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ON THE METRIC DIMENSION OF THE CHARACTER DEGREE GRAPH OF A SOLVABLE GROUP

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arXiv 2024年

作者： Cameron, Peter J. Sivanesan, G. Selvaraj, C. Chelvam, T. Tamizh Laubacher, Jacob School of Mathematics and Statistics University of St Andrews North Haugh St Andrews FifeKY16 9SS United Kingdom Department of Mathematics Government College of Engineering Tamil Nadu Salem636011 India Department of Mathematics Periyar University Tamil Nadu Salem636011 India Department of Mathematics Manonmaniam Sundaranar University Tamil Nadu Tirunelveli627 012 India Department of Mathematics St. Norbert College De PereWI54115 United States

Let G be a finite solvable group and let ∆(G) be the character degree graph of G. In this paper, we obtain the metric dimension of certain character degree graphs. Specifically, we calculate the metric dimension for a regular character degree graph, a character degree graph with a diameter of 2 that is not a block, a character degree graph with a diameter of 3 that also has a cut vertex and a character degree graph with Fitting height 2. We also consider two related parameters, base size and adjacency dimension, and their relation to metric dimension for character degree graphs of solvable *** Codes 05C25 © 2024, CC BY.

关键词： Graph algorithms

Training Integer-Only Deep Recurrent Neural Networks

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SN Computer Science 2023年第5期4卷 1-16页

作者： Nia, Vahid Partovi Sari, Eyyüb Courville, Vanessa Asgharian, Masoud Huawei Noah’s Ark Lab Montreal Research Centre 7101 Park Avenue Montreal H3N 1X9 QC Canada Department of Mathematics and Industrial Engineering Polytechnique Montreal 2500 Chem. Polytechnique Montreal H3T 1J4 QC Canada Department of Mathematics and Statistics McGill University 805 Sherbrooke Street West Montreal H3A 0B9 QC Canada

Recurrent neural networks (RNN) are the backbone of many text and speech applications. These architectures are typically made up of several computationally complex components such as;non-linear activation functions, normalization, bi-directional dependence and attention. In order to maintain good accuracy, these components are frequently run using full-precision floating-point computation, making them slow, inefficient and difficult to deploy on edge devices. In addition, the complex nature of these operations makes them challenging to quantize using standard quantization methods without a significant performance drop. We present a quantization-aware training method for obtaining a highly accurate integer-only recurrent neural network (iRNN). Our approach supports layer normalization, attention, and an adaptive piecewise linear (PWL) approximation of activation functions, to serve a wide range of state-of-the-art RNNs. The proposed method enables RNN-based language models to run on edge devices with 2 × improvement in runtime, and 4 × reduction in model size while maintaining similar accuracy as its full-precision counterpart. © 2023, The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.

关键词： ASR LSTM Model compression NLP Quantization Recurrent neural network

An Exploratory Computational Approach for Elucidating a Nonstructural Protein Interaction in Dengue Virus 2 9th

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An Exploratory Computational Approach for Elucidating a Nons...

9th International Conference on Computer Science and Computational Intelligence, ICCSCI 2024

作者： Hidayat, Alam Ahmad Nirwantono, Rudi Pardamean, Bens Mathematics Department School of Computer Science Bina Nusantara University 11480 Indonesia Biotechnology Department Faculty of Engineering Bina Nusantara University 11480 Indonesia Bioinformatics and Data Science Research Center Bina Nusantara University Jakarta11480 Indonesia Computer Science Department BINUS Graduate Program Bina Nusantara University Jakarta11480 Indonesia

As the dengue infection still impacts hundreds of millions of people globally, unprecedented efforts in dengue drug development have been more progressive in recent decades. Computational methods provide a fast, sustainable, and efficient screening of active compounds and newly created drug molecules, including those specifically targeting nonstructural proteins (NS) of dengue viruses. In this work, protein modeling for the NS proteins of DENV-2/16681 strain was performed using a template-based homology modeling for the NS3 protein and an Artificial Intelligence (AI)-based prediction via AlphaFold for the NS4B protein. Moreover, the protein-protein interaction between the two structures was predicted using the HADDOCK server, which employs information about active and passive residues of the interaction interface to guide the docking process. After the modeling and its respective refinement process, the predicted structures of NS3 and NS4B improved their steric clashing scoring from MolProbity assessment. The refined models were then docked, and the resulting docking pose was analyzed to extract the interacting residues based on the polar contacts within the interface of the two proteins. Our result presents a preliminary study to create a dataset related to in silico molecular interactions of the NS3-NS4B interaction of different DENV types. It is helpful for building a computational pipeline for elucidating protein-ligand problems in dengue drug screenings. © 2024 The Authors.

关键词： Molecular docking

Existence of Ε-Nash Equilibria in Nonzero-Sum Borel Stochastic Games and Equilibria of Quantized Models

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arXiv 2024年

作者： Saldi, Naci Arslan, Gürdal Yüksel, Serdar Bilkent University Department of Mathematics Ankara06800 Turkey University of Hawaii at Manoa Department of Electrical Engineering HonoluluHI96822 United States Queen’s University Department of Mathematics and Statistics KingstonONK7L 3N6 Canada

Establishing the existence of exact or near Markov or stationary perfect Nash equilibria in nonzero-sum Markov games over Borel spaces remains a challenging problem, with few positive results to date. In this paper, we establish the existence of approximate Markov and stationary Nash equilibria for nonzero-sum stochastic games over Borel spaces, assuming only mild regularity conditions on the model. Our approach involves analyzing a quantized version of the game, for which we provide an explicit construction under both finite-horizon and discounted cost criteria. This work has significant implications for emerging applications such as multi-agent learning. Our results apply to both compact and non-compact state spaces. For the compact state space case, we first approximate the standard Borel model with a finite state-action model. Using the existence of Markov and stationary perfect Nash equilibria for these finite models under finite-horizon and discounted cost criteria, we demonstrate that these joint policies constitute approximate Markov and stationary perfect equilibria under mild continuity conditions on the one-stage costs and transition probabilities. For the non-compact state space case, we achieve similar results by first approximating the model with a compact-state model. Compared with previous results in the literature, which we comprehensively review, we provide more general and complementary conditions, along with explicit approximation models whose equilibria are Ε-equilibria for the original model. Copyright © 2024, The Authors. All rights reserved.

关键词： Nash equilibrium

A Fourth-Order Degradation Tensor for an Anisotropic Damage Phase Field Model

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SSRN

SSRN 2023年

作者： Bittencourt, Marco Lúcio Petrini, Ana L.E.R. Esteves, Carlos L.C.S. Boldrini, José L. Department of Integrated Systems School of Mechanical Engineering University of Campinas SP 13083-970 Brazil Department of Applied Mathematics Institute of Mathematics Statistics and Scientific Computing University of Campinas SP 13083-859 Brazil

This work proposes a thermodynamically consistent phase-field model for anisotropic brittle material under the hypotheses of plane stress, small deformation and constant temperature. The model is derived from the principle of virtual power, the first and second laws of thermodynamics in the form of the Clausius-Duhem inequality. The degradation effect on the material behavior is given by a fourth-order degradation tensor introduced as an internal variable that evolves according to the current strain state rather than the conventional scalar degradation function of phase-field models. Therefore, local anisotropy can be induced, changing the material mechanical behavior differently in all directions organically. The proposed degradation tensor is defined in the global coordinate system and therefore is sensitive to any change in the principal directions of the strain and stress states. To demonstrate the model's capability of representing damage in isotropic and transversely isotropic materials, some benchmark examples were carried out. The evolution of the damage components was also analyzed. © 2023, The Authors. All rights reserved.

关键词： Tensors

Sparse Sets in Triangle-free Graphs

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arXiv 2024年

作者： Ekim, Tınaz Erdem, Burak Nur Gimbel, John Department of Industrial Engineering Bogaziçi University Bebek Istanbul34342 Turkey Mathematics and Statistics University of Alaska FairbanksAK99775-6660 United States

A set of vertices is k-sparse if it induces a graph with a maximum degree of at most k. In this missive, we consider the order of the largest k-sparse set in a triangle-free graph of fixed order. We show, for example, that every triangle-free graph of order 11 contains a 1-sparse 5-set;every triangle-free graph of order 13 contains a 2-sparse 7-set;and every triangle-free graph of order 8 contains a 3-sparse 6-set. Further, these are all best possible. For fixed k, we consider the growth rate of the largest k-sparse set of a triangle-free graph of order n. Also, we consider Ramsey numbers of the following type. Given i, what is the smallest n having the property that all triangle-free graphs of order n contain a 4-cycle or a k-sparse set of order i. We use both direct proof techniques and an efficient graph enumeration algorithm to obtain several values for defective Ramsey numbers and a parameter related to largest sparse sets in triangle-free graphs, along with their extremal graphs. © 2024, CC BY-NC-SA.

关键词： Defects

Cupolets in a Chaotic Neuron Model

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arXiv 2022年

作者： Parker, John E. Short, Kevin M. Department of Mathematics University of Pittsburgh PittsburghPA15260 United States Integrated Applied Mathematics Program Department of Mathematics and Statistics University of New Hampshire DurhamNH03824 United States

This paper reports the first finding of cupolets in a chaotic Hindmarsh-Rose neural model. Cupolets (chaotic, unstable, periodic, orbit-lets) are unstable periodic orbits that have been stabilized through a particular control scheme applying a binary control sequence. We demonstrate different neural dynamics (periodic or chaotic) of the Hindmarsh-Rose model through a bifurcation diagram where the external input current, I, is the bifurcation parameter. We select a region in the chaotic parameter space and provide the results of numerical simulations. In this chosen parameter space, a control scheme is applied when the trajectory intersects with either of the two control planes. The size of the control is determined by a bit in a binary control sequence. The control is either a small microcontrol (0) or a large macrocontrol (1) that adjusts the future dynamics of the trajectory. We report the discovery of many cupolets with corresponding control sequences and comment on the differences with previously reported cupolets in the double scroll system. We provide some examples of the generated cupolets and conclude by discussing potential implications for biological neurons. © 2022, CC BY.

关键词： Bifurcation (mathematics)

A New Cross-Space Total Variation Regularization Model for Color Image Restoration with Quaternion Blur Operator

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arXiv 2024年

作者： Jia, Zhigang Xiang, Yuelian Zhao, Meixiang Wu, Tingting Ng, Michael K. School of Mathematics and Statistics & RIMS Jiangsu Normal University Xuzhou221116 China School of Mathematics and Statistics Jiangsu Normal University Xuzhou221116 China General Education School Wuhan Vocational College of Software and Engineering Wuhan430205 China School of Science Nanjing University of Posts and Telecommunications Nanjing210003 China Department of Mathematics Hong Kong Baptist University Hong Kong

The cross-channel deblurring problem in color image processing is difficult to solve due to the complex coupling and structural blurring of color pixels. Until now, there are few efficient algorithms that can reduce color artifacts in deblurring process. To solve this challenging problem, we present a novel cross-space total variation (CSTV) regularization model for color image deblurring by introducing a quaternion blur operator and a cross-color space regularization functional. The existence and uniqueness of the solution are proved and a new L-curve method is proposed to find a balance of regularization terms on different color spaces. The Euler-Lagrange equation is derived to show that CSTV has taken into account the coupling of all color channels and the local smoothing within each color channel. A quaternion operator splitting method is firstly proposed to enhance the ability of color artifacts reduction of the CSTV regularization model. This strategy also applies to the well-known color deblurring models. Numerical experiments on color image databases illustrate the efficiency and effectiveness of the new model and algorithms. The color images restored by them successfully maintain the color and spatial information and are of higher quality in terms of PSNR, SSIM, MSE and CIEde2000 than the restorations of the-state-of-the-art methods. Copyright © 2024, The Authors. All rights reserved.

关键词： Image reconstruction

On seeded subgraph-to-subgraph matching: The ssSGM Algorithm and matchability information theory

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arXiv 2023年

作者： Meng, Lingyao Lou, Mengqi Lin, Jianyu Lyzinski, Vince Fishkind, Donniell E. Johns Hopkins University Department of Applied Mathematics and Statistics United States Georgia Institute of Technology School of Industrial and Systems Engineering United States University of Maryland Department of Mathematics College Park United States

The subgraph-subgraph matching problem is, given a pair of graphs and a positive integer K, to find K vertices in the first graph, K vertices in the second graph, and a bijection between them, so as to minimize the number of adjacency disagreements across the bijection;it is "seeded" if some of this bijection is fixed. The problem is intractable, and we present the ssSGM algorithm, which uses Frank-Wolfe methodology to efficiently find an approximate solution. Then, in the context of a generalized correlated random Bernoulli graph model, in which the pair of graphs naturally have a core of K matched pairs of vertices, we provide and prove mild conditions for the subgraph-subgraph matching problem solution to almost always be the correct K matched pairs of *** Codes 05C60, 05C80, 90C35 © 2023, CC BY.

关键词： Information theory