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Relativistic stars in f(Q)-gravity

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arXiv 2025年

作者： Dimakis, Nikolaos Giacomini, Alex Paliathanasis, Andronikos Panotopoulos, Grigorios Departamento de Ciencias Físicas Universidad de la Frontera Casilla 54-D Temuco4811186 Chile Instituto de Ciencias Físicas y Matemáticas Universidad Austral de Chile Valdivia Chile Institute of Systems Science Department of Mathematics Faculty of Applied Sciences Durban University of Technology Durban4000 South Africa School for Data Science and Computational Thinking Stellenbosch University 44 Banghoek Rd Stellenbosch7600 South Africa Departamento de Matemáticas Universidad Católica del Norte Avda. Angamos 0610 Casilla Antofagasta1280 Chile South Africa

We investigate static spherically symmetric spacetimes within the framework of symmetric teleparallel f(Q) gravity in order to describe relativistic stars. We adopt a specific ansatz for the background geometry corresponding to a singularity-free space-time. We obtain an expression for the connection, which allows the derivation of solutions for any f(Q) theory in this context. Our approach aims to address a recurring error appearing in the literature, where even when a connection compatible with spherical symmetry is adopted, the field equation for the connection is systematically omitted and not checked if it is satisfied. For the stellar configuration, we concentrate on the power-law model f(Q) = Q + αQ0（QQ0）ν. The de Sitter-Schwarzschild geometry naturally emerges as an attractor beyond a certain radius, we thus utilize it as the external solution beyond the boundary of the star. We perform a detailed investigation of the physical characteristics of the interior solution, explicitly determining the mass function, analyzing the resulting gravitational fluid properties and deriving the angular and radial speed of sound. © 2025, CC BY.

关键词： Spheres

Dynamic network analysis improves protein 3D structural classification

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arXiv 2021年

作者： Newaz, Khalique Piland, Jacob Clark, Patricia L. Emrich, Scott J. Li, Jun Milenković, Tijana Department of Computer Science and Engineering University of Notre Dame Notre DameIN46556 United States Department of Chemistry and Biochemistry University of Notre Dame Notre DameIN46556 United States Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States Department of Electrical Engineering and Computer Science University of Tennessee KnoxvilleTN37996 United States

Protein structural classification (PSC) is a supervised problem of assigning proteins into pre-defined structural (e.g., CATH or SCOPe) classes based on the proteins' sequence or 3D structural features. We recently proposed PSC approaches that model protein 3D structures as protein structure networks (PSNs) and analyze PSN-based protein features, which performed better than or comparable to state-of-the-art sequence or other 3D structure-based approaches in the task of PSC. However, existing PSN-based PSC approaches model the whole 3D structure of a protein as a static PSN. Because folding of a protein is a dynamic process, where some parts of a protein fold before others, modeling the 3D structure of a protein as a dynamic PSN might further help improvethe existing PSC performance. Here, we propose for the first time a way to model 3D structures of proteins as dynamic PSNs, with the hypothesis that this will improve upon the current state-of-the-art PSC approaches that are based on static PSNs (and thus upon the existing state-of-the-art sequence and other 3D structural approaches). Indeed, we confirm this on 71 datasets spanning ∼44,000 protein domains from CATH and SCOPe. © 2021, CC BY.

关键词： Proteins

GENERALISED SYMMETRIES AND BASES FOR DUNKL MONOGENICS

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arXiv 2022年

作者： de Bie, Hendrik Langlois-Rémillard, Alexis Oste, Roy van der Jeugt, Joris Clifford Research Group Department of Electronics and Information Systems Faculty of Engineering and Architecture Ghent University Krijgslaan 281–S8 Gent9000 Belgium Department of Applied Mathematics Computer Science and Statistics Faculty of Sciences Ghent University Krijgslaan 281–S9 Gent9000 Belgium

We introduce a family of commuting generalised symmetries of the Dunkl–Dirac operator inspired by the Maxwell construction in harmonic analysis. As an application, we use these generalised symmetries to construct bases of the polynomial null-solutions of the Dunkl–Dirac operator. These polynomial spaces form representation spaces of the Dunkl–Dirac symmetry algebra. For the Zd2 case, the results are compared with previous *** Codes 20F55, 43A32, 30G35, 33C52, 33C55 Copyright © 2022, The Authors. All rights reserved.

关键词： Polynomials

Insegt fibre: A user-friendly software for individual fibre segmentation 22

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Insegt fibre: A user-friendly software for individual fibre ...

22nd International Conference on Composite Materials, ICCM 2019

作者： Emerson, Monica J. Dahl, Anders B. Conradsen, Knut Dahl, Vedrana A. Department of Applied Mathematics and Computer Science Technical University of Denmark Kongens Lyngby Denmark

Insegt Fibre is a software toolbox for volumetric fibre segmentation. The toolbox comes with scripts to detect the centres of individual fibres in 2D and 3D from tomograms acquired through X-ray imaging, and a graphical user interface to verify the accuracy of the resulting 3D tracks. In addition, there is a script to characterise fibre orientations in 3D and a script to match corresponding fibres across a 4D time-lapse sequence, which enables the characterisation of composite micro-structural changes of individual fibres. Insegt Fibre is based on a segmentation method that uses a dictionary of image patches which has been trained to model the patterns/features that are repeated in the image data at a certain scale defined by the patch size. Thus, the dictionary-learning segmentation algorithm has proven highly successful in modelling fibres that have regular cross-sections, commonly found in fibre reinforced composite materials. The algorithm is robust to noise and artefacts in the data and therefore excels in measuring fibre geometry from a variety of scan qualities, even when fibres are densely packed and the boundaries between them are unclear. Insegt Fibre is simple to use, it comes with a manual and it requires minimal input from the user. Besides presenting the recent user-friendly version of this robust method for measuring the 3D tracks of fibres from X-ray CT data, the paper gives an overview of the possibilities that the method gives with regards to characterisation of composite micro-structure and fibre behaviour under load. Thanks to the precision to which fibre geometry can be characterised with this method, it is now possible to follow how each individual fibre changes across data-sets acquired under progressive loading conditions. All in all, Insegt Fibre makes image-based characterisation of fibrous materials simpler, more accessible and applicable to a broader range of studies. © 2019 International Committee on Composite Materials. All rights reser

关键词： Fibers

A monotonic optimization approach for solving strictly quasiconvex multiobjective programming problems

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A monotonic optimization approach for solving strictly quasi...

作者： Thang, Tran Ngoc Solanki, Vijender Kumar Dao, Tuan Anh Thi Ngoc Anh, Nguyen Van Hai, Pham School of Applied Mathematics and Informatics Hanoi University of Science and Technology Hanoi Viet Nam Department of Computer Science and Engineering CMR Institute of Technology Hyderabad TS India Department of Information Technology Uppsala University Uppsala Sweden School of Information and Communication Technology Hanoi University of Science and Technology Hanoi Viet Nam

In this article, we use a monotonic optimization approach to propose an outcome-space outer approximation by copolyblocks for solving strictly quasiconvex multiobjective programming problems which include many classes of captivating problems, for example when the criterion functions are nonlinear fractional. After the algorithm is terminated, with any given tolerance, an approximation of the weakly efficient solution set is obtained containing the whole weakly efficient solution set of the problem. The algorithm is proved to be convergent and it is suitable to be implemented in parallel using convex programming tools. Some computational experiments are reported to show the accuracy and efficiency of the algorithm. © 2020 - IOS Press and the authors. All rights reserved.

关键词： Multiobjective optimization

Multi-phase volume segmentation with tetrahedral mesh 29

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Multi-phase volume segmentation with tetrahedral mesh

29th British Machine Vision Conference, BMVC 2018

作者： Nguyen, Tuan T. Dahl, Vedrana A. Andreas Brentzen, J. Trinderup, Camilla H. Department of Applied Mathematics and Computer Science Technical University of Denmark Kgs Lyngby Denmark

In life science and material science, it is often desirable to segment a volumetric data set in such a way that multiple materials (phases) are segmented and a tetrahedral mesh representation is obtained for each segment for downstream applications. Unfortunately, obtaining a mesh, typically from CT or MRI scan, is challenging, especially in 3D. This paper proposes a novel approach for volume segmentation using a tetrahedral mesh. Our method employs a deformable model that minimizes the Mumford-Shah energy function. We apply our method to several CT data sets in order to demonstrate its advantages: multi-phase support, robustness to noise, and adaptive resolution outputs. Our method is based on the Deformable Simplicial Complex (DSC) method for tracking deformable interfaces which is designed specifically to deal with topology changes. © 2018. The copyright of this document resides with its authors. It may be distributed unchanged freely in print or electronic forms.

关键词： Volumetric analysis

On a problem involving the squares of odd harmonic numbers

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arXiv 2022年

作者： Campbell, John M. Levrie, Paul Xu, Ce Zhao, Jianqiang Department of Mathematics and Statistics York University 4700 Keele St TorontoONM3J 1P3 Canada Faculty of Applied Engineering UAntwerpen Groenenborgerlaan 171 Antwerp2020 Belgium Department of Computer Science KU Leuven Celestijnenlaan 200A P. O. Box 2402 Heverlee Leuven3001 Belgium School of Mathematics and Statistics Anhui Normal University Wuhu241002 China Department of Mathematics The Bishop's School La Jolla CA92037 United States

We introduce a full solution to a problem considered by Wang and Chu concerning series involving the squares of finite sums of the form 1 + 1/3 + · · · + 1/2n-1. Our proof involves techniques from the t... 详细信息

关键词： Harmonic analysis

Graph clustering in all parameter regimes 45

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Graph clustering in all parameter regimes

45th International Symposium on Mathematical Foundations of computer science, MFCS 2020

作者： Gan, Junhao Gleich, David F. Veldt, Nate Wirth, Anthony Zhang, Xin School of Computing and Information Systems University of Melbourne Victoria Australia Department of Computer Science Purdue University West LafayetteIN United States Center for Applied Mathematics Cornell University IthacaNY United States

ISBN: (纸本)9783959771597

Resolution parameters in graph clustering control the size and structure of clusters formed by solving a parametric objective function. Typically there is more than one meaningful way to cluster a graph, and solving the same objective function for different resolution parameters produces clusterings at different levels of granularity, each of which can be meaningful depending on the application. In this paper, we address the task of efficiently solving a parameterized graph clustering objective for all values of a resolution parameter. Specifically, we consider a new analysis-friendly objective we call LambdaPrime, involving a parameter λ ∈ (0, 1). LambdaPrime is an adaptation of LambdaCC, a significant family of instances of the Correlation Clustering (minimization) problem. Indeed, LambdaPrime and LambdaCC are closely related to other parameterized clustering problems, such as parametric generalizations of modularity. They capture a number of specific clustering problems as special cases, including sparsest cut and cluster deletion. While previous work provides approximation results for a single value of the resolution parameter, we seek a set of approximately optimal clusterings for all values of λ in polynomial time. More specifically, we show that when a graph has m edges and n nodes, there exists a set of at most m clusterings such that, for every λ ∈ (0, 1), the family contains an optimal solution to the LambdaPrime objective. This bound is tight on star graphs. We obtain a family of O(log n) clusterings by solving the parametric linear programming (LP) relaxation of LambdaPrime at O(log n) λ values, and rounding each LP solution using existing approximation algorithms. We prove that this is asymptotically tight: for a certain class of ring graphs, for all values of λ, Ω(log n) feasible solutions are required to provide a constant-factor approximation for the LambdaPrime LP relaxation. To minimize the size of the clustering family, we further propose an algor

关键词： Linear programming

Universal methods for variational inequalities: deterministic and stochastic cases

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arXiv 2024年

作者： Klimza, Anton Gasnikov, Alexander Stonyakin, Fedor Alkousa, Mohammad Moscow Institute of Physics and Technology Department of Applied Mathematics and Computer Science Institutsky lane 9 Dolgoprudny141701 Russia Innopolis University Universitetskaya Str. Innopolis420500 Russia Institute for Information Transmission Problems RAS Bolshoy Karetny per. 19 build.1 Moscow127051 Russia V. I. Vernadsky Crimean Federal University 4 Academician Vernadsky Avenue Simferopol295007 Russia

In this paper, we propose universal proximal mirror methods to solve the variational inequality problem with Hölder-continuous operators in both deterministic and stochastic settings. The proposed methods automatically adapt not only to the oracle’s noise (in the stochastic setting of the problem) but also to the Hölder continuity of the operator without having prior knowledge of either the problem class or the nature of the operator information. We analyzed the proposed algorithms in both deterministic and stochastic settings and obtained estimates for the required number of iterations to achieve a given quality of a solution to the variational inequality. We showed that, without knowing the Hölder exponent and Hölder constant of the operators, the proposed algorithms have the least possible in the worst-case sense complexity for the considered class of variational inequalities. We also compared the resulting stochastic algorithm with other popular optimizers for the task of image classification. © 2024, CC BY.

关键词： Mirrors