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 Showing 601 - 538 of 538 Journals sorted alphabetically Research in the Mathematical Sciences Research Journal of Pure Algebra       (Followers: 1) Researches in Mathematics Results in Control and Optimization Results in Mathematics Results in Nonlinear Analysis Review of Symbolic Logic       (Followers: 2) Reviews in Mathematical Physics       (Followers: 1) Revista Baiana de Educação Matemática Revista Bases de la Ciencia Revista BoEM - Boletim online de Educação Matemática Revista Colombiana de Matemáticas       (Followers: 1) Revista de Ciencias Revista de Educación Matemática Revista de la Escuela de Perfeccionamiento en Investigación Operativa Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Revista de Matemática : Teoría y Aplicaciones       (Followers: 1) Revista Digital: Matemática, Educación e Internet Revista Electrónica de Conocimientos, Saberes y Prácticas Revista Integración : Temas de Matemáticas Revista Internacional de Sistemas Revista Latinoamericana de Etnomatemática Revista Latinoamericana de Investigación en Matemática Educativa Revista Matemática Complutense Revista REAMEC : Rede Amazônica de Educação em Ciências e Matemática Revista SIGMA Ricerche di Matematica RMS : Research in Mathematics & Statistics Royal Society Open Science       (Followers: 7) Russian Journal of Mathematical Physics Russian Mathematics Sahand Communications in Mathematical Analysis Sampling Theory, Signal Processing, and Data Analysis São Paulo Journal of Mathematical Sciences Science China Mathematics       (Followers: 1) Science Progress       (Followers: 1) Sciences & Technologie A : sciences exactes Selecta Mathematica       (Followers: 1) SeMA Journal Semigroup Forum       (Followers: 1) Set-Valued and Variational Analysis SIAM Journal on Applied Mathematics       (Followers: 11) SIAM Journal on Computing       (Followers: 11) SIAM Journal on Control and Optimization       (Followers: 19) SIAM Journal on Discrete Mathematics       (Followers: 8) SIAM Journal on Financial Mathematics       (Followers: 3) SIAM Journal on Mathematics of Data Science       (Followers: 1) SIAM Journal on Matrix Analysis and Applications       (Followers: 3) SIAM Journal on Optimization       (Followers: 13) Siberian Advances in Mathematics Siberian Mathematical Journal Sigmae SILICON SN Partial Differential Equations and Applications Soft Computing       (Followers: 7) Statistics and Computing       (Followers: 14) Stochastic Analysis and Applications       (Followers: 3) Stochastic Partial Differential Equations : Analysis and Computations       (Followers: 2) Stochastic Processes and their Applications       (Followers: 6) Stochastics and Dynamics       (Followers: 2) Studia Scientiarum Mathematicarum Hungarica       (Followers: 1) Studia Universitatis Babeș-Bolyai Informatica Studies In Applied Mathematics       (Followers: 1) Studies in Mathematical Sciences       (Followers: 1) Superficies y vacio Suska Journal of Mathematics Education       (Followers: 1) Swiss Journal of Geosciences       (Followers: 1) Synthesis Lectures on Algorithms and Software in Engineering       (Followers: 2) Synthesis Lectures on Mathematics and Statistics       (Followers: 1) Tamkang Journal of Mathematics Tatra Mountains Mathematical Publications Teaching Mathematics       (Followers: 10) Teaching Mathematics and its Applications: An International Journal of the IMA       (Followers: 4) Teaching Statistics       (Followers: 8) Technometrics       (Followers: 8) The Journal of Supercomputing       (Followers: 1) The Mathematica journal The Mathematical Gazette       (Followers: 1) The Mathematical Intelligencer       (Followers: 1) The Ramanujan Journal The VLDB Journal       (Followers: 2) Theoretical and Mathematical Physics       (Followers: 7) Theory and Applications of Graphs Topological Methods in Nonlinear Analysis Transactions of the London Mathematical Society       (Followers: 1) Transformation Groups Turkish Journal of Mathematics Ukrainian Mathematical Journal Uniciencia Uniform Distribution Theory Unisda Journal of Mathematics and Computer Science Unnes Journal of Mathematics       (Followers: 1) Unnes Journal of Mathematics Education       (Followers: 2) Unnes Journal of Mathematics Education Research       (Followers: 1) Ural Mathematical Journal Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Vestnik St. Petersburg University: Mathematics VFAST Transactions on Mathematics       (Followers: 1) Vietnam Journal of Mathematics Vinculum Visnyk of V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics       (Followers: 2) Water SA       (Followers: 1) Water Waves Zamm-Zeitschrift Fuer Angewandte Mathematik Und Mechanik       (Followers: 1) ZDM       (Followers: 2) Zeitschrift für angewandte Mathematik und Physik       (Followers: 2) Zeitschrift fur Energiewirtschaft Zetetike

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Similar Journals
 Research in the Mathematical SciencesNumber of Followers: 0     Open Access journal ISSN (Print) 2522-0144 - ISSN (Online) 2197-9847 Published by SpringerOpen  [228 journals]
• Serre duality for tame Deligne–Mumford stacks

• Abstract: Abstract Using the exceptional inverse image functor for quasi-finite proper morphisms of separated tame Deligne–Mumford stacks of finite type over a field k, Serre duality is obtained in varying degrees of generality for tame Deligne–Mumford stacks. The approach follows that for schemes.
PubDate: 2022-11-19

• Discontinuous Galerkin method with Voronoi partitioning for quantum
simulation of chemistry

• Abstract: Abstract To circumvent a potentially dense two-body interaction tensor and obtain lower asymptotic costs for quantum simulations of chemistry, the discontinuous Galerkin (DG) basis set with a rectangular partitioning strategy was recently introduced [McClean et al, New J. Phys. 22, 093015, 2020]. We propose and numerically scrutinize a more general DG basis set construction based on a Voronoi decomposition with respect to the nuclear coordinates. This allows the construction of DG basis sets for arbitrary molecular and crystalline configurations. We here employ the planewave dual basis set as primitive basis set in the supercell model; as a set of grid-based nascent delta functions, the planewave dual functions provide sufficient flexibility for the Voronoi partitioning. The presented implementation of this DG-Voronoi approach is in Python and solely based on PySCF. We numerically investigate the performance, at the mean-field and correlated level of theory for quasi-1D, quasi-2D and fully 3D systems, and exemplify the application to crystalline systems.
PubDate: 2022-11-19

• The algebraic parts of the central values of quadratic twists of modular
L-functions modulo $$\ell$$

• Abstract: Abstract Let F be a newform of weight 2k on $$\Gamma _0(N)$$ with an odd integer N and a positive integer k, and $$\ell$$ be a prime larger than or equal to 5 with $$(\ell ,N)=1$$ . For each fundamental discriminant D, let $$\chi _{D}$$ be a quadratic character associated with quadratic field $$\mathbb {Q}(\sqrt{D})$$ . Assume that for each D, the $$\ell$$ -adic valuation of the algebraic part of $$L(F\otimes \chi _{D},k)$$ is non-negative. Let $$W_{\ell }^{+}$$ (resp. $$W_{\ell }^{-}$$ ) be the set of positive (resp. negative) fundamental discriminants D with $$(D,N)=1$$ such that the $$\ell$$ -adic valuation of the algebraic part of $$L(F\otimes \chi _{D},k)$$ is zero. We prove that for each sign $$\epsilon$$ , if $$W_{\ell }^{\epsilon }$$ is a non-empty finite set, then \begin{aligned} W_{\ell }^{\epsilon } \subset \left\{ 1, (-1)^{\frac{\ell -1}{2}}\ell \right\} .\end{aligned} By this result, we prove that if $$\epsilon$$ is the sign of $$(-1)^k$$ , then \begin{aligned}k\ge \ell -1 \text { or } k=\frac{\ell -1}{2}. \end{aligned} These are applied to obtain a lower bound for $$\#\{D\in W_{\ell }^{\epsilon } : D \le X \}$$ and the indivisibility of the order of the Shafarevich–Tate group of an elliptic curve over $$\mathbb {Q}$$ . To prove these results, first we refine Waldspurger’s formula on the Shimura correspondence for general odd levels N. Next we study mod $$\ell$$ modular forms of half-integral weight with few non-vanishing coefficients. To do this, we use the filtration of mod $$\ell$$ modular forms and mod $$\ell$$ Galois representations.
PubDate: 2022-11-02

• Distribution of rational points on toric varieties: all the heights

• Abstract: Abstract In this paper we prove a formula for the number of rational points in a certain height box for a split toric variety over a number field.
PubDate: 2022-11-02

• Derivatives of L-series of weakly holomorphic cusp forms

• Abstract: Abstract Based on the theory of L-series associated with weakly holomorphic modular forms in Diamantis et al. (L-series of harmonic Maass forms and a summation formula for harmonic lifts. arXiv:2107.12366), we derive explicit formulas for central values of derivatives of L-series as integrals with limits inside the upper half-plane. This has computational advantages, already in the case of classical holomorphic cusp forms and, in the last section, we discuss computational aspects and explicit examples.
PubDate: 2022-10-26

• $${}_{4}F_{3}$$ -Gaussian hypergeometric series and traces of Frobenius
for elliptic curves

• Abstract: Abstract In this article, we obtain finite field analogues of classical summation identities connecting $$F_3$$ -Appell series and $${_4} F_3$$ -classical hypergeometric series. As an application, we establish a new summation formula satisfied by the $${_4} F_3$$ -Gaussian hypergeometric series. We further express certain special values of $${_4} F_3$$ -Gaussian hypergeometric series in terms of traces of the Frobenius endomorphisms of certain families of elliptic curves. We also explicitly find some special values of $${{}_4} F_3$$ -Gaussian hypergeometric series.
PubDate: 2022-10-05

• Performance assessment of the maximum likelihood ensemble filter and the
ensemble Kalman filters for nonlinear problems

• Abstract: Abstract This study presents a thorough investigation of the performance comparison of three ensemble data assimilation (DA) methods, including the maximum likelihood ensemble filter (MLEF), the ensemble Kalman filter (EnKF), and the iterative EnKF (IEnKF), with respect to solution accuracy and computational efficiency for nonlinear problems. The convection–diffusion–reaction (CDR) problem is first tested, and then, the chaotic Lorenz 96 model is solved. Both linear and nonlinear observation operators are considered. The study demonstrates that MLEF consistently produces more accurate and efficient solution than the other two methods and provides more information on both states and their uncertainties. The IEnKF and MLEF are used to estimate model parameters and uncertainty in initial conditions using a nonlinear observation operator. The assimilation performance is assessed based on the quality metrics, such as the squared true error, the trace of the error covariance matrix, and the root-mean-square (RMS) error. Based on these DA performance assessments, MLEF demonstrates better convergence and higher accuracy. Results of the CDR problem show significant improvements in the estimate of model parameters and the solution accuracy by MLEF compared to the EnKF family. This study provides evidence supporting the choice of MLEF when solving large nonlinear problems.
PubDate: 2022-10-03

• Asymptotics for the twisted eta-product and applications to sign changes
in partitions

• Abstract: Abstract We prove asymptotic formulas for the complex coefficients of $$(\zeta q;q)_\infty ^{-1}$$ , where $$\zeta$$ is a root of unity, and apply our results to determine secondary terms in the asymptotics for p(a, b, n), the number of integer partitions of n with number of parts congruent a modulo b. Our results imply that, as $$n \rightarrow \infty$$ , the difference $$p(a_1,b,n)-p(a_2,b,n)$$ for $$a_1 \ne a_2$$ oscillates like a cosine when renormalized by elementary functions. Moreover, we give asymptotic formulas for arbitrary linear combinations of $$\{p(a,b,n)\}_{1 \le a \le b}.$$
PubDate: 2022-09-24

• Fully hyperbolic convolutional neural networks

• Abstract: Abstract Convolutional neural networks (CNN) have recently seen tremendous success in various computer vision tasks. However, their application to problems with high dimensional input and output, such as high-resolution image and video segmentation or 3D medical imaging, has been limited by various factors. Primarily, in the training stage, it is necessary to store network activations for back-propagation. In these settings, the memory requirements associated with storing activations can exceed what is feasible with current hardware, especially for problems in 3D. Motivated by the propagation of signals over physical networks, that are governed by the hyperbolic Telegraph equation, in this work we introduce a fully conservative hyperbolic network for problems with high-dimensional input and output. We introduce a coarsening operation that allows completely reversible CNNs by using a learnable discrete wavelet transform and its inverse to both coarsen and interpolate the network state and change the number of channels. We show that fully reversible networks are able to achieve results comparable to the state of the art in 4D time-lapse hyper-spectral image segmentation and full 3D video segmentation, with a much lower memory footprint that is a constant independent of the network depth. We also extend the use of such networks to variational auto-encoders, where optimization begins from an exact recovery and we discover the level of compression through optimization.
PubDate: 2022-09-23

• Extendable orthogonal sets of integral vectors

• Abstract: Abstract Motivated by a model in quantum computation, we study orthogonal sets of integral vectors of the same norm that can be extended with new vectors keeping the norm and the orthogonality. Our approach involves some arithmetic properties of the quaternions and other hypercomplex numbers.
PubDate: 2022-09-22

• Quantized convolutional neural networks through the lens of partial
differential equations

• Abstract: Abstract Quantization of convolutional neural networks (CNNs) is a common approach to ease the computational burden involved in the deployment of CNNs, especially on low-resource edge devices. However, fixed-point arithmetic is not natural to the type of computations involved in neural networks. In this work, we explore ways to improve quantized CNNs using PDE-based perspective and analysis. First, we harness the total variation (TV) approach to apply edge-aware smoothing to the feature maps throughout the network. This aims to reduce outliers in the distribution of values and promote piecewise constant maps, which are more suitable for quantization. Secondly, we consider symmetric and stable variants of common CNNs for image classification and graph convolutional networks for graph node classification. We demonstrate through several experiments that the property of forward stability preserves the action of a network under different quantization rates. As a result, stable quantized networks behave similarly to their non-quantized counterparts even though they rely on fewer parameters. We also find that at times, stability even aids in improving accuracy. These properties are of particular interest for sensitive, resource-constrained, low-power or real-time applications like autonomous driving.
PubDate: 2022-09-06

• How does momentum benefit deep neural networks architecture design' A
few case studies

• Abstract: Abstract We present and review an algorithmic and theoretical framework for improving neural network architecture design via momentum. As case studies, we consider how momentum can improve the architecture design for recurrent neural networks (RNNs), neural ordinary differential equations (ODEs), and transformers. We show that integrating momentum into neural network architectures has several remarkable theoretical and empirical benefits, including (1) integrating momentum into RNNs and neural ODEs can overcome the vanishing gradient issues in training RNNs and neural ODEs, resulting in effective learning long-term dependencies; (2) momentum in neural ODEs can reduce the stiffness of the ODE dynamics, which significantly enhances the computational efficiency in training and testing; (3) momentum can improve the efficiency and accuracy of transformers.
PubDate: 2022-08-26

• Tight closure and strongly F-regular rings

• Abstract: Abstract We describe several aspects of the theory of strongly F-regular rings, including how they should be defined without the hypothesis of F-finiteness, and its relationship to tight closure theory, to F-signature, and to cluster algebras. As a necessary prerequisite, we give a quick introduction to tight closure theory, without proofs, but with discussion of underlying ideas. This treatment includes characterizations, important applications, and material concerning the existence of various kinds of test elements, since test elements play a considerable role in the theory of strongly F-regular rings. We introduce both weakly F-regular and strongly F-regular rings. We give a number of characterizations of strong F-regularity. We discuss techniques for proving strong F-regularity, including Glassbrenner’s criterion and several methods that have been used in the literature. Many open questions are raised.
PubDate: 2022-08-22

• Abstract: Abstract We propose a class of very simple modifications of gradient descent and stochastic gradient descent leveraging Laplacian smoothing. We show that when applied to a large variety of machine learning problems, ranging from logistic regression to deep neural nets, the proposed surrogates can dramatically reduce the variance, allow to take a larger step size, and improve the generalization accuracy. The methods only involve multiplying the usual (stochastic) gradient by the inverse of a positive definitive matrix (which can be computed efficiently by FFT) with a low condition number coming from a one-dimensional discrete Laplacian or its high-order generalizations. Given any vector, e.g., gradient vector, Laplacian smoothing preserves the mean and increases the smallest component and decreases the largest component. Moreover, we show that optimization algorithms with these surrogates converge uniformly in the discrete Sobolev $$H_\sigma ^p$$ sense and reduce the optimality gap for convex optimization problems. The code is available at: https://github.com/BaoWangMath/LaplacianSmoothing-GradientDescent.
PubDate: 2022-08-12

• On the regularized risk of distributionally robust learning over deep
neural networks

• Abstract: Abstract In this paper, we explore the relation between distributionally robust learning and different forms of regularization to enforce robustness of deep neural networks. In particular, starting from a concrete min-max distributionally robust problem, and using tools from optimal transport theory, we derive first-order and second-order approximations to the distributionally robust problem in terms of appropriate regularized risk minimization problems. In the context of deep ResNet models, we identify the structure of the resulting regularization problems as mean-field optimal control problems where the number and dimension of state variables are within a dimension-free factor of the dimension of the original unrobust problem. Using the Pontryagin maximum principles associated with these problems, we motivate a family of scalable algorithms for the training of robust neural networks. Our analysis recovers some results and algorithms known in the literature (in settings explained throughout the paper) and provides many other theoretical and algorithmic insights that to our knowledge are novel. In our analysis, we employ tools that we deem useful for a future analysis of more general adversarial learning problems.
PubDate: 2022-08-08

• Loop space decompositions of $$(2n-2)$$ ( 2 n - 2 ) -connected $$(4n-1)$$
( 4 n - 1 ) -dimensional Poincaré Duality complexes

• Abstract: Abstract Beben and Wu showed that if M is a $$(2n-2)$$ -connected $$(4n-1)$$ -dimensional Poincaré Duality complex such that $$n\ge 3$$ and $$H^{2n}(M;{{\mathbb {Z}}})$$ consists only of odd torsion, then $$\Omega M$$ can be decomposed up to homotopy as a product of simpler, well-studied spaces. We use a result from Beben and Theriault (Doc Math 27:183-211, 2022) to greatly simplify and enhance Beben and Wu’s work and to extend it in various directions.
PubDate: 2022-08-05

• Designing rotationally invariant neural networks from PDEs and variational
methods

• Abstract: Abstract Partial differential equation models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which is desirable in applications such as image analysis. Convolutional neural networks (CNNs) do not share this property, and existing remedies are often complex. The goal of our paper is to investigate how diffusion and variational models achieve rotation invariance and transfer these ideas to neural networks. As a core novelty, we propose activation functions which couple network channels by combining information from several oriented filters. This guarantees rotation invariance within the basic building blocks of the networks while still allowing for directional filtering. The resulting neural architectures are inherently rotationally invariant. With only a few small filters, they can achieve the same invariance as existing techniques which require a fine-grained sampling of orientations. Our findings help to translate diffusion and variational models into mathematically well-founded network architectures and provide novel concepts for model-based CNN design.
PubDate: 2022-08-04

• Mean field control problems for vaccine distribution

• Abstract: Abstract With the invention of the COVID-19 vaccine, shipping and distributing are crucial in controlling the pandemic. In this paper, we build a mean-field variational problem in a spatial domain, which controls the propagation of pandemics by the optimal transportation strategy of vaccine distribution. Here, we integrate the vaccine distribution into the mean-field SIR model designed in Lee W, Liu S, Tembine H, Li W, Osher S (2020) Controlling propagation of epidemics via mean-field games. arXiv preprint arXiv:2006.01249. Numerical examples demonstrate that the proposed model provides practical strategies for vaccine distribution in a spatial domain.
PubDate: 2022-07-27

• On the growth of Fourier coefficientsof Siegel cusp forms of degree two

• PubDate: 2022-07-25

• Merge trees in discrete Morse theory

• Abstract: Abstract In this paper, we study merge trees induced by a discrete Morse function on a tree. Given a discrete Morse function, we provide a method to constructing an induced merge tree and define a new notion of equivalence of discrete Morse functions based on the induced merge tree. We then relate the matching number of a tree to a certain invariant of the induced merge tree. Finally, we count the number of merge trees that can be induced on a star graph and characterize the induced merge tree.
PubDate: 2022-07-22

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