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Contracting edges to destroy a pattern: A complexity study

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arXiv 2023年

作者： Chakraborty, Dipayan Sandeep, R.B. LIMOS Université Clermont Auvergne France Department of Mathematics and Applied Mathematics University of Johannesburg South Africa Department of Computer Science and Engineering Indian Institute of Technology Dharwad India

Given a graph G and an integer k, the objective of the Π-Contraction problem is to check whether there exists at most k edges in G such that contracting them in G results in a graph satisfying the property Π. We investigate the problem where Π is ‘H-free’ (without any induced copies of H). It is trivial that H-free Contraction is polynomial-time solvable if H is a complete graph of at most two vertices. We prove that, in all other cases, the problem is NP-complete. We then investigate the fixed-parameter tractability of these problems. We prove that whenever H is a tree, except for seven trees, H-free Contraction is W[2]-hard. This result along with the known results leaves behind only three unknown cases among trees. Copyright © 2023, The Authors. All rights reserved.

关键词： Polynomial approximation

Photovoltaic Module Parameter Estimation by Using Wild Horse Optimizer

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Procedia computer Science 2025年 258卷 2808-2816页

作者： Anuj Kumar Tina Sharma Manoj K. Singh Sangeeta Pant Hitesh Kumar Sharma School of Computer Science Engineering & Applications D Y Patil International University (DYPIU) Pune India- 411044 Department of Mathematics Birla Institute of Technology and Science Pilani India School of Computer Science Engineering and Technology Bennett University Greater Noida India- 201310 Department of Applied Sciences Symbiosis Institute of Technology Symbiosis International (Deemed University) (SIU) Pune India- 412115 School of Computer Science University of Petroleum & Energy Studies Dehradun India-248007

The development of highly accurate models is essential for optimizing the performance and efficiency of photovoltaic (PV) modules, which are integral to renewable energy systems. In this context, metaheuristic algorithms have become indispensable tools for tackling complex engineering challenges, particularly in the areas of evaluation, simulation, and parameter estimation. These algorithms excel at finding optimal or near-optimal solutions for problems where traditional methods may struggle due to their complexity or computational intensity. This article presents a novel framework for estimating the parameters of PV modules using the Wild Horse Optimizer (WHO), a recently introduced metaheuristic algorithm known for its robustness and efficiency. Specifically, the framework is applied to the Double Diode Model (DDM) of a solar cell, a widely recognized model for representing the electrical behavior of PV modules. The simulation results clearly illustrate that the proposed framework based on WHO algorithm offers significant improvements in the accuracy and effectiveness of parameter estimation for PV modules, compared to Artificial Bee Swarm Optimization (ABSO), the Flower Pollination Algorithm (FPA), and several others, thereby validating the proposed approach.

关键词： Optimization Photovoltaic (PV) modules Double diode model (DDM) metaheuristics Wild Horse Optimizer (WHO)

Semantic Data Representation for Explainable Windows Malware Detection Models

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arXiv 2024年

作者： Švec, Peter Balogh, Štefan Homola, Martin Kľuka, Ján Bisták, Tomáš Institute of Computer Science and Mathematics Faculty of Electrical Engineering and Information Technology Slovak University of Technology Ilkovičova 3 Bratislava Slovakia Department of Applied Informatics Faculty of Mathematics Physics and Informatics Comenius University in Bratislava Mlynská dolina Bratislava Slovakia

Ontologies are a standard tool for creating semantic schemata in many knowledge intensive domains of human interest. They are becoming increasingly important also in the areas that have been until very recently dominated by subsymbolic knowledge representation and machine-learning (ML) based data processing. One such area is information security, and specifically, malware detection. We thus propose PE Malware Ontology that offers a reusable semantic schema for Portable Executable (PE – the Windows binary format) malware files. This ontology is inspired by the structure of the EMBER dataset, which focuses on the static malware analysis of PE files. With this proposal, we hope to provide a unified semantic representation for the existing and future PE-malware datasets and facilitate the application of symbolic, neuro-symbolic, or otherwise explainable approaches in the PE-malware-detection domain, which may produce interpretable results described by the terms defined in our ontology. In addition, we also publish semantically treated EMBER data, including fractional datasets, to support the reproducibility of experiments on EMBER. We supplement our work with a preliminary case study, conducted using concept learning, to show the general feasibility of our approach. While we were not able to match the precision of the state-of-the-art ML tools, the learned malware discriminators were interesting and highly interpretable. Copyright © 2024, The Authors. All rights reserved.

关键词： Ontology

computer-aided diagnosis of breast cancer from mammogram images using deep learning algorithms

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Journal of Electrical Systems and Information technology 2024年第1期11卷 1-16页

作者： Dada, Emmanuel Gbenga Oyewola, David Opeoluwa Misra, Sanjay Department of Mathematical Sciences University of Maiduguri Maiduguri Nigeria Department of Mathematics and Computer Science Federal University Kashere Gombe Nigeria Department of Computer Science and Communication Østfold University College Halden Norway Department of Applied Data Science Institute for Energy Technology Halden Norway

Even though accurate detection of dangerous malignancies from mammogram images is mostly dependent on radiologists' experience, specialists occasionally differ in their assessments. computer-aided diagnosis provides a better solution for image diagnosis that can help experts make more reliable decisions. In medical applications for diagnosing cancerous growths from mammogram images, computerized and accurate classification of breast cancer mammogram images is critical. The deep learning approach has been widely applied in medical image processing and has had considerable success in biological image classification. The Convolutional Neural Network (CNN), Inception, and EfficientNet are proposed in this paper. The proposed models attain better performance compared to the conventional CNN. The models are used to automatically classify breast cancer mammogram images from Kaggle into benign and malignant. Simulation results demonstrated that EfficientNet, with an accuracy between 97.13 and 99.27%, and overall accuracy of 98.29%, perform better than the other models in this paper.

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Threaded Gröbner bases: a Macaulay2 package

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Journal of Software for Algebra and Geometry 2021年第1期11卷 123-127页

作者： Petrović, Sonja Zelenberg, Shahrzad Department of Applied Mathematics Illinois Institute of Technology Chicago IL United States Lake Forest College Department of Mathematics and Computer Science Lake Forest IL United States

The complexity of Gröbner computations has inspired many improvements to Buchberger’s algorithm over the years. Looking for further insights into the algorithm’s performance, we offer a threaded implementation of the classical Buchberger algorithm in Macaulay2. The output of the main function of the package includes information about lineages of nonzero remainders that are added to the basis during the computation. This information can be used for further algorithm improvements and optimization. © 2021, Mathematical Sciences Publishers. All rights reserved.

关键词： distributed computation Gröbner basis lineages S-pairs. ThreadedGB version 1.1

PACMANN: Point Adaptive Collocation Method for Artificial Neural Networks

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arXiv 2024年

作者： Visser, Coen Heinlein, Alexander Giovanardi, Bianca Faculty of Aerospace Engineering Delft University of Technology Delft2629 HS Netherlands Delft Institute of Applied Mathematics Faculty of Electrical Engineering Mathematics and Computer Science Delft University of Technology Delft2628 CD Netherlands Delft Institute for Computational Science and Engineering Delft University of Technology 2628 CD Netherlands

MSC Codes 65M22, 68T07, 65M50Physics-Informed Neural Networks (PINNs) are an emerging tool for approximating the solution of Partial Differential Equations (PDEs) in both forward and inverse problems. PINNs minimize a loss function which includes the PDE residual determined for a set of collocation points. Previous work has shown that the number and distribution of these collocation points have a significant influence on the accuracy of the PINN solution. Therefore, the effective placement of these collocation points is an active area of research. Specifically, adaptive collocation point sampling methods have been proposed, which have been reported to scale poorly to higher dimensions. In this work, we address this issue and present the Point Adaptive Collocation Method for Artificial Neural Networks (PACMANN). Inspired by classic optimization problems, this approach incrementally moves collocation points toward regions of higher residuals using gradient-based optimization algorithms guided by the gradient of the squared residual. We apply PACMANN for forward and inverse problems, and demonstrate that this method matches the performance of state-of-the-art methods in terms of the accuracy/efficiency tradeoff for the low-dimensional problems, while outperforming available approaches for high-dimensional problems;the best performance is observed for the Adam optimizer. Key features of the method include its low computational cost and simplicity of integration in existing physics-informed neural network pipelines. Copyright © 2024, The Authors. All rights reserved.

关键词： Inverse problems

Disjoint Compatibility via graph classes

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arXiv 2024年

作者： Aichholzer, Oswin Obmann, Julia Paták, Pavel Perz, Daniel Tkadlec, Josef Vogtenhuber, Birgit Graz University of Technology Institute of Software Technology Austria Czech Technical University in Prague Department of Applied Mathematics Czech Republic University of Perugia Department of Engineering Italy Charles University Prague Computer Science Institute Czech Republic

Two plane drawings of graphs on the same set of points are called disjoint compatible if their union is plane and they do not have an edge in common. Let S be a convex point set of 2n ≥ 10 points and let H be a family of plane drawings on S. Two plane perfect matchings M1 and M2 on S (which do not need to be disjoint nor compatible) are disjoint H-compatible if there exists a drawing in H which is disjoint compatible to both M1 and M2. In this work, we consider the graph which has all plane perfect matchings as vertices and where two vertices are connected by an edge if the matchings are disjoint H-compatible. We study the diameter of this graph when H is the family of all plane spanning trees, caterpillars or paths. We show that in the first two cases the graph is connected with constant and linear diameter, respectively, while in the third case it is disconnected. © 2024, CC BY-NC-ND.

关键词： Graphic methods

On a class of nonlinear BGK-type kinetic equations with density dependent collision rates

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arXiv 2025年

作者： Evans, Josephine Morris, Daniel Yoldaş, Havva Warwick Mathematics Institute University of Warwick Zeeman Building CoventryCV4 7AL United Kingdom Delft Institute of Applied Mathematics Faculty of Electrical Engineering Mathematics and Computer Science Delft University of Technology Mekelweg 4 Delft2628CD Netherlands Okinawa Institute of Science and Technology Graduate University Onna904-0495 Japan

We consider a class of nonlinear, spatially inhomogeneous kinetic equations of BGK-type with density dependent collision rates. These equations share the same superlinearity as the Boltzmann equation, and fall into the class of run and tumble equations appearing in mathematical biology. We prove that the Cauchy problem is well-posed, and the solutions propagate Maxwellian bounds over time. Moreover, we show that the solutions approach to equilibrium with an exponential rate, known as a hypocoercivity result. Lastly, we derive a class of nonlinear diffusion equations as the hydrodynamic limit of the kinetic equations in the diffusive scaling, employing both hypocoercivity and relative entropy methods. The limit equations cover a wide range of nonlinear diffusion equations including both the porous medium and the fast diffusion *** Codes 35A01, 82C40, 35B40, 35Q35 © 2025, CC BY.

关键词： Entropy

An analytical investigation of nonlinear time-fractional Schrödinger and coupled Schrödinger–KdV equations

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Results in Physics 2025年 70卷

作者： Patel, Yogeshwari F. Izadi, Mohammad Department of Mathematical Sciences P D Patel Institute of Applied Sciences Charotar University of Science and Technology Changa Anand Gujarat 388421 India Department of Applied Mathematics Faculty of Mathematics and Computer Shahid Bahonar University of Kerman Kerman Iran

This study applies the Fractional Reduced Differential Transform Method (FRDTM) to solve two nonlinear fractional equations: the time-fractional Schrödinger equation (TFSE) and the coupled Schrödinger–KdV (Sch–KdV) equation, which are prominent in quantum mechanics, plasma physics, and wave propagation studies. These equations model various wave phenomena, including dust-acoustic waves, electromagnetic waves, and Langmuir waves, in plasma physics. Using the Liouville–Caputo fractional derivative, FRDTM effectively incorporates nonlocality and memory effects. The solutions are derived as rapidly convergent infinite series with terms that are straightforward to compute, ensuring both accuracy and efficiency. Numerical examples highlight the method's ability to closely approximate exact solutions, with graphical and tabular comparisons illustrating the effect of the fractional order on solution behavior and validating the approach through computed absolute errors. Additionally, discussions on the modulation instability of the models reinforce the robustness of FRDTM as a powerful tool for solving complex nonlinear fractional systems. © 2025 The Authors

关键词： Analytical solutions Fractional PDEs Liouville–Caputo fractional derivative Modulational instability Nonlinear Schrödinger equation Schrödinger–KdV equation