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software defined networking ( sdn ) is a promising approach for improving the performance and manageability of future network architectures. however, little work has gone into using sdn to improve the performance and manageability of existing networks without requiring a major overhaul of the existing network infrastructure. in this paper, we show how we can dramatically improve, or supercharge, the performance of existing ip routers by combining them with sdn - enabled equipment in a novel way. more particularly, our supercharged solution substantially reduces the convergence time of an ip router upon link or node failure without inducing any reconfiguration of the ip router itself. our key insight is to use the sdn controller to precompute backup forwarding entries and immediately activate them upon failure, enabling almost immediate data - plane recovery, while letting the router converge at its typical slow pace. by boosting existing equipment ' s performance, we not only increase their lifetime but also provide new incentives for network operators to kickstart sdn deployment. we implemented a fully functional " supercharger " and use it to boost the convergence performance of a cisco nexus 7k router. using a fpga - based traffic generator, we show that our supercharged router systematically converges within ~ 150ms, a 900x reduction with respect to its normal convergence time under similar conditions.
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arxiv:1505.06630
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accurate detection and diagnosis of abnormal behaviors such as network attacks from multivariate time series ( mts ) are crucial for ensuring the stable and effective operation of industrial cyber - physical systems ( cps ). however, existing researches pay little attention to the logical dependencies among system working states, and have difficulties in explaining the evolution mechanisms of abnormal signals. to reveal the spatio - temporal association relationships and evolution mechanisms of the working states of industrial cps, this paper proposes a fine - grained adaptive anomaly diagnosis method ( i. e. mad - transformer ) to identify and diagnose anomalies in mts. mad - transformer first constructs a temporal state matrix to characterize and estimate the change patterns of the system states in the temporal dimension. then, to better locate the anomalies, a spatial state matrix is also constructed to capture the inter - sensor state correlation relationships within the system. subsequently, based on these two types of state matrices, a three - branch structure of series - temporal - spatial attention module is designed to simultaneously capture the series, temporal, and space dependencies among mts. afterwards, three associated alignment loss functions and a reconstruction loss are constructed to jointly optimize the model. finally, anomalies are determined and diagnosed by comparing the residual matrices with the original matrices. we conducted comparative experiments on five publicly datasets spanning three application domains ( service monitoring, spatial and earth exploration, and water treatment ), along with a petroleum refining simulation dataset collected by ourselves. the results demonstrate that mad - transformer can adaptively detect fine - grained anomalies with short duration, and outperforms the state - of - the - art baselines in terms of noise robustness and localization performance.
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arxiv:2403.02616
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computing the probability of an edge ' s existence in a graph network is known as link prediction. while traditional methods calculate the similarity between two given nodes in a static network, recent research has focused on evaluating networks that evolve dynamically. although deep learning techniques and network representation learning algorithms, such as node2vec, show remarkable improvements in prediction accuracy, the stochastic gradient descent ( sgd ) method of node2vec tends to fall into a mediocre local optimum value due to a shortage of prior network information, resulting in failure to capture the global structure of the network. to tackle this problem, we propose noddle ( integration of node2vec and deep learning method ), a deep learning model which incorporates the features extracted by node2vec and feeds them into a four layer hidden neural network. noddle takes advantage of adaptive learning optimizers such as adam, adamax, adadelta, and adagrad to improve the performance of link prediction. experimental results show that this method yields better results than the traditional methods on various social network datasets.
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arxiv:2305.16421
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the large scale pattern in the arrival directions of extragalactic cosmic rays that reach the earth is different from that of the flux arriving to the halo of the galaxy as a result of the propagation through the galactic magnetic field. two different effects are relevant in this process : deflections of trajectories and ( de ) acceleration by the electric field component due to the galactic rotation. the deflection of the cosmic ray trajectories makes the flux intensity arriving to the halo from some direction to appear reaching the earth from another direction. this applies to any intrinsic anisotropy in the extragalactic distribution or, even in the absence of intrinsic anisotropies, to the dipolar compton - getting anisotropy induced when the observer is moving with respect to the cosmic rays rest frame. for an observer moving with the solar system, cosmic rays traveling through far away regions of the galaxy also experience an electric force coming from the relative motion ( due to the rotation of the galaxy ) of the local system in which the field can be considered as being purely magnetic. this produces small changes in the particles momentum that can originate large scale anisotropies even for an isotropic extragalactic flux.
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arxiv:1009.5891
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some test amplification tools extend a manually created test suite with additional test cases to increase the code coverage. the technique is effective, in the sense that it suggests strong and understandable test cases, generally adopted by software engineers. unfortunately, the current state - of - the - art for test amplification heavily relies on program analysis techniques which benefit a lot from explicit type declarations present in statically typed languages. in dynamically typed languages, such type declarations are not available and as a consequence test amplification has yet to find its way to programming languages like smalltalk, python, ruby and javascript. we propose to exploit profiling information - - readily obtainable by executing the associated test suite - - to infer the necessary type information creating special test inputs with corresponding assertions. we evaluated this approach on 52 selected test classes from 13 mature projects in the pharo ecosystem containing approximately 400 test methods. we show the improvement in killing new mutants and mutation coverage at least in 28 out of 52 test classes ( 53 % ). moreover, these generated tests are understandable by humans : 8 out of 11 pull - requests submitted were merged into the main code base ( 72 % ). these results are comparable to the state - of - the - art, hence we conclude that test amplification is feasible for dynamically typed languages.
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arxiv:2108.05663
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the radial velocity technique is currently used to classify transiting objects. while capable of identifying grazing binary eclipses, this technique cannot reliably identify blends, a chance overlap of a faint background eclipsing binary with an ordinary foreground star. blends generally have no observable radial velocity shifts, as the foreground star is brighter by several magnitudes and therefore dominates the spectrum, but their combined light can produce events that closely resemble those produced by transiting exoplanets. the radial velocity technique takes advantage of the mass difference between planets and stars to classify exoplanet candidates. however, the existence of blends renders this difference an unreliable discriminator. another difference must therefore be utilized for this classification - - the physical size of the transiting body. due to the dependence of limb darkening on color, planets and stars produce subtly different transit shapes. these differences can be relatively weak, little more than 1 / 10th the transit depth. however, the presence of even small color differences between the individual components of the blend increases this difference. this paper will show that this color difference is capable of discriminating between exoplanets and blends reliably, theoretically capable of classifying even terrestrial - class transits, unlike the radial velocity technique.
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arxiv:astro-ph/0406201
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we consider convex relaxations for recovering low - rank tensors based on constrained minimization over a ball induced by the tensor nuclear norm, recently introduced in \ cite { tensor _ tsvd }. we build on a recent line of results that considered convex relaxations for the recovery of low - rank matrices and established that under a strict complementarity condition ( sc ), both the convergence rate and per - iteration runtime of standard gradient methods may improve dramatically. we develop the appropriate strict complementarity condition for the tensor nuclear norm ball and obtain the following main results under this condition : 1. when the objective to minimize is of the form $ f ( \ mx ) = g ( \ ma \ mx ) + \ langle { \ mc, \ mx } \ rangle $, where $ g $ is strongly convex and $ \ ma $ is a linear map ( e. g., least squares ), a quadratic growth bound holds, which implies linear convergence rates for standard projected gradient methods, despite the fact that $ f $ need not be strongly convex. 2. for a smooth objective function, when initialized in certain proximity of an optimal solution which satisfies sc, standard projected gradient methods only require svd computations ( for projecting onto the tensor nuclear norm ball ) of rank that matches the tubal rank of the optimal solution. in particular, when the tubal rank is constant, this implies nearly linear ( in the size of the tensor ) runtime per iteration, as opposed to super linear without further assumptions. 3. for a nonsmooth objective function which admits a popular smooth saddle - point formulation, we derive similar results to the latter for the well known extragradient method. an additional contribution which may be of independent interest, is the rigorous extension of many basic results regarding tensors of arbitrary order, which were previously obtained only for third - order tensors.
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arxiv:2308.01677
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in this work we present a review of the state of the art of information theoretic feature selection methods. the concepts of feature relevance, redundance and complementarity ( synergy ) are clearly defined, as well as markov blanket. the problem of optimal feature selection is defined. a unifying theoretical framework is described, which can retrofit successful heuristic criteria, indicating the approximations made by each method. a number of open problems in the field are presented.
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arxiv:1509.07577
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the efficiency of energy conversion during magnetic reconnection is related to the reconnection rate. while the stable reconnection rate has been studied extensively, its growth between the time of reconnection onset and the peak reconnection rate has not been thoroughly discussed. we use a 2d particle - in - cell ( pic ) simulation to examine how the non - ideal reconnection electric field evolves during the growth process and how it relates to changes near the x - line. we identify three phases of growth : 1 ) slow quasi - linear growth, 2 ) rapid exponential growth, and 3 ) tapered growth followed by negative growth after the reconnection rate peaks. through analysis of the structural changes of the edr, we associate the early phases with the breaking of x - line symmetry through the erosion of the pre - onset bipolar ez and the emergence of a diverging ex pattern at the neutral line in phase 1 followed by the expansion of the inflow region and the enhancement of inflow poynting flux sz associated with the out - of - plane electric field ey in phase 2. we show how the hall fields facilitate rapid growth in phase 2 by opening up the exhaust, relieving the electron - scale bottleneck and allowing large poynting flux across the separatrices. we find that the rapid inflow of electromagnetic energy accumulates until the downstream electromagnetic energy density in phase 3 approaches the initial upstream asymptotic value. finally, we examine how the electron outflow and the downstream ion populations interact in phase 3 and how each species exchanges energy with the local field structures in the exhaust.
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arxiv:2208.08470
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perfect cooper pair splitting is proposed, based on crossed andreev reflection ( car ) in a p - type semiconductor - superconductor - n - type semiconductor ( psn ) junction. the ideal splitting is caused by the energy filtering that is enforced by the bandstructure of the electrodes. the psn junction is modeled by the bogoliubov - de gennes equations and an extension of the blonder - tinkham - klapwijk theory beyond the andreev approximation. despite a large momentum mismatch, the car current is predicted to be large. the proposed straightforward experimental design and the 100 % degree of pureness of the nonlocal current open the way to psn structures as high quality sources of entanglement.
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arxiv:1112.3742
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the spectral statistics of the circular billiard with a point - scatterer is investigated. in the semiclassical limit, the spectrum is demonstrated to be composed of two uncorrelated level sequences. the first corresponds to states for which the scatterer is located in the classically forbidden region and its energy levels are not affected by the scatterer in the semiclassical limit while the second sequence contains the levels which are affected by the point - scatterer. the nearest neighbor spacing distribution which results from the superposition of these sequences is calculated analytically within some approximation and good agreement with the distribution that was computed numerically is found.
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arxiv:nlin/0309061
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in this article, a combinatorial characterization of the family of planes of $ \ pg ( 3, q ) $ which meet a hyperbolic quadric in an irreducible conic, using their intersection properties with the points and lines of $ \ pg ( 3, q ) $, is given.
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arxiv:2102.03813
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we study two classes of dynamical systems with holes : expanding maps of the interval and collet - eckmann maps with singularities. in both cases, we prove that there is a natural absolutely continuous conditionally invariant measure $ \ mu $ ( a. c. c. i. m. ) with the physical property that strictly positive h \ " { o } lder continuous functions converge to the density of $ \ mu $ under the renormalized dynamics of the system. in addition, we construct an invariant measure $ \ nu $, supported on the cantor set of points that never escape from the system, that is ergodic and enjoys exponential decay of correlations for h \ " { o } lder observables. we show that $ \ nu $ satisfies an equilibrium principle which implies that the escape rate formula, familiar to the thermodynamic formalism, holds outside the usual setting. in particular, it holds for collet - eckmann maps with holes, which are not uniformly hyperbolic and do not admit a finite markov partition. we use a general framework of young towers with holes and first prove results about the \ accim and the invariant measure on the tower. then we show how to transfer results to the original dynamical system. this approach can be expected to generalize to other dynamical systems than the two above classes.
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arxiv:0705.4271
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in this article, we study the stochastic wave equation in spatial dimensions $ d \ le 2 $ with multiplicative l \ ' evy noise that can have infinite $ p $ - th moments. using the past light - cone property of the wave equation, we prove the existence and uniqueness of a solution, considering only the $ p $ - integrability of the l \ ' evy measure $ \ nu $ for the region corresponding to the small jumps of the noise. for $ d = 1 $, there are no restrictions on $ \ nu $. for $ d = 2 $, we assume that there exists a value $ p \ in ( 0, 2 ) $ for which $ \ int _ { \ { | z | \ le 1 \ } } | z | ^ p \ nu ( dz ) < + \ infty $.
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arxiv:2310.05907
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vine copula models have become highly popular practical tools for modeling multivariate dependencies. to maintain tractability, a commonly employed simplifying assumption is that conditional copulas remain unchanged by the conditioning variables. this assumption has sparked a somewhat polarizing debate within the copula community. the fact that much of this dispute occurs outside the public record has placed the field in an unfortunate position, impeding scientific progress. in this article, i will review what we know about the flexibility and limitations of simplified vine copula models, explore the broader implications, and offer my own, hopefully reconciling, perspective on the issue.
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arxiv:2410.16806
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we study non - univalent solutions of the polubarinova - galin equation, describing the time evolution of the conformal map from the unit disk onto a hele - shaw blob of fluid subject to injection at one point. in particular, we tackle the difficulties arising when the map is not even locally univalent, in which case one has to pass to weak solutions developing on a branched covering surface of the complex plane. one major concern is the construction of this riemann surface, which is not given in advance but has to be constantly up - dated along with the solution. once the riemann surface is constructed the weak solution is automatically global in time, but we have had to leave open the question whether the weak solution can be kept simply connected all the time ( as is necessary to connect to the polubarinova - galin equation ). a certain crucial statement, a kind of stability statement for free boundaries, has therefore been left as a conjecture only. another major part of the paper concerns the structure of rational solutions ( as for the derivative of the mapping function ). here we have fairly complete results on the dynamics. several examples are given.
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arxiv:1411.1909
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the new super - kamiokande - gadolinium ( sk - gd ) project is an upgrade of the super - kamiokande ( sk ) detector. in the sk - gd project, 0. 2 \ % gd $ _ 2 $ ( so $ _ 4 $ ) $ _ 3 $ is loaded into the 50 kton water tank of the sk. one of the main purposes of the project is to discover supernova relic neutrinos. neutrino measurements and proton decay searches will also be performed in the sk - gd. in order to measure solar neutrinos with a low energy threshold of $ \ sim $ 3. 5 mev in the sk - gd, the main radioactive contaminations, $ ^ { 238 } $ u and $ ^ { 232 } $ th, in gd $ _ 2 $ ( so $ _ 4 $ ) $ _ 3 { \ cdot } $ 8h $ _ 2 $ o, should be minimized before loading. our maximum levels for u and th are 5 mbq ( u ) / kg ( gd $ _ 2 $ ( so $ _ 4 $ ) $ _ 3 { \ cdot } $ 8h $ _ 2 $ o ) and 0. 05 mbq ( th ) / kg ( gd $ _ 2 $ ( so $ _ 4 $ ) $ _ 3 { \ cdot } $ 8h $ _ 2 $ o ). in order to measure such low concentrations of u and th in gd $ _ 2 $ ( so $ _ 4 $ ) $ _ 3 { \ cdot } $ 8h $ _ 2 $ o, we developed the solid - phase extraction technique. using this method, about 90 \ % or more u and th could be efficiently extracted while gd was reduced by a factor of about $ 10 ^ { 4 } $. this allowed these radioactivity contaminations to be measured precisely as 0. 04 mbq / kg ( gd $ _ 2 $ ( so $ _ 4 $ ) $ _ 3 { \ cdot } $ 8h $ _ 2 $ o ) for u and 0. 01 mbq / kg ( gd $ _ 2 $ ( so $ _ 4 $ ) $ _ 3 { \ cdot } $ 8h $ _ 2 $ o ) for th. we measured three pure gd $ _ 2 $ ( so $ _ 4 $ ) $ _ 3 { \ cdot } $ 8h $ _ 2 $ o
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arxiv:1709.03417
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in this paper, we develop the proof theory of skew prounital closed categories. these are variants of the skew closed categories of street where the unit is not represented. skew closed categories in turn are a weakening of the closed categories of eilenberg and kelly where no structural law is required to be invertible. the presence of a monoidal structure in these categories is not required. we construct several equivalent presentations of the free skew prounital closed category on a given set of generating objects : a categorical calculus ( hilbert - style system ), a cut - free sequent calculus and a natural deduction system corresponding to a variant of planar ( = non - commutative linear ) typed lambda - calculus. we solve the coherence problem for skew prounital closed categories by showing that the sequent calculus admits focusing and presenting two reduction - free normalization procedures for the natural deduction calculus : normalization by evaluation and hereditary substitutions. normal natural deduction derivations ( beta - eta - long forms ) are in one - to - one correspondence with derivations in the focused sequent calculus. unexpectedly, the free skew prounital closed category on a set satisfies a left - normality condition which makes it lose its skew aspect. this pitfall can be avoided by considering the free skew prounital closed category on a skew multicategory instead. the latter has a presentation as a cut - free sequent calculus for which it is easy to see that the left - normality condition generally fails. the whole development has been fully formalized in the dependently typed programming language agda.
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arxiv:2101.03809
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in this paper, we will show that the limit of some quasilocal mass integrals of the coordinate spheres in an asymptotically hyperbolic ( ah ) manifold is the mass integral of the ah manifold. this is the analogue of the well known result that the limit of the brown - york mass of coordinate spheres is the adm mass in an asymptotically flat manifold.
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arxiv:1010.6130
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we consider 3 - webs, hyper - para - complex structures and integrable segre structures on manifolds of even dimension and generalise the second heavenly pleba \ ' nski equation in the context of higher - dimensional hyper - para - complex structures. we also characterise the segre structures admitting a compatible hyper - para - complex structure in terms of systems of ordinary differential equations.
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arxiv:1508.05234
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in this work we consider regularized wasserstein barycenters ( average in wasserstein distance ) in fourier basis. we prove that random fourier parameters of the barycenter converge to some gaussian random vector by distribution. the convergence rate has been derived in finite - sample case with explicit dependence on measures count ( $ n $ ) and the dimension of parameters ( $ p $ ).
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arxiv:1904.00891
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in earlier work, we used a gauge independent abelian decomposition to show that abelian degrees of freedom are wholly responsible for the static quark potential. the restricted abelian field can be split into two terms, a maxwell term and a $ \ theta $ ( dirac ) term. the $ \ theta $ term ' s contribution to the string tension can be analysed theoretically and numerically, and arises because of the existence of a certain type of monopole. while the abelian field can be constructed without gauge fixing, its two component parts are gauge - dependent, with a gauge transformation moving the topological features from one part to another. this allows us to isolate and identify the topological objects responsible for confinement by constructing a gauge where the $ \ theta $ term wholly accounts for the string tension. we confirm the presence of these monopoles in lattice simulations of su ( 2 ) yang - mills theory.
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arxiv:1610.09708
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the existing core methods, which are employed by the popular ctl model checking tools, are facing the famous state explode problem. in our previous study, a method based on the machine learning ( ml ) algorithms was proposed to address this problem. however, the accuracy is not satisfactory. first, we conduct a comprehensive experiment on graph lab to seek the optimal accuracy using the five machine learning algorithms. second, given the optimal accuracy, the average time is seeked. the results show that the logistic regressive ( lr ) - based approach can simulate ctl model checking with the accuracy of 98. 8 %, and its average efficiency is 459 times higher than that of the existing method, as well as the boosted tree ( bt ) - based approach can simulate ctl model checking with the accuracy of 98. 7 %, and its average efficiency is 639 times higher than that of the existing method.
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arxiv:1902.08789
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due to the incompatibility of the nonlinear realization of superconformal symmetry and dilatation symmetry with the dilaton as the compensator field, in the present paper it shows an alternative mechanism of spontaneous breaking the n = 2 superconformal symmetry to the n = 0 case. by using the approach of nonlinear transformations it is found that it leads to a space - filling brane theory with weyl scale w ( 1, 3 ) symmetry. the dynamics of the resulting weyl scale invariant brane, along with that of other nambu - goldstone fields, is derived in terms of the building blocks of the vierbein and the covariant derivative from the maurer - cartan oneforms. a general coupling of the matter fields localized on the brane world volume to these ng fields is also constructed.
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arxiv:0802.1299
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globular clusters ( gcs ) are old massive star clusters that serve as ` fossils ' of galaxy formation. the advent of gaia observatory has enabled detailed kinematics studies of the galactic gcs and revolutionized our understanding of the connections between gc properties and galaxy assembly. however, lack of kinematic measurements of extragalactic gcs limits the sample size of gc systems that we can fully study. in this work, we present a model for gc formation and evolution, which includes positional and kinematic information of individual gcs by assigning them to particles in the illustris tng50 - 1 simulation based on age and location. we calibrate the three adjustable model parameters using observed properties of the galactic and extragalactic gc systems, including the distributions of position, systemic velocity, velocity dispersion, anisotropy parameter, orbital actions, and metallicities. we also analyze the properties of gcs from different origins. in outer galaxy, ex - situ clusters are more dominant than the clusters formed in - situ. this leads to the gc metallicities decreasing outwards due to the increasing abundance of accreted, metal - poor clusters. we also find the ex - situ gcs to have greater velocity dispersions and orbital actions, in agreement with their accretion origin.
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arxiv:2203.00599
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we prove that the $ \ ell $ - adic chern classes of canonical extensions of automorphic vector bundles, over toroidal compactifications of shimura varieties of hodge type over $ \ bar { \ mathbb { q } } _ p $, descend to classes in the $ \ ell $ - adic cohomology of the minimal compactifications. these are invariant under the galois group of the $ p $ - adic field above which the variety and the bundle are defined.
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arxiv:1801.08219
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if omega _ tot = 1 and structure formed from adiabatic initial conditions then the age of the universe, as constrained by measurements of the cosmic microwave background ( cmb ), is t _ 0 = 14. 0 + / - 0. 5 gyr. the uncertainty is surprisingly small given that cmb data alone constrain neither h nor omega _ lambda significantly. it is due to the tight ( and accidental ) correlation, in these models, of the age with the angle subtended by the sound horizon on the last - - scattering surface and thus with the well - determined acoustic peak locations. if we assume either the hst key project result h = 0. 72 \ pm. 08 or simply that h > 0. 55, we find omega _ lambda > 0. 4 at 95 % confidence - - another argument for dark energy, independent of supernovae observations. our analysis is greatly simplified by the monte carlo markov chain approach to bayesian inference combined with a fast method for calculating angular power spectra.
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arxiv:astro-ph/0109232
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we propose a nonparametric algorithm to detect structural breaks in the conditional mean and / or variance of a time series. our method does not assume any specific parametric form for the dependence structure of the regressor, the time series model, or the distribution of the model noise. this flexibility allows our algorithm to be applicable to a wide range of time series structures commonly encountered in financial econometrics. the effectiveness of the proposed algorithm is validated through an extensive simulation study and a real data application in detecting structural breaks in the mean and volatility of bitcoin returns. the algorithm ' s ability to identify structural breaks in the data highlights its practical utility in econometric analysis and financial modeling.
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arxiv:2410.15713
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parametric mathematical models such as parameterizations of partial differential equations with random coefficients have received a lot of attention within the field of uncertainty quantification. the model uncertainties are often represented via a series expansion in terms of the parametric variables. in practice, this series expansion needs to be truncated to a finite number of terms, introducing a dimension truncation error to the numerical simulation of a parametric mathematical model. there have been several studies of the dimension truncation error corresponding to different models of the input random field in recent years, but many of these analyses have been carried out within the context of numerical integration. in this paper, we study the $ l ^ 2 $ dimension truncation error of the parametric model problem. estimates of this kind arise in the assessment of the dimension truncation error for function approximation in high dimensions. in addition, we show that the dimension truncation error rate is invariant with respect to certain transformations of the parametric variables. numerical results are presented which showcase the sharpness of the theoretical results.
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arxiv:2301.13693
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we develop a new low - level, first - order probabilistic programming language ( lf - ppl ) suited for models containing a mix of continuous, discrete, and / or piecewise - continuous variables. the key success of this language and its compilation scheme is in its ability to automatically distinguish parameters the density function is discontinuous with respect to, while further providing runtime checks for boundary crossings. this enables the introduction of new inference engines that are able to exploit gradient information, while remaining efficient for models which are not everywhere differentiable. we demonstrate this ability by incorporating a discontinuous hamiltonian monte carlo ( dhmc ) inference engine that is able to deliver automated and efficient inference for non - differentiable models. our system is backed up by a mathematical formalism that ensures that any model expressed in this language has a density with measure zero discontinuities to maintain the validity of the inference engine.
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arxiv:1903.02482
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it is shown that there exists a normal uniform algebra, on a compact metrizable space, that fails to be strongly regular at some peak point. this answers a 31 - year - old question of joel feinstein. our example is r ( k ) for a certain compact planar set k. furthermore, it has a totally ordered one - parameter family of closed primary ideals whose hull is a peak point. general results regarding lifting ideals under cole root extensions are established. these results are applied to obtain a normal uniform algebra, on a compact metrizable space, with every point a peak point but again having a totally ordered one - parameter family of closed primary ideals.
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arxiv:2308.13951
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let $ fh $ be a supersolvable frobenius group with kernel $ f $ and complement $ h $. suppose that a finite group $ g $ admits $ fh $ as a group of automorphisms in such a manner that $ c _ g ( f ) = 1 $ and $ c _ { g } ( h ) $ is nilpotent of class $ c $. we show that $ g $ is nilpotent of $ ( c, \ left | fh \ right | ) $ - bounded class.
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arxiv:1805.05812
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environmental data science for spatial extremes has traditionally relied heavily on max - stable processes. even though the popularity of these models has perhaps peaked with statisticians, they are still perceived and considered as the ` state - of - the - art ' in many applied fields. however, while the asymptotic theory supporting the use of max - stable processes is mathematically rigorous and comprehensive, we think that it has also been overused, if not misused, in environmental applications, to the detriment of more purposeful and meticulously validated models. in this paper, we review the main limitations of max - stable process models, and strongly argue against their systematic use in environmental studies. alternative solutions based on more flexible frameworks using the exceedances of variables above appropriately chosen high thresholds are discussed, and an outlook on future research is given, highlighting recommendations moving forward and the opportunities offered by hybridizing machine learning with extreme - value statistics.
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arxiv:2401.17430
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in this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of $ s $ - spectrum. the proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and then using a transformation which maps a quaternionic unbounded normal operator to a quaternionic bounded normal operator. with this paper we complete the foundation of spectral analysis of quaternionic operators. the $ s $ - spectrum has been introduced to define the quaternionic functional calculus but it turns out to be the correct object also for the spectral theorem for quaternionic normal operators. the fact that the correct notion of spectrum for quaternionic operators was not previously known has been one of the main obstructions to fully understanding the spectral theorem in this setting. a prime motivation for studying the spectral theorem for quaternionic unbounded normal operators is given by the subclass of unbounded anti - self adjoint quaternionic operators which play a crucial role in the quaternionic quantum mechanics.
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arxiv:1409.7010
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photomechanical liquid crystal elastomers ( lces ) are responsive polymers that can convert light directly into mechanical deformation. this unique feature makes these materials an attractive candidate for soft actuators capable of remote and multi - mode actuation. in this work, we propose a three - dimensional multi - scale model of the nonlinear and nonlocal dynamics of fibers of photomechanical lces under illumination. we use the model to show that a pre - stressed helix - like fibers immersed in a fluid can undergo a periodic whirling motion under steady illumination. we analyze the photo - driven spatiotemporal pattern and stability of the whirling deformation, and provide a parametric study. unlike previous work on photo - driven periodic motion, this whirling motion does not exploit instabilities in the form of snap - through phenomena, or gravity as in rolling. we then show that such motion can be exploited in developing remote controlled bio - inspired microswimmers and novel micromixers.
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arxiv:2207.13908
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we obtain a generalized euler - lagrange differential equation and transversality optimality conditions for herglotz - type higher - order variational problems. illustrative examples of the new results are given.
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arxiv:1309.6518
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we study the phonon modes in single - walled mos $ _ { 2 } $ nanotubes via the lattice dynamics calculation and molecular dynamics simulation. the phonon spectra for tubes of arbitrary chiralities are calculated from the dynamical matrix constructed by the combination of an empirical potential with the conserved helical quantum numbers $ ( \ kappa, n ) $. in particular, we show that the frequency ( $ \ omega $ ) of the radial breathing mode is inversely proportional to the tube diameter ( $ d $ ) as $ \ omega = 665. 3 / d $ { cm $ ^ { - 1 } $ }. the eigen vectors of the first twenty lowest - frequency phonon modes are illustrated. based on these eigen vectors, we demonstrate that the radial breathing oscillation is disturbed by phonon modes of three - fold symmetry initially, and the tube is squashed by the modes of two - fold symmetry eventually. our study provides fundamental knowledge for further investigations of the thermal and mechanical properties of the mos $ _ { 2 } $ nanotubes.
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arxiv:1401.0577
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we theoretically consider a josephson junction formed by a ferromagnetic spacer with a strong spin - orbit interaction or a magnetic spin valve, i. e., a bilayer with one static and one free layer. electron spin transport facilitates a nonlinear dynamical coupling between the magnetic moment and charge current, which consists of normal and superfluid components. by phenomenologically adding reactive and dissipative interactions ( guided by structural and onsager symmetries ), we construct magnetic torques and charge pumping, whose microscopic origins are also discussed. a stability analysis of our coupled nonlinear systems generates a rich phase diagram with fixed points, limit cycles, and quasiperiodic states. our findings reduce to the known phase diagrams for current - biased nonmagnetic josephson junctions, on the one hand, and spin - torque driven magnetic films, on the other, in the absence of coupling between the magnetic and superconducting order parameters.
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arxiv:1110.1680
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lidars play a critical role in autonomous vehicles ' ( avs ) perception and their safe operations. recent works have demonstrated that it is possible to spoof lidar return signals to elicit fake objects. in this work we demonstrate how the same physical capabilities can be used to mount a new, even more dangerous class of attacks, namely object removal attacks ( oras ). oras aim to force 3d object detectors to fail. we leverage the default setting of lidars that record a single return signal per direction to perturb point clouds in the region of interest ( roi ) of 3d objects. by injecting illegitimate points behind the target object, we effectively shift points away from the target objects ' rois. our initial results using a simple random point selection strategy show that the attack is effective in degrading the performance of commonly used 3d object detection models.
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arxiv:2102.03722
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the exploration of flatband in photonics is fundamentally important, aiming to control the localization of light for potential applications in optical communications. we study the flatband physics in a synthetic space including the frequency axis of light. a ring - resonator array is used to construct a synthetic lieb - type lattice, where the modulation phase distribution supports a locally non - zero effective magnetic flux pointing into the synthetic space. we find that the flatband is isolated from other dispersive bands and the light can still be localized even with the perturbation from the group velocity dispersion of the waveguide. our work points out a route towards manipulating the localization performance of a wavepacket of light along both the spatial dimension and the frequency dimension, which holds the potential implication for controlling the storage of optical information in dispersive materials.
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arxiv:2004.12542
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( abridged ) in the framework of the binamics project, we have begun a study of the magnetic properties of a sample of intermediate - mass and massive short - period binary systems, as a function of binarity properties. we report in this paper the characterisation of the magnetic field of hd 5550, a double - lined spectroscopic binary system of intermediate - mass, using high - resolution spectropolarimetric narval observations of hd 5550. we first fit the intensity spectra using zeeman / atlas9 lte synthetic spectra to estimate the effective temperatures, microturbulent velocities, and the abundances of some elements of both components, as well as the light - ratio of the system. we then fit the least - square deconvolved $ i $ profiles to determine the radial and projected rotational velocities of both stars. we then analysed the shape and evolution of the lsd $ v $ profiles using the oblique rotator model to characterise the magnetic fields of both stars. we confirm the ap nature of the primary, previously reported in the literature, and find that the secondary displays spectral characteristics typical of an am star. while a magnetic field is clearly detected in the lines of the primary, no magnetic field is detected in the secondary, in any of our observation. if a dipolar field were present at the surface of the am star, its polar strength must be below 40 g. the faint variability observed in the stokes $ v $ profiles of the ap star allowed us to propose a rotation period of $ 6. 84 _ { - 0. 39 } ^ { + 0. 61 } $ d, close to the orbital period ( $ \ sim $ 6. 82 d ), suggesting that the star is synchronised with its orbit. by fitting the variability of the $ v $ profiles, we propose that the ap component hosts a dipolar field inclined with the rotation axis at an angle $ \ beta = 156 \ pm17 $ $ ^ { \ circ } $ and a polar strength $ b _ { \ rm d } = 65 \ pm 20 $ g. the field strength is the weakest known for an ap star.
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arxiv:1601.07762
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mesh denoising is a fundamental problem in digital geometry processing. it seeks to remove surface noise, while preserving surface intrinsic signals as accurately as possible. while the traditional wisdom has been built upon specialized priors to smooth surfaces, learning - based approaches are making their debut with great success in generalization and automation. in this work, we provide a comprehensive review of the advances in mesh denoising, containing both traditional geometric approaches and recent learning - based methods. first, to familiarize readers with the denoising tasks, we summarize four common issues in mesh denoising. we then provide two categorizations of the existing denoising methods. furthermore, three important categories, including optimization -, filter -, and data - driven - based techniques, are introduced and analyzed in detail, respectively. both qualitative and quantitative comparisons are illustrated, to demonstrate the effectiveness of the state - of - the - art denoising methods. finally, potential directions of future work are pointed out to solve the common problems of these approaches. a mesh denoising benchmark is also built in this work, and future researchers will easily and conveniently evaluate their methods with the state - of - the - art approaches.
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arxiv:2209.00841
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reaction - diffusion - advection media on semi - infinite domains are important in chemical, biological and ecological applications, yet remain a challenge for pattern formation theory. to demonstrate the rich emergence of nonlinear traveling waves and stationary periodic states, we review results obtained using a membrane reactor as a case model. such solutions coexist in overlapping parameter regimes and their temporal stability is determined by the boundary conditions ( periodic vs. mixed ) which either preserve or destroy the translational symmetry, i. e., selection mechanisms under realistic danckwerts boundary conditions. a brief outlook is given at the end.
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arxiv:1802.02367
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variable selection in high - dimensional scenarios is of great interested in statistics. one application involves identifying differentially expressed genes in genomic analysis. existing methods for addressing this problem have some limits or disadvantages. in this paper, we propose distance based variable importance measures to deal with these problems, which is inspired by the multi - response permutation procedure ( mrpp ). the proposed variable importance assessments can effectively measure the importance of an individual dimension by quantifying its influence on the differences between multivariate distributions. a backward selection algorithm is developed that can be used in high - dimensional variable selection to discover important variables. both simulations and real data applications demonstrate that our proposed method enjoys good properties and has advantages over other methods.
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arxiv:1806.06468
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sxp4. 78 was originally discovered in 2000 as a pulsar in the small magellanic cloud ( smc ) by the rossi x - ray timing explorer ( rxte ) but it was not spatially located at that time. a new detection in 2018 with the neil gehrels swift observatory during a type ii outburst permitted its position to be accurately located and its optical counterpart identified. we report x - ray and optical monitoring covering epochs before and during the outburst. using photometric data we show the long - term variability of the be disc where we present flux and colour changes associated with the disc growth and decay over a period of ~ 6000 days. we show evidence of disc growth during the recent outburst through an increase in the h - alpha equivalent width and photometric flux. period analysis was performed using both optical photometric and spectroscopic data, but with no significant detection of an orbital period. a modest periodic signature of 2. 65 days was detected from the ogle i band data, however, but we attribute that to the non - radial pulsations ( nrps ) of the be star. we also obtained a blue spectrum from the southern african large telescope ( salt ) which permits us to classify the spectral type as b0. 5 iv - v.
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arxiv:1902.00677
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an article for the springer encyclopedia of complexity and system science
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arxiv:0708.2203
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eccentric black - hole binaries are among the most awaited sources of gravitational waves, yet their dynamics lack a consistent framework that provides a detailed and physically robust evolutionary description due to gauge issues. we present a new set of non - orbit - averaged equations, free from radiation - reaction gauge ambiguities, that accurately describe the evolution of orbital elements for eccentric, non - spinning black - hole binaries. we derive these equations by mapping the keplerian orbital elements to a new set of characteristic parameters using energy and angular momentum definitions combined with near - identity transformations. the resulting framework is valid for arbitrary eccentricities, including parabolic and hyperbolic limits. using this framework, we demonstrate the strictly observable effects of the non - adiabatic emission of gravitational waves - - characteristic of eccentric binaries - - on the orbital parameters. furthermore, we assess the regime of validity of the widely used orbit - averaged equations first derived by peters in 1964. importantly, their breakdown becomes evident at the first pericenter passage, implying that the validity of the orbit - averaged approximation cannot be inferred solely from binary initial conditions. the formalism we introduce, accurate up to 2. 5 post - newtonian order, aims to provide a robust tool for making reliable astrophysical predictions and accurately interpreting current and future gravitational wave data, paving the way for deeper insights into the dynamics of eccentric black hole binaries.
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arxiv:2502.06952
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reinforcement learning ( rl ) is pivotal for enabling large language models ( llms ) to generate long chains of thought ( cot ) for complex tasks like math and reasoning. however, proximal policy optimization ( ppo ), effective in many rl scenarios, fails in long cot tasks. this paper identifies that value initialization bias and reward signal decay are the root causes of ppo ' s failure. we propose value - calibrated ppo ( vc - ppo ) to address these issues. in vc - ppo, the value model is pretrained to tackle initialization bias, and the generalized advantage estimation ( gae ) computation is decoupled between the actor and critic to mitigate reward signal decay. experiments on the american invitational mathematics examination ( aime ) show that vc - ppo significantly boosts ppo performance. ablation studies show that techniques in vc - ppo are essential in enhancing ppo for long cot tasks.
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arxiv:2503.01491
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we show that reconstructing a curve in $ \ mathbb { r } ^ d $ for $ d \ geq 2 $ from a $ 0. 66 $ - sample is always possible using an algorithm similar to the classical nn - crust algorithm. previously, this was only known to be possible for $ 0. 47 $ - samples in $ \ mathbb { r } ^ 2 $ and $ \ frac { 1 } { 3 } $ - samples in $ \ mathbb { r } ^ d $ for $ d \ geq 3 $. in addition, we show that there is not always a unique way to reconstruct a curve from a $ 0. 72 $ - sample ; this was previously only known for $ 1 $ - samples. we also extend this non - uniqueness result to hypersurfaces in all higher dimensions.
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arxiv:2112.03656
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we consider the two categories of termination problems of quantum programs with nondeterminism : 1 ) is an input of a program terminating with probability one under all schedulers? if not, how can a scheduler be synthesized to evidence the nontermination? 2 ) are all inputs terminating with probability one under their respective schedulers? if yes, a further question asks whether there is a scheduler that forces all inputs to be terminating with probability one together with how to synthesize it ; otherwise, how can an input be provided to refute the universal termination? for the effective verification of the first category, we over - approximate the reachable set of quantum program states by the reachable subspace, whose algebraic structure is a linear space. on the other hand, we study the set of divergent states from which the program terminates with probability zero under some scheduler. the divergent set has an explicit algebraic structure. exploiting them, we address the decision problem by a necessary and sufficient condition, i. e. the disjointness of the reachable subspace and the divergent set. furthermore, the scheduler synthesis is completed in exponential time. for the second category, we reduce the decision problem to the existence of invariant subspace, from which the program terminates with probability zero under all schedulers. the invariant subspace is characterized by linear equations. the states on that invariant subspace are evidence of the nontermination. furthermore, the scheduler synthesis is completed by seeking a pattern of finite schedulers that forces all inputs to be terminating with positive probability. the repetition of that pattern yields the desired universal scheduler that forces all inputs to be terminating with probability one. all the problems in the second category are shown to be solved in polynomial time.
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arxiv:2402.15827
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we introduce a relativization of the secant sheaves used by ein, green and lazarsfeld and apply this construction to the study of syzygies of canonical curves. as a first application, we give a simpler proof of voisin ' s theorem for general canonical curves. this completely determines the terms of the minimal free resolution of the coordinate ring of such curves. secondly, in the case of curves of even genus, we enhance voisin ' s theorem by providing a structure theorem for the last syzygy space, resolving the geometric syzygy conjecture in even genus.
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arxiv:2003.05849
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we obtain an inverse of furstenberg ' s correspondence principle in the setting of countable cancellative, amenable semigroups. besides being of intrinsic interest on its own, this result allows us to answer a variety of questions concerning sets of recurrence and van der corput ( vdc ) sets, which were posed by bergelson and lesigne \ cite { bl }, bergelson and ferr \ ' e moragues \ cite { bf }, kelly and l \ ^ e \ cite { kl }, and moreira \ cite { mor }. we also prove a spectral characterization of vdc sets and prove some of their basic properties in the context of countable amenable groups. several results in this article were independently found by sohail farhangi and robin tucker - drob, see \ cite { ft }.
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arxiv:2409.00885
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gamma - ray burst ( grb ) progenitors are observationally linked to the death of massive stars. x - ray studies of the grb afterglows can deepen our knowledge of the ionization status and metal abundances of the matter in the grb environment. moreover, the presence of local matter can be inferred through its fingerprints in the x - ray spectrum, i. e. the presence of absorption higher than the galactic value. a few studies based on bepposax and xmm - newton found evidence of higher than galactic values for the column density in a number of grb afterglows. here we report on a systematic analysis of 17 grbs observed by swift up to april 15, 2005. we observed a large number of grbs with an excess of column density. our sample, together with previous determinations of the intrinsic column densities for grbs with known redshift, provides evidence for a distribution of absorption consistent with that predicted for randomly occurring grb within molecular clouds.
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arxiv:astro-ph/0511750
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spin - wave excitations in ensembles of atoms are gaining attention as a quantum information resource. however, current techniques with atomic spin waves do not achieve universal quantum information processing. we conduct a theoretical analysis of methods to create a high - capacity universal quantum processor and network node using an ensemble of laser - cooled atoms, trapped in a one - dimensional periodic potential and coupled to a ring cavity. we describe how to establish linear quantum processing using a lambda - scheme in a rubidium - atom system, calculate the expected experimental operational fidelities. second, we derive an efficient method to achieve linear controllability with a single ensemble of atoms, rather than two - ensembles as proposed in [ k. c. cox et al. spin - wave quantum computing with atoms in a single - mode cavity, preprint 2021 ]. finally, we propose to use the spin - wave processor for continuous - variable quantum information processing and present a scheme to generate large dual - rail cluster states useful for deterministic computing.
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arxiv:2109.15246
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we discuss the effects of open boundary conditions and boundary induced drift on condensation phenomena in the pair - factorized steady states transport process, a versatile model for stochastic transport with tunable nearest - neighbour interactions. varying the specific type of the boundary implementation as well as the presence of a particle drift, we observe phase diagrams that are similar but richer compared to those of the simpler zero - range process with open boundary conditions. tuning our model towards zero - range - process - like properties we are able to study boundary induced effects in the transition regime from zero - range interactions to short - range interactions. we discuss the emerging phase structure where spatially extended condensates can be observed at the boundaries as well as in the bulk system and compare it to the situation with periodic boundaries, where the dynamics leads to the formation of a single condensate in the bulk.
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arxiv:1508.00619
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we study stochastic integrals driven by a general subordinator and establish a zero - one law for the finiteness of the resulting integral as well as moment estimates. as an application, we use these results to obtain structural properties of spdes driven by multiplicative pure jump noise, which include ( 1 ) a maximal inequality for a multiplicative stochastic convolution $ z _ t $, ( 2 ) a small ball probability of $ z _ t $, ( 3 ) the existence of invariant measures and accessibility to zero of spdes, and ( 4 ) a galerkin approximation of solutions to spdes.
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arxiv:2009.04785
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we propose and investigate a one - parameter probabilistic mixture of one - dimensional elementary cellular automata under the guise of a model for the dynamics of a single - species unstructured population with nonoverlapping generations in which individuals have smaller probability of reproducing and surviving in a crowded neighbourhood but also suffer from isolation and dispersal. remarkably, the first - order mean field approximation to the dynamics of the model yields a cubic map containing terms representing both logistic and weak allee effects. the model has a single absorbing state devoid of individuals, but depending on the reproduction and survival probabilities can achieve a stable population. we determine the critical probability separating these two phases and find that the phase transition between them is in the directed percolation universality class of critical behaviour.
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arxiv:1710.11305
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in this paper we continue to advance the theory regarding the riesz fractional gradient in the calculus of variations and fractional partial differential equations begun in an earlier work of the same name. in particular we here establish an $ l ^ 1 $ hardy inequality, obtain further regularity results for solutions of certain fractional pde, demonstrate the existence of minimizers for integral functionals of the fractional gradient with non - linear dependence in the field, and also establish the existence of solutions to corresponding euler - lagrange equations obtained as conditions of minimality. in addition we pose a number of open problems, the answers to which would fill in some gaps in the theory as well as to establish connections with more classical areas of study, including interpolation and the theory of dirichlet forms.
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arxiv:1611.07204
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or solid as is the case with water ( h2o ) ; a liquid at room temperature because its molecules are bound by hydrogen bonds. whereas hydrogen sulfide ( h2s ) is a gas at room temperature and standard pressure, as its molecules are bound by weaker dipole – dipole interactions. the transfer of energy from one chemical substance to another depends on the size of energy quanta emitted from one substance. however, heat energy is often transferred more easily from almost any substance to another because the phonons responsible for vibrational and rotational energy levels in a substance have much less energy than photons invoked for the electronic energy transfer. thus, because vibrational and rotational energy levels are more closely spaced than electronic energy levels, heat is more easily transferred between substances relative to light or other forms of electronic energy. for example, ultraviolet electromagnetic radiation is not transferred with as much efficacy from one substance to another as thermal or electrical energy. the existence of characteristic energy levels for different chemical substances is useful for their identification by the analysis of spectral lines. different kinds of spectra are often used in chemical spectroscopy, e. g. ir, microwave, nmr, esr, etc. spectroscopy is also used to identify the composition of remote objects – like stars and distant galaxies – by analyzing their radiation spectra. the term chemical energy is often used to indicate the potential of a chemical substance to undergo a transformation through a chemical reaction or to transform other chemical substances. = = = reaction = = = when a chemical substance is transformed as a result of its interaction with another substance or with energy, a chemical reaction is said to have occurred. a chemical reaction is therefore a concept related to the " reaction " of a substance when it comes in close contact with another, whether as a mixture or a solution ; exposure to some form of energy, or both. it results in some energy exchange between the constituents of the reaction as well as with the system environment, which may be designed vessels — often laboratory glassware. chemical reactions can result in the formation or dissociation of molecules, that is, molecules breaking apart to form two or more molecules or rearrangement of atoms within or across molecules. chemical reactions usually involve the making or breaking of chemical bonds. oxidation, reduction, dissociation, acid – base neutralization and molecular rearrangement are some examples of common chemical reactions. a chemical reaction can be symbolically depicted through a chemical equation. while in a non - nuclear chemical reaction the number and kind of atoms on both sides of the equation are equal, for
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https://en.wikipedia.org/wiki/Chemistry
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we present a set of equations describing the evolution of the scalar - type cosmological perturbation in a gravity with general quadratic order curvature coupling terms. equations are presented in a gauge ready form, thus are ready to implement various temporal gauge conditions depending on the problems. the ricci - curvature square term leads to a fourth - order differential equation for describing the spacetime fluctuations in a spatially homogeneous and isotropic cosmological background.
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arxiv:gr-qc/9811013
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let $ - d $ be a a negative discriminant and let $ t $ vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms of discriminant $ - d $. we prove an asymptotic formula for $ d \ to \ infty $ for the average over $ t $ of the number of representations of $ t $ by an integral positive definite quaternary quadratic form and obtain results on averages of fourier coefficients of linear combinations of siegel theta series. we also find an asymptotic bound from below on the number of binary forms of fixed discriminant $ - d $ which are represented by a given quaternary form. in particular, we can show that for growing $ d $ a positive proportion of the binary quadratic forms of discriminant $ - d $ is represented by the given quaternary quadratic form.
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arxiv:1202.4909
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we report the observation and characterization of field emission current from individual single - and few - layer graphene flakes laid on a flat sio2 / si substrate. measurements were performed in a scanning electron microscope chamber equipped with nanoprobes, used as electrodes to realize local measurements of the field emission current. we achieved field emission currents up to 1 { \ mu } a from the flat part of graphene flakes at applied fields of few hundred v / { \ mu } m. we found that emission process is stable over a period of several hours and that it is well described by a fowler - nordheim model for currents over 5 orders of magnitude.
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arxiv:1102.3273
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according to the formal holographic principle, a modification to the assumption of holographic principle in verlinder ' s investigation of entropy force is obtained. a more precise relation between entropy and area in the holographic system is proposed. with the entropy corrections to the area - relation, we derivate newton ' s laws and einstein equation with a static spherically symmetric holographic screen. furthermore we derived the correction terms to the modified friedmann equation of the frw universe starting from the holographic principle and the debye model.
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arxiv:1010.3429
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we report the successful test flight of a device for generating and monitoring correlated photon pairs under near - space conditions up to 35. 5km altitude. data from ground based qualification tests and the high altitude experiment demonstrate that the device continues to operate even under harsh environmental conditions. the design of the rugged, compact and power - efficient photon pair system is presented. this design enables autonomous photon pair systems to be deployed on low - resource platforms such as nanosatellites hosting remote nodes of a quantum key distribution network. these results pave the way for tests of entangled photon technology in low earth orbit.
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arxiv:1404.3971
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during design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e. g., wave propagation or fluid - structure interaction. a levelset description of the boundary, when combined with an enriched finite element formulation, offers a smoother description of the design than traditional density - based methods. however, existing enriched methods have drawbacks, including ill - conditioning and difficulties in prescribing essential boundary conditions. in this work we introduce a new enriched topology optimization methodology that overcomes the aforementioned drawbacks ; boundaries are resolved accurately by means of the interface - enriched generalized finite element method ( igfem ), coupled to a levelset function constructed by radial basis functions. the enriched method used in this new approach to topology optimization has the same level of accuracy in the analysis as standard the finite element method with matching meshes, but without the need for remeshing. we derive the analytical sensitivities and we discuss the behavior of the optimization process in detail. we establish that igfem - based levelset topology optimization generates correct topologies for well - known compliance minimization problems.
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arxiv:2003.13751
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although rdbs store vast amounts of rich, informative data spread across interconnected tables, the progress of predictive machine learning models as applied to such tasks arguably falls well behind advances in other domains such as computer vision or natural language processing. this deficit stems, at least in part, from the lack of established / public rdb benchmarks as needed for training and evaluation purposes. as a result, related model development thus far often defaults to tabular approaches trained on ubiquitous single - table benchmarks, or on the relational side, graph - based alternatives such as gnns applied to a completely different set of graph datasets devoid of tabular characteristics. to more precisely target rdbs lying at the nexus of these two complementary regimes, we explore a broad class of baseline models predicated on : ( i ) converting multi - table datasets into graphs using various strategies equipped with efficient subsampling, while preserving tabular characteristics ; and ( ii ) trainable models with well - matched inductive biases that output predictions based on these input subgraphs. then, to address the dearth of suitable public benchmarks and reduce siloed comparisons, we assemble a diverse collection of ( i ) large - scale rdb datasets and ( ii ) coincident predictive tasks. from a delivery standpoint, we operationalize the above four dimensions ( 4d ) of exploration within a unified, scalable open - source toolbox called 4dbinfer. we conclude by presenting evaluations using 4dbinfer, the results of which highlight the importance of considering each such dimension in the design of rdb predictive models, as well as the limitations of more naive approaches such as simply joining adjacent tables. our source code is released at https : / / github. com / awslabs / multi - table - benchmark.
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arxiv:2404.18209
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the three - sphere swimmer by najafi and golestanian is composed of three spheres connected by two arms. the case in which the swimmer can control the lengths of the two arms has been studied in detail. here we study a variation of the model in which the swimmer ' s arms are constructed according to hill ' s model of muscular contraction. the swimmer is able to control the tension developed in the active components of the arms. the two shape parameters and the tensions acting on the two arms are then obtained by solving a system of ordinary differential equations. we study the qualitative properties of the solutions, compute analytically their leading order approximation and compare them with numerical simulations. we also formulate and solve some optimisation problems, aimed at finding the actuation strategies maximising performance, for various performance measures. finally, we discuss the structure of the governing equations of our microswimmers from the point of view of control theory. we show that our systems are control affine systems with drift.
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arxiv:1702.00365
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a novel spherical convolution is defined through the sifting property of the dirac delta on the sphere. the so - called sifting convolution is defined by the inner product of one function with a translated version of another, but with the adoption of an alternative translation operator on the sphere. this translation operator follows by analogy with the euclidean translation when viewed in harmonic space. the sifting convolution satisfies a variety of desirable properties that are lacking in alternate definitions, namely : it supports directional kernels ; it has an output which remains on the sphere ; and is efficient to compute. an illustration of the sifting convolution on a topographic map of the earth demonstrates that it supports directional kernels to perform anisotropic filtering, while its output remains on the sphere.
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arxiv:2007.12153
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a metric graph is a 1 - dimensional stratified metric space consisting of vertices and edges or loops glued together. metric graphs can be naturally used to represent and model data that take the form of noisy filamentary structures, such as street maps, neurons, networks of rivers and galaxies. we consider the statistical problem of reconstructing the topology of a metric graph embedded in r ^ d from a random sample. we derive lower and upper bounds on the minimax risk for the noiseless case and tubular noise case. the upper bound is based on the reconstruction algorithm given in aanjaneya et al. ( 2012 ).
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arxiv:1305.1212
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the settling of highly elastic non - brownian closed fibres ( called loops ) under gravity in a viscous fluid is investigated numerically. the loops are represented using a bead - spring model with harmonic bending potential and finitely extensible nonlinear elastic ( fene ) stretching potential. numerical solutions to the stokes equations are obtained with the use of hydromultipole numerical codes, which are based on the multipole method corrected for lubrication to calculate hydrodynamic interactions between spherical particles with high precision. depending on the elasto - gravitation number b, a ratio of gravitation to bending forces, the loop approaches different attracting dynamical modes, as described by gruziel - slomka et al. ( soft matter, vol. 15, 2019, pp. 7262 - 7274 ) with the use of the rotne - prager mobility of the elastic loop made of beads. here, using a more precise method, we find and characterise a new mode, analyse typical timescales, velocities, and orientations of all the modes, compare them, and investigate their coexistence. we analyse the transitions ( bifurcations ) to a different mode at certain critical values of the elasto - gravitation number b.
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arxiv:2411.13563
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animal vocalisations contain important information about health, emotional state, and behaviour, thus can be potentially used for animal welfare monitoring. motivated by the spectro - temporal patterns of chick calls in the time $ - $ frequency domain, in this paper we propose an automatic system for chick call recognition using the joint time $ - $ frequency scattering transform ( jtfs ). taking full - length recordings as input, the system first extracts chick call candidates by an onset detector and silence removal. after computing their jtfs features, a support vector machine classifier groups each candidate into different chick call types. evaluating on a dataset comprising 3013 chick calls collected in laboratory conditions, the proposed recognition system using the jtfs features improves the frame - and event - based macro f - measures by 9. 5 % and 11. 7 %, respectively, than that of a mel - frequency cepstral coefficients baseline.
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arxiv:2110.03965
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we analyzed the localized charge dynamics in the system of $ n $ interacting single - level quantum dots ( qds ) coupled to the continuous spectrum states in the presence of coulomb interaction between electrons within the dots. different dots geometry and initial charge configurations were considered. the analysis was performed by means of heisenberg equations for localized electrons pair correlators. we revealed that charge trapping takes place for a wide range of system parameters and we suggested the qds geometry for experimental observations of this phenomenon. we demonstrated significant suppression of coulomb correlations with the increasing of qds number. we found the appearance of several time scales with the strongly different relaxation rates for a wide range of the coulomb interaction values.
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arxiv:1209.5262
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in this paper we study the boltzmann equation near global maxwellians in the $ d $ - dimensional whole space. a unique global - in - time mild solution to the cauchy problem of the equation is established in a chemin - lerner type space with respect to the phase variable $ ( x, v ) $. both hard and soft potentials with angular cutoff are considered. the new function space for global well - posedness is introduced to essentially treat the case of soft potentials, and the key point is that the velocity variable is taken in the weighted supremum norm, and the space variable is in the $ s $ - order besov space with $ s \ geq d / 2 $ including the spatially critical regularity. the proof is based on the time - decay properties of solutions to the linearized equation together with the bootstrap argument. particularly, the linear analysis in case of hard potentials is due to the semigroup theory, where the extra time - decay plays a role in coping with initial data in $ l ^ 2 $ with respect to space variable. in case of soft potentials, for the time - decay of linear equations we borrow the results basing on the pure energy method and further extend them to those in $ l ^ \ infty $ framework through the technique of $ l ^ 2 $ - - $ l ^ \ infty $ interplay. in contrast to hard potentials, $ l ^ 1 $ integrability in $ x $ of initial data is necessary for soft potentials in order to obtain global solutions to the nonlinear cauchy problem.
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arxiv:1709.09908
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autonomous vehicles ( avs ) are about to be used in transportation systems in the near future. to increase the level of safety and throughput of these vehicles, dedicated lanes for avs have been suggested in past studies as exclusive mobility infrastructure for these types of vehicles. although these lanes can bring obvious advantages in a transportation network, overall performance of these lanes, especially in urban areas and in micro level sight, is not clear. this study aims to examine the efficiency of dedicated lanes for avs in roundabout with an unbalanced traffic flow pattern. four factors of travel time, delay time, speed of vehicles, and queue of vehicles have been selected as variables of traffic performance at the roundabout. two microscopic traffic simulation software, aimsun and sidra intersection, were used to examine the impact of the av dedicated lanes at the roundabout. this study shows that the effects of an imbalanced traffic pattern in a roundabout are higher when the penetration rate of avs is lower and also dedicated lanes in roundabout ' s leg may improve traffic performance indicators when the penetration rate of avs is higher, but this improvement is not significant.
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arxiv:1904.07025
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optical see - through head - mounted displays ( ost hmds ) are a major output medium for augmented reality, which have seen significant growth in popularity and usage among the general public due to the growing release of consumer - oriented models, such as the microsoft hololens. unlike virtual reality headsets, ost hmds inherently support the addition of computer - generated graphics directly into the light path between a user ' s eyes and their view of the physical world. as with most augmented and virtual reality systems, the physical position of an ost hmd is typically determined by an external or embedded 6 - degree - of - freedom tracking system. however, in order to properly render virtual objects, which are perceived as spatially aligned with the physical environment, it is also necessary to accurately measure the position of the user ' s eyes within the tracking system ' s coordinate frame. for over 20 years, researchers have proposed various calibration methods to determine this needed eye position. however, to date, there has not been a comprehensive overview of these procedures and their requirements. hence, this paper surveys the field of calibration methods for ost hmds. specifically, it provides insights into the fundamentals of calibration techniques, and presents an overview of both manual and automatic approaches, as well as evaluation methods and metrics. finally, it also identifies opportunities for future research. % relative to the tracking coordinate system, and, hence, its position in 3d space.
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arxiv:1709.04299
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raman scattering is used to observe pronounced electronic excitations around 230 mev - well above the two - phonon range - in the mott insulators latio $ _ 3 $ and ytio $ _ 3 $. based on the temperature, polarization, and photon energy dependence, the modes are identified as orbital excitations. the observed profiles bear a striking resemblance to magnetic raman modes in the insulating parent compounds of the superconducting cuprates, indicating an unanticipated universality of the electronic excitations in transition metal oxides.
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arxiv:cond-mat/0503106
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natural language and images are commonly used as goal representations in goal - conditioned imitation learning ( il ). however, natural language can be ambiguous and images can be over - specified. in this work, we propose hand - drawn sketches as a modality for goal specification in visual imitation learning. sketches are easy for users to provide on the fly like language, but similar to images they can also help a downstream policy to be spatially - aware and even go beyond images to disambiguate task - relevant from task - irrelevant objects. we present rt - sketch, a goal - conditioned policy for manipulation that takes a hand - drawn sketch of the desired scene as input, and outputs actions. we train rt - sketch on a dataset of paired trajectories and corresponding synthetically generated goal sketches. we evaluate this approach on six manipulation skills involving tabletop object rearrangements on an articulated countertop. experimentally we find that rt - sketch is able to perform on a similar level to image or language - conditioned agents in straightforward settings, while achieving greater robustness when language goals are ambiguous or visual distractors are present. additionally, we show that rt - sketch has the capacity to interpret and act upon sketches with varied levels of specificity, ranging from minimal line drawings to detailed, colored drawings. for supplementary material and videos, please refer to our website : http : / / rt - sketch. github. io.
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arxiv:2403.02709
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to better understanding the principal features of collisionless damping / growing plasma waves we have implemented a demonstrative calculation for the simplest cases of electron waves in two - stream plasmas with the delta - function type electron velocity distribution function of each of the streams with velocities v ( 1 ) and v ( 2 ). the traditional dispersion equation is reduced to an algebraic 4th order equation, for which numerical solutions are presented for a variant of equal stream densities. in the case of uniform half - infinite slab one finds two dominant type solutions : non - damping forward waves and forward complex conjugated exponentially both damping and growing waves. beside it in this case there is no necessity of calculation any logarithmically divergent indefinite integrals. the possibility of wave amplifying might be useful in practical applications.
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arxiv:0708.0767
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the curvature and twisting of spacetime rotate the angle of polarization and imprint orbital angular momentum to photons emitted by the accretion disk near rotating black holes. considering polarization and orbital angular momentum as two degrees of freedom of single - photons that can encode quantum information, we emphasize that the particular shape of spacetime around rotating black holes implements quantum gates and simple quantum circuits. consequently, we demonstrate the implementation of some elementary quantum gates, like hadamard or c - not, and simple quantum circuits, like bell states, with photons in the presence of spinning black holes. detection and measurement of quantum information encoded in photons emitted in the accretion disk around rotating black holes may be performed by actual quantum information technology.
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arxiv:1702.04640
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eye - tracking data is a very useful source of information to study cognition and especially language comprehension in humans. in this paper, we describe our systems for the cmcl 2022 shared task on predicting eye - tracking information. we describe our experiments with pretrained models like bert and xlm and the different ways in which we used those representations to predict four eye - tracking features. along with analysing the effect of using two different kinds of pretrained multilingual language models and different ways of pooling the tokenlevel representations, we also explore how contextual information affects the performance of the systems. finally, we also explore if factors like augmenting linguistic information affect the predictions. our submissions achieved an average mae of 5. 72 and ranked 5th in the shared task. the average mae showed further reduction to 5. 25 in post task evaluation.
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arxiv:2204.04998
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through basin - scale circulations, the ocean regulates global distributions of heat, nutrients, and greenhouse gases. to properly predict the future of the ocean under climate change, we need to develop a thorough understanding of the underlying mechanisms that drive global circulations. an estimated 2 tw of power is required to support interior mixing. roughly half of this power is believed to come from tidal flow over topography, producing internal gravity waves ( igw ' s ), which can radiate energy throughout the ocean interior. but it is difficult to track the subsequent journey from tidal injection to dissipation, as the energy cascade spans an enormous range of spatio - temporal scales and multiple different nonlinear transfer mechanisms. to investigate the full energy pathway from topographic forcing to irreversible mixing, we built a model ocean in a large - scale laboratory wavetank ( 9 m x 2. 9 m x 0. 75 m ) allowing reynolds numbers up to o ( 10 $ ^ 5 $ ). we replicate the tidal forcing by oscillating an idealized ocean ridge. we track energy transfer across the first cascade, driven by wave turbulence, using background oriented schlieren ( bos ) over the full tank. through the bos we observe the formation of various sets of subharmonics, driven by triadic resonant instabilities ( tri ). at later times, the subharmonics born from tri engage in different interactions, which ultimately develop a continuum of waves at frequencies up to $ n $. we validate the three - wave resonant conditions through a fourier decomposition and confirm a backward cascade in frequency but a forward cascade in vertical wavenumber. through our spatial analysis, we identify relevant three - wave interactions and show the significance of elastic scattering, a nonlocal interaction, in our fully evolved system. we note however that the majority of our triads are local, which have been historically overlooked.
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arxiv:2408.05593
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an alternative to density functional theory are wavefunction based electronic structure calculations for solids. in order to perform them the exponential wall ( ew ) problem has to be resolved. it is caused by an exponential increase of the number of configurations with increasing electron number n. there are different routes one may follow. one is to characterize a many - electron wavefunction by a vector in liouville space with a cumulant metric rather than in hilbert space. this removes the ew problem. another is to model the solid by an { \ it impurity } or { \ it fragment } embedded in a { \ it bath } which is treated at a much lower level than the former. this is the case in density matrix embedding theory ( dmet ) or density embedding theory ( det ). the latter are closely related to a schmidt decomposition of a system and to the determination of the associated entanglement. we show here the connection between the two approaches. it turns out that the dmet ( or det ) has an identical active space as a previously used local ansatz, based on a projection and partitioning approach. yet, the ew problem is resolved differently in the two cases. by studying a $ h _ { 10 } $ ring these differences are analyzed with the help of the method of increments.
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arxiv:1703.02572
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in an exact conformal theory there is no particle. the excitations have continuum spectra and are called " unparticles " by georgi. we consider supersymmetric extensions of the standard model with approximate conformal sectors. the conformal symmetry is softly broken in the infrared which generates a gap. however, the spectrum can still have a continuum above the gap if there is no confinement. using the ads / cft correspondence this can be achieved with a soft wall in the warped extra dimension. when supersymmetry is broken the superpartners of the standard model particles may simply be a continuum above gap. the collider signals can be quite different from the standard supersymmetric scenarios and the experimental searches for the continuum superpartners can be very challenging.
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arxiv:1003.1163
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we show that the variance of a probability measure $ \ mu $ on a compact subset $ x $ of a complete metric space $ m $ is bounded by the square of the circumradius $ r $ of the canonical embedding of $ x $ into the space $ p ( m ) $ of probability measures on $ m $, equipped with the wasserstein metric. when barycenters of measures on $ x $ are unique ( such as on cat ( $ 0 $ ) spaces ), our approach shows that $ r $ in fact coincides with the circumradius of $ x $ and so this result extends a recent result of lim - mccann from euclidean space. our approach involves bi - linear minimax theory on $ p ( x ) \ times p ( m ) $ and extends easily to the case when the variance is replaced by very general moments. as an application, we provide a simple proof of jung ' s theorem on cat ( $ k $ ) spaces, a result originally due to dekster and lang - schroeder.
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arxiv:2006.02984
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here, we address the essential question of whether, in the context of evolving populations, ecosystems attain properties that enable persistence of the ecosystem itself. we use a simple ecosystem model describing resource, producer, and consumer dynamics to analyze how evolution affects dynamical stability properties of the ecosystem. in particular, we compare resilience of the entire system after allowing the producer and consumer populations to evolve to their evolutionarily stable strategy ( ess ), to the maximum attainable resilience. we find a substantial reduction in ecosystem resilience when producers and consumers are allowed to evolve compared to the maximal attainable resilience. this study illustrates the inherent difference and possible conflict between maximizing individual - level fitness and maximizing resilience of entire ecosystems.
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arxiv:1407.7412
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in this paper we propose a bayesian, information theoretic approach to dimensionality reduction. the approach is formulated as a variational principle on mutual information, and seamlessly addresses the notions of sufficiency, relevance, and representation. maximally informative statistics are shown to minimize a kullback - leibler distance between posterior distributions. illustrating the approach, we derive the maximally informative one dimensional statistic for a random sample from the cauchy distribution.
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arxiv:physics/0010039
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we investigate the su ( $ n $ ) hubbard model for the multi - component fermionic optical lattice system, combining dynamical mean - field theory with the continuous - time quantum monte carlo method. we obtain the finite temperature phase diagrams with $ n \ le 6 $ and find that low temperature properties depends on the parity of the components. the magnetically ordered state competes with the correlated metallic state in the system with the even number of components $ ( n \ ge 4 ) $, yielding the first - order phase transition. it is also clarified that, in the odd - component system, the ordered state is realized at relatively lower temperatures and the critical temperature is constant in the strong coupling limit.
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arxiv:1603.02647
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superclimbing modes are hallmark degrees of freedom of transverse quantum fluids describing wide superfluid one - dimensional interfaces and / or edges with negligible peierls barrier. we report the first direct numeric evidence of quantum shape fluctuations - - caused by superclimbing modes - - in simple lattice models, as well as at the free edge of an incomplete solid monolayer of $ ^ 4 $ he adsorbed on graphite. our data unambiguously reveals the defining feature of the superclimbing modes - - canonical conjugation of the edge displacement field to the field of superfluid phase - - and its unexpected implication, i. e., that superfluid stiffness can be inferred from density snapshots.
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arxiv:2404.03465
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this is the second paper in our series of five in which we test the master constraint programme for solving the hamiltonian constraint in loop quantum gravity. in this work we begin with the simplest examples : finite dimensional models with a finite number of first or second class constraints, abelean or non - - abelean, with or without structure functions.
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arxiv:gr-qc/0411139
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in loop quantum gravity in the connection representation, the quantum configuration space $ \ bar { \ mathcal { a } / \ mathcal { g } } $, which is a compact space, is much larger than the classical configuration space $ \ mathcal { a } / % \ mathcal { g } $ of connections modulo gauge transformations. one finds that $ % \ bar { \ mathcal { a } / \ mathcal { g } } $ is homeomorphic to the space $ hom ( % \ mathcal { l } _ { \ ast }, g ) ) / ad $. we give a new, natural proof of this result, suggesting the extension of the hoop group $ \ mathcal { l } _ { \ ast } $ to a larger, compact group $ \ mathcal { m } ( \ mathcal { l } _ { \ ast } ) $ that contains $ % \ mathcal { l } _ { \ ast } $ as a dense subset. this construction is based on almost periodic functions. we introduce the hilbert algebra $ l _ { 2 } ( \ mathcal { m } ( % \ mathcal { l } _ { \ ast } ) ) $ of $ \ mathcal { m } ( \ mathcal { l } _ { \ ast } ) $ with respect to the haar measure $ \ xi $ on $ \ mathcal { m } ( \ mathcal { l } _ { \ ast } ) $. the measure $ % \ xi $ is shown to be invariant under 3 - diffeomorphisms. this is the first step in a proof that $ l _ { 2 } ( \ mathcal { m } ( \ mathcal { l } _ { \ ast } ) ) $ is the appropriate hilbert space for loop quantum gravity in the loop representation. in a subsequent paper, we will reinforce this claim by defining an extended loop transform and its inverse.
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arxiv:gr-qc/0112072
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we investigate the optical detection of single atoms held in a microscopic atom trap close to a surface. laser light is guided by optical fibers or optical micro - structures via the atom to a photo - detector. our results suggest that with present - day technology, micro - cavities can be built around the atom with sufficiently high finesse to permit unambiguous detection of a single atom in the trap with 10 $ \ mu $ s of integration. we compare resonant and non - resonant detection schemes and we discuss the requirements for detecting an atom without causing it to undergo spontaneous emission.
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arxiv:quant-ph/0210090
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we study the convergence of $ q $ - learning with linear function approximation. our key contribution is the introduction of a novel multi - bellman operator that extends the traditional bellman operator. by exploring the properties of this operator, we identify conditions under which the projected multi - bellman operator becomes contractive, providing improved fixed - point guarantees compared to the bellman operator. to leverage these insights, we propose the multi $ q $ - learning algorithm with linear function approximation. we demonstrate that this algorithm converges to the fixed - point of the projected multi - bellman operator, yielding solutions of arbitrary accuracy. finally, we validate our approach by applying it to well - known environments, showcasing the effectiveness and applicability of our findings.
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arxiv:2309.16819
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the bepposax wide field cameras detected a transient in ngc6440 on 1998 aug 22. rosat did not detect this source on 1998 sep 8, indicating that the x - ray flux had decreased by a factor 400 at least, and / or that the x - ray spectrum had become appreciably softer. analysis of archival rosat hri data reveals two sources associated with ngc6440 ; one of these may be the transient in quiescence. we have also obtained b and r images of ngc6440 on 1998 aug 26 and again on 1999 july 15, when the transient had returned to quiescence. subtraction of these images reveals one object in the core which was brighter in b, but not in r, during the x - ray outburst. we estimate b = 22. 7 and ( b - r ) o < 0 on 1998 aug 26, which makes it a viable candidate counterpart.
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arxiv:astro-ph/0005337
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we say that a set of points $ s \ subset \ mathbb { r } ^ d $ is an $ \ varepsilon $ - nearly $ k $ - distance set if there exist $ 1 \ le t _ 1 \ le \ ldots \ le t _ k, $ such that the distance between any two distinct points in $ s $ falls into $ [ t _ 1, t _ 1 + \ varepsilon ] \ cup \ ldots \ cup [ t _ k, t _ k + \ varepsilon ] $. in this paper, we study the quantity $ m _ k ( d ) = \ lim _ { \ varepsilon \ to 0 } \ max \ { | s | \ : \ s \ text { is an } \ varepsilon \ text { - nearly } k \ text { - distance set in } \ mathbb { r } ^ d \ } $ and its relation to the classical quantity $ m _ k ( d ) $ : the size of the largest $ k $ - distance set in $ \ mathbb { r } ^ d $. we obtain that $ m _ k ( d ) = m _ k ( d ) $ for $ k = 2, 3 $, as well as for any fixed $ k $, provided that $ d $ is sufficiently large. the last result answers a question, proposed by erd \ h { o } s, makai and pach. we also address a closely related tur \ ' an - type problem, studied by erd \ h { o } s, makai, pach, and spencer in the 80 ' s : given $ n $ points in $ \ mathbb { r } ^ d $, how many pairs of them form a distance that belongs to $ [ t _ 1, t _ 1 + 1 ] \ cup \ ldots \ cup [ t _ k, t _ k + 1 ], $ where $ t _ 1, \ ldots, t _ k $ are fixed and any two points in the set are at distance at least $ 1 $ apart? we establish the connection between this quantity and a quantity closely related to $ m _ k ( d - 1 ) $, as well as obtain an exact answer for the same ranges $ k, d $ as above.
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arxiv:1906.02574
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we prove that the eulerian polynomial satisfies certain polynomial congruences. furthermore, these congruences characterize the eulerian polynomial.
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arxiv:1611.10147
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given the euclidean space $ \ r ^ { 2n + 2 } $ endowed with a constant symplectic structure and the standard flat connection, and given a polynomial of degree 2 on that space, baguis and cahen have defined a reduction procedure which yields a symplectic manifold endowed with a ricci - type connection. we observe that any symplectic manifold of dimension greater than 2 endowed with a symplectic connection of ricci - type is locally given by a local version of such a reduction. we also consider the reverse of this reduction procedure, an induction procedure : we construct globally on a symplectic manifold endowed with a connection of ricci - type $ ( m, \ omega, \ nabla ) $ a circle or a line bundle which embeds in a flat symplectic manifold $ ( p, \ mu, \ nabla ^ 1 ) $ as the zero set of a function whose third covariant derivative vanishes, in such a way that $ ( m, \ omega, \ nabla ) $ is obtained by reduction from $ ( p, \ mu, \ nabla ^ 1 ) $. we further develop the particular case of symmetric symplectic manifolds with ricci - type connections.
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arxiv:math/0310375
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we revisit some issues about existence and regularity for the wave equation in noncylindrical domains. using a method of diffeomorphisms, we show how, through increasing regularity assumptions, the existence of weak solutions, their improved regularity and an energy balance can be derived. as an application, we give a rigorous definition of dynamic energy release rate density for some problems of debonding, and we formulate a proper notion of solution for such problems. we discuss the consistence of such formulation with previous ones, given in literature for particular cases.
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arxiv:2203.03738
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researchers have recently achieved significant advances in deep learning techniques, which in turn has substantially advanced other research disciplines, such as natural language processing, image processing, speech recognition, and software engineering. various deep learning techniques have been successfully employed to facilitate software engineering tasks, including code generation, software refactoring, and fault localization. many papers have also been presented in top conferences and journals, demonstrating the applications of deep learning techniques in resolving various software engineering tasks. however, although several surveys have provided overall pictures of the application of deep learning techniques in software engineering, they focus more on learning techniques, that is, what kind of deep learning techniques are employed and how deep models are trained or fine - tuned for software engineering tasks. we still lack surveys explaining the advances of subareas in software engineering driven by deep learning techniques, as well as challenges and opportunities in each subarea. to this end, in this paper, we present the first task - oriented survey on deep learning - based software engineering. it covers twelve major software engineering subareas significantly impacted by deep learning techniques. such subareas spread out the through the whole lifecycle of software development and maintenance, including requirements engineering, software development, testing, maintenance, and developer collaboration. as we believe that deep learning may provide an opportunity to revolutionize the whole discipline of software engineering, providing one survey covering as many subareas as possible in software engineering can help future research push forward the frontier of deep learning - based software engineering more systematically.
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arxiv:2410.13110
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parker solar probes ' s ( psp ) ' s unique orbital path allows us to observe the solar wind closer to the sun than ever before. essential to advancing our knowledge of solar wind and energetic particle formation is identifying the sources of psp observations. we report on results for the first two psp solar encounters derived using the wang - sheeley - arge ( wsa ) model driven by air force data assimilative photospheric flux transport ( adapt ) model maps. we derive the coronal magnetic field and the 1 rs source regions of the psp - observed solar wind. we validate our results with the solar wind speed and magnetic polarity observed at psp. when modeling results are very reliable, we derive time series of model - derived spacecraft separation from the heliospheric current sheet, magnetic expansion factor, coronal hole boundary distance, and photospheric field strength along the field lines estimated to be connected to the spacecraft. we present new results for encounter 1, which show time evolution of the far - side mid - latitude coronal hole that psp co - rotates with. we discuss how this evolution coincides with solar wind speed, density, and temperature observed at the spacecraft. during encounter 2, a new active region emerges on the far - side, making it difficult to model. we show that adapt - wsa output agrees well with psp observations once this active region rotates onto the near - side, allowing us to reliably estimate the solar wind sources retrospectively for most of the encounter. we close with ways in which coronal modeling enables scientific interpretation of these encounters that would otherwise not have been possible.
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arxiv:2205.13010
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the prospect of using the quantum nature of light for secure communication keeps spurring the search and investigation of suitable sources of entangled - photons. semiconductor quantum dots are arguably the most attractive. they can generate indistinguishable entangled - photons deterministically, and are compatible with current photonic - integration technologies, a set of properties not shared by any other entanglement resource. however, as no two quantum dots are identical, they emit entangled - photons with random energies. this hinders their exploitation in communication protocols requiring entangled - states with well - defined energies. here, we introduce scalable quantum - dot - based sources of polarization - entangled - photons whose energy can be controlled via dynamic strain - engineering without degrading the degree of entanglement of the source. as a test - bench, we interface quantum dots with clouds of atomic vapours, and we demonstrate slow - entangled - photons from a single quantum emitter. these results pave the way towards the implementation of hybrid quantum networks where entanglement is distributed among distant parties using scalable optoelectronic devices.
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arxiv:1507.06612
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