregory - laflamme instability and the black hole / string transition. | arxiv:hep-th/0309230 |
we establish new hoelder and lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro - differential equations, by the classical ishii - lions ' s method. we thus extend the hoelder regularity results recently obtained by barles, chasseigne and imbert ( 2011 ). in addition, we deal with a new class of nonlocal equations that we term mixed integro - differential equations. these equations are particularly interesting, as they are degenerate both in the local and nonlocal term, but their overall behavior is driven by the local - nonlocal interaction, e. g. the fractional diffusion may give the ellipticity in one direction and the classical diffusion in the complementary one. | arxiv:1107.3228 |
we establish a mathematical framework that formally validates the two - phase ` ` super - population viewpoint ' ' proposed by hartley and sielken [ biometrics 31 ( 1975 ) 411 - - 422 ] by defining a product probability space which includes both the design space and the model space. the methodology we develop combines finite population sampling theory and the classical theory of infinite population sampling to account for the underlying processes that produce the data under a unified approach. our key results are the following : first, if the sample estimators converge in the design law and the model statistics converge in the model, then, under certain conditions, they are asymptotically independent, and they converge jointly in the product space ; second, the sample estimating equation estimator is asymptotically normal around a super - population parameter. | arxiv:math/0603078 |
we consider the interference of two photons with different colors in the context of a hong - ou - mandel experiment, in which single photons enter each of the input ports of a beam splitter, and exit in the same, albeit undetermined, output port. such interference is possible if one uses an active ( energy - non - conserving ) beam splitter. we find scenarios in which one " red " and one " blue " photon enter the beam splitter, and either two red or two blue photons exit, but never one of each color. we show how the precise form of the active beam - splitter transformation determines in what way the spectral degrees of freedom of the input photons should be related to each other for perfect destructive interference of the different - color components in the output. we discuss two examples of active beam splitters : one is a gedanken experiment involving a moving mirror and the other is a more realistic example involving four - wave mixing in an optical fiber. | arxiv:1002.0350 |
we consider the low energy description of five dimensional models of supergravity with boundaries comprising a vector multiplet and the universal hypermultiplet in the bulk. we analyse the spontaneous breaking of supersymmetry induced by the vacuum expectation value of superpotentials on the boundary branes. when supersymmetry is broken, the moduli corresponding to the radion, the zero mode of the vector multiplet scalar field and the dilaton develop a potential in the effective action. we compute the resulting soft breaking terms and give some indications on the features of the corresponding particle spectrum. we consider some of the possible phenomenological implications when supersymmetry is broken on the hidden brane. | arxiv:hep-th/0405143 |
in the colliding - wind region of massive binaries, non - thermal radio emission occurs. this non - thermal radio emission ( due to synchrotron radiation ) has so far been observed at centimetre wavelengths. at millimetre wavelengths, the stellar winds and the colliding - wind region emit more thermal free - free radiation, and it is expected that any non - thermal contribution will be difficult or impossible to detect. we aim to determine if the material in the colliding - wind region contributes substantially to the observed millimetre fluxes of a colliding - wind binary. we also try to distinguish the synchrotron emission from the free - free emission. we monitored the massive binary cyg ob2 # 8a at 3 mm with the northern extended millimeter array ( noema ) interferometer of the institut de radioastronomie millimetrique ( iram ). the data were collected in 14 separate observing runs ( in 2014 and 2016 ), and provide good coverage of the orbital period. the observed millimetre fluxes range between 1. 1 and 2. 3 mjy, and show phase - locked variability, clearly indicating that a large part of the emission is due to the colliding - wind region. a simple synchrotron model gives fluxes with the correct order of magnitude, but with a maximum that is phase - shifted with respect to the observations. qualitatively this phase shift can be explained by our neglect of orbital motion on the shape of the colliding - wind region. a model using only free - free emission results in only a slightly worse explanation of the observations. additionally, on the map of our observations we also detect the o6. 5 iii star cyg ob2 # 8b, for which we determine a 3 mm flux of 0. 21 + - 0. 033 mjy. the question of whether synchrotron radiation or free - free emission dominates the millimetre fluxes of cyg ob2 # 8a remains open. more detailed modelling of this system, based on solving the hydrodynamical equations, is required to give a definite answer. | arxiv:1708.04834 |
we present the extension of our previous results for three - loop yukawa coupling beta - functions to the case of complex yukawa matrices describing the flavour structure of the sm. the calculation is carried out in the context of unbroken phase of the sm with the help of the mincer program in a general linear gauge and cross - checked by means of matad / bamba codes. in addition, ambiguities in yukawa matrix beta - functions are studied. | arxiv:1406.7171 |
we investigate electromechanical properties of two - dimensional mos $ _ 2 $ monolayers in the 1h, 1t, and 1t $ ^ \ prime $ structures as a function of charge doping by using density functional theory. we find isotropic elastic moduli in the 1h and 1t structures, while the 1t $ ^ \ prime $ structure exhibits an anisotropic elastic modulus. moreover, the 1t structure is shown to have a negative poisson ' s ratio, while poisson ' s ratios of the 1h and 1t $ ^ \ prime $ are positive. by charge doping, the monolayer mos $ _ 2 $ shows a reversibly strain and work density per cycle ranging from - 0. 68 % to 2. 67 % and from 4. 4 to 36. 9 mj / m $ ^ 3 $, respectively, making them suitable for applications in electromechanical actuators. stress generated is also examined in this work and we find that 1t and 1t $ ^ \ prime $ mos $ _ 2 $ monolayers relatively have better performance than 1h mos $ _ 2 $ monolayer. we argue that such excellent electromechanical performance originate from the electrical conductivity of the metallic 1t and semimetallic 1t $ ^ \ prime $ structures high young ' s modulus of about $ 150 - 200 $ gpa. | arxiv:1711.00188 |
we present the coupling of two frameworks - - the pseudo - open boundary simulation method known as constant potential molecular dynamics simulations ( c $ \ mu $ md ), combined with qmmd calculations - - to describe the properties of graphene electrodes in contact with electrolytes. the resulting c $ \ mu $ qmmd model was then applied to three ionic solutions ( licl, nacl and kcl in water ) at bulk solution concentrations ranging from 0. 5 m up to 6 m in contact with a charged graphene electrode. the new approach we are describing here provides a simulation protocol to control the concentration of the electrolyte solutions while including the effects of a fully polarizable electrode surface. thanks to this coupling, we are able to accurately model both the electrode and solution side of the double layer and provide a thorough analysis of the properties of electrolytes at charged interfaces, such as the screening ability of the electrolyte and the electrostatic potential profile. we also report the calculation of the integral electrochemical double layer capacitance in the whole range of concentrations analysed for each ionic species, while the qm simulations provide access to the differential and integral quantum capacitance. we highlight how subtle features, such as the adsorption of potassium at the interface or the tendency of the ions to form clusters, emerge from our simulations, contribute to explaining the ability of graphene to store charge and suggest implications for desalination. | arxiv:2212.03990 |
real - time data collection and analysis in large experimental facilities present a great challenge across multiple domains, including high energy physics, nuclear physics, and cosmology. to address this, machine learning ( ml ) - based methods for real - time data compression have drawn significant attention. however, unlike natural image data, such as cifar and imagenet that are relatively small - sized and continuous, scientific data often come in as three - dimensional data volumes at high rates with high sparsity ( many zeros ) and non - gaussian value distribution. this makes direct application of popular ml compression methods, as well as conventional data compression methods, suboptimal. to address these obstacles, this work introduces a dual - head autoencoder to resolve sparsity and regression simultaneously, called \ textit { bicephalous convolutional autoencoder } ( bcae ). this method shows advantages both in compression fidelity and ratio compared to traditional data compression methods, such as mgard, sz, and zfp. to achieve similar fidelity, the best performer among the traditional methods can reach only half the compression ratio of bcae. moreover, a thorough ablation study of the bcae method shows that a dedicated segmentation decoder improves the reconstruction. | arxiv:2111.05423 |
we show that first order semilinear pdes by stochastic perturbation are well - posedness for globally holder continuous and bounded vector field, with an integrability condition on the divergence. this result extends the liner case presented in [ 2 ]. the proof is based on in the stochastic characteristics method and a version of the commuting lemma. | arxiv:1310.7404 |
optical imaging polarimetry was conducted on the hydrogen poor superluminous supernova 2020znr during 3 phases after maximum light ( approximately + 34 days, + 288 days and + 289 days ). after instrumental and interstellar polarization correction, all measurements are consistent with null - polarization detection. modelling the light curve with a magnetar spin - down model shows that sn 2020znr has similar magnetar and ejecta parameters to other slsne. a comparison of the best - fit values discussed in the literature on sn 2017egm and sn 2015bn, two hydrogen poor slsne showing an increase of polarization after maximum light, suggests that sn 2020znr has higher mass ejecta that may prevent access to the geometry of the inner ejecta with optical polarimetry. the combined information provided by spectroscopy and light curve analysis of type i slsne may be an interesting avenue to categorize the polarization properties of this class of transients. this approach would require to expand the sample of slsne polarimetry data currently available with early and late time epochs new measurements. | arxiv:2201.03887 |
glass, a ubiquitous state of matter like a frozen liquid, is a seminal issue across fundamental and applied sciences and has long been investigated in the framework of classical mechanics. a challenge in glass physics is the exploration of the quantum - mechanical behaviour of glass. experimentally, however, the real quantum manifestation of glass and the relationship between classical and quantum glass are totally unknown and remain to be observed in real systems. here, we report the direct observation of classical - to - quantum evolution in the frustration - induced charge glass state exhibited by interacting electrons in organic materials. we employ raman spectroscopy to capture a snapshot of the charge density distribution of each molecule in a series of charge glasses formed on triangular lattices with different geometrical frustrations. in less frustrated glass, the charge density profile exhibits a particle - like two - valued distribution ; however, it becomes continuous and narrowed with increasing frustration, demonstrating the classical - to - quantum crossover. moreover, the charge density distribution shows contrasting temperature evolution in classical and quantum glasses, enabling us to delineate energy landscapes with distinct features. the present result is the first to experimentally identify the quantum charge glass and show how it emerges from classical glass. | arxiv:2205.10795 |
this paper shows how particle hopping models fit into the context of traffic flow theory. connections between fluid - dynamical traffic flow models, which derive from the navier - stokes - equations, and particle hopping models are shown. in some cases, these connections are exact and have long been established, but have never been viewed in the context of traffic theory. in other cases, critical behavior of traffic jam clusters can be compared to instabilities in the partial differential equations. finally, it is shown how this leads to a consistent picture of traffic jam dynamics. | arxiv:cond-mat/9509075 |
a microscopic configuration - interaction ( ci ) methodology is introduced to enable bottom - up schroedinger - equation emulation of unconventional superconductivity in ultracold optical traps. we illustrate the method by exploring the properties of lithium - 6 atoms in a single square plaquette in the hole - pairing regime, and by analyzing the entanglement ( symmetry - preserving ) and disentanglement physics ( via symmetry - breaking, associated with the separation of charge and spin density waves ) of two coupled plaquettes in the same regime. the single - occupancy rvb states contribute only partially to the exact many - body solutions, and the ci results map onto a hubbard hamiltonian, but not onto the double - occupancy - excluding t - j one. for the double - plaquette case, effects brought about by breaking the symmetry between two weakly - interacting plaquettes, either by distorting, or by tilting and detuning, one of the plaquettes with respect to the other, as well as spectral changes caused by increased coupling between the two plaquettes, are explored. | arxiv:1703.10128 |
stimulated emission depletion ( sted ) microscopy has become a powerful imaging and localized excitation method beating the diffraction barrier for improved lateral spatial resolution in cellular imaging, lithography, etc. due to specimen - induced aberrations and scattering distortion, it has been a great challenge for sted to maintain consistent lateral resolution deeply inside the specimens. here we report on a deep imaging sted microscopy by using gaussian beam for excitation and hollow bessel beam for depletion ( gb - sted ). the proposed scheme shows the improved imaging depth up to ~ 155 { \ mu } m in solid agarose sample, ~ 115 { \ mu } m in pdms and ~ 100 { \ mu } m in phantom of gray matter in brain tissue with consistent super resolution, while the standard sted microscopy shown a significantly reduced lateral resolution at the same imaging depth. the results indicate the excellent imaging penetration capability of gb - sted, making it a promising tool for deep 3d imaging optical nanoscopy and laser fabrication. | arxiv:1510.04076 |
fairness - aware machine learning has garnered significant attention in recent years because of extensive use of machine learning in sensitive applications like judiciary systems. various heuristics, and optimization frameworks have been proposed to enforce fairness in classification \ cite { del2020review } where the later approaches either provides empirical results or provides fairness guarantee for the exact minimizer of the objective function \ cite { celis2019classification }. in modern machine learning, stochastic gradient descent ( sgd ) type algorithms are almost always used as training algorithms implying that the learned model, and consequently, its fairness properties are random. hence, especially for crucial applications, it is imperative to construct confidence interval ( ci ) for the fairness of the learned model. in this work we provide ci for test unfairness when a group - fairness - aware, specifically, disparate impact ( di ), and disparate mistreatment ( dm ) aware linear binary classifier is trained using online sgd - type algorithms. we show that asymptotically a central limit theorem holds for the estimated model parameter of both di and dm - aware models. we provide online multiplier bootstrap method to estimate the asymptotic covariance to construct online ci. to do so, we extend the known theoretical guarantees shown on the consistency of the online bootstrap method for unconstrained sgd to constrained optimization which could be of independent interest. we illustrate our results on synthetic and real datasets. | arxiv:2304.13950 |
in fiber reinforced composites ( frc ) fiber breakage is a common phenomenon resulting in stress concentration. this high stress gets transfer in the vicinity of the breakage which is quantified by stress transfer coefficient ( stc ). in this paper, an attempt is made to check the effect of fiber volume fraction and the distribution of the fibers on stc and ineffective length. the fiber volume fraction is changed considering three cases : 1 ) by changing the number of fibers, 2 ) by changing the dimension of the represntative volume element ( rve ) and 3 ) by changing the fiber radius. cases with change in dimension of rve and change in fiber radius, periodic and semi - random arrangents of fibers are considered. from the analysis of 200 rve ' s for each volume fraction in random and semi - random arrangements, it is observed that the distribution of stc does not follow any standard distribution, even if the fiber arrangement follows the normal distribution. the fiber cross - sectional dimension plays a critical role in regaining the broken fiber strength. the periodic arrangement of fibers can be said to be beneficial over the random arrangement considering the stress transfer from the broken fiber. | arxiv:2209.09801 |
considering a charged black hole ( bh ) surrounded by a perfect fluid radiation field ( pfrf ) in rastall gravity, we investigate this bh shadow and photon sphere on different spherical accretions backgrounds. the effect of the pfrf parameter / bh charge on the critical impact parameter is studied by investigating the light deflection near this bh. the luminosity of these bh shadows in different spherical accretions is obtained, respectively. it is found that the shadow of this bh with infalling spherical accretion is darker than static spherical accretion, and the photon sphere with infalling spherical accretion is brighter than a static one. we creatively investigate the effects of the bh charge / pfrf parameter on the luminosity of bh shadow and photon sphere. the results implying that the bh shadow is a signature of space - time geometry, and the photon sphere luminosity is affected by accretion materials and bh itself. | arxiv:2205.07242 |
parallel i / o refers to the ability of scientific programs to concurrently read / write from / to a single file from multiple processes executing on distributed memory platforms like compute clusters. in the hpc world, i / o becomes a significant bottleneck for many real - world scientific applications. in the last two decades, there has been significant research in improving the performance of i / o operations in scientific computing for traditional languages including c, c + +, and fortran. as a result of this, several mature and high - performance libraries including romio ( implementation of mpi - io ), parallel hdf5, parallel i / o ( pio ), and parallel netcdf are available today that provide efficient i / o for scientific applications. however, there is very little research done to evaluate and improve i / o performance of java - based hpc applications. the main hindrance in the development of efficient parallel i / o java libraries is the lack of a standard api ( something equivalent to mpi - io ). some adhoc solutions have been developed and used in proprietary applications, but there is no general - purpose solution that can be used by performance hungry applications. as part of this project, we plan to develop a java - based parallel i / o api inspired by the mpi - io bindings ( mpi 2. 0 standard document ) for c, c + +, and fortran. once the java equivalent api of mpi - io has been developed, we will develop a reference implementation on top of existing java messaging libraries. later, we will evaluate and compare performance of our reference java parallel i / o library with c / c + + counterparts using benchmarks and real - world applications. | arxiv:2305.07414 |
we use the holographic hardwall model to calculate the masses of light glueball states with odd spin and p = c = - 1 associated with odderons. considering dirichlet and neumann boundary conditions we obtain expressions for the odderon regge trajectories consistent with those calculated using other approaches. | arxiv:1301.4457 |
we study mazur rotations problem focusing on the metric aspects of the action of the isometry group and semitransitivity properties. | arxiv:2109.01906 |
we study the susceptible - infected - recovered model of epidemics in the vicinity of the threshold infectivity. we derive the distribution of total outbreak size in the limit of large population size $ n $. this is accomplished by mapping the problem to the first passage time of a random walker subject to a drift that increases linearly with time. we recover the scaling results of ben - naim and krapivsky that the effective maximal size of the outbreak scales as $ n ^ { 2 / 3 } $, with the average scaling as $ n ^ { 1 / 3 } $, with an explicit form for the scaling function. | arxiv:q-bio/0701024 |
in this paper, we introduce a new conception of pseudorandom phase ensemble to simulate a quantum ensemble. a pseudorandom sequence is inseparability and integral that are demonstrated only for a whole sequence not for a single phase unit, which is similar to that of quantum ensembles and a quantum particle. by using the ensemble conception, we demonstrate non - locality properties for classical fields similar to quantum entanglement. | arxiv:1604.07652 |
the search for an application of near - term quantum devices is widespread. quantum machine learning is touted as a potential utilisation of such devices, particularly those which are out of the reach of the simulation capabilities of classical computers. in this work, we propose a generative quantum machine learning model, called the ising born machine ( ibm ), which we show cannot, in the worst case, and up to suitable notions of error, be simulated efficiently by a classical device. we also show this holds for all the circuit families encountered during training. in particular, we explore quantum circuit learning using non - universal circuits derived from ising model hamiltonians, which are implementable on near term quantum devices. we propose two novel training methods for the ibm by utilising the stein discrepancy and the sinkhorn divergence cost functions. we show numerically, both using a simulator within rigetti ' s forest platform and on the aspen - 1 16q chip, that the cost functions we suggest outperform the more commonly used maximum mean discrepancy ( mmd ) for differentiable training. we also propose an improvement to the mmd by proposing a novel utilisation of quantum kernels which we demonstrate provides improvements over its classical counterpart. we discuss the potential of these methods to learn ` hard ' quantum distributions, a feat which would demonstrate the advantage of quantum over classical computers, and provide the first formal definitions for what we call ` quantum learning supremacy '. finally, we propose a novel view on the area of quantum circuit compilation by using the ibm to ` mimic ' target quantum circuits using classical output data only. | arxiv:1904.02214 |
solar magnetic activity follows regular cycles of about 11 years with an inversion of polarity in the poles every 22 years. this changing surface magnetism impacts the properties of the acoustic modes. the acoustic mode frequency shifts are a good proxy of the magnetic cycle. in this letter we investigate solar magnetic activity cycles 23 and 24 through the evolution of the frequency shifts of low - degree modes ( l = 0, 1, and 2 ) in three frequency bands. these bands probe properties between 74 and 1575 km beneath the surface. the analysis was carried out using observations from the space instrument global oscillations at low frequency and the ground - based birmingham solar oscillations network and global oscillation network group. the frequency shifts of radial modes suggest that changes in the magnetic field amplitude and configuration likely occur near the sun ' s surface rather than near its core. the maximum shifts of solar cycle 24 occurred earlier at mid and high latitudes ( relative to the equator ) and about 1550 km beneath the photosphere. at this depth but near the equator, this maximum aligns with the surface activity but has a stronger magnitude. at around 74 km deep, the behaviour near the equator mirrors the behaviour at the surface, while at higher latitudes, it matches the strength of cycle 23. | arxiv:2410.23928 |
bcs theory has been widely successful at describing elemental bulk superconductors. yet, as the length scales of such superconductors approach the atomic limit, dimensionality as well as the environment of the superconductor can lead to drastically different and unpredictable superconducting behavior. here, we report a threefold enhancement of the superconducting critical temperature and gap size in ultrathin epitaxial al films on si ( 111 ), when approaching the 2d limit, based on high - resolution scanning tunneling microscopy / spectroscopy ( stm / sts ) measurements. in magnetic field, the al films show type ii behavior and the meservey - tedrow - fulde ( mtf ) effect for in - plane magnetic fields. using spatially resolved spectroscopy, we characterize the vortex structure in the mtf regime and find strong deviations from the typical abrikosov vortex. we corroborate these findings with calculations that unveil the role of odd - frequency pairing and a paramagnetic meissner effect. these results illustrate two striking influences of reduced dimensionality on a bcs superconductor and present a new platform to study bcs superconductivity in large magnetic fields. | arxiv:2210.10645 |
the orbital period of the recurrent nova u sco has been observed to decrease during the 1999 outburst. in an outburst mass is ejected from the surface of the white dwarf. the separation of the binary system widens and the orbital period increases. we find that magnetic braking between outbursts, mass transfer to the companion, and frictional angular momentum losses during outbursts are all too small to account for this unexpected change. we find, however, that if the secondary has a sufficiently strong magnetic field, b = 8x10 ^ 3 g, then the ejected material can couple to it and corrotate with the system. the ejected material gains angular momentum while the binary system loses it and the period decreases. if such a strong magnetic field is indeed present, then we predict that a period decrease should be observed also during the current 2010 outburst. if, however, the presence of such a field can be ruled out observationally, then the cause for the period decrease ( if confirmed ) remains unknown. | arxiv:1003.4207 |
we present a theoretical model and experimental demonstration of thin liquid film deformations due to a dielectric force distribution established by surface electrodes. we model the spatial electric field produced by a pair of parallel electrodes and use it to evaluate the stress on the interface through maxwell stresses. by coupling this force with the young - laplace equation, we obtain the deformation of the interface. to validate our theory, we design an experimental setup which uses microfabricated electrodes to achieve spatial dielectrophoretic actuation of a thin liquid film, while providing measurements of microscale deformations through digital holographic microscopy. we characterize the deformation as a function of the electrode - pair geometry and film thickness, showing very good agreement with the model. based on the insights from the characterization of the system, we pattern conductive lines of electrode pairs on the surface of a microfluidic chamber and demonstrate the ability to produce complex two - dimensional deformations. the films can remain in liquid form and be dynamically modulated between different configurations or polymerized to create solid structures with high surface quality. | arxiv:2102.11019 |
the primary challenge of density - functional - theory exploration of alloy systems concerns the size of computational model. small alloy models can hardly exhibit the chemical disorder properly, while large models induce difficulty in sampling the alignments within the massive material space. we study this problem with the { \ gamma } phase of the mixed halide inorganic perovskite alloy cspbbr $ _ 2 $ cl. the distribution of alloy formation energy becomes narrower when the size of the model system increases along $ \ sqrt { 2 } \ times \ sqrt { 2 } \ times2 $, $ 2 \ times2 \ times2 $, and $ 2 \ sqrt { 2 } \ times2 \ sqrt { 2 } \ times2 $ models. this is primarily because the distribution of br distribution parameters, which plays a leading role in determining the formation energy range, is more narrow for larger models. as a result, larger entropy stability effect can be observed with larger models especially at high temperatures, for which the approximation using mixing entropy based on the ideal solution model becomes better. | arxiv:2406.18013 |
we consider solutions to the linear wave equation on a ( maximally extended ) schwarzschild spacetime, assuming only that the solution decays suitably at spatial infinity on a complete cauchy hypersurface. ( in particular, we allow the support of the solution to contain the bifurcate event horizon. ) we prove uniform decay bounds for the solution in the exterior regions, including the uniform bound cv _ + ^ { - 1 }, where v _ + denotes max { v, 1 } and v denotes eddington - finkelstein advanced time. we also prove uniform decay bounds for the flux of energy through the event horizon and null infinity. the estimates near the event horizon exploit an integral energy identity normalized to local observers. this estimate can be thought to quantify the celebrated red - shift effect. the results in particular give an independent proof of the classical uniform boundedness theorem of kay and wald, without recourse to the discrete isometries of spacetime. | arxiv:gr-qc/0512119 |
using the categorical description of supergeometry we give an explicit construction of the diffeomorphism supergroup of a compact finite - dimensional supermanifold. the construction provides the diffeomorphism supergroup with the structure of a frechet supermanifold. in addition, we derive results about the structure of diffeomorphism supergroups. | arxiv:0904.2726 |
this paper proposes a definition of gravitational observables and of their path integral formula within the framework of adm foliation and the choice of unimodular gauge classes. the method enforces a brst invariant gauge fixing of the lapse and shift fields. it yields the quantum level extension of the known classical property that the conformal classes of internal metrics of constant lorentz time leafs define the gravitational physical degrees of freedom. | arxiv:2012.01116 |
extending our previous work ( rosu, mancas, chen, ann. phys. 343 ( 2014 ) 87 - 102 ), we define supersymmetric partner potentials through a particular riccati solution of the form f ( x ) = ( x - c ) ^ 2 - 1, where c is a real shift parameter, and work out the quartic double - well family of one - parameter isospectral potentials obtained by using the corresponding general riccati solution. for these parametric double well potentials, we study how the localization properties of the two wells depend on the parameter of the potentials for various values of the shifting parameter. we also consider the supersymmetric parametric family of the first double - well potential in the razavy chain of double well potentials corresponding to f ( x ) = ( 1 / 2 ) sinh 2x - 2 ( 1 + sqrt 2 ) sinh 2x / [ ( 1 + sqrt 2 ) cosh 2x + 1 ], both unshifted and shifted, to test and compare the localization properties | arxiv:1311.6866 |
light scalar fields can naturally couple disformally to standard model fields without giving rise to the unacceptably large fifth forces usually associated with light scalars. we show that these scalar fields can still be studied and constrained through their interaction with photons, and focus particularly on changes to the cosmic microwave background spectral distortions and violations of the distance duality relation. we then specialise our constraints to scalars which could play the role of axionic quintessence. | arxiv:1306.4168 |
there exists two distinct off - shell $ { \ mathcal { n } } = 2 $ supergravities in three dimensions. they are also referred to as $ { \ mathcal { n } } = ( 1, 1 ) $ and $ { \ mathcal { n } } = ( 2, 0 ) $ supergravities, and they arise from the coupling of the weyl multiplet to a compensating scalar or vector multiplet, respectively, followed by fixing of conformal symmetries. the $ { \ mathcal { n } } = ( p, q ) $ terminology refers to the underlying anti - de sitter superalgebras $ osp ( 2, p ) \ oplus osp ( 2, q ) $ with $ r $ - symmetry group $ so ( p ) \ times so ( q ) $. we construct off - shell invariants of these theories up to fourth order in derivatives. as an application of these results, we determine the special combinations of the $ { \ mathcal { n } } = ( 1, 1 ) $ invariants that admit anti - de sitter vacuum solution about which there is a ghost - free massive spin - 2 multiplet of propagating modes. we also show that the $ { \ mathcal { n } } = ( 2, 0 ) $ invariants do not allow such possibility. | arxiv:1412.3118 |
deep reinforcement learning ( rl ) algorithms can solve complex sequential decision tasks successfully. however, they have a major drawback of having poor sample efficiency which can often be tackled by knowledge reuse. in multi - agent reinforcement learning ( marl ) this drawback becomes worse, but at the same time, a new set of opportunities to leverage knowledge are also presented through agent interactions. one promising approach among these is peer - to - peer action advising through a teacher - student framework. despite being introduced for single - agent rl originally, recent studies show that it can also be applied to multi - agent scenarios with promising empirical results. however, studies in this line of research are currently very limited. in this paper, we propose heuristics - based action advising techniques in cooperative decentralised marl, using a nonlinear function approximation based task - level policy. by adopting random network distillation technique, we devise a measurement for agents to assess their knowledge in any given state and be able to initiate the teacher - student dynamics with no prior role assumptions. experimental results in a gridworld environment show that such an approach may indeed be useful and needs to be further investigated. | arxiv:1905.01357 |
entanglement appears in two different ways in quantum mechanics, namely as a property of states and as a property of measurement outcomes in joint measurements. by combining these two aspects of entanglement, it is possible to generate nonlocality between particles that never interacted, using the protocol of entanglement swapping. we investigate the communication cost of classically simulating this process. while the communication cost of simulating nonlocal correlations of entangled states appears to be generally quite low, we show here that infinite communication is required to simulate entanglement swapping. this result is derived in the scenario of bilocality, where distant sources of particles are assumed to be independent, and takes advantage of a previous result of massar et al. [ phys. rev. a { \ bf 63 }, 052305 ( 2001 ) ]. our result implies that any classical model simulating entanglement swapping must either assume that ( i ) infinite shared randomness is available between any two locations in the universe, or that ( ii ) infinite communication takes place. | arxiv:1103.5058 |
in this paper we present a new bootstrap procedure for elliptic systems with two unknown functions. combining with the $ l ^ p $ - $ l ^ q $ - estimates, it yields the optimal $ l ^ \ infty $ - regularity conditions for the three well - known types of weak solutions : $ h _ 0 ^ 1 $ - solutions, $ l ^ 1 $ - solutions and $ l ^ 1 _ \ delta $ - solutions. thanks to the linear theory in $ l ^ p _ \ delta ( \ omega ) $, it also yields the optimal conditions for a priori estimates for $ l ^ 1 _ \ delta $ - solutions. based on the a priori estimates, we improve known existence theorems for some classes of elliptic systems. | arxiv:0805.4550 |
in this paper, we studied systematically the semileptonic decays $ b _ s \ to \ phi l ^ + l ^ - $ with $ l ^ - = ( e ^ -, \ mu ^ -, \ tau ^ - ) $ by using the perturbative qcd ( pqcd ) and the " pqcd + lattice " factorization approach, respectively. we first evaluated all relevant form factors $ f _ i ( q ^ 2 ) $ in the low $ q ^ 2 $ region using the pqcd approach, and we also took the available lattice qcd results at the high - $ q ^ 2 $ region as additional input to improve the extrapolation of $ f _ i ( q ^ 2 ) $ from the low - $ q ^ 2 $ region to the endpoint $ q ^ 2 _ { max } $. we then calculated the branching ratios and many other physical observables : $ a _ { fb } ^ { l } $, $ f _ l ^ { \ phi } $, $ s _ { 3, 4, 7 } $, $ a _ { 5, 6, 8, 9 } $ and the clean angular observables $ p _ { 1, 2, 3 } $ and $ p ^ { \ prime } _ { 4, 5, 6, 8 } $. from our studies, we find the following points : ( a ) the pqcd and " pqcd + lattice " predictions of $ { \ cal b } ( b _ s \ to \ phi \ mu ^ + \ mu ^ - ) $ are about $ 7 \ times 10 ^ { - 7 } $, which agree well with the lhcb measured values and the qcd sum rule prediction within still large errors ; ( b ) we defined and calculated the ratios of the branching ratios $ r _ \ phi ^ { e \ mu } $ and $ r _ \ phi ^ { \ mu \ tau } $ ; ( c ) the pqcd and " pqcd + lattice " predictions of the longitudinal polarization $ f _ l $, the cp averaged angular coefficients $ s _ { 3, 4, 7 } $ and the cp asymmetry angular coefficients $ a _ { 5, 6, 8, 9 } $, agree with the lhcb measurements in all considered bins within the still large experimental errors ; and ( d ) for those currently still unknown observables $ r _ \ phi ^ { e | arxiv:2011.11409 |
glaucoma remains among the leading causes of blindness despite many treatment options available today. effective treatment requires early diagnosis, which is difficult to achieve with existing imaging technologies that detect the already inflicted irreversible posterior eye damage. one improved approach could be to detect the changes in trabecular meshwork of the anterior eye that precede the intraocular pressure buildup and vision loss. here we report a device that enables in vivo exploration of trabecular meshwork at cell resolution. the instrument combines two orthogonal views : en face view of time - domain full - field oct for high - resolution and cross - sectional view of spectral - domain oct for aligning to the meshwork. the device resolves micron - level corneoscleral and uveal pores, meshwork beams and internal elastic fibers, ciliary body tendons and trabecular cell nuclei. capable of detecting blockage of trabecular pores, orthogonal view oct presents a promising solution to the long - standing problem of early glaucoma diagnosis. future clinical adoption of the device is facilitated by the compact footprint and broad functionality that includes corneal imaging in healthy subjects and patients ( with keratoconus, fuchs endothelial dystrophy ) using the same design. | arxiv:2209.11803 |
in this article we show that the holevo capacity of a classical quantum channel, can be reached not only by a povm but by von neumann measurement too. furthermore we show two use of this fact 1 ) we can generalize the classical compound channel to quantum environment and with this new measure technique we can give an optimal coding / decoding algorithm to it. 2 ) we give an algorithm, with it a classical system can be decoded by quantum apparatus in linear time, which is a surprising result, because best known optimal classical decoding algorithm need n * log ( n ) time. this means that if a quantum machine can perform arbitrarily von neumann measurement with only two possible outcome, then it can solve non - polynomial classical problems in linear time. | arxiv:0704.2513 |
we derive the gravitational waveform from the collapse of a rapidly rotating supermassive star ( sms ) core leading directly to a seed of a supermassive black hole ( smbh ) in axisymmetric numerical - relativity simulations. we find that the peak strain amplitude of gravitational waves emitted during the black - hole formation is $ \ approx 5 \ times 10 ^ { - 21 } $ at the frequency $ f \ approx 5 $ \, mhz for an event at the cosmological redshift $ z = 3 $, if the collapsing sms core is in the hydrogen - burning phase. such gravitational waves will be detectable by space laser interferometric detectors like elisa with signal - to - noise ratio $ \ approx 10 $, if the sensitivity is as high as lisa for $ f = 1 $ - - 10 \, mhz. the detection of the gravitational - wave signal will provide a potential opportunity for testing the direct - collapse scenario for the formation of a seed of smbhs. | arxiv:1606.07147 |
it is pointed out that the " counter example " presented in the comment is a family of probe wave functions which are increasingly broad as the shift becomes large. furthermore, the author ' s variational calculation is not correct in the sense that we have to gauge fix the freedom of the phase translation. it is shown that there are two kinds of solutions, normalizable and un - normalizable. the former is our optimal solution, and the latter is what he found. it seems only the former is relevant from a practical point of view. | arxiv:1304.1352 |
this paper analyzes the suitability of a beamed propulsion concept having properties consistent with the impulse gravity generator described by podkletnov et al. [ physics / 0108005 ]. the use of this propulsion concept for orbital maneuver, earth - to - orbit, interplanetary, and interstellar applications based on presently available experimental results and theory is considered, and areas for future research needed to better characterize this phenomenon are discussed. a beam of radiation or particles with the properties described for the impulse gravity generator would appear to be an excellent candidate for use in beamed spacecraft propulsion. besides the usual benefits of beamed propulsion, it would not need sails or other special spacecraft components to function, could safely provide high accelerations to delicate components, and might operate at higher efficiencies than other beamed propulsion concepts. | arxiv:physics/0209023 |
some estimates for the transverse single spin asymmetry, a _ n, in the inclusive processes l p ( transv. pol. ) - - > h x, given in a previous paper, are expanded and compared with new experimental data. the predictions are based on the sivers distributions and the collins fragmentation functions which fit the azimuthal asymmetries measured in semi - inclusive deep inelastic scattering ( sidis ) processes ( l p ( transv. pol. ) - - > l ' h x ). the factorisation in terms of transverse momentum dependent distribution and fragmentation functions ( tmd factorisation ) - - i. e., the theoretical framework in which sidis azimuthal asymmetries are analysed - - is assumed to hold also for the inclusive process l p - - > h x at large p _ t. the values of a _ n thus obtained agree in sign and shape with the data. some predictions are given for future experiments. | arxiv:1404.6465 |
the initial mass function ( imf ) of the first pop iii stars remains a persistent mystery. their predicted massive nature implies the existence of stars exploding as pair - instability supernovae ( pisn ), but no observational evidence had been found. now, the lamost survey claims to have discovered a pure pisn descendant, j1010 + 2358, at $ { \ rm [ fe / h ] } = - 2. 4 $. here we confirm that a massive 250 - 260 $ { \ rm m _ \ odot } $ pisn is needed to reproduce the abundance pattern of j1010 + 2358. however, the pisn contribution can be as low as 10 %, since key elements are missing to discriminate between scenarios. we investigate the implications of this discovery for the pop iii imf, by statistical comparison with the predictions of our cosmological galaxy formation model, nefertiti. first, we show that the non - detection of mono - enriched pisn descendants at $ { \ rm [ fe / h ] } < - 2. 5 $ allows us to exclude : ( i ) a flat imf at a 90 % confidence level ; and ( ii ) a larson type imf with characteristic mass $ m _ { \ rm ch } / { \ rm m _ \ odot } > 191. 16x - 132. 44 $, where x is the slope, at a 75 % confidence level. secondly, we show that if j1010 + 2358 has only inherited < 70 % of its metals from a massive pisn, no further constraints can be put on the pop iii imf. if, instead, j1010 + 2358 will be confirmed to be a nearly pure ( > 90 % ) pisn descendant, it will offer strong and complementary constraints on the pop iii imf, excluding the steepest and bottom - heaviest imfs : $ m _ { \ rm ch } / { \ rm m _ \ odot } < 143. 21x - 225. 94 $. our work shows that even a single detection of a pure pisn descendant can be crucial to our understanding of the mass distribution of the first stars. | arxiv:2312.05309 |
let $ \ mathcal { a } \ subseteq { [ n ] \ choose a } $ and $ \ mathcal { b } \ subseteq { [ n ] \ choose b } $ be two families of subsets of $ [ n ] $, we say $ \ mathcal { a } $ and $ \ mathcal { b } $ are cross - intersecting if $ a \ cap b \ neq \ emptyset $ for all $ a \ in \ mathcal { a } $, $ b \ in \ mathcal { b } $. in this paper, we study cross - intersecting families in the multi - part setting. by characterizing the independent sets of vertex - transitive graphs and their direct products, we determine the sizes and structures of maximum - sized multi - part cross - intersecting families. this generalizes the results of hilton ' s and frankl - - tohushige ' s on cross - intersecting families in the single - part setting. | arxiv:1809.08756 |
we employ quantum molecular dynamic simulations to investigate the behavior of benzene under shock conditions. the principal hugoniot derived from the equation of state is determined. we compare our firs - principles results with available experimental data and provide predictions of chemical reactions for shocked benzene. the decomposition of benzene is found under the pressure of 11 gpa. the nonmetal - metal transition, which is associated with the rapid c - h bond breaking and the formation of atomic and molecular hydrogen, occurs under the pressure around 50 gpa. additionally, optical properties are also studied. | arxiv:0912.5272 |
we present a full description of the n - probability density function of the galaxy number density fluctuations. this n - pdf is given in terms, on the one hand, of the cold dark matter correlations and, on the other hand, of the galaxy bias parameter. the method relies on the assumption commonly adopted that the dark matter density fluctuations follow a local non - linear transformation of the initial energy density perturbations. the n - pdf of the galaxy number density fluctuations allows for an optimal estimation of the bias parameter ( e. g., via maximum - likelihood estimation, or bayesian inference if there exists any a priori information on the bias parameter ), and of those parameters defining the dark matter correlations, in particular its amplitude ( $ \ sigma _ 8 $ ). it also provides the proper framework to perform model selection between two competitive hypotheses. the parameters estimation capabilities of the n - pdf are proved by sdss - like simulations ( both ideal log - normal simulations and mocks obtained from las damas simulations ), showing that our estimator is unbiased. we apply our formalism to the 7th release of the sdss main sample ( for a volume - limited subset with absolute magnitudes $ m _ r \ leq - 20 $ ). we obtain $ \ hat { b } = 1. 193 \ pm 0. 074 $ and $ \ hat { \ sigma _ 8 } = 0. 862 \ pm 0. 080 $, for galaxy number density fluctuations in cells of a size of $ 30h ^ { - 1 } $ mpc. different model selection criteria show that galaxy biasing is clearly favoured. | arxiv:1506.07794 |
we analyze the phemomenon of induced fermion number at finite temperature. at finite temperature, the induced fermion number $ < n > $ is a thermal expectation value, and we compute the finite temperature fluctuations, $ ( \ delta n ) ^ 2 = < n ^ 2 > - < n > ^ 2 $. while the zero temperature induced fermion number is topological and is a sharp observable, the finite temperature induced fermion number is generically nontopological, and is not a sharp observable. the fluctuations are due to the mixing of states inherent in any finite temperature expectation value. we analyze in detail two different cases in 1 + 1 dimensional field theory : fermions in a kink background, and fermions in a chiral sigma model background. at zero temperature the induced fermion numbers for these two cases are very similar, but at finite temperature they are very different. the sigma model case is generic and the induced fermion number is nontopological, but the kink case is special and the fermion number is topological, even at finite temperature. there is a simple physical interpretation of all these results in terms of the spectrum of the fermions in the relevant background, and many of the results generalize to higher dimensional models. | arxiv:hep-th/0103061 |
methods for the analysis of the control process. = = = industrial engineering = = = industrial engineering is a branch of engineering that concerns the development, improvement, implementation, and evaluation of integrated systems of people, money, knowledge, information, equipment, energy, material, and process. industrial engineering draws upon the principles and methods of engineering analysis and synthesis, as well as mathematical, physical, and social sciences together with the principles and methods of engineering analysis and design to specify, predict, and evaluate results obtained from such systems. = = = production systems engineering = = = production systems engineering ( pse ) is an emerging branch of engineering intended to uncover fundamental principles of production systems and utilize them for analysis, continuous improvement, and design. = = = interface design = = = interface design and its specification are concerned with assuring that the pieces of a system connect and inter - operate with other parts of the system and with external systems as necessary. interface design also includes assuring that system interfaces are able to accept new features, including mechanical, electrical, and logical interfaces, including reserved wires, plug - space, command codes, and bits in communication protocols. this is known as extensibility. human - computer interaction ( hci ) or human - machine interface ( hmi ) is another aspect of interface design and is a critical aspect of modern systems engineering. systems engineering principles are applied in the design of communication protocols for local area networks and wide area networks. = = = mechatronic engineering = = = mechatronic engineering, like systems engineering, is a multidisciplinary field of engineering that uses dynamic systems modeling to express tangible constructs. in that regard, it is almost indistinguishable from systems engineering, but what sets it apart is the focus on smaller details rather than larger generalizations and relationships. as such, both fields are distinguished by the scope of their projects rather than the methodology of their practice. = = = operations research = = = operations research supports systems engineering. operations research, briefly, is concerned with the optimization of a process under multiple constraints. = = = performance engineering = = = performance engineering is the discipline of ensuring a system meets customer expectations for performance throughout its life. performance is usually defined as the speed with which a certain operation is executed or the capability of executing a number of such operations in a unit of time. performance may be degraded when operations queued to execute are throttled by limited system capacity. for example, the performance of a packet - switched network is characterized by the end - | https://en.wikipedia.org/wiki/Systems_engineering |
in this paper, we continue to develop aubry - mather and weak kam theories for contact hamiltonian systems $ h ( x, u, p ) $ with certain dependence on the contact variable $ u $. for the lipschitz dependence case, we obtain some properties of the ma \ ~ { n } \ ' { e } set. for the non - decreasing case, we provide some information on the aubry set, such as the comparison property, graph property and a partially ordered relation for the collection of all projected aubry sets with respect to backward weak kam solutions. moreover, we find a new flow - invariant set $ \ tilde { \ mathcal { s } } _ s $ consists of strongly static orbits, which coincides with the aubry set $ \ tilde { \ mathcal { a } } $ in classical hamiltonian systems. nevertheless, a class of examples are constructed to show $ \ tilde { \ mathcal { s } } _ s \ subsetneqq \ tilde { \ mathcal { a } } $ in the contact case. as their applications, we find some new phenomena appear even if the strictly increasing dependence of $ h $ on $ u $ fails at only one point, and we show that there is a difference for the vanishing discount problem from the negative direction between the minimal viscosity solution and non - minimal ones. | arxiv:2107.07088 |
this paper disproves a conjecture of wang, wu, yan and xie, and answers in negative a question in dvorak, pekarek and sereni. in return, we pose five open problems. | arxiv:2002.07998 |
we propose a novel algorithm for selection of dangerous n - 2 contingencies associated with line or generator failures. the algorithm is based on iterative filtering of the set of all possible double contingencies. it is certified to identify all the dangerous contingencies, and has the complexity comparable to the n - 1 contingency screening. tests performed on realistic model of polish power grid with about 3000 buses show that only two iterations of algorithm allow one to certify the safety of 99. 9 % of all double contingencies, leaving only 0. 1 % of the most dangerous ones for direct analysis. | arxiv:1303.3938 |
this is a review of searches for supersymmetry ( susy ) with the atlas detector in proton - proton collisions at a center - of - mass energy of 7 tev at the large hadron collider at cern. the review covers results that have been published, or submitted for publication, up to september 2012, many of which cover the full 7 tev data - taking period. no evidence for susy has been seen ; some possibilities for future directions are discussed. | arxiv:1209.1742 |
employing the data from orbital periods and masses of extra - solar planets in 166 multiple planetary systems, the period - ratio and mass - ratio of adjacent planet pairs are studied. the correlation between the period - ratio and mass - ratio is confirmed and found to have a correlation coefficient of 0. 5303 with a 99 % confidence interval ( 0. 3807, 0. 6528 ). a comparison with the distribution of synthetic samples from a monte carlo simulation reveals the imprint of planet - planet interactions on the formation of adjacent planet pairs in multiple planetary systems. | arxiv:1501.03562 |
we present a multihistogram reweighting technique for nonequilibrium markov chains with discrete energies. the method generalizes the single histogram method of yin et al. [ phys. rev. e72, 036122 ( 2005 ) ], making it possible to calculate the time evolution of observables at a posteriori chosen couplings based on a set of simulations performed at other couplings. in the same way as multihistogram reweighting in an equilibrium setting improves the practical reweighting range as well as use of available data compared to single histogram reweighting, the method generalizes the multihistogram advantages to nonequilibrium simulations. we demonstrate the procedure for the ising model with metropolis dynamics, but stress that the method is generally applicable to a range of models and monte carlo update schemes. | arxiv:1304.1656 |
we prove that fargues - scholze ' s semisimplified local langlands correspondence ( for quasisplit groups ) with $ \ overline { \ mathbb { f } } _ \ ell $ - coefficients is compatible with deligne and kazhdan ' s philosophy of close fields. from this, we deduce that the same holds with $ \ overline { \ mathbb { q } } _ \ ell $ - coefficients after restricting to wild inertia, addressing questions of gan - harris - sawin and scholze. the proof involves constructing a moduli space of nonarchimedean local fields and then extending fargues - scholze ' s work to this context. | arxiv:2407.07063 |
a method of transitional automorphic mapping of the genome on itself ( tamgi ) is aimed at combining detection and reconstruction of correlational and quasi - periodic motifs in the viral genomic rna / dna sequences. the motifs reconstructed by tamgi are robust with respect to indels and point mutations and can be tried as putative therapeutic targets. we developed and tested the relevant theory and statistical criteria for tamgi applications. the applications of tamgi are illustrated by the study of motifs in the genomes of the severe acute respiratory syndrome coronaviruses sars - cov and sars - cov - 2 ( the latter coronavirus sars - cov - 2 being responsible for the covid - 19 pandemic ) packaged within filament - like helical capsid. such ribonucleocapsid is transported into spherical membrane envelope with incorporated spike glycoproteins. two other examples concern the genomes of viruses with icosahedral capsids, satellite tobacco mosaic virus ( stmv ) and bacteriophage phix174. a part of the quasi - periodic motifs in these viral genomes was evolved due to weakly specific cooperative interaction between genomic ssrna / ssdna and nucleocapsid proteins. the symmetry of the capsids leads to the natural selection of specific quasi - periodic motifs in the related genomic sequences. generally, tamgi provides a convenient tool for the study of numerous molecular mechanisms with participation of both quasi - periodic motifs and complete repeats, the genome organization, contextual analysis of cis / trans regulatory elements, data mining, and correlations in the genomic sequences. | arxiv:2010.07006 |
in four dimensions there are 4 different types of extremal maxwell / scalar black holes characterized by a scalar coupling parameter $ a $ with $ a = 0, 1 / \ sqrt { 3 }, 1, \ sqrt { 3 } $. these black holes can be described as intersections of ten - - dimensional non - singular ramond - ramond objects, i. e. ~ $ d $ - branes, waves and taub - nut solitons. using this description it can be shown that the four - - dimensional black holes decompactify near the core to higher - - dimensional { \ em non - singular } solutions. in terms of these higher - - dimensional non - singular solutions we define a non - vanishing entropy for all four black hole types from a four - - dimensional point of view. | arxiv:hep-th/9605216 |
the state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. how can one visualize such operators for coupled spin systems? a general approach is presented which consists of several shapes representing linear combinations of spherical harmonics. it is applicable to an arbitrary number of spins and can be interpreted as a generalization of wigner functions. the corresponding visualization transforms naturally under non - selective spin rotations as well as spin permutations. examples and applications are illustrated for the case of three spins 1 / 2. | arxiv:1409.5417 |
analog quantum simulators rely on programmable quantum devices to emulate hamiltonians describing various physical phenomenon. photonic coupled cavity arrays are a promising platform for realizing such devices. using a silicon photonic coupled cavity array made up of 8 high quality - factor resonators and equipped with specially designed thermo - optic island heaters for independent control of cavities, we demonstrate a programmable device implementing tight - binding hamiltonians with access to the full eigen - energy spectrum. we report a ~ 50 % reduction in the thermal crosstalk between neighboring sites of the cavity array compared to traditional heaters, and then present a control scheme to program the cavity array to a given tight - binding hamiltonian. | arxiv:2210.05070 |
we study public goods games played on networks with possibly non - reciprocal relationships between players. examples for this type of interactions include one - sided relationships, mutual but unequal relationships, and parasitism. it is well known that many simple learning processes converge to a nash equilibrium if interactions are reciprocal, but this is not true in general for directed networks. however, by a simple tool of rescaling the strategy space, we generalize the convergence result for a class of directed networks and show that it is characterized by transitive weight matrices. additionally, we show convergence in a second class of networks ; those rescalable into networks with weak externalities. we characterize the latter class by the spectral properties of the absolute value of the network ' s weight matrix and show that it includes all directed acyclic networks. | arxiv:2101.03863 |
the recently - discovered, nearby young supernova remnant in the southeast corner of the older vela supernova remnant may have been seen in measurements of nitrate abundances in antarctic ice cores. such an interpretation of this twenty - year - old ice - core data would provide a more accurate dating of this supernova than is possible purely using astrophysical techniques. it permits an inference of the supernova4s $ { } ^ { 44 } $ ti yield purely on an observational basis, without reference to supernova modelling. the resulting estimates of the supernova distance and light - arrival time are 200 pc and 700 years ago, implying an expansion speed of 5, 000 km / s for the supernova remnant. such an expansion speed has been argued elsewhere to imply the explosion to have been a 15 $ m _ \ odot $ type ii supernova. this interpretation also adds new evidence to the debate as to whether nearby supernovae can measurably affect nitrate abundances in polar ice cores. | arxiv:astro-ph/9909010 |
remote sensing change captioning ( rsicc ) aims to describe changes between bitemporal images in natural language. existing methods often fail under challenges like illumination differences, viewpoint changes, blur effects, leading to inaccuracies, especially in no - change regions. moreover, the images acquired at different spatial resolutions and have registration errors tend to affect the captions. to address these issues, we introduce second - cc, a novel rsicc dataset featuring high - resolution rgb image pairs, semantic segmentation maps, and diverse real - world scenarios. second - cc which contains 6, 041 pairs of bitemporal rs images and 30, 205 sentences describing the differences between images. additionally, we propose mmodalcc, a multimodal framework that integrates semantic and visual data using advanced attention mechanisms, including cross - modal cross attention ( cmca ) and multimodal gated cross attention ( mgca ). detailed ablation studies and attention visualizations further demonstrate its effectiveness and ability to address rsicc challenges. comprehensive experiments show that mmodalcc outperforms state - of - the - art rsicc methods, including rsiccformer, chg2cap, and psnet with + 4. 6 % improvement on bleu4 score and + 9. 6 % improvement on cider score. we will make our dataset and codebase publicly available to facilitate future research at https : / / github. com / changecapsinrs / secondcc | arxiv:2501.10075 |
this paper addresses well - posedness issues for the initial value problem ( ivp ) associated with the generalized zakharov - kuznetsov equation, namely, \ { equation * } \ quad \ left \ { \ { array } { lll } { \ displaystyle u _ t + \ partial _ x \ delta u + u ^ ku _ x = 0, } \ qquad ( x, y ) \ in \ mathbb { r } ^ 2, \, \, \, \, t > 0, { \ displaystyle u ( x, y, 0 ) = u _ 0 ( x, y ) }. \ { array } \ right. \ { equation * } for $ 2 \ leq k \ leq 7 $, the ivp above is shown to be locally well - posed for data in $ h ^ s ( \ mathbb { r } ^ 2 ) $, $ s > 3 / 4 $. for $ k \ geq8 $, local well - posedness is shown to hold for data in $ h ^ s ( \ mathbb { r } ^ 2 ) $, $ s > s _ k $, where $ s _ k = 1 - 3 / ( 2k - 4 ) $. furthermore, for $ k \ geq3 $, if $ u _ 0 \ in h ^ 1 ( \ mathbb { r } ^ 2 ) $ and satisfies $ \ | u _ 0 \ | _ { h ^ 1 } \ ll1 $, then the solution is shown to be global in $ h ^ 1 ( \ mathbb { r } ^ 2 ) $. for $ k = 2 $, if $ u _ 0 \ in h ^ s ( \ mathbb { r } ^ 2 ) $, $ s > 53 / 63 $, and satisfies $ \ | u _ 0 \ | _ { l ^ 2 } < \ sqrt3 \, \ | \ phi \ | _ { l ^ 2 } $, where $ \ phi $ is the corresponding ground state solution, then the solution is shown to be global in $ h ^ s ( \ mathbb { r } ^ 2 ) $. | arxiv:1010.5404 |
bergman ' s ring $ e _ p $, parameterized by a prime number $ p $, is a ring with $ p ^ 5 $ elements that cannot be embedded in a ring of matrices over any commutative ring. this ring was discovered in 1974. in 2011, climent, navarro and tortosa described an efficient implementation of $ e _ p $ using simple modular arithmetic, and suggested that this ring may be a useful source for intractable cryptographic problems. we present a deterministic polynomial time reduction of the discrete logarithm problem in $ e _ p $ to the classical discrete logarithm problem in $ \ zp $, the $ p $ - element field. in particular, the discrete logarithm problem in $ e _ p $ can be solved, by conventional computers, in sub - exponential time. | arxiv:1206.1077 |
a model in which the soft collisions of the nucleon are described in terms of interactions of its two constituents ( a quark and a diquark ) is proposed. when adjusted to describe precisely the elastic proton - proton scattering data and supplemented with the idea of wounded constituents, the model accounts rather well for the centrality dependence of particle production in the central rapidity region at rhic energies. | arxiv:nucl-th/0611021 |
the anomalies of a very general class of non local dirac operators are computed using the $ \ zeta $ - function definition of the fermionic determinant and an asymmetric version of the wigner transformation. for the axial anomaly all new terms introduced by the non locality can be brought to the standard minimal bardeen ' s form. some extensions of the present techniques are also commented. | arxiv:hep-th/9910230 |
non - equilibrium dynamics in an interacting fe - c nanoparticle sample, exhibiting a low temperature spin glass like phase, has been studied by low frequency ac - susceptibility and magnetic relaxation experiments. the non - equilibrium behavior shows characteristic spin glass features, but some qualitative differences exist. the nature of these differences is discussed. | arxiv:cond-mat/9909123 |
let $ x $ be a ball quasi - banach function space on $ { \ mathbb r } ^ n $ satisfying some mild assumptions and let $ \ alpha \ in ( 0, n ) $ and $ \ beta \ in ( 1, \ infty ) $. in this article, when $ \ alpha \ in ( 0, 1 ) $, the authors first find a reasonable version $ \ widetilde { i } _ { \ alpha } $ of the fractional integral $ i _ { \ alpha } $ on the ball campanato - type function space $ \ mathcal { l } _ { x, q, s, d } ( \ mathbb { r } ^ n ) $ with $ q \ in [ 1, \ infty ) $, $ s \ in \ mathbb { z } _ + ^ n $, and $ d \ in ( 0, \ infty ) $. then the authors prove that $ \ widetilde { i } _ { \ alpha } $ is bounded from $ \ mathcal { l } _ { x ^ { \ beta }, q, s, d } ( \ mathbb { r } ^ n ) $ to $ \ mathcal { l } _ { x, q, s, d } ( \ mathbb { r } ^ n ) $ if and only if there exists a positive constant $ c $ such that, for any ball $ b \ subset \ mathbb { r } ^ n $, $ | b | ^ { \ frac { \ alpha } { n } } \ leq c \ | \ mathbf { 1 } _ b \ | _ x ^ { \ frac { \ beta - 1 } { \ beta } } $, where $ x ^ { \ beta } $ denotes the $ \ beta $ - convexification of $ x $. furthermore, the authors extend the range $ \ alpha \ in ( 0, 1 ) $ in $ \ widetilde { i } _ { \ alpha } $ to the range $ \ alpha \ in ( 0, n ) $ and also obtain the corresponding boundedness in this case. moreover, $ \ widetilde { i } _ { \ alpha } $ is proved to be the adjoint operator of $ i _ \ alpha $. all these results have a wide range of applications. particularly, even when they are applied, respectively, to morrey spaces, mixed - norm lebesgue spaces, local generalized herz | arxiv:2206.06551 |
the present work deals with the study of structural, ferroelectric, dielectric and electro - caloric effects in lead free ferroelectric polycrystalline ba1 - xcaxti0. 95sn0. 05o3 ( x = 2, 5 and 10 % ) i. e., ca, sn co - doped batio3 ( bto ). phase purity of the samples is confirmed from x - ray data by using rietveld refinement. 119sn m \ " ossbauer reveals homogenous phase as well as iso - valent substitution of sn at ti site. enhancements in ferroelectric and dielectric properties have been observed. indirect method which is based on maxwell equation has been used to determine the electro - caloric ( ec ) effect in the studied ferroelectric ceramics and maximum ec coefficient is observed for ba0. 95ca0. 05ti0. 95sn0. 05o3. | arxiv:1704.05475 |
the paper has been withdrawn by the author. | arxiv:cond-mat/9810090 |
we study the conditions under which the majorana phase of the two flavor neutrino mixing matrix appears in the oscillation probabilities and causes $ cp $ violation. we find that the majorana phase remains in the neutrino evolution equation if the neutrino decay eigenstates are not aligned with the mass eigenstates. we show that, in general, two kinds of $ cp $ violation are possible : one due to the majorana phase and the other due to the phase of the off - diagonal element of the neutrino decay matrix. we find that the $ cp $ violating terms in the oscillation probabilities are also sensitive to neutrino mass ordering. | arxiv:2207.09480 |
conversion rate optimization means designing web interfaces such that more visitors perform a desired action ( such as register or purchase ) on the site. one promising approach, implemented in sentient ascend, is to optimize the design using evolutionary algorithms, evaluating each candidate design online with actual visitors. because such evaluations are costly and noisy, several challenges emerge : how can available visitor traffic be used most efficiently? how can good solutions be identified most reliably? how can a high conversion rate be maintained during optimization? this paper proposes a new technique to address these issues. traffic is allocated to candidate solutions using a multi - armed bandit algorithm, using more traffic on those evaluations that are most useful. in a best - arm identification mode, the best candidate can be identified reliably at the end of evolution, and in a campaign mode, the overall conversion rate can be optimized throughout the entire evolution process. multi - armed bandit algorithms thus improve performance and reliability of machine discovery in noisy real - world environments. | arxiv:1803.03737 |
semidefinite programming ( sdp ) with diagonal constraints arise in many optimization problems, such as max - cut, community detection and group synchronization. although sdps can be solved to arbitrary precision in polynomial time, generic convex solvers do not scale well with the dimension of the problem. in order to address this issue, burer and monteiro proposed to reduce the dimension of the problem by appealing to a low - rank factorization and solve the subsequent non - convex problem instead. in this paper, we present coordinate ascent based methods to solve this non - convex problem with provable convergence guarantees. more specifically, we prove that the block - coordinate maximization algorithm applied to the non - convex burer - monteiro method globally converges to a first - order stationary point with a sublinear rate without any assumptions on the problem. we further show that this algorithm converges linearly around a local maximum provided that the objective function exhibits quadratic decay. we establish that this condition generically holds when the rank of the factorization is sufficiently large. furthermore, incorporating lanczos method to the block - coordinate maximization, we propose an algorithm that is guaranteed to return a solution that provides $ 1 - o ( 1 / r ) $ approximation to the original sdp without any assumptions, where $ r $ is the rank of the factorization. this approximation ratio is known to be optimal ( up to constants ) under the unique games conjecture, and we can explicitly quantify the number of iterations to obtain such a solution. | arxiv:1807.04428 |
context : the detailed chemical abundances of extremely metal - poor ( emp ) stars are key guides to understanding the early chemical evolution of the galaxy. most existing data are, however, for giant stars which may have experienced internal mixing later. aims : we aim to compare the results for giants with new, accurate abundances for all observable elements in 18 emp turnoff stars. methods : vlt / uves spectra at r ~ 45, 000 and s / n ~ 130 per pixel ( 330 - 1000 nm ) are analysed with osmarcs model atmospheres and the turbospectrum code to derive abundances for c, mg, si, ca, sc, ti, cr, mn, co, ni, zn, sr, and ba. results : for ca, ni, sr, and ba, we find excellent consistency with our earlier sample of emp giants, at all metallicities. however, our abundances of c, sc, ti, cr, mn and co are ~ 0. 2 dex larger than in giants of similar metallicity. mg and si abundances are ~ 0. 2 dex lower ( the giant [ mg / fe ] values are slightly revised ), while zn is again ~ 0. 4 dex higher than in giants of similar [ fe / h ] ( 6 stars only ). conclusions : for c, the dwarf / giant discrepancy could possibly have an astrophysical cause, but for the other elements it must arise from shortcomings in the analysis. approximate computations of granulation ( 3d ) effects yield smaller corrections for giants than for dwarfs, but suggest that this is an unlikely explanation, except perhaps for c, cr, and mn. nlte computations for na and al provide consistent abundances between dwarfs and giants, unlike the lte results, and would be highly desirable for the other discrepant elements as well. meanwhile, we recommend using the giant abundances as reference data for galactic chemical evolution models. | arxiv:0903.4174 |
we report on the extraction of $ \ sin ^ 2 \ theta ^ { \ rm lept } _ { \ rm eff } ( m _ z ) $ and an indirect measurement of the mass of the w boson from the forward - backward asymmetry of dilepton events in the $ z $ boson mass region at the tevatron. the data samples of $ e ^ + e ^ - $ and $ \ mu ^ + \ mu ^ - $ events collected by the cdf detector correspond to the full 9. 4 fb $ ^ { - 1 } $ run ii sample and yield an effective electroweak mixing angle $ \ sin ^ 2 \ theta ^ { \ rm lept } _ { \ rm eff } ( m _ z ) = 0. 23222 \ pm 0. 00046 $. the corresponding result reported by the d0 collaboration with the full 9. 4 fb $ ^ { - 1 } $ $ e ^ + e - $ sample is $ \ sin ^ 2 \ theta ^ { \ rm lept } _ { \ rm eff } ( m _ z ) = 0. 23146 \ pm 0. 00047 $. the cdf collaboration also extracts the on - shell electroweak mixing angle $ \ sin ^ 2 \ theta _ w = 0. 22401 \ pm 0. 00044 $ which corresponds to an indirect measurement of the w boson mass $ m _ w ( { \ rm indirect } ) = 80. 327 \ pm 0. 023 \ ; { \ rm gev } $. the quoted uncertainties include both statistical and systematic contributions. | arxiv:1512.08256 |
the hausdorff dimension of the set of points that are covered infinitely many times by a sequence of randomly distributed balls in the unit cube can be expressed in terms of the sizes of the balls. this note presents a new proof of the formula. | arxiv:1910.12319 |
recurrence quantification analysis ( rqa ) can help to detect significant events and phase transitions of a dynamical system, but choosing a suitable set of parameters is crucial for the success. from recurrence plots different rqa variables can be obtained and analysed. currently, most of the methods for rqa radius optimisation are focusing on a single rqa variable. in this work we are proposing two new methods for radius optimisation that look for an optimum in the higher dimensional space of the rqa variables, therefore synchronously optimising across several variables. we illustrate our approach using two case studies : a well known lorenz dynamical system, and a time - series obtained from monitoring energy consumption of a small enterprise. our case studies show that both methods result in plausible values and can be used to analyse energy data. | arxiv:1807.02896 |
we consider the sum - of - squares hierarchy of approximations for the problem of minimizing a polynomial $ f $ over the boolean hypercube $ \ mathbb { b } ^ { n } = \ { 0, 1 \ } ^ n $. this hierarchy provides for each integer $ r \ in \ mathbb { n } $ a lower bound $ f _ { ( r ) } $ on the minimum $ f _ { \ min } $ of $ f $, given by the largest scalar $ \ lambda $ for which the polynomial $ f - \ lambda $ is a sum - of - squares on $ \ mathbb { b } ^ { n } $ with degree at most $ 2r $. we analyze the quality of these bounds by estimating the worst - case error $ f _ { \ min } - f _ { ( r ) } $ in terms of the least roots of the krawtchouk polynomials. as a consequence, for fixed $ t \ in [ 0, 1 / 2 ] $, we can show that this worst - case error in the regime $ r \ approx t \ cdot n $ is of the order $ 1 / 2 - \ sqrt { t ( 1 - t ) } $ as $ n $ tends to $ \ infty $. our proof combines classical fourier analysis on $ \ mathbb { b } ^ { n } $ with the polynomial kernel technique and existing results on the extremal roots of krawtchouk polynomials. this link to roots of orthogonal polynomials relies on a connection between the hierarchy of lower bounds $ f _ { ( r ) } $ and another hierarchy of upper bounds $ f ^ { ( r ) } $, for which we are also able to establish the same error analysis. our analysis extends to the minimization of a polynomial over the $ q $ - ary cube $ ( \ mathbb { z } / q \ mathbb { z } ) ^ { n } $. | arxiv:2011.04027 |
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