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arXiv 2024年

作者： Culf, Eric Mastel, Kieran Institute for Quantum Computing University of Waterloo Canada Department of Applied Mathematics University of Waterloo Canada Department of Pure Mathematics University of Waterloo Canada

Constraint satisfaction problems (CSPs) are a natural class of decision problems where one must decide whether there is an assignment to variables that satisfies a given formula. Schaefer’s dichotomy theorem, and its extension to all alphabets due to Bulatov and Zhuk, shows that CSP languages are either efficiently decidable, or NP-complete. It is possible to extend CSP languages to quantum assignments using the formalism of nonlocal games. Due to the equality of complexity classes MIP∗ = RE, general succinctly-presented entangled CSPs become RE-complete. In this work, we show that a wide range of NP-complete CSPs become RE-complete in this setting, including all boolean CSPs, such as 3SAT, and all CSPs with two variables per constraint (2-CSPs), such as k-colouring. This also implies that these CSP languages remain undecidable even when not succinctly presented. To show this, we work in the weighted algebra framework introduced by Mastel and Slofstra, where synchronous strategies for a nonlocal game are represented by tracial states on an algebra. Along the way, we improve the subdivision technique in order to be able to separate constraints in the CSP while preserving constant soundness, and we show a variety of relations between the different ways of presenting CSPs as games. In particular, we show that all 2-CSP games are oracularizable, wherein the two players’ operators for questions asked at the same time must commute for a perfect strategy. Copyright © 2024, The Authors. All rights reserved.

关键词： Constraint satisfaction problems

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Forward-backward-forward dynamics for bilevel equilibrium problem

arXiv

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arXiv 2024年

作者： Mittal, Kanchan Gautam, Pankaj Vetrivel, V. Department of Mathematics Indian Institute of Technology Madras Chennai India Department of Applied Mathematics and Scientific Computing Indian Institute of Technology Roorkee India

We introduce a forward-backward-forward (FBF) algorithm for solving bilevel equilibrium problem associated with bifunctions on a real Hilbert space. This modifies the forward-backward algorithm by relaxing cocoercivity with monotone and Lipschitzness. Further, we present the FBF dynamical system and investigate the generated trajectory’s existence, uniqueness and weak convergence. We illustrate the proposed method for equilibrium problem under saddle point constraint. © 2024, CC BY.

关键词： Dynamical systems

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On the Practical Power of Automata in Pattern Matching

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SN Computer Science 2024年第4期5卷 400页

作者： Amir, Ora Amir, Amihood Fraenkel, Aviezri Sarne, David Department of Computer Science Bar-Ilan University Ramat-Gan 52900 Israel Camtek Migdal HaEmek Israel College of Computing Georgia Tech Atlanta 30332 GA United States Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot 76100 Israel

Many papers in the intersection of theoretical and applied algorithms show that the simple, asymptotically less efficient algorithm, performs better than the bestcomplex theoretical algorithms on random data or in specialized “real world” applications. This paper considers the Knuth–Morris–Pratt automaton, and shows a counter-intuitive practical result. The classical pattern matching paradigm is that of seeking occurrences of one string—the pattern, in another—the text, where both strings are drawn from an alphabet set Σ. Assuming the text length is n and the pattern length is m, this problem can naively be solved in time O(nm). In Knuth, Morris and Pratt’s seminal paper of 1977, an automaton, was developed that allows solving this problem in time O(n) for any alphabet. This automaton, which we will refer to as the KMP-automaton, has proven useful in solving many other problems. A notable example is the parameterized pattern matching model. In this model, a consistent renaming of symbols from Σ is allowed in a match. The parameterized matching paradigm has proven useful in problems in software engineering, computer vision, and other applications. It has long been believed that for texts where the symbols are uniformly random, the naive algorithm will perform as well as the KMP algorithm. In this paper, we examine the practical efficiency of the KMP algorithm versus the naive algorithm on a randomly generated text. We analyze the time under various parameters, such as alphabet size, pattern length, and the distribution of pattern occurrences in the text. We do this for both the original exact matching problem and parameterized matching. While the folklore wisdom is vindicated by these findings for the exact matching case, surprisingly, the KMP algorithm always works significantly faster than the naive in the parameterized matching case. We check this hypothesis for DNA texts and image data and observe a similar behavior as in the random text. We also show a very stru

关键词： Knuth–Morris–Pratt automaton Parameterized matching Simple algorithms Uniformly random text

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Towards Improving mathematics Learning Using the Deep Learning Models 1

Towards Improving Mathematics Learning Using the Deep Learni...

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1st IEEE International Conference on Advances in Data-Driven Analytics and Intelligent Systems, ADACIS 2023

作者： Lmati, Imane Khoulimi, Hind Hassan First University IR2M Laboratory Faculty of Sciences and Techniques Settat Morocco Hassan Ii University of Casablanca Applied Mathematics and Computing Laboratory Higher Normal School Morocco

ISBN: (纸本)9798350344158

Nowadays, the majority of intelligent tutoring systems (ITS) have significantly advanced in terms of capabilities and technologies. These systems have evolved to provide personalized and adaptive learning experiences for students. In mathematics, ITS can provide hints or messages to facilitate problem solving, but they do not provide feedback on educational concepts useful for resolving (such as theorems, definitions, etc.). Our methodology enables the generation of feedback in human learning environments. It makes it possible to predict the didactic concepts relevant to solving a given question Q(i) in an exercise based on existing or previously demonstrated data (Q(i-1), Q(i-2),...) using the Math-Bridge ontology. To extract knowledge from mathematical text, we use vectorization with SBERT models to calculate the semantic similarity between ontology concepts and exercises. We tested our approach on a set of exercises from mathematics teaching platforms and compared the number of concepts generated by our approach with those of experts. The results highlight the encouraging potential of our exercise solution method. © 2023 IEEE.

关键词： Ontology

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Non-Newtonian Effect on Mixed Convection Flow Over an Elliptical Cylinder with Uniform Heat Flux

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International Journal of applied and Computational mathematics 2022年第2期8卷 1-20页

作者： Nag, Preetom Molla, M. Mamun Hossain, M. Anwar Department of Mathematics and Physics North South University Dhaka 1229 Bangladesh Center for Applied Scientific Computing (CASC) North South University Dhaka 1229 Bangladesh Department of Mathematics University of Dhaka Dhaka 1000 Bangladesh

A numerical study about the convective non-Newtonian flow over a cylinder of elliptical cross-sections is conducted with uniform surface heat flux conditions. The non-Newtonian characteristics of the flow are predicted by the empirically defined modified power-law model that has overcome the singularity raised for the original version. The governing non-dimensional boundary layer equations are obtained in non-similar form employing dimensionless transformations. The resulting non-dimensional equations are numerically resolved by using an implicit finite difference scheme for various pertinent parameters. Numerical results have shown that the boundary layer separation over the cylinder is an active function of the mixed convection parameter and the geometry of the cylinder. Besides, the wall shear stress and surface heat transfer rate are investigated as a function of the eccentric angle. The wall shear-stress gets attenuated, and the rate of energy transfer becomes enhanced for non-Newtonian shear-thinning fluids than the Newtonian fluids and shear-thickening fluids. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.

关键词： Boundary layer flow Elliptical cylinder Finite difference method Mixed convection Non-Newtonian fluid Surface heat flux

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Tensor parametric Hamiltonian operator inference

arXiv

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arXiv 2025年

作者： Vijaywargiya, Arjun McQuarrie, Shane A. Gruber, Anthony Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States Computational Mathematics Center for Computing Research Sandia National Laboratories Scientific Machine Learning Center for Computing Research Sandia National Laboratories

This work presents a tensor-based approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with affine dependence as contractions of a generalized parameter vector against a constant tensor, this method leverages the operator inference framework to capture parametric dependence in the learned reduced-order model via the solution to a convex, least-squares optimization problem. This leads to a concise and straightforward implementation which compactifies previous parametric operator inference approaches and directly extends to learning parametric operators with symmetry constraints—a key feature required for constructing structure-preserving surrogates of Hamiltonian systems. The proposed approach is demonstrated on both a (non-Hamiltonian) heat equation with variable diffusion coefficient as well as a Hamiltonian wave equation with variable wave *** Codes 15A69, 35B30, 65P10 © 2025, CC BY.

关键词： Tensors

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Interference of communication and field correlations in entanglement harvesting

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Physical Review D 2024年第2期110卷 025016-025016页

作者： Matheus H. Zambianco Adam Teixidó-Bonfill Eduardo Martín-Martínez Department of Applied Mathematics Institute for Quantum Computing Waterloo Ontario N2L 2Y5 Canada

We reveal that the information exchange between particle detectors and their ability to harvest correlations from a quantum field can interfere constructively and destructively. This allows for scenarios where the presence of entanglement in the quantum field is actually detrimental to the process of getting the two detectors entangled.

关键词： Entanglement in field theory Quantum entanglement Quantum field theory Quantum fields in curved spacetime Relativistic quantum information

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Towards Highly Compressed CNN Models for Human Activity Recognition in Wearable Devices 26

Towards Highly Compressed CNN Models for Human Activity Reco...

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26th IEEE Signal Processing: Algorithms, Architectures, Arrangements, and Applications, SPA 2023

作者： Gkountelos, Dimitrios Kokhazadeh, Milad Bournas, Charalampos Keramidas, Georgios Kelefouras, Vasilios Aristotle University of Thessaloniki School of Informatics Thessaloniki Greece An Applied Materials Company Think Silicon S.A. Patras Greece University of Plymouth School of Engineering Computing and Mathematics Plymouth United Kingdom

ISBN: (纸本)9798350304985

The widespread usage of wearables set the foundations for many new applications that process the wearable sensor data. Human Activity Recognition (HAR) is a well-studied application that targets to classify the data captured by multiple wearable sensors into one of a predefined set of activity classes. Earlier approaches in the area relied on Machine Learning (ML) classifiers, while many researchers proposed solutions based on Deep Neural Networks (DNNs), e.g., using Long Short-Term Memory (LSTMs) or Convolution Neural Network (CNNs). Even though the usage of DNNs for HAR is a widely explored field, the problem of compressing (thus reducing the computational requirements) the resulting DNN models has been disregarded by the research community. This is of paramount importance if we consider that wearables are characterized by scarce memory and computational resources. In this work, we first analyze the impact of the size of the various CNN components (focusing on the convolution and dense layers) to the model validation performance. As a second step, we focus on two CNN models with diverse memory characteristics (the lean and the fat model) and we employ three different compression techniques (Filter-Based Pruning -FBP,- Low Rank Factorization -LRF,- and dynamic range quantization) assuming various compressibility scenarios. © 2023 Division of Signal Processing and Electronic Systems, Poznan University of Technology (DSPES PUT).

关键词： Neural network models

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Nonseparating Independent Sets and Maximum Genus of Graphs

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Acta Mathematicae Applicatae Sinica 2022年第3期38卷 719-728页

作者： Chao YANG Han REN Er-ling WEI Center of Intelligent Computing and Applied Statistics School of MathematicsPhysics and StatisticsShanghai University of Engineering ScienceShanghai 201620China School of Mathematical Sciences East China Normal UniversityShanghai 200241China Shanghai Key Laboratory of PMMP Shanghai 200241China School of Mathematics Renmin University of ChinaBeijing 100872China

A subset I of vertices of an undirected connected graph G is a nonseparating independent set(NSIS)if no two vertices of I are adjacent and G􀀀I is *** Z(G)denote the cardinality of a maximum NSIS of G.A nonseparating independent set containing Z(G)vertices is called the maximum nonseparating independent *** this paper,we firstly give an upper bound for Z(G)of regular graphs and determine Z(G)for some types of circular ***,we show a relationship between Z(G)and the maximum genus M(G)of a general ***,an important formula is provided to compute Z(G),i.e.,Z(G)=Σx∈I dI(x)+2(M(G-I)-γM(G))+(ξ(G-I)-ξ(G));where I is the maximum nonseparating independent set and ξ(G)is the Betti deficiency(Xuong,1979)of G.

关键词： nonseparating independent sets maximum genus graph embedding decycling set

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Neighbor Embedding Projection and Rank-Based Manifold Learning for Image Retrieval

Neighbor Embedding Projection and Rank-Based Manifold Learni...

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Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI)

作者： Vinicius Atsushi Sato Kawai Gustavo Rosseto Leticio Lucas Pascotti Valem Daniel Carlos Guimarães Pedronette Department of Statistics Applied Mathematics and Computing State University of São Paulo (UNESP) Rio Claro Brazil

ISBN: (数字)9798350376036

ISBN: (纸本)9798350376043

Despite the impressive advances in image under-standing approaches, defining similarity among images remains a challenging task, crucial for many applications such as classification and retrieval. Mainly supported by Convolution Neural Networks (CNNs) and Transformer-based models, image representation techniques are the main reason for the advances. On the other hand, comparisons are mostly computed based on traditional pairwise measures, such as the Euclidean distance, while contextual similarity approaches can lead to effective results in defining similarity between points in high-dimensional spaces. This paper introduces a novel approach to contextual similarity by combining two techniques: neighbor embedding projection methods and rank-based manifold learning. High-dimensional features are projected in a 2D space used for efficiently ranking computation. Subsequently, manifold learning methods are exploited for a re-ranking step. An experimental evaluation conducted on different datasets and visual features indicates that the proposed approach leads to significant gains in comparison to the original feature representations and the neighbor embedding method in isolation.

关键词： Visualization Convolution Image retrieval Neural networks Euclidean distance Image representation Transformers Extraterrestrial measurements Manifold learning Convolutional neural networks

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