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A Framework for Self-Intersecting Surfaces (SOS): Symmetric Optimisation for Stability 自相交曲面的框架:稳定性的对称优化
arXiv - CS - Mathematical Software Pub Date : 2023-12-04 DOI: arxiv-2312.02113
Christian Amend, Tom Goertzen
{"title":"A Framework for Self-Intersecting Surfaces (SOS): Symmetric Optimisation for Stability","authors":"Christian Amend, Tom Goertzen","doi":"arxiv-2312.02113","DOIUrl":"https://doi.org/arxiv-2312.02113","url":null,"abstract":"In this paper, we give a stable and efficient method for fixing\u0000self-intersections and non-manifold parts in a given embedded simplicial\u0000complex. In addition, we show how symmetric properties can be used for further\u0000optimisation. We prove an initialisation criterion for computation of the outer\u0000hull of an embedded simplicial complex. To regularise the outer hull of the\u0000retriangulated surface, we present a method to remedy non-manifold edges and\u0000points. We also give a modification of the outer hull algorithm to determine\u0000chambers of complexes which gives rise to many new insights. All of these\u0000methods have applications in many areas, for example in 3D-printing, artistic\u0000realisations of 3D models or fixing errors introduced by scanning equipment\u0000applied for tomography. Implementations of the proposed algorithms are given in\u0000the computer algebra system GAP4. For verification of our methods, we use a\u0000data-set of highly self-intersecting symmetric icosahedra.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"18 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Scale Ratio Tuning of Group Based Job Scheduling in HPC Systems HPC系统中基于组的作业调度比例调整
arXiv - CS - Mathematical Software Pub Date : 2023-11-29 DOI: arxiv-2311.17889
Lyakhovets D. S., Baranov A. V., Telegin P. N
{"title":"Scale Ratio Tuning of Group Based Job Scheduling in HPC Systems","authors":"Lyakhovets D. S., Baranov A. V., Telegin P. N","doi":"arxiv-2311.17889","DOIUrl":"https://doi.org/arxiv-2311.17889","url":null,"abstract":"During the initialization of a supercomputer job, no useful calculations are\u0000performed. A high proportion of initialization time results in idle computing\u0000resources and less computational efficiency. Certain methods and algorithms\u0000combining jobs into groups are used to optimize scheduling of jobs with high\u0000initialization proportion. The article considers the influence of the scale\u0000ratio setting in algorithm for the job groups formation, on the performance\u0000metrics of the workload manager. The study was carried out on the developed by\u0000authors Aleabased workload manager model. The model makes it possible to\u0000conduct a large number of experiments in reasonable time without losing the\u0000accuracy of the simulation. We performed a series of experiments involving\u0000various characteristics of the workload. The article represents the results of\u0000a study of the scale ratio influence on efficiency metrics for different\u0000initialization time proportions and input workflows with varying intensity and\u0000homogeneity. The presented results allow the workload managers administrators\u0000to set a scale ratio that provides an appropriate balance with contradictory\u0000efficiency metrics.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lineax: unified linear solves and linear least-squares in JAX and Equinox Lineax: JAX和Equinox中统一的线性解和线性最小二乘
arXiv - CS - Mathematical Software Pub Date : 2023-11-28 DOI: arxiv-2311.17283
Jason Rader, Terry Lyons, Patrick Kidger
{"title":"Lineax: unified linear solves and linear least-squares in JAX and Equinox","authors":"Jason Rader, Terry Lyons, Patrick Kidger","doi":"arxiv-2311.17283","DOIUrl":"https://doi.org/arxiv-2311.17283","url":null,"abstract":"We introduce Lineax, a library bringing linear solves and linear\u0000least-squares to the JAX+Equinox scientific computing ecosystem. Lineax uses\u0000general linear operators, and unifies linear solves and least-squares into a\u0000single, autodifferentiable API. Solvers and operators are user-extensible,\u0000without requiring the user to implement any custom derivative rules to get\u0000differentiability. Lineax is available at https://github.com/google/lineax.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"11 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mathematical Modelling and a Numerical Solution for High Precision Satellite Ephemeris Determination 高精度卫星星历确定的数学模型和数值解
arXiv - CS - Mathematical Software Pub Date : 2023-11-25 DOI: arxiv-2311.15028
Aravind Gundakaram, Abhirath Sangala, Aditya Sai Ellendula, Prachi Kansal, Lanii Lakshitaa, Suchir Reddy Punuru, Nethra Naveen, Sanjitha Jaggumantri
{"title":"Mathematical Modelling and a Numerical Solution for High Precision Satellite Ephemeris Determination","authors":"Aravind Gundakaram, Abhirath Sangala, Aditya Sai Ellendula, Prachi Kansal, Lanii Lakshitaa, Suchir Reddy Punuru, Nethra Naveen, Sanjitha Jaggumantri","doi":"arxiv-2311.15028","DOIUrl":"https://doi.org/arxiv-2311.15028","url":null,"abstract":"In this paper, we develop a high-precision satellite orbit determination\u0000model for satellites orbiting the Earth. Solving this model entails numerically\u0000integrating the differential equation of motion governing a two-body system,\u0000employing Fehlberg's formulation and the Runge-Kutta class of embedded\u0000integrators with adaptive stepsize control. Relevant primary perturbing forces\u0000included in this mathematical model are the full force gravitational field\u0000model, Earth's atmospheric drag, third body gravitational effects and solar\u0000radiation pressure. Development of the high-precision model required accounting\u0000for the perturbing influences of Earth radiation pressure, Earth tides and\u0000relativistic effects. The model is then implemented to obtain a high-fidelity\u0000Earth orbiting satellite propagator, namely the Satellite Ephemeris Determiner\u0000(SED), which is comparable to the popular High Precision Orbit Propagator\u0000(HPOP). The architecture of SED, the methodology employed, and the numerical\u0000results obtained are presented.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"14 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exact Combinatorial Optimization with Temporo-Attentional Graph Neural Networks 时间-注意力图神经网络的精确组合优化
arXiv - CS - Mathematical Software Pub Date : 2023-11-23 DOI: arxiv-2311.13843
Mehdi Seyfi, Amin Banitalebi-Dehkordi, Zirui Zhou, Yong Zhang
{"title":"Exact Combinatorial Optimization with Temporo-Attentional Graph Neural Networks","authors":"Mehdi Seyfi, Amin Banitalebi-Dehkordi, Zirui Zhou, Yong Zhang","doi":"arxiv-2311.13843","DOIUrl":"https://doi.org/arxiv-2311.13843","url":null,"abstract":"Combinatorial optimization finds an optimal solution within a discrete set of\u0000variables and constraints. The field has seen tremendous progress both in\u0000research and industry. With the success of deep learning in the past decade, a\u0000recent trend in combinatorial optimization has been to improve state-of-the-art\u0000combinatorial optimization solvers by replacing key heuristic components with\u0000machine learning (ML) models. In this paper, we investigate two essential\u0000aspects of machine learning algorithms for combinatorial optimization: temporal\u0000characteristics and attention. We argue that for the task of variable selection\u0000in the branch-and-bound (B&B) algorithm, incorporating the temporal information\u0000as well as the bipartite graph attention improves the solver's performance. We\u0000support our claims with intuitions and numerical results over several standard\u0000datasets used in the literature and competitions. Code is available at:\u0000https://developer.huaweicloud.com/develop/aigallery/notebook/detail?id=047c6cf2-8463-40d7-b92f-7b2ca998e935","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Assessment of PC-mer's Performance in Alignment-Free Phylogenetic Tree Construction PC-mer在无比对系统发育树构建中的性能评价
arXiv - CS - Mathematical Software Pub Date : 2023-11-21 DOI: arxiv-2311.12898
Saeedeh Akbari Rokn Abadi, Melika Honarmand, Ali Hajialinaghi, Somayyeh Koohi
{"title":"An Assessment of PC-mer's Performance in Alignment-Free Phylogenetic Tree Construction","authors":"Saeedeh Akbari Rokn Abadi, Melika Honarmand, Ali Hajialinaghi, Somayyeh Koohi","doi":"arxiv-2311.12898","DOIUrl":"https://doi.org/arxiv-2311.12898","url":null,"abstract":"Background: Sequence comparison is essential in bioinformatics, serving\u0000various purposes such as taxonomy, functional inference, and drug discovery.\u0000The traditional method of aligning sequences for comparison is time-consuming,\u0000especially with large datasets. To overcome this, alignment-free methods have\u0000emerged as an alternative approach, prioritizing comparison scores over\u0000alignment itself. These methods directly compare sequences without the need for\u0000alignment. However, accurately representing the relationships between sequences\u0000is a significant challenge in the design of these tools. Methods:One of the\u0000alignment-free comparison approaches utilizes the frequency of fixed-length\u0000substrings, known as K-mers, which serves as the foundation for many sequence\u0000comparison methods. However, a challenge arises in these methods when\u0000increasing the length of the substring (K), as it leads to an exponential\u0000growth in the number of possible states. In this work, we explore the PC-mer\u0000method, which utilizes a more limited set of words that experience slower\u0000growth 2^k instead of 4^k compared to K. We conducted a comparison of sequences\u0000and evaluated how the reduced input vector size influenced the performance of\u0000the PC-mer method. Results: For the evaluation, we selected the Clustal Omega\u0000method as our reference approach, alongside three alignment-free methods:\u0000kmacs, FFP, and alfpy (word count). These methods also leverage the frequency\u0000of K-mers. We applied all five methods to 9 datasets for comprehensive\u0000analysis. The results were compared using phylogenetic trees and metrics such\u0000as Robinson-Foulds and normalized quartet distance (nQD). Conclusion: Our\u0000findings indicate that, unlike reducing the input features in other\u0000alignment-independent methods, the PC-mer method exhibits competitive\u0000performance when compared to the aforementioned methods especially when input\u0000sequences are very varied.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"10 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
p-adaptive discontinuous Galerkin method for the shallow water equations on heterogeneous computing architectures 异构计算结构下浅水方程的p-自适应间断Galerkin方法
arXiv - CS - Mathematical Software Pub Date : 2023-11-19 DOI: arxiv-2311.11348
Sara Faghih-Naini, Vadym Aizinger, Sebastian Kuckuk, Richard Angersbach, Harald Köstler
{"title":"p-adaptive discontinuous Galerkin method for the shallow water equations on heterogeneous computing architectures","authors":"Sara Faghih-Naini, Vadym Aizinger, Sebastian Kuckuk, Richard Angersbach, Harald Köstler","doi":"arxiv-2311.11348","DOIUrl":"https://doi.org/arxiv-2311.11348","url":null,"abstract":"Heterogeneous computing and exploiting integrated CPU-GPU architectures has\u0000become a clear current trend since the flattening of Moore's Law. In this work,\u0000we propose a numerical and algorithmic re-design of a p-adaptive\u0000quadrature-free discontinuous Galerkin method (DG) for the shallow water\u0000equations (SWE). Our new approach separates the computations of the\u0000non-adaptive (lower-order) and adaptive (higher-order) parts of the\u0000discretization form each other. Thereby, we can overlap computations of the\u0000lower-order and the higher-order DG solution components. Furthermore, we\u0000investigate execution times of main computational kernels and use automatic\u0000code generation to optimize their distribution between the CPU and GPU. Several\u0000setups, including a prototype of a tsunami simulation in a tide-driven flow\u0000scenario, are investigated, and the results show that significant performance\u0000improvements can be achieved in suitable setups.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"13 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deriving Algorithms for Triangular Tridiagonalization a (Skew-)Symmetric Matrix (斜)对称矩阵三角三角对角化的推导算法
arXiv - CS - Mathematical Software Pub Date : 2023-11-17 DOI: arxiv-2311.10700
Robert van de Geijn, Maggie Myers, RuQing G. Xu, Devin Matthews
{"title":"Deriving Algorithms for Triangular Tridiagonalization a (Skew-)Symmetric Matrix","authors":"Robert van de Geijn, Maggie Myers, RuQing G. Xu, Devin Matthews","doi":"arxiv-2311.10700","DOIUrl":"https://doi.org/arxiv-2311.10700","url":null,"abstract":"We apply the FLAME methodology to derive algorithms hand in hand with their\u0000proofs of correctness for the computation of the $ L T L^T $ decomposition\u0000(with and without pivoting) of a skew-symmetric matrix. The approach yields\u0000known as well as new algorithms, presented using the FLAME notation. A number\u0000of BLAS-like primitives are exposed at the core of blocked algorithms that can\u0000attain high performance. The insights can be easily extended to yield\u0000algorithms for computing the $ L T L^T $ decomposition of a symmetric matrix.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"12 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
DisCoPy: the Hierarchy of Graphical Languages in Python DisCoPy: Python中图形语言的层次结构
arXiv - CS - Mathematical Software Pub Date : 2023-11-17 DOI: arxiv-2311.10608
Alexis Toumi, Richie Yeung, Boldizsár Poór, Giovanni de Felice
{"title":"DisCoPy: the Hierarchy of Graphical Languages in Python","authors":"Alexis Toumi, Richie Yeung, Boldizsár Poór, Giovanni de Felice","doi":"arxiv-2311.10608","DOIUrl":"https://doi.org/arxiv-2311.10608","url":null,"abstract":"DisCoPy is a Python toolkit for computing with monoidal categories. It comes\u0000with two flexible data structures for string diagrams: the first one for planar\u0000monoidal categories based on lists of layers, the second one for symmetric\u0000monoidal categories based on cospans of hypergraphs. Algorithms for functor\u0000application then allow to translate string diagrams into code for numerical\u0000computation, be it differentiable, probabilistic or quantum. This report gives\u0000an overview of the library and the new developments released in its version\u00001.0. In particular, we showcase the implementation of diagram equality for a\u0000large fragment of the hierarchy of graphical languages for monoidal categories,\u0000as well as a new syntax for defining string diagrams as Python functions.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fast multiplication by two's complement addition of numbers represented as a set of polynomial radix 2 indexes, stored as an integer list for massively parallel computation 以多项式基数2索引的集合表示的数字的2的补加的快速乘法，存储为大规模并行计算的整数列表
arXiv - CS - Mathematical Software Pub Date : 2023-11-16 DOI: arxiv-2311.09922
Mark Stocks
{"title":"Fast multiplication by two's complement addition of numbers represented as a set of polynomial radix 2 indexes, stored as an integer list for massively parallel computation","authors":"Mark Stocks","doi":"arxiv-2311.09922","DOIUrl":"https://doi.org/arxiv-2311.09922","url":null,"abstract":"We demonstrate a multiplication method based on numbers represented as set of\u0000polynomial radix 2 indices stored as an integer list. The 'polynomial integer\u0000index multiplication' method is a set of algorithms implemented in python code.\u0000We demonstrate the method to be faster than both the Number Theoretic Transform\u0000(NTT) and Karatsuba for multiplication within a certain bit range. Also\u0000implemented in python code for comparison purposes with the polynomial radix 2\u0000integer method. We demonstrate that it is possible to express any integer or\u0000real number as a list of integer indices, representing a finite series in base\u0000two. The finite series of integer index representation of a number can then be\u0000stored and distributed across multiple CPUs / GPUs. We show that operations of\u0000addition and multiplication can be applied as two's complement additions\u0000operating on the index integer representations and can be fully distributed\u0000across a given CPU / GPU architecture. We demonstrate fully distributed\u0000arithmetic operations such that the 'polynomial integer index multiplication'\u0000method overcomes the current limitation of parallel multiplication methods. Ie,\u0000the need to share common core memory and common disk for the calculation of\u0000results and intermediate results.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"13 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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