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Efficient Calculations for k-diagonal Circulant Matrices and Cyclic Banded Matrices arXiv.cs.MS Pub Date : 2024-03-08 Chen Wang, Chao Wang
Calculating the inverse of $k$-diagonal circulant matrices and cyclic banded matrices is a more challenging problem than calculating their determinants. Algorithms that directly involve or specify linear or quadratic complexity for the inverses of these two types of matrices are rare. This paper presents two fast algorithms that can compute the complexity of a $k$-diagonal circulant matrix within complexity
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TopoX: A Suite of Python Packages for Machine Learning on Topological Domains arXiv.cs.MS Pub Date : 2024-02-04 Mustafa Hajij, Mathilde Papillon, Florian Frantzen, Jens Agerberg, Ibrahem AlJabea, Ruben Ballester, Claudio Battiloro, Guillermo Bernárdez, Tolga Birdal, Aiden Brent, Peter Chin, Sergio Escalera, Simone Fiorellino, Odin Hoff Gardaa, Gurusankar Gopalakrishnan, Devendra Govil, Josef Hoppe, Maneel Reddy Karri, Jude Khouja, Manuel Lecha, Neal Livesay, Jan Meißner, Soham Mukherjee, Alexander Nikitin, Theodore
We introduce topox, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes. topox consists of three packages: toponetx facilitates constructing and computing on these domains, including working with nodes, edges and higher-order
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Reproducibility, energy efficiency and performance of pseudorandom number generators in machine learning: a comparative study of python, numpy, tensorflow, and pytorch implementations arXiv.cs.MS Pub Date : 2024-01-30 Benjamin Antunes, David R. C Hill
Pseudo-Random Number Generators (PRNGs) have become ubiquitous in machine learning technologies because they are interesting for numerous methods. The field of machine learning holds the potential for substantial advancements across various domains, as exemplified by recent breakthroughs in Large Language Models (LLMs). However, despite the growing interest, persistent concerns include issues related
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Shortcutting Cross-Validation: Efficiently Deriving Column-Wise Centered and Scaled Training Set $\mathbf{X}^\mathbf{T}\mathbf{X}$ and $\mathbf{X}^\mathbf{T}\mathbf{Y}$ Without Full Recomputation of Matrix Products or Statistical Moments arXiv.cs.MS Pub Date : 2024-01-24 Ole-Christian Galbo Engstrøm
Cross-validation is a widely used technique for assessing the performance of predictive models on unseen data. Many predictive models, such as Kernel-Based Partial Least-Squares (PLS) models, require the computation of $\mathbf{X}^{\mathbf{T}}\mathbf{X}$ and $\mathbf{X}^{\mathbf{T}}\mathbf{Y}$ using only training set samples from the input and output matrices, $\mathbf{X}$ and $\mathbf{Y}$, respectively
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Theorem Discovery Amongst Cyclic Polygons arXiv.cs.MS Pub Date : 2024-01-22 Philip ToddSaltire Software
We examine a class of geometric theorems on cyclic 2n-gons. We prove that if we take n disjoint pairs of sides, each pair separated by an even number of polygon sides, then there is a linear combination of the angles between those sides which is constant. We present a formula for the linear combination, which provides a theorem statement in terms of those angles. We describe a program which uses this
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PlasmoData.jl -- A Julia Framework for Modeling and Analyzing Complex Data as Graphs arXiv.cs.MS Pub Date : 2024-01-21 David L Cole, Victor M Zavala
Datasets encountered in scientific and engineering applications appear in complex formats (e.g., images, multivariate time series, molecules, video, text strings, networks). Graph theory provides a unifying framework to model such datasets and enables the use of powerful tools that can help analyze, visualize, and extract value from data. In this work, we present PlasmoData.jl, an open-source, Julia
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Scalable Automated Verification for Cyber-Physical Systems in Isabelle/HOL arXiv.cs.MS Pub Date : 2024-01-22 Jonathan Julián Huerta y Munive, Simon Foster, Mario Gleirscher, Georg Struth, Christian Pardillo Laursen, Thomas Hickman
We formally introduce IsaVODEs (Isabelle verification with Ordinary Differential Equations), a framework for the verification of cyber-physical systems. We describe the semantic foundations of the framework's formalisation in the Isabelle/HOL proof assistant. A user-friendly language specification based on a robust state model makes our framework flexible and adaptable to various engineering workflows
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A Simulation of Optimal Dryness When Moving in the Rain or Snow Using MATLAB arXiv.cs.MS Pub Date : 2024-01-22 Neil Zhao, Emilee Brockner, Asia Winslow, Megan Seraydarian
The classic question of whether one should walk or run in the rain to remain the least wet has inspired a myriad of solutions ranging from physically performing test runs in raining conditions to mathematically modeling human movement through rain. This manuscript approaches the classical problem by simulating movement through rainfall using MATLAB. Our simulation was generalizable to include snowfall
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Automated Completion of Statements and Proofs in Synthetic Geometry: an Approach based on Constraint Solving arXiv.cs.MS Pub Date : 2024-01-22 Salwa Tabet GonzalezUniversity of Strasbourg, Predrag JaničićUniversity of Belgrade, Julien NarbouxUniversity of Strasbourg
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn a conjecture with missing assumptions and with an under-specified goal into a proper theorem. Also, the proposed framework can help in completing a proof sketch
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Proceedings 14th International Conference on Automated Deduction in Geometry arXiv.cs.MS Pub Date : 2024-01-19 Pedro QuaresmaUniversity of Coimbra, Portugal, Zoltán KovácsThe Private University College of Education of the Diocese of Linz, Austria
ADG is a forum to exchange ideas and views, to present research results and progress, and to demonstrate software tools at the intersection between geometry and automated deduction. The conference is held every two years. The previous editions of ADG were held in Hagenberg in 2021 (online, postponed from 2020 due to COVID-19), Nanning in 2018, Strasbourg in 2016, Coimbra in 2014, Edinburgh in 2012
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Efficient N-to-M Checkpointing Algorithm for Finite Element Simulations arXiv.cs.MS Pub Date : 2024-01-11 David A. Ham, Vaclav Hapla, Matthew G. Knepley, Lawrence Mitchell, Koki Sagiyama
In this work, we introduce a new algorithm for N-to-M checkpointing in finite element simulations. This new algorithm allows efficient saving/loading of functions representing physical quantities associated with the mesh representing the physical domain. Specifically, the algorithm allows for using different numbers of parallel processes for saving and loading, allowing for restarting and post-processing
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Toward a comprehensive simulation framework for hypergraphs: a Python-base approach arXiv.cs.MS Pub Date : 2024-01-08 Quoc Chuong Nguyen, Trung Kien Le
Hypergraphs, or generalization of graphs such that edges can contain more than two nodes, have become increasingly prominent in understanding complex network analysis. Unlike graphs, hypergraphs have relatively few supporting platforms, and such dearth presents a barrier to more widespread adaptation of hypergraph computational toolboxes that could enable further research in several areas. Here, we
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KAXAI: An Integrated Environment for Knowledge Analysis and Explainable AI arXiv.cs.MS Pub Date : 2023-12-30 Saikat Barua, Dr. Sifat Momen
In order to fully harness the potential of machine learning, it is crucial to establish a system that renders the field more accessible and less daunting for individuals who may not possess a comprehensive understanding of its intricacies. The paper describes the design of a system that integrates AutoML, XAI, and synthetic data generation to provide a great UX design for users. The system allows users
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Ricci-Notation Tensor Framework for Model-Based Approaches to Imaging arXiv.cs.MS Pub Date : 2023-12-07 Dileepan JosephElectrical and Computer Engineering, University of Alberta
Model-based approaches to imaging, like specialized image enhancements in astronomy, favour physics-based models which facilitate explanations of relationships between observed inputs and computed outputs. While this paper features a tutorial example, inspired by exoplanet imaging, that reveals embedded 2D fast Fourier transforms in an image enhancement model, the work is actually about the tensor
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Impact of parallel code optimization on computer power consumption arXiv.cs.MS Pub Date : 2023-12-06 E. A. Kiselev, P. N. Telegin, A. V. Baranov
The increase in performance and power of computing systems requires the wider use of program optimizations. The goal of performing optimizations is not only to reduce program runtime, but also to reduce other computer resources including power consumption. The goal of the study was to evaluate the impact of different optimization levels and various optimization strategies on power consumption. In a
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Mathematical Supplement for the $\texttt{gsplat}$ Library arXiv.cs.MS Pub Date : 2023-12-04 Vickie Ye, Angjoo Kanazawa
This report provides the mathematical details of the gsplat library, a modular toolbox for efficient differentiable Gaussian splatting, as proposed by Kerbl et al. It provides a self-contained reference for the computations involved in the forward and backward passes of differentiable Gaussian splatting. To facilitate practical usage and development, we provide a user friendly Python API that exposes
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A Framework for Self-Intersecting Surfaces (SOS): Symmetric Optimisation for Stability arXiv.cs.MS Pub Date : 2023-12-04 Christian Amend, Tom Goertzen
In this paper, we give a stable and efficient method for fixing self-intersections and non-manifold parts in a given embedded simplicial complex. In addition, we show how symmetric properties can be used for further optimisation. We prove an initialisation criterion for computation of the outer hull of an embedded simplicial complex. To regularise the outer hull of the retriangulated surface, we present
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A New Challenging Curve Fitting Benchmark Test Set for Global Optimization Solvers arXiv.cs.MS Pub Date : 2023-12-04 Peicong Cheng, Peicheng Cheng
Benchmark sets are extremely important for evaluating and developing global optimization algorithms and related solvers. A new test set named PCC benchmark is proposed especially for optimization problem of nonlinear curve fitting for the first time, with the aspiration of investigating and comparing the performance of different global optimization solvers. Compared with the well-known classical nonlinear
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Lineax: unified linear solves and linear least-squares in JAX and Equinox arXiv.cs.MS Pub Date : 2023-11-28 Jason Rader, Terry Lyons, Patrick Kidger
We introduce Lineax, a library bringing linear solves and linear least-squares to the JAX+Equinox scientific computing ecosystem. Lineax uses general linear operators, and unifies linear solves and least-squares into a single, autodifferentiable API. Solvers and operators are user-extensible, without requiring the user to implement any custom derivative rules to get differentiability. Lineax is available
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Scale Ratio Tuning of Group Based Job Scheduling in HPC Systems arXiv.cs.MS Pub Date : 2023-11-29 Lyakhovets D. S., Baranov A. V., Telegin P. N
During the initialization of a supercomputer job, no useful calculations are performed. A high proportion of initialization time results in idle computing resources and less computational efficiency. Certain methods and algorithms combining jobs into groups are used to optimize scheduling of jobs with high initialization proportion. The article considers the influence of the scale ratio setting in
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Mathematical Modelling and a Numerical Solution for High Precision Satellite Ephemeris Determination arXiv.cs.MS Pub Date : 2023-11-25 Aravind Gundakaram, Abhirath Sangala, Aditya Sai Ellendula, Prachi Kansal, Lanii Lakshitaa, Suchir Reddy Punuru, Nethra Naveen, Sanjitha Jaggumantri
In this paper, we develop a high-precision satellite orbit determination model for satellites orbiting the Earth. Solving this model entails numerically integrating the differential equation of motion governing a two-body system, employing Fehlberg's formulation and the Runge-Kutta class of embedded integrators with adaptive stepsize control. Relevant primary perturbing forces included in this mathematical
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Exact Combinatorial Optimization with Temporo-Attentional Graph Neural Networks arXiv.cs.MS Pub Date : 2023-11-23 Mehdi Seyfi, Amin Banitalebi-Dehkordi, Zirui Zhou, Yong Zhang
Combinatorial optimization finds an optimal solution within a discrete set of variables and constraints. The field has seen tremendous progress both in research and industry. With the success of deep learning in the past decade, a recent trend in combinatorial optimization has been to improve state-of-the-art combinatorial optimization solvers by replacing key heuristic components with machine learning
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An Assessment of PC-mer's Performance in Alignment-Free Phylogenetic Tree Construction arXiv.cs.MS Pub Date : 2023-11-21 Saeedeh Akbari Rokn Abadi, Melika Honarmand, Ali Hajialinaghi, Somayyeh Koohi
Background: Sequence comparison is essential in bioinformatics, serving various purposes such as taxonomy, functional inference, and drug discovery. The traditional method of aligning sequences for comparison is time-consuming, especially with large datasets. To overcome this, alignment-free methods have emerged as an alternative approach, prioritizing comparison scores over alignment itself. These
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p-adaptive discontinuous Galerkin method for the shallow water equations on heterogeneous computing architectures arXiv.cs.MS Pub Date : 2023-11-19 Sara Faghih-Naini, Vadym Aizinger, Sebastian Kuckuk, Richard Angersbach, Harald Köstler
Heterogeneous computing and exploiting integrated CPU-GPU architectures has become a clear current trend since the flattening of Moore's Law. In this work, we propose a numerical and algorithmic re-design of a p-adaptive quadrature-free discontinuous Galerkin method (DG) for the shallow water equations (SWE). Our new approach separates the computations of the non-adaptive (lower-order) and adaptive
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Deriving Algorithms for Triangular Tridiagonalization a (Skew-)Symmetric Matrix arXiv.cs.MS Pub Date : 2023-11-17 Robert van de Geijn, Maggie Myers, RuQing G. Xu, Devin Matthews
We apply the FLAME methodology to derive algorithms hand in hand with their proofs of correctness for the computation of the $ L T L^T $ decomposition (with and without pivoting) of a skew-symmetric matrix. The approach yields known as well as new algorithms, presented using the FLAME notation. A number of BLAS-like primitives are exposed at the core of blocked algorithms that can attain high performance
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DisCoPy: the Hierarchy of Graphical Languages in Python arXiv.cs.MS Pub Date : 2023-11-17 Alexis Toumi, Richie Yeung, Boldizsár Poór, Giovanni de Felice
DisCoPy is a Python toolkit for computing with monoidal categories. It comes with two flexible data structures for string diagrams: the first one for planar monoidal categories based on lists of layers, the second one for symmetric monoidal categories based on cospans of hypergraphs. Algorithms for functor application then allow to translate string diagrams into code for numerical computation, be it
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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 arXiv.cs.MS Pub Date : 2023-11-16 Mark Stocks
We demonstrate a multiplication method based on numbers represented as set of polynomial radix 2 indices stored as an integer list. The 'polynomial integer index multiplication' method is a set of algorithms implemented in python code. We demonstrate the method to be faster than both the Number Theoretic Transform (NTT) and Karatsuba for multiplication within a certain bit range. Also implemented in
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Semidefinite Programming by Projective Cutting Planes arXiv.cs.MS Pub Date : 2023-11-15 Daniel Porumbel
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is still significantly harder to solve than a similar-size Linear Program (LP). It is well-known that a semidefinite program can be written as an LP with infinitely-many
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A Case Study in Analytic Protocol Analysis in ACL2 arXiv.cs.MS Pub Date : 2023-11-15 Max von HippelNortheastern University, Panagiotis ManoliosNortheastern University, Kenneth L. McMillanUniversity of Texas at Austin, Cristina Nita-RotaruNortheastern University, Lenore ZuckUniversity of Illinois Chicago
When verifying computer systems we sometimes want to study their asymptotic behaviors, i.e., how they behave in the long run. In such cases, we need real analysis, the area of mathematics that deals with limits and the foundations of calculus. In a prior work, we used real analysis in ACL2s to study the asymptotic behavior of the RTO computation, commonly used in congestion control algorithms across
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Cache Optimization and Performance Modeling of Batched, Small, and Rectangular Matrix Multiplication on Intel, AMD, and Fujitsu Processors arXiv.cs.MS Pub Date : 2023-11-11 Sameer Deshmukh, Rio Yokota, George Bosilca
Factorization and multiplication of dense matrices and tensors are critical, yet extremely expensive pieces of the scientific toolbox. Careful use of low rank approximation can drastically reduce the computation and memory requirements of these operations. In addition to a lower arithmetic complexity, such methods can, by their structure, be designed to efficiently exploit modern hardware architectures
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An Efficient Framework for Global Non-Convex Polynomial Optimization with Nonlinear Polynomial Constraints arXiv.cs.MS Pub Date : 2023-11-03 Mitchell Tong Harris, Pierre-David Letourneau, Dalton Jones, M. Harper Langston
We present an efficient framework for solving constrained global non-convex polynomial optimization problems. We prove the existence of an equivalent nonlinear reformulation of such problems that possesses essentially no spurious local minima. We show through numerical experiments that polynomial scaling in dimension and degree is achievable for computing the optimal value and location of previously
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$O(N)$ distributed direct factorization of structured dense matrices using runtime systems arXiv.cs.MS Pub Date : 2023-11-02 Sameer Deshmukh, Qinxiang Ma, Rio Yokota, George Bosilca
Structured dense matrices result from boundary integral problems in electrostatics and geostatistics, and also Schur complements in sparse preconditioners such as multi-frontal methods. Exploiting the structure of such matrices can reduce the time for dense direct factorization from $O(N^3)$ to $O(N)$. The Hierarchically Semi-Separable (HSS) matrix is one such low rank matrix format that can be factorized
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NoMoPy: Noise Modeling in Python arXiv.cs.MS Pub Date : 2023-10-31 Dylan Albrecht, N. Tobias Jacobson
NoMoPy is a code for fitting, analyzing, and generating noise modeled as a hidden Markov model (HMM) or, more generally, factorial hidden Markov model (FHMM). This code, written in Python, implements approximate and exact expectation maximization (EM) algorithms for performing the parameter estimation process, model selection procedures via cross-validation, and parameter confidence region estimation
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Performance Optimization of Deep Learning Sparse Matrix Kernels on Intel Max Series GPU arXiv.cs.MS Pub Date : 2023-11-01 Mohammad Zubair, Christoph Bauinger
In this paper, we focus on three sparse matrix operations that are relevant for machine learning applications, namely, the sparse-dense matrix multiplication (SPMM), the sampled dense-dense matrix multiplication (SDDMM), and the composition of the SDDMM with SPMM, also termed as FusedMM. We develop optimized implementations for SPMM, SDDMM, and FusedMM operations utilizing Intel oneAPI's Explicit SIMD
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Factor Fitting, Rank Allocation, and Partitioning in Multilevel Low Rank Matrices arXiv.cs.MS Pub Date : 2023-10-30 Tetiana Parshakova, Trevor Hastie, Eric Darve, Stephen Boyd
We consider multilevel low rank (MLR) matrices, defined as a row and column permutation of a sum of matrices, each one a block diagonal refinement of the previous one, with all blocks low rank given in factored form. MLR matrices extend low rank matrices but share many of their properties, such as the total storage required and complexity of matrix-vector multiplication. We address three problems that
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A Survey of Methods for Estimating Hurst Exponent of Time Sequence arXiv.cs.MS Pub Date : 2023-10-29 Hong-Yan Zhang, Zhi-Qiang Feng, Si-Yu Feng, Yu Zhou
The Hurst exponent is a significant indicator for characterizing the self-similarity and long-term memory properties of time sequences. It has wide applications in physics, technologies, engineering, mathematics, statistics, economics, psychology and so on. Currently, available methods for estimating the Hurst exponent of time sequences can be divided into different categories: time-domain methods
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Tackling the Matrix Multiplication Micro-kernel Generation with Exo arXiv.cs.MS Pub Date : 2023-10-26 Adrián Castelló, Julian Bellavita, Grace Dinh, Yuka Ikarashi, Héctor Martínez
The optimization of the matrix multiplication (or GEMM) has been a need during the last decades. This operation is considered the flagship of current linear algebra libraries such as BLIS, OpenBLAS, or Intel OneAPI because of its widespread use in a large variety of scientific applications. The GEMM is usually implemented following the GotoBLAS philosophy, which tiles the GEMM operands and uses a series
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HyperNetX: A Python package for modeling complex network data as hypergraphs arXiv.cs.MS Pub Date : 2023-10-17 Brenda Praggastis, Sinan Aksoy, Dustin Arendt, Mark Bonicillo, Cliff Joslyn, Emilie Purvine, Madelyn Shapiro, Ji Young Yun
HyperNetX (HNX) is an open source Python library for the analysis and visualization of complex network data modeled as hypergraphs. Initially released in 2019, HNX facilitates exploratory data analysis of complex networks using algebraic topology, combinatorics, and generalized hypergraph and graph theoretical methods on structured data inputs. With its 2023 release, the library supports attaching
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A Number Representation Systems Library Supporting New Representations Based on Morris Tapered Floating-point with Hidden Exponent Bit arXiv.cs.MS Pub Date : 2023-10-15 Stefan-Dan Ciocirlan, Dumitrel Loghin
The introduction of posit reopened the debate about the utility of IEEE754 in specific domains. In this context, we propose a high-level language (Scala) library that aims to reduce the effort of designing and testing new number representation systems (NRSs). The library's efficiency is tested with three new NRSs derived from Morris Tapered Floating-Point by adding a hidden exponent bit. We call these
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Algorithm xxxx: HiPPIS A High-Order Positivity-Preserving Mapping Software for Structured Meshes arXiv.cs.MS Pub Date : 2023-10-13 Timbwaoga A. J. Ouermi, Robert M Kirby, Martin Berzins
Polynomial interpolation is an important component of many computational problems. In several of these computational problems, failure to preserve positivity when using polynomials to approximate or map data values between meshes can lead to negative unphysical quantities. Currently, most polynomial-based methods for enforcing positivity are based on splines and polynomial rescaling. The spline-based
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A Generic Software Framework for Distributed Topological Analysis Pipelines arXiv.cs.MS Pub Date : 2023-10-12 Eve Le Guillou, Michael Will, Pierre Guillou, Jonas Lukasczyk, Pierre Fortin, Christoph Garth, Julien Tierny
This system paper presents a software framework for the support of topological analysis pipelines in a distributed-memory model. While several recent papers introduced topology-based approaches for distributed-memory environments, these were reporting experiments obtained with tailored, mono-algorithm implementations. In contrast, we describe in this paper a general-purpose, generic framework for topological
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Smoothing Methods for Automatic Differentiation Across Conditional Branches arXiv.cs.MS Pub Date : 2023-10-05 Justin N. Kreikemeyer, Philipp Andelfinger
Programs involving discontinuities introduced by control flow constructs such as conditional branches pose challenges to mathematical optimization methods that assume a degree of smoothness in the objective function's response surface. Smooth interpretation (SI) is a form of abstract interpretation that approximates the convolution of a program's output with a Gaussian kernel, thus smoothing its output
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A directional regularization method for the limited-angle Helsinki Tomography Challenge using the Core Imaging Library (CIL) arXiv.cs.MS Pub Date : 2023-10-02 Jakob Sauer Jørgensen, Evangelos Papoutsellis, Laura Murgatroyd, Gemma Fardell, Edoardo Pasca
This article presents the algorithms developed by the Core Imaging Library (CIL) developer team for the Helsinki Tomography Challenge 2022. The challenge focused on reconstructing 2D phantom shapes from limited-angle computed tomography (CT) data. The CIL team designed and implemented five reconstruction methods using CIL (https://ccpi.ac.uk/cil/), an open-source Python package for tomographic imaging
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CausalGPS: An R Package for Causal Inference With Continuous Exposures arXiv.cs.MS Pub Date : 2023-10-01 Naeem Khoshnevis, Xiao Wu, Danielle Braun
Quantifying the causal effects of continuous exposures on outcomes of interest is critical for social, economic, health, and medical research. However, most existing software packages focus on binary exposures. We develop the CausalGPS R package that implements a collection of algorithms to provide algorithmic solutions for causal inference with continuous exposures. CausalGPS implements a causal inference
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Implicit Gaussian process representation of vector fields over arbitrary latent manifolds arXiv.cs.MS Pub Date : 2023-09-28 Robert L. Peach, Matteo Vinao-Carl, Nir Grossman, Michael David, Emma Mallas, David Sharp, Paresh A. Malhotra, Pierre Vandergheynst, Adam Gosztolai
Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed over non-Euclidean domains, including smooth manifolds appearing in numerous fields such as computer vision, dynamical systems, and neuroscience. However, these approaches
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Asymptote-based scientific animation arXiv.cs.MS Pub Date : 2023-09-30 Migran N. Gevorkyan, Anna V. Korolkova, Dmitry S. Kulyabov
This article discusses a universal way to create animation using Asymptote the language for vector graphics. The Asymptote language itself has a built-in library for creating animations, but its practical use is complicated by an extremely brief description in the official documentation and unstable execution of existing examples. The purpose of this article is to eliminate this gap. The method we
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Parallel local time stepping for rigid bodies represented by triangulated meshes arXiv.cs.MS Pub Date : 2023-09-27 Peter Noble, Tobias Weinzierl
Discrete Element Methods (DEM), i.e.~the simulation of many rigid particles, suffer from very stiff differential equations plus multiscale challenges in space and time. The particles move smoothly through space until they interact almost instantaneously due to collisions. Dense particle packings hence require tiny time step sizes, while free particles can advance with large time steps. Admissible time
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A Sparse Fast Chebyshev Transform for High-Dimensional Approximation arXiv.cs.MS Pub Date : 2023-09-26 Dalton Jones, Pierre-David Letourneau, Matthew J. Morse, M. Harper Langston
We present the Fast Chebyshev Transform (FCT), a fast, randomized algorithm to compute a Chebyshev approximation of functions in high-dimensions from the knowledge of the location of its nonzero Chebyshev coefficients. Rather than sampling a full-resolution Chebyshev grid in each dimension, we randomly sample several grids with varied resolutions and solve a least-squares problem in coefficient space
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pyPPG: A Python toolbox for comprehensive photoplethysmography signal analysis arXiv.cs.MS Pub Date : 2023-09-24 Marton A. Goda, Peter H. Charlton, Joachim A. Behar
Photoplethysmography is a non-invasive optical technique that measures changes in blood volume within tissues. It is commonly and increasingly used for in a variety of research and clinical application to assess vascular dynamics and physiological parameters. Yet, contrary to heart rate variability measures, a field which has seen the development of stable standards and advanced toolboxes and software
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Physics Informed Neural Network Code for 2D Transient Problems (PINN-2DT) Compatible with Google Colab arXiv.cs.MS Pub Date : 2023-09-24 Paweł Maczuga, Maciej Skoczeń, Przemysław Rożnawski, Filip Tłuszcz, Marcin Szubert, Marcin Łoś, Witold Dzwinel, Keshav Pingali, Maciej Paszyński
We present an open-source Physics Informed Neural Network environment for simulations of transient phenomena on two-dimensional rectangular domains, with the following features: (1) it is compatible with Google Colab which allows automatic execution on cloud environment; (2) it supports two dimensional time-dependent PDEs; (3) it provides simple interface for definition of the residual loss, boundary
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Unlocking massively parallel spectral proper orthogonal decompositions in the PySPOD package arXiv.cs.MS Pub Date : 2023-09-21 Marcin Rogowski, Brandon C. Y. Yeung, Oliver T. Schmidt, Romit Maulik, Lisandro Dalcin, Matteo Parsani, Gianmarco Mengaldo
We propose a parallel (distributed) version of the spectral proper orthogonal decomposition (SPOD) technique. The parallel SPOD algorithm distributes the spatial dimension of the dataset preserving time. This approach is adopted to preserve the non-distributed fast Fourier transform of the data in time, thereby avoiding the associated bottlenecks. The parallel SPOD algorithm is implemented in the PySPOD
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Ensemble Differential Evolution with Simulation-Based Hybridization and Self-Adaptation for Inventory Management Under Uncertainty arXiv.cs.MS Pub Date : 2023-09-22 Sarit Maitra, Vivek Mishra, Sukanya Kundu
This study proposes an Ensemble Differential Evolution with Simula-tion-Based Hybridization and Self-Adaptation (EDESH-SA) approach for inven-tory management (IM) under uncertainty. In this study, DE with multiple runs is combined with a simulation-based hybridization method that includes a self-adaptive mechanism that dynamically alters mutation and crossover rates based on the success or failure
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Satisfiability.jl: Satisfiability Modulo Theories in Julia arXiv.cs.MS Pub Date : 2023-09-15 Emiko Soroka, Mykel J. Kochenderfer, Sanjay Lall
Satisfiability modulo theories (SMT) is a core tool in formal verification. While the SMT-LIB specification language can be used to interact with theorem proving software, a high-level interface allows for faster and easier specifications of complex SMT formulae. In this paper we discuss the design and implementation of a novel publicly-available interface for interacting with SMT-LIB compliant solvers
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$\texttt{ChisholmD.wl}$- Automated rational approximant for bi-variate series arXiv.cs.MS Pub Date : 2023-09-14 Souvik Bera, Tanay Pathak
The Chisholm rational approximant is a natural generalization to two variables of the well-known single variable Pad\'e approximant, and has the advantage of reducing to the latter when one of the variables is set equals to 0. We present, to our knowledge, the first automated Mathematica package to evaluate diagonal Chisholm approximants of two variable series. For the moment, the package can only
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CDL: A fast and flexible library for the study of permutation sets with structural restrictions arXiv.cs.MS Pub Date : 2023-09-12 Bei Zhou, Klas Markstrōm, Søren Riis
In this paper, we introduce CDL, a software library designed for the analysis of permutations and linear orders subject to various structural restrictions. Prominent examples of these restrictions include pattern avoidance, a topic of interest in both computer science and combinatorics, and "never conditions" utilized in social choice and voting theory. CDL offers a range of fundamental functionalities
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Integration of Quantum Accelerators with High Performance Computing $\unicode{x2013}$ A Review of Quantum Programming Tools arXiv.cs.MS Pub Date : 2023-09-12 Amr Elsharkawy, Xiao-Ting Michelle To, Philipp Seitz, Yanbin Chen, Yannick Stade, Manuel Geiger, Qunsheng Huang, Xiaorang Guo, Muhammad Arslan Ansari, Christian B. Mendl, Dieter Kranzlmüller, Martin Schulz
Quantum computing (QC) introduces a novel mode of computation with the possibility of greater computational power that remains to be exploited $\unicode{x2013}$ presenting exciting opportunities for high performance computing (HPC) applications. However, recent advancements in the field have made clear that QC does not supplant conventional HPC, but can rather be incorporated into current heterogeneous
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A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale arXiv.cs.MS Pub Date : 2023-09-12 Hao-Jun Michael Shi, Tsung-Hsien Lee, Shintaro Iwasaki, Jose Gallego-Posada, Zhijing Li, Kaushik Rangadurai, Dheevatsa Mudigere, Michael Rabbat
Shampoo is an online and stochastic optimization algorithm belonging to the AdaGrad family of methods for training neural networks. It constructs a block-diagonal preconditioner where each block consists of a coarse Kronecker product approximation to full-matrix AdaGrad for each parameter of the neural network. In this work, we provide a complete description of the algorithm as well as the performance
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A Distributed Algebra System for Time Integration on Parallel Computers arXiv.cs.MS Pub Date : 2023-09-11 Abhinav Singh, Landfried Kraatz, Pietro Incardona, Ivo F. Sbalzarini
We present a distributed algebra system for efficient and compact implementation of numerical time integration schemes on parallel computers and graphics processing units (GPU). The software implementation combines the time integration library Odeint from Boost with the OpenFPM framework for scalable scientific computing. Implementing multi-stage, multi-step, or adaptive time integration methods in
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A Novel Immersed Boundary Approach for Irregular Topography with Acoustic Wave Equations arXiv.cs.MS Pub Date : 2023-09-07 Edward Caunt, Rhodri Nelson, Fabio Luporini, Gerard Gorman
Irregular terrain has a pronounced effect on the propagation of seismic and acoustic wavefields but is not straightforwardly reconciled with structured finite-difference (FD) methods used to model such phenomena. Methods currently detailed in the literature are generally limited in scope application-wise or non-trivial to apply to real-world geometries. With this in mind, a general immersed boundary
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Enhancing Missing Data Imputation of Non-stationary Signals with Harmonic Decomposition arXiv.cs.MS Pub Date : 2023-09-08 Joaquin Ruiz, Hau-tieng Wu, Marcelo A. Colominas
Dealing with time series with missing values, including those afflicted by low quality or over-saturation, presents a significant signal processing challenge. The task of recovering these missing values, known as imputation, has led to the development of several algorithms. However, we have observed that the efficacy of these algorithms tends to diminish when the time series exhibit non-stationary