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arXiv 2024年

作者： Hyeon, Sieun Jung, Kyudan Won, Jaehee Kim, Nam-Joon Ryu, Hyun Gon Lee, Hyuk-Jae Do, Jaeyoung Department of Electrical and Computer Engineering Seoul National University Korea Republic of Department of Mathematics Chung-Ang University Korea Republic of College of Liberal Studies Seoul National University Korea Republic of NVIDIA United States Interdisciplinary Program in Artificial Intelligence Seoul National University Korea Republic of

In various academic and professional settings, such as mathematics lectures or research presentations, it is often necessary to convey mathematical expressions orally. However, reading mathematical expressions aloud without accompanying visuals can significantly hinder comprehension, especially for those who are hearing-impaired or rely on subtitles due to language barriers. For instance, when a presenter reads Euler’s Formula, current Automatic Speech Recognition (ASR) models often produce a verbose and error-prone textual description (e.g., e to the power of i x equals cosine of x plus i side of x), instead of the concise LATEX format (i.e., eix = cos(x) + isin(x)), which hampers clear understanding and communication. To address this issue, we introduce MathSpeech, a novel pipeline that integrates ASR models with small Language Models (sLMs) to correct errors in mathematical expressions and accurately convert spoken expressions into structured LATEX representations. Evaluated on a new dataset derived from lecture recordings, MathSpeech demonstrates LATEX generation capabilities comparable to leading commercial Large Language Models (LLMs), while leveraging fine-tuned small language models of only 120M parameters. Specifically, in terms of CER, BLEU, and ROUGE scores for LATEX translation, MathSpeech demonstrated significantly superior capabilities compared to GPT-4o. We observed a decrease in CER from 0.390 to 0.298, and higher ROUGE/BLEU scores compared to GPT-4o. Copyright © 2024, The Authors. All rights reserved.

关键词： Speech recognition

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Random Measures, ANOVA Models and Quantifying Uncertainty in Randomized Controlled Trials

arXiv

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arXiv 2023年

作者： Bastian, Caleb Deen Rabitz, Herschel Rempala, Grzegorz A. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Mathematics The Ohio State University ColumbusOH43210 United States Division of Biostatistics The Ohio State University ColumbusOH43210 United States

This short paper introduces a novel approach to global sensitivity analysis, grounded in the variance-covariance structure of random variables derived from random measures. The proposed methodology facilitates the application of information-theoretic rules for uncertainty quantification, offering several advantages. Specifically, the approach provides valuable insights into the decomposition of variance within discrete subspaces, similar to the standard ANOVA analysis. To illustrate this point, the method is applied to datasets obtained from the analysis of randomized controlled trials on evaluating the efficacy of the COVID-19 vaccine and assessing clinical endpoints in a lung cancer *** Codes 92-05, 92-11 Copyright © 2023, The Authors. All rights reserved.

关键词： Sensitivity analysis

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Interactions of solitary waves in the Adlam-Allen model

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Physical Review E 2022年第3期106卷 034209-034209页

作者： Boris A. Malomed Panayotis G. Kevrekidis Vassilis Koukouloyannis Nathaniel Whitaker Dimitrios J. Frantzeskakis Department of Interdisciplinary Studies Faculty of Engineering Tel Aviv University Tel Aviv 69978 Israel Instituto de Alta Investigación Universidad de Tarapacá Casilla 7D Arica Chile Department of Mathematics Statistics University of Massachusetts Amherst Massachusetts 01003-4515 USA Department of Mathematics Laboratory of Applied Mathematics and Mathematical Modelling University of the Aegean Karlovasi 83200 Samos Greece Department of Physics National and Kapodistrian University of Athens Panepistimiopolis Zografos Athens 15784 Greece

We study the interactions of two or more solitary waves in the Adlam-Allen model describing the evolution of a (cold) plasma of positive and negative charges, in the presence of electric and transverse magnetic fields. In order to show that the interactions feature an exponentially repulsive nature, we elaborate two distinct approaches: (a) using energetic considerations and the Hamiltonian structure of the model, and (b) using the so-called Manton method. We compare these findings with results of direct simulations, and we identify adjustments necessary to achieve a quantitative match between them. Additional connections are made, such as with solitons of the Korteweg–de Vries equation. New challenges are identified in connection to this model and its solitary waves.

关键词： Pattern formation

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Atomistic Behavior of Deformed Au Thin Film during the Indentation Process 4

Atomistic Behavior of Deformed Au Thin Film during the Inden...

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4th International Conference on Innovative Research in applied Science, Engineering and Technology, IRASET 2024

作者： Ou-Khouya, Abdelkarim Mes-Adi, Hassane Taoufiki, Meryem Ibrahim, Imane Ait El Harfouf, Amin Herbazi, Rachid Tahiri, Mohamed Khouribga National School Of Applied Sciences Sultan Moulay Slimane University Process Engineering Computer Science And Mathematics Laboratory Khouribga25000 Morocco Sultan Moulay Slimane University Faculty Of Sciences And Techniques Sustainable Development Laboratory Beni-Mellal Morocco Mohamed V University Laboratory Of Condensed Matter And Interdisciplinary Sciences Cnrst Labeled Research Unit Faculty Of Sciences Departement Of Physics Rabat Morocco University Of Sultan Moulay Slimane Polydisciplinary Faculty Of Khouribga Department Of Physics Khouribga Morocco Tangier Morocco

ISBN: (纸本)9798350309508

In this study, we investigate the mechanical properties of gold (Au) materials using molecular dynamics simulations. In this simulation, the nanoindentation process was performed to analyze the deformation defects and hardness properties of Au under different indentation velocities. The results suggest that the deformation behavior of the Au specimen was affected by different indentation velocities. These findings were confirmed by examining the load-displacement curve, which indicated elastic deformation through the appearance of a linear load-displacement relationship at low indentation velocities. In contrast, plastic deformation was identified by the presence of intensified serrations in the load-displacement curve at higher indentation velocities. Under such conditions, the hardness exhibited minimal variation when the indenter velocity increased from 5 mls to 10 mls. However, a significant increase in hardness was noted when the indentation velocity was further raised to 15 mls. © 2024 IEEE.

关键词： Molecular dynamics

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Fast decisions reflect biases, slow decisions do not

arXiv

引用

arXiv 2023年

作者： Linn, Samantha Lawley, Sean D. Karamched, Bhargav R. Kilpatrick, Zachary P. Josić, Krešimir Department of Mathematics University of Utah Salt Lake CityUT United States Department of Mathematics Florida State University TallahasseeFL32306 United States Institute of Molecular Biophysics Florida State University TallahasseeFL32306 United States Program in Neuroscience Florida State University TallahasseeFL32306 United States Department of Applied Mathematics University of Colorado Boulder BoulderCO80309 United States Department of Mathematics University of Houston HoustonTX77004 United States Department of Biology and Biochemistry University of Houston HoustonTX77004 United States

Decisions are often made by heterogeneous groups of individuals, each with distinct initial biases and access to information of different quality. We show that in large groups of independent agents who accumulate evidence the first to decide are those with the strongest initial biases. Their decisions align with their initial bias, regardless of the underlying truth. In contrast, agents who decide last make decisions as if they were initially unbiased, and hence make better choices. We obtain asymptotic expressions in the large population limit that quantify how agents’ initial inclinations shape early decisions. Our analysis shows how bias, information quality, and decision order interact in non-trivial ways to determine the reliability of decisions in a group. © 2023, CC BY.

关键词： Reliability analysis

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Benchmarking the Immersed Boundary Method for Viscoelastic Flows

arXiv

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arXiv 2023年

作者： Gruninger, Cole Barrett, Aaron Fang, Fuhui Forest, M. Gregory Griffith, Boyce E. Department of Mathematics University North Carolina Chapel HillNC United States Department of Mathematics University of Utah Salt Lake CityUT United States Department of Applied Physical Sciences University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

We present and analyze a series of benchmark tests regarding the application of the immersed boundary (IB) method to viscoelastic flows through and around non-trivial, stationary geometries. The IB method is widely used for the simulation of biological fluid dynamics and other modeling scenarios where a structure is immersed in a fluid. Although the IB method has been most commonly used to model systems with viscous incompressible fluids, it also can be applied to visoelastic fluids, and has enabled the study of a wide variety of dynamical problems including the settling of vesicles and the swimming of elastic filaments in fluids modeled by the Oldroyd-B constuitive equation. However, to date, relatively little work has explored the accuracy or convergence properties of the numerical scheme. Herein, we present benchmarking results for an IB solver applied to viscoelastic flows in and around non-trivial geometries using the idealized Oldroyd-B and more realistic, polymer-entanglement-based Rolie-Poly constitutive equations. We use two-dimensional numerical test cases along with results from rheology experiments to benchmark the IB method and compare it to more complex finite element and finite volume viscoelastic flow solvers. Additionally, we analyze different choices of regularized delta function and relative Lagrangian grid spacings which allow us to identify and recommend the key choices of these numerical parameters depending on the present flow regime. Copyright © 2023, The Authors. All rights reserved.

关键词： Benchmarking

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HiPoNet: A Topology-Preserving Multi-View Neural Network For High Dimensional Point Cloud and Single-Cell Data

arXiv

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arXiv 2025年

作者： Viswanath, Siddharth Madhu, Hiren Bhaskar, Dhananjay Kovalic, Jake Johnson, Dave Ying, Rex Tape, Christopher Adelstein, Ian Perlmutter, Michael Krishnaswamy, Smita Department of Computer Science Yale University New Haven United States Department of Genetics Yale University New Haven United States Department of Applied Physics Yale University New Haven United States Program in Computing Boise State University Idaho United States Cell Communication Lab Department of Oncology University College London Cancer Institute London United Kingdom Department of Mathematics Yale University New Haven United States Department of Mathematics Boise State University Idaho United States Computational Biology and Bioinformatics Program Yale University New Haven United States Wu-Tsai Institute Yale University New Haven United States Program for Applied Math Yale University New Haven United States

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Single-cell data can have high dimensionality exceeding the capabilities of existing methods for point clouds which are tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e. one on every patient), necessitating models that can process large, high-dimensional point clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric information. In contrast, HiPoNet forms higher-order simplicial complexes through learnable feature reweighting, generating multiple data views that disentangle distinct biological processes. It then employs simplicial wavelet transforms to extract multiscale features—capturing both local and global topology. We empirically show that these components preserve topological information in the learned representations, and that HiPoNet significantly outperforms state-of-the-art point-cloud and graph-based models on single cell. We also show an application of HiPoNet on spatial transcriptomics datasets using spatial co-ordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis. © 2025, CC BY.

关键词： Network topology

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Modeling High-Resolution Spatio-Temporal Wind with Deep Echo State Networks and Stochastic Partial Differential Equations

arXiv

引用

arXiv 2024年

作者： Wang, Kesen Kim, Minwoo Castruccio, Stefano Genton, Marc G. Statistics Program King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistics Pusan National University Busan46241 Korea Republic of Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States

In the past decades, clean and renewable energy has gained increasing attention due to a global effort on carbon footprint reduction. In particular, Saudi Arabia is gradually shifting its energy portfolio from an exclusive use of oil to a reliance on renewable energy, and, in particular, wind. Modeling wind for assessing potential energy output in a country as large, geographically diverse and understudied as Saudi Arabia is a challenge which implies highly non-linear dynamic structures in both space and time. To address this, we propose a spatio-temporal model whose spatial information is first reduced via an energy distance-based approach and then its dynamical behavior is informed by a sparse and stochastic recurrent neural network (Echo State Network). Finally, the full spatial data is reconstructed by means of a non-stationary stochastic partial differential equation-based approach. Our model can capture the fine scale wind structure and produce more accurate forecasts of both wind speed and energy in lead times of interest for energy grid management and save annually as much as one million dollar against the closest competitive model. © 2024, CC BY.

关键词： Clean energy

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Commercial Versus Natural Activated Carbon Fabricated Sheets: applied to Dyes Removal Application

引用

Macromolecular Symposia 2024年第2期413卷 2300046-2300046页

作者： Alrefaey, Khlood A. Mohamed, Nora Husien, Sh. Fahim, Irene Samy Said, Lobna A. Radwan, Ahmed G. School of Engineering and Applied Sciences Nile University Giza12613 Egypt Industrial Engineering program SESC Research Center Nile University Giza12613 Egypt Nile University Giza12613 Egypt Engineering Mathematics and Physics Department Faculty of Engineering Cairo University Giza12613 Egypt

Industrial dyes are considered one of the main causes of increased water pollution of water. Many businesses, such as steel and paper, are located along riverbanks because they require large amounts of water in their manufacturing processes, and their wastes, which contain acids, alkalis, dyes, and other chemicals, are dumped and poured into rivers as effluents. For example, chemical enterprises producing aluminum emit a significant quantity of fluoride into the air and effluents into water bodies. Fertilizer facilities produce a lot of ammonia, whereas steel plants produce cyanide. Many nations consider employing wastewater treatment plants using physical, biological, and chemical methods to clean the wastewater to address environmental crises. The treated water can be used for targeting the irrigation systems in its majority, as it is biologically acceptable for that specific use, industrial dyes are considered one of the leading causes of increased water pollution of water. Many businesses, such as steel and paper, are located along riverbanks because they require large amounts of water in their manufacturing processes, and their wastes, which contain acids, alkalis, dyes, and other chemicals, are dumped and poured into rivers as effluents. For example, chemical enterprises producing aluminum emit a significant quantity of fluoride into the air and effluents into water bodies. Fertilizer facilities produce much ammonia, whereas steel plants produce cyanide. Chromium salts are used in. Many nations consider employing wastewater treatment plants using physical, biological, and chemical methods to clean the wastewater to address environmental crises. The treated water can target the majority of irrigation systems, as it is biologically acceptable for that specific use, which economizes the use of freshwater sources for municipal use. This study presents a novel method for fabricating an efficient adsorbent sheet for wastewater treatment. The sheets are fabricated by

关键词： Activated carbon

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Discrete null field equation methods for solving Laplace's equation: Boundary layer computations

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Numerical Methods for Partial Differential Equations 2024年第4期40卷 e23092-e23092页

作者： Zhang, Li-Ping Li, Zi-Cai Lee, Ming-Gong Huang, Hung-Tsai School of Mathematical Sciences Qufu Normal University Shandong Qufu China Department of Applied Mathematics National Sun Yat-sen University Kaohsiung Taiwan Department of Tourism and Leisure/Ph.D. Program in Engineering Science Chung Hua University Hsinchu Taiwan Department of Data Science and Analytics I-Shou University Kaohsiung Taiwan

Consider Dirichlet problems of Laplace's equation in a bounded simply-connected domain (Formula presented.), and use the null field equation (NFE) of Green's representation formulation, where the source nodes (Formula presented.) are located on a pseudo-boundary (Formula presented.) outside (Formula presented.) but not close to its boundary (Formula presented.). Simple algorithms are proposed in this article by using the central rule for the NFE, and the normal derivatives (Formula presented.) of the solutions on the boundary (Formula presented.) can be easily obtained. These algorithms are called the discrete null field equation method (DNFEM) because the collocation equations are, indeed, the direct discrete form of the NFE. The bounds of the condition number are like those by the method of fundamental solutions (MFS) yielding the exponential growth as the number of unknowns increases. One trouble of the DNFEM is the near singularity of integrations for the solutions in boundary layers in Green's representation formulation. The traditional BEM also suffers from the same trouble. To deal with the near singularity, quadrature by expansions and the sinh transformation are often used. To handle this trouble, however, we develop two kinds of new techniques: (I) the interpolation techniques by Taylor's formulas with piecewise (Formula presented.) -degree polynomials and the Fourier series, and (II) the mini-rules of integrals, such as the mini-Simpson's and the mini-Gaussian rules. Error analysis is made for technique I to achieve optimal convergence rates. Numerical experiments are carried out for disk domains to support the theoretical analysis made. The numerical performance of the DNFEM is excellent for disk domains to compete with the MFS. The errors with (Formula presented.) can be obtained by combination algorithms, which are satisfactory for most engineering problems. In summary, the new simple DNFEM is based on the NFE, which is different from the boundary elem

关键词： Fourier series

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