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Critical (P5, W4)-Free Graphs

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arXiv 2025年

作者： Xia, Wen Jooken, Jorik Goedgebeur, Jan Beaton, Iain Cameron, Ben Huang, Shenwei College of Computer Science Nankai University Tianjin300071 China Tianjin Key Laboratory of Network and Data Security Technology Nankai University Tianjin300071 China Department of Computer Science KU Leuven Campus Kulak-Kortrijk Kortrijk8500 Belgium Department of Applied Mathematics Computer Science and Statistics Ghent University Ghent9000 Belgium Department of Mathematics and Statistics Acadia University WolfvilleNS Canada School of Mathematical and Computational Sciences University of Prince Edward Island CharlottetownPE Canada

A graph G is k-vertex-critical if χ(G) = k but χ(G − v) 1, H2)-free if it contains no induced subgraph isomorphic to H1 nor H2. A W4 is the graph consisting of a C4 plus an additional vertex adjacent to all the vertices of the C4. We show that there are finitely many k-vertex-critical (P5, W4)-free graphs for all k ≥ 1 and we characterize all 5-vertex-critical (P5, W4)-free graphs. Our results imply the existence of a polynomial-time certifying algorithm to decide the k-colorability of (P5, W4)-free graphs for each k ≥ 1 where the certificate is either a k-coloring or a (k + 1)-vertex-critical induced subgraph. Copyright © 2025, The Authors. All rights reserved.

关键词： Graph algorithms

A Nonlinear, Conservative, Entropic Fokker-Planck Model for Multi-Species Collisions

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arXiv 2024年

作者： Habbershaw, Evan Hauck, Cory D. Hu, Jingwei Haack, Jeffrey R. Department of Mathematics The University of Tennessee KnoxvilleTN37996 United States Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Department of Applied Mathematics University of Washington SeattleWA98195 United States Computer Computational and Statistical Sciences Division Los Alamos National Laboratory Los AlamosNM87545 United States

A multi-species Fokker-Planck model for simulating particle collisions in a plasma is presented. The model includes various parameters that must be tuned. Under reasonable assumptions on these parameters, the model satisfies appropriate conservation laws, dissipates an entropy, and satisfies an H-Theorem. In addition, the model parameters provide the additional flexibility that is used to match simultaneously momentum and temperature relaxation formulas derived from the Boltzmann collision operator for a binary mixture with Coulomb potentials. A numerical method for solving the resulting space-homogeneous kinetic equation is presented and two examples are provided to demonstrate the relaxation of species bulk velocities and temperatures to their equilibrium values. © 2024, CC BY.

关键词： Numerical methods

An FPT-Algorithm for Longest Common Subsequence Parameterized by the Maximum Number of Deletions 33

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An FPT-Algorithm for Longest Common Subsequence Parameterize...

33rd Annual Symposium on Combinatorial Pattern Matching, CPM 2022

作者： Bulteau, Laurent Jones, Mark Niedermeier, Rolf Tantau, Till LIGM CNRS Université Gustave Eiffel Marne-la-vallée F77454 France Delft Institute of Applied Mathematics Delft University of Technology Netherlands Algorithmics and Computational Complexity Faculty IV TU Berlin Germany Institute of Theoretical Computer Science University of Lübeck Germany

ISBN: (纸本)9783959772341

In the NP-hard Longest Common Subsequence problem (LCS), given a set of strings, the task is to find a string that can be obtained from every input string using as few deletions as possible. LCS is one of the most fundamental string problems with numerous applications in various areas, having gained a lot of attention in the algorithms and complexity research community. Significantly improving on an algorithm by Irving and Fraser [CPM'92], featured as a research challenge in a 2014 survey paper, we show that LCS is fixed-parameter tractable (FPT) when parameterized by the maximum number of deletions per input string. Given the relatively moderate running time of our algorithm (linear time when the parameter is a constant) and small parameter values to be expected in several applications, we believe that our purely theoretical analysis could finally pave the way to a new, exact and practically useful algorithm for this notoriously hard string problem. © Laurent Bulteau, Mark Jones, Rolf Niedermeier, and Till Tantau;licensed under Creative Commons License CC-BY 4.0

关键词： Parameter estimation

A deterministic model of COVID-19 with differential infectivity and vaccination booster

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Decision Analytics Journal 2024年 10卷

作者： Tchoumi, Stephane Y. Schwartz, Elissa J. Tchuenche, Jean M. Department of Mathematics and Computer Sciences ENSAI University of NGaoundéré PO Box 455 Ngaoundéré Cameroon Department of Mathematics and Applied Mathematics University of Pretoria South Africa Department of Mathematics & Statistics and School of Biological Sciences Washington State University PO Box 643113 Pullman 99164-3113 WA United States School of Computer Science and Applied Mathematics University of the Witwatersrand Johannesburg South Africa School of Computational and Communication Sciences and Engineering Nelson Mandela African Institution of Science and Technology Arusha Tanzania

Vaccine boosters have been recommended to mitigate the spread of the coronavirus disease 2019 (COVID-19) pandemic. A mathematical model with three vaccine doses and susceptibility is formulated. The model is calibrated using the cumulative number of hospitalized cases from Alberta, Canada. Estimated values from the fitting are used to explore the potential impact of the booster doses to mitigate the spread of COVID-19. Sensitivity analysis on initial disease transmission shows that the most sensitive parameters are the contact rate, the vaccine efficacy, the proportion of exposed individuals moving into the symptomatic and asymptomatic classes, and the recovery rate from asymptomatic infection. Simulation results support the positive population-level impact of the second and third COVID-19 vaccine boosters to reduce the number of infections and hospitalizations. Public health policy and decision-makers should continue advocating and encouraging people to get booster doses. As the end of the pandemic is in sight, there should be no complacency before it resolves. © 2023 The Author(s)

关键词： Basic reproduction number COVID-19 Non-linear mathematical model Sensitivity analysis Simulation Vaccination

PARAMETERIZED PROXIMAL-GRADIENT ALGORITHMS FOR L1/L2 SPARSE SIGNAL RECOVERY

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arXiv 2023年

作者： Zhang, Na Liu, Xinrui Li, Qia Department of Applied Mathematics College of Mathematics and Informatics South China Agricultural University Guangzhou510642 China School of Mathematics and Statistics Shandong Normal University Jinan250358 China Guangdong Province Key Laboratory of Computational Science School of Computer Science and Engineering Sun Yat-sen University Guangzhou510275 China

The ratio of 1 and 2 norms (1/2), serving as a sparse promoting function, receives considerable attentions recently due to its effectiveness for sparse signal recovery. In this paper, we propose an 1/2 based penalty model for recovering sparse signals from noiseless or noisy observations. It is proven that stationary points of the proposed problem tend to those of the elliptically constrained 1/2 minimization problem as the smoothing parameter goes to zero. Moreover, inspired by the parametric approach for the fractional programming, we design a parameterized proximal-gradient algorithm (PPGA) as well as its line search counterpart (PPGA_L) for solving the proposed model. The closed-form solution of the involved proximity operator is derived, which enable the efficiency of the proposed algorithms. We establish the global convergence of the entire sequences generated by PPGA and PPGA_L with monotone objective values by taking advantage of the fact that the objective of the proposed model is a KL function. Numerical experiments show the efficiency of the proposed algorithms over the state-of-the-art methods in both noiseless and noisy sparse signal recovery problems. Copyright © 2023, The Authors. All rights reserved.

关键词： Efficiency

A Hybridized Approach on Physics Informed Neural Networks and Symbolic Regression for Simulating Nonlinear Wave Dynamics in Arterial Blood Flow

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SSRN

SSRN 2024年

作者： Changdar, Satyasaran Bhaumik, Bivas Sadhukhan, Nabanita Pandey, Sumit Mukhopadhyay, Sabyasachi De, Soumen Bakalis, Serafim Department of Food Science University of Copenhagen Copenhagen Denmark Department of Mathematics National Institute of Technology Odisha Rourkela India Department of Applied Mathematics University of Calcutta 92 A.P.C. Road Kolkata India Department of Computer Science University of Copenhagen Copenhagen Denmark Centre For Computational And Data Sciences Indian Institute of Technology Kharag India

This study explores a comprehensive hybrid framework integrating machine learning techniques and symbolic regression via genetic programming for analyzing the nonlinear propagation of waves in arterial blood flow. We employ a mathematical framework to simulate viscoelastic arterial flow, incorporating assumptions of long wavelength and large Reynolds numbers. We derive a fifth-order nonlinear evolutionary equation using reductive perturbation to represent the behavior of nonlinear waves in a viscoelastic tube, considering the tube wall's bending. We obtain solutions through physics-informed neural networks (PINNs), an artificial intelligence (AI)-driven approach that optimizes via Bayesian hyperparameter optimization across three distinct initial conditions. We found that physics-informed neural network-based models are proficient at predicting the solutions of higher-order nonlinear partial differential equations in the spatial-temporal domain [-1,1] x [0,2]. This is evidenced by graphical results and a residual validation showing a mean absolute residue error of O(0.001). We thoroughly examine the impacts of various initial conditions. Furthermore, the three solutions are combined into a single model using the random forest machine learning algorithm, achieving an impressive accuracy of 99% on the testing dataset and compared with another model using an artificial neural network. Finally, the analytical form of the solutions is estimated using symbolic regression, a type of AI that provides interpretable models. These insights contribute to the interpretation of cardiovascular parameters, potentially advancing AI-driven machine learning applications within the medical domain. © 2024, The Authors. All rights reserved.

关键词： Genetic programming

Unbiased Estimation using Underdamped Langevin Dynamics

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arXiv 2022年

作者： Ruzayqat, Hamza Chada, Neil K. Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this work we consider the unbiased estimation of expectations w.r.t. probability measures that have non-negative Lebesgue density, and which are known point-wise up-to a normalizing constant. We focus upon developing an unbiased method via the underdamped Langevin dynamics, which has proven to be popular of late due to applications in statistics and machine learning. Specifically in continuous-time, the dynamics can be constructed so that as the time goes to infinity they admit the probability of interest as a stationary measure. In many cases, time-discretized versions of the underdamped Langevin dynamics are used in practice which are run only with a fixed number of iterations. We develop a novel scheme based upon doubly randomized estimation as in [17, 19], which requires access only to time-discretized versions of the dynamics. The proposed scheme aims to remove the dicretization bias and the bias resulting from running the dynamics for a finite number of iterations. We prove, under standard assumptions, that our estimator is of finite variance and either has finite expected cost, or has finite cost with a high probability. To illustrate our theoretical findings we provide numerical experiments which verify our theory, which include challenging examples from Bayesian statistics and statistical *** Codes 60J22, 65C05, 65C40, 82C31, 62G08, 35Q56 © 2022, CC BY.

关键词： Dynamics

On the uniqueness of collections of pennies and marbles

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arXiv 2023年

作者： Dewar, Sean Grasegger, Georg Kubjas, Kaie Mohammadi, Fatemeh Nixon, Anthony School of Mathematics University of Bristol Bristol United Kingdom Johann Radon Institute for Computational and Applied Mathematics Austria Department of Mathematics and Systems Analysis Aalto University Finland Departments of Mathematics and Computer Science KU Leuven Belgium Mathematics and Statistics Lancaster University LancasterLA1 4YF United Kingdom

In this note we study the uniqueness problem for collections of pennies and marbles. More generally, consider a collection of unit d-spheres that may touch but not overlap. Given the existence of such a collection, one may analyse the contact graph of the collection. In particular we consider the uniqueness of the collection arising from the contact graph. Using the language of graph rigidity theory, we prove a precise characterisation of uniqueness (global rigidity) in dimensions 2 and 3 when the contact graph is additionally chordal. We then illustrate a wide range of examples in these cases. That is, we illustrate collections of marbles and pennies that can be perturbed continuously (flexible), are locally unique (rigid) and are unique (globally rigid). We also contrast these examples with the usual generic setting of graph *** Codes 05C10, 52C25, 52C17 Copyright © 2023, The Authors. All rights reserved.

关键词： Marble

A SPECTRAL LEVENBERG-MARQUARDT-DEFLATION METHOD FOR MULTIPLE SOLUTIONS OF SEMILINEAR ELLIPTIC SYSTEMS

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arXiv 2025年

作者： Li, Lin Zhou, Yuheng Xie, Pengcheng Li, Huiyuan School of Mathematics and Physics University of South China Hengyang China Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory 1 Cyclotron Road BerkeleyCA94720 United States State Key Laboratory of Computer Science Laboratory of Parallel Computing Institute of Software Chinese Academy of Sciences Beijing100190 China

Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve some applications. Developing an efficient numerical method for finding multiple solutions is very necessary due to the nonlinearity and multiple solutions of these equations. Moreover, providing an efficient iteration plays an important role in successfully obtaining multiple solutions with fast and stable convergence. In the current paper, an efficient algorithm for finding multiple solutions of semilinear elliptic systems is proposed, where the trust region Levenberg-Marquardt method is firstly used to iterate the resulted nonlinear algebraic system. When the nonlinear term in these equations has only the first derivative, our algorithm can efficiently find multiple solutions as well. Several numerical experiments are tested to show the efficiency of our algorithm, and some solutions which have not been shown in the literature are also found and *** Codes 65N35, 65N22, 65F05, 65L10 Copyright © 2025, The Authors. All rights reserved.

关键词： Nonlinear equations