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AN ALGEBRAIC CHARACTERIZATION OF k–COLORABILITY

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arXiv 2020年

作者： Flores, Ramón Kahrobaei, Delaram Koberda, Thomas Department of Geometry and Topology University of Seville Spain Department of Computer Science University of York UK New York University Tandon School of Engineering PhD Program in Computer Science CUNY Graduate Center Mathematics Department University of Virginia CharlottesvilleVA22904

We characterize k–colorability of a simplicial graph via the intrinsic algebraic structure of the associated right-angled Artin group. As a consequence, we show that a certain problem about the existence of homomorphisms from right-angled Artin groups to products of free groups is NP–complete. Copyright © 2020, The Authors. All rights reserved.

关键词： Algebra

A parallel evolutionary multiple-try metropolis Markov chain monte carlo algorithm for sampling spatial partitions

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arXiv 2020年

作者： Tam Cho, Wendy K. Liu, Yan Y. Department of Political Science Department of Statistics Department of Mathematics Department of Asian American Studies College of Law National Center for Supercomputing Applications University of Illinois at Urbana-Champaign United States Computational Urban Sciences Group Computational Science and Engineering Division Oak Ridge National Laboratory United States

We develop an Evolutionary Markov Chain Monte Carlo (EMCMC) algorithm for sampling spatial partitions that lie within a large and complex spatial state space. Our algorithm combines the advantages of evolutionary algorithms (EAs) as optimization heuristics for state space traversal and the theoretical convergence properties of Markov Chain Monte Carlo algorithms for sampling from unknown distributions. Local optimality information that is identified via a directed search by our optimization heuristic is used to adaptively update a Markov chain in a promising direction within the framework of a Multiple-Try Metropolis Markov Chain model that incorporates a generalized Metropolis-Hasting ratio. We further expand the reach of our EMCMC algorithm by harnessing the computational power afforded by massively parallel architecture through the integration of a parallel EA framework that guides Markov chains running in parallel. Copyright © 2020, The Authors. All rights reserved.

关键词： Evolutionary algorithms

Space-time theory of retail gravitation in economics of sun-earth relationships 18

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Space-time theory of retail gravitation in economics of sun-...

18th Conference on Applied mathematics, APLIMAT 2019

作者： Zeithamer, Tomáš R. Pospíšil, Jiří Faculty of Informatics and Statistics Department of Mathematics Economic University Prague Ekonomická 957 Prague140 00 Czech Republic Faculty of Civil Engineering Czech Technical University in Prague Thákurova 7 Prague166 29 Czech Republic

ISBN: (纸本)9781510882140

This paper is dealing with space-time theory of retail gravitation in economics of Sun-Earth Relationships. The mathematical model for physical space-time with the field of retail gravitation is based on a four-dimensional differentiable manifold on which a symmetric covariant second-order tensor field is defined, i.e. metric tensor having Lorentzian signature. © Applied mathematics, APLIMAT *** right reserved.

关键词： Tensors

Sub-Exact Sequence On Hilbert Space

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Journal of Physics: Conference Series 2021年第1期1751卷

作者： B H S Utami Fitriani M Usman Warsono J I Daoud Doctoral Program of Mathematics and Natural Science Faculty of Mathematics and Natural Science University of Lampung Bandar Lampung Indonesia Department of Information System STMIK Pringsewu Pringsewu Indonesia Department of Mathematics and Natural Science Faculty of Mathematics and Natural Science University of Lampung Bandar Lampung Indonesia Department of Science and Engineering Faculty of Engineering International Islamic University Malaysia P.O. Box 10 50728 Kuala Lumpur Malaysia

The notion of the sub-exact sequence is the generalization of exact sequence in algebra especially on a module. A module over a ring R is a generalization of the notion of vector space over a field F. Refers to a special vector space over field F when we have a complete inner product space, it is called a Hilbert space. A space is complete if every Cauchy sequence converges. Now, we introduce the sub-exact sequence on Hilbert space which can later be useful in statistics. This paper aims to investigate the properties of the sub-exact sequence and their relation to direct summand on Hilbert space. As the result, we get two properties of isometric isomorphism sub-exact sequence on Hilbert space.

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Multiwavelength Afterglow Analysis of GRB 221009A: Unveiling the Evolution of a Cooling Break in a Wind-like Medium

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arXiv 2024年

作者： Tak, Donggeun Uhm, Z. Lucas Paek, Gregory S.H. Im, Myungshin Arimoto, Makoto Choi, Hyeonho Kim, Sophia Omodei, Nicola Racusin, Judith Urata, Yuji Zhang, Bing SNU Astronomy Research Center Seoul National University Seoul08826 Korea Republic of Korea Astronomy and Space Science Institute Daejeon34055 Korea Republic of Astronomy Program Department of Physics and Astronomy Seoul National University Gwanak-gu Seoul08826 Korea Republic of Faculty of Mathematics and Physics Institute of Science and Engineering Kanazawa University Kakuma Ishikawa Kanazawa920-1192 Japan W. W. Hansen Experimental Physics Laboratory Kavli Institute for Particle Astrophysics and Cosmology Department of Physics SLAC National Accelerator Laboratory Stanford University StanfordCA94305 United States NASA Goddard Space Flight Center GreenbeltMD20771 United States Institute of Astronomy National Central University Chung-Li32054 Taiwan The Nevada Center for Astrophysics University of Nevada Las VegasNV89154 United States Department of Physics and Astronomy University of Nevada Las VegasNV89154 United States

Gamma-ray bursts (GRBs) are the most energetic explosions in the universe, and their afterglow emission provides an opportunity to probe the physics of relativistic shock waves in an extreme environment. Several key pieces for completing the picture of the GRB afterglow physics are still missing, including jet properties, emission mechanism, and particle acceleration. Here we present a study of the afterglow emission of GRB 221009A, the most energetic GRB ever observed. Using optical, X-ray, and gamma-ray data up to approximately two days after the trigger, we trace the evolution of the multi-wavelength spectrum and the physical parameters behind the emission process. The broadband spectrum is consistent with the synchrotron emission emitted by relativistic electrons with its index of p = 2.29 ± 0.02. We identify a break energy at keV and an exponential cutoff at GeV in the observed multi-wavelength spectrum. The break energy increases in time from 16.0+7.1−4.9 keV at 0.65 days to 46.8+25.0−15.5 keV at 1.68 days, favoring a stellar wind-like profile of the circumburst medium with k = 2.4 ± 0.1 as in ρ(r) ∝ r−k. The high-energy attenuation at around 0.4 to 4 GeV is attributed to the maximum of the particle acceleration in the relativistic shock wave. This study confirms that the synchrotron process can explain the multi-wavelength afterglow emission and its evolution. Copyright © 2024, The Authors. All rights reserved.

关键词： Gamma rays

Graph Kolmogorov-Arnold Networks for Multi-Cancer Classification and Biomarker Identification, An Interpretable Multi-Omics Approach

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arXiv 2025年

作者： Alharbi, Fadi Budhiraja, Nishant Vakanski, Aleksandar Zhang, Boyu Elbashir, Murtada K. Mohammed, Mohanad College of Engineering Department of Computer Science University of Idaho MoscowID83844 United States College of Computer and Information Sciences Department of Computer Science Jouf University Aljouf Sakaka72441 Saudi Arabia College of Computer and Information Sciences Department of Information Systems Jouf University Aljouf Sakaka72441 Saudi Arabia Faculty of Mathematical and Computer Sciences University of Gezira Wad Madani Sudan School of Mathematics Statistics and Computer Science University of KwaZulu-Natal Scottsville Pietermaritzburg3209 South Africa

The integration of multi-omics data presents a major challenge in precision medicine, requiring advanced computational methods for accurate disease classification and biological interpretation. This study introduces the Multi-Omics Graph Kolmogorov–Arnold Network (MOGKAN), a deep learning model that integrates messenger-RNA, micro-RNA sequences, and DNA methylation data with Protein-Protein Interaction (PPI) networks for accurate and interpretable cancer classification across 31 cancer types. MOGKAN employs a hybrid approach combining differential expression with DESeq2, Linear Models for Microarray (LIMMA), and Least Absolute Shrinkage and Selection Operator (LASSO) regression to reduce multi-omics data dimensionality while preserving relevant biological features. The model architecture is based on the Kolmogorov–Arnold theorem principle, using trainable univariate functions to enhance interpretability and feature analysis. MOGKAN achieves classification accuracy of 96.28% and demonstrates low experimental variability with a standard deviation that is reduced by 1.58–7.30% points compared to Convolutional Neural Networks (CNNs) and Graph Neural Networks (GNNs). The biomarkers identified by MOGKAN have been validated as cancer-related markers through Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analysis. The proposed model presents an ability to uncover molecular oncogenesis mechanisms by detecting phosphoinositide-binding substances and regulating sphingolipid cellular processes. By integrating multi-omics data with graph-based deep learning, our proposed approach demonstrates superior predictive performance and interpretability that has the potential to enhance the translation of complex multi-omics data into clinically actionable cancer *** Codes 68 Copyright © 2025, The Authors. All rights reserved.

关键词： Convolutional neural networks

On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources

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arXiv 2022年

作者： Berta, Mario Brandão, Fernando G.S.L. Gour, Gilad Lami, Ludovico Plenio, Martin B. Regula, Bartosz Tomamichel, Marco Institute for Quantum Information RWTH Aachen University Aachen Germany Department of Computing Imperial College London London United Kingdom Institute for Quantum Information and Matter California Institute of Technology PasadenaCA United States AWS Center for Quantum Computing PasadenaCA United States Department of Mathematics and Statistics Institute for Quantum Science and Technology University of Calgary ABT2N 1N4 Canada Institut für Theoretische Physik und IQST Universität Ulm Albert-Einstein-Allee 11 UlmD-89069 Germany QuSoft Science Park 123 Amsterdam1098 XG Netherlands Korteweg–de Vries Institute for Mathematics University of Amsterdam Science Park 105-107 Amsterdam1098 XG Netherlands Institute for Theoretical Physics University of Amsterdam Science Park 904 Amsterdam1098 XH Netherlands Saitama Wako351-0198 Japan Department of Physics Graduate School of Science The University of Tokyo Bunkyo-ku Tokyo113-0033 Japan Center for Quantum Technologies National University of Singapore Singapore Department of Electrical and Computer Engineering College of Design and Engineering National University of Singapore Singapore

We show that the proof of the generalised quantum Stein’s lemma [Brandão & Plenio, Commun. Math. Phys. 295, 791 (2010)] is not correct due to a gap in the argument leading to Lemma III.9. Hence, the main achievability result of Brandão & Plenio is not known to hold. This puts into question a number of established results in the literature, in particular the reversibility of quantum entanglement [Brandão & Plenio, Commun. Math. Phys. 295, 829 (2010);Nat. Phys. 4, 873 (2008)] and of general quantum resources [Brandão & Gour, Phys. Rev. Lett. 115, 070503 (2015)] under asymptotically resource non-generating operations. We discuss potential ways to recover variants of the newly unsettled results using other approaches. © 2022, CC BY.

关键词： Quantum entanglement

Autonomous Multi-Modal Chemical Tomography using Bayesian Optimization

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Microscopy and Microanalysis 2024年第SUPPLEMENT_1期30卷

作者： Millsaps, William Schwartz, Jonathan Manassa, Jason Wendy Di, Zichao Jiang, Yi Hovden, Robert Department of Nuclear Engineering Radiological Sciences University of Michigan Ann Arbor MI US Chan Zuckerberg Imaging Institute Redwood City CA USA Department of Materials Science and Engineering University of Michigan Ann Arbor MI US Mathematics and Computer Science Division Argonne National Laboratory Lemont IL US Advanced Photon Source Facility Argonne National Laboratory Lemont IL US Applied Physics Program University of Michigan Ann Arbor MI US

Asymptotics of reinforcement learning with neural networks

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arXiv 2019年

作者： Sirignano, Justin Spiliopoulos, Konstantinos Mathematics University of Oxford United Kingdom Department of Industrial & Systems Engineering University of Illinois at Urbana-Champaign United States Department of Mathematics and Statistics Boston University Boston United States

We prove that a single-layer neural network trained with the Q-learning algorithm converges in distribution to a random ordinary differential equation as the size of the model and the number of training steps become large. Analysis of the limit differential equation shows that it has a unique stationary solution which is the solution of the Bellman equation, thus giving the optimal control for the problem. In addition, we study the convergence of the limit differential equation to the stationary solution. As a by-product of our analysis, we obtain the limiting behavior of single-layer neural networks when trained on i.i.d. data with stochastic gradient descent under the widely-used Xavier initialization. Copyright © 2019, The Authors. All rights reserved.

关键词： Ordinary differential equations