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Reactive particle-tracking solutions to a benchmark problem on heavy metal cycling in lake sediments

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arXiv 2019年

作者： Schmidt, Michael J. Pankavich, Stephen D. Navarre-Sitchler, Alexis Engdah, Nicholas B. Bolster, Diogo Benson, David A. Department of Civil and Environmental Engineering and Earth Sciences University of Notre Dame Notre DameIN46556 United States Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States Hydrologic Science and Engineering Program Department of Geology and Geological Engineering Colorado School of Mines GoldenCO80401 United States Department of Civil and Environmental Engineering Washington State University PullmanWA99164 United States

Geochemical systems are known to exhibit highly variable spatiotemporal behavior. This may be observed both in non-smooth concentration curves in space for a single sampling time and also in variability between samples taken from the same location at different times. However, most models that are designed to simulate these systems provide only single-solution smooth curves and fail to capture the noise and variability seen in the data. We apply a recently developed reactive particle-tracking method to a system that displays highly-complex geochemical behavior. When the method is made to most closely resemble a corresponding Eulerian method, in its unperturbed form, we see near-exact match between solutions of the two models. More importantly, we consider two approaches for perturbing the model and find that the spatially-perturbed condition is able to capture a greater degree of the variability present in the data. This method of perturbation is a task to which particle methods are uniquely suited and Eulerian models are not well-suited. Additionally, because of the nature of the algorithm, noisy spatial gradients can be highly resolved by a large number of mobile particles, and this incurs negligible computational cost, as compared to expensive chemistry calculations. Copyright © 2019, The Authors. All rights reserved.

关键词： Heavy metals

Identifying Equivalent Training Dynamics

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arXiv 2023年

作者： Redman, William T. Bello-Rivas, Juan Fonoberova, Maria Mohr, Ryan Kevrekidis, Yannis Mezić, Igor AIMdyn Inc. United States Interdepartmental Program in Dynamical Neuroscience UC Santa Barbara United States Department of Chemical and Biomolecular Engineering Whiting School of Engineering Johns Hopkins University United States Departments of Applied Mathematics and Statistics Johns Hopkins University United States Department of Mechanical Engineering UC Santa Barbara United States Department of Mathematics UC Santa Barbara United States

Study of the nonlinear evolution deep neural network (DNN) parameters undergo during training has uncovered regimes of distinct dynamical behavior. While a detailed understanding of these phenomena has the potential to advance improvements in training efficiency and robustness, the lack of methods for identifying when DNN models have equivalent dynamics limits the insight that can be gained from prior work. Topological conjugacy, a notion from dynamical systems theory, provides a precise definition of dynamical equivalence, offering a possible route to address this need. However, topological conjugacies have historically been challenging to compute. By leveraging advances in Koopman operator theory, we develop a framework for identifying conjugate and non-conjugate training dynamics. To validate our approach, we demonstrate that comparing Koopman eigenvalues can correctly identify a known equivalence between online mirror descent and online gradient descent. We then utilize our approach to: (a) identify non-conjugate training dynamics between shallow and wide fully connected neural networks;(b) characterize the early phase of training dynamics in convolutional neural networks;(c) uncover non-conjugate training dynamics in Transformers that do and do not undergo grokking. Our results, across a range of DNN architectures, illustrate the flexibility of our framework and highlight its potential for shedding new light on training dynamics. © 2023, CC BY.

关键词： Topology

Simulating local fields in carbon nanotube reinforced composites for infinite strip with voids

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arXiv 2021年

作者： Nasser, Mohamed M.S. Kalmoun, El Mostafa Mityushev, Vladimir Rylko, Natalia Mathematics Program Department of Mathematics Statistics and Physics College of Arts and Sciences Qatar University Doha Qatar School of Science and Engineering Al Akhawayn University in Ifrane PO Box 104 Ifrane53000 Morocco Faculty of Computer Science and Telecommunications Cracow University of Technology Kraków Poland

We consider the steady heat conduction problem within a thermal isotropic and homogeneous infinite strip composite reinforced by uniformly and randomly distributed non-overlapping carbon nanotubes (CNTs) and containing voids. We treat the CNTs as thin perfectly conducting elliptic inclusions and assume the voids to be of circular shape and act as barriers to heat flow. We also impose isothermal conditions on the external boundaries by assuming the lower infinite wall to be a heater under a given temperature, and the upper wall to be a cooler that can be held at a lower fixed temperature. The equations for the temperature distribution are governed by the two-dimensional Laplace equation with mixed Dirichlet-Neumann boundary conditions. The resulting boundary value problem is solved using the boundary integral equation with the generalized Neumann kernel. We illustrate the performance of the proposed method through several numerical examples including the case of the presence a large number of CNTs and voids. © 2021, CC BY-NC-ND.

关键词： Carbon nanotubes

Modeling of Measurement Error in Financial Returns Data

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arXiv 2024年

作者： Jasra, Ajay Maama, Mohamed Mijatović, Aleksandar School of Data Science The Chinese University of Hong Kong Shenzhen China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistics University of Warwick United Kingdom

In this paper we consider the modeling of measurement error for fund returns data. In particular, given access to a time-series of discretely observed log-returns and the associated maximum over the observation period, we develop a stochastic model which models the true log-returns and maximum via a Lévy process and the data as a measurement error there-of. The main technical difficulty of trying to infer this model, for instance Bayesian parameter estimation, is that the joint transition density of the return and maximum is seldom known, nor can it be simulated exactly. Based upon the novel stick breaking representation of [12] we provide an approximation of the model. We develop a Markov chain Monte Carlo (MCMC) algorithm to sample from the Bayesian posterior of the approximated posterior and then extend this to a multilevel MCMC method which can reduce the computational cost to approximate posterior expectations, relative to ordinary MCMC. We implement our methodology on several applications including for real data. Copyright © 2024, The Authors. All rights reserved.

关键词： Markov chains

Electric Vehicle Charging Diversity Factors

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Electric Vehicle Charging Diversity Factors

Compatibility in Power Electronics (CPE)

作者： Luiz Artur Pecorelli Peres José Francisco Moreira Pessanha Antonio Guilherme Garcia Lima Windson Braga Pereira Electrical Engineering Department UERJ - State University of Rio de Janeiro (Professor) Rio de Janeiro Brazil UERJ - State University of Rio de Janeiro (Professor) IME - Institute of Mathematics and Statistics Rio de Janeiro Brazil UERJ - State University of Rio de Janeiro (Student) Mechanical Engineering Postgraduate Program Rio de Janeiro Brazil

ISBN: (数字)9781728142180

ISBN: (纸本)9781728142197

This paper presents the determination of diversity factors related to the increased demand when charging EVs, electric vehicles, and focuses on the adequacy of distribution network capacity. The work aimed to meet the R&D project "Smart City Búzios" proposed by ENEL Distribuição Rio within the scope of the National Electric Energy Agency - ANEEL. The treated results of several measurements of EV charging characteristics provided the basis to estimate the increase in electricity demand. Deterministic and stochastic analyzes considering the influence of the distance previously traveled by the vehicle and the moment of its connection to the network were compared, allowed to obtain the diversity factor. This study shows the influence of the connection moment to recharge EVs in predicting the capacity of transformers as well as the need for their stochastic treatment. Therefore, the results recommended implementing communication systems to offer attractive tariffs aiming at shifting the recharging of EVs to daily times of lower demand.

关键词： Batteries Load modeling Electric vehicle charging Standards Reactive power Charge measurement

Sixth-order Compact Extended Trapezoidal Rules for 2D Schr(o)dinger Equation

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数学研究 2015年第1期48卷 30-52页

作者： Xiao-Hui Liu Yu-Jiang Wu Jin-Yun Yuan Raimundo J.B.de Sampaio Yan-Tao Wang School of Mathematics and Statistics Lanzhou University Lanzhou 730000 GansuP.R.China School of Mathematics and Statistics Lanzhou University Lanzhou 730000 GansuP.R.China Key Laboratory of Applied Mathematics and Complex Systems Lanzhou 730000Gansu P.R.China Department of Mathematics Federal University of Paraná Centro Politecnico CP:19.081 81531-980 Curitiba PR Brazil Graduate Program in Production and Systems Engineering Pontifical Catholic University of Paraná CEP: 81611-970 Curitiba PR Brazil

Based on high-order linear multistep methods (LMMs), we use the class of extended trapezoidal rules (ETRs) to solve boundary value problems of ordinary differential equations (ODEs), whose numerical solutions can be approximated by boundary value methods (BVMs). Then we combine this technique with fourth-order Padé compact approximation to discrete 2D Schrödinger equation. We propose a scheme with sixth-order accuracy in time and fourth-order accuracy in space. It is unconditionally stable due to the favourable property of BVMs and ETRs. Furthermore, with Richardson extrapolation, we can increase the scheme to order 6 accuracy both in time and space. Numerical results are presented to illustrate the accuracy of our scheme.

关键词： Schr(o)dinger equation BVMs ETRs compact scheme Richardson extrapolation

Bridging the Gap: Towards an Expanded Toolkit for AI-Driven Decision-Making in the Public Sector

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arXiv 2023年

作者： Fischer-Abaigar, Unai Kern, Christoph Barda, Noam Kreuter, Frauke Dept. of Statistics LMU Munich Germany Munich Center for Machine Learning Germany Joint Program in Survey Methodology University of Maryland United States Dept. of Software and Information Systems Engineering Dept. of Epidemiology Biostatistics and Community Health Sciences Ben-Gurion University of the Negev Israel

AI-driven decision-making systems are becoming instrumental in the public sector, with applications spanning areas like criminal justice, social welfare, financial fraud detection, and public health. While these systems offer great potential benefits to institutional decision-making processes, such as improved efficiency and reliability, these systems face the challenge of aligning machine learning (ML) models with the complex realities of public sector decision-making. In this paper, we examine five key challenges where misalignment can occur, including distribution shifts, label bias, the influence of past decision-making on the data side, as well as competing objectives and human-in-the-loop on the model output side. Our findings suggest that standard ML methods often rely on assumptions that do not fully account for these complexities, potentially leading to unreliable and harmful predictions. To address this, we propose a shift in modeling efforts from focusing solely on predictive accuracy to improving decision-making outcomes. We offer guidance for selecting appropriate modeling frameworks, including counterfactual prediction and policy learning, by considering how the model estimand connects to the decision-maker’s utility. Additionally, we outline technical methods that address specific challenges within each modeling approach. Finally, we argue for the importance of external input from domain experts and stakeholders to ensure that model assumptions and design choices align with real-world policy objectives, taking a step towards harmonizing AI and public sector objectives. © 2023, CC BY-NC-ND.

关键词： Crime

Parallel Approximations for High-Dimensional Multivariate Normal Probability Computation in Confidence Region Detection Applications

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Parallel Approximations for High-Dimensional Multivariate No...

International Symposium on Parallel and Distributed Processing (IPDPS)

作者： Xiran Zhang Sameh Abdulah Jian Cao Hatem Ltaief Ying Sun Marc G. Genton David E. Keyes Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Statistics Program King Abdullah University of Science and Technology Extreme Computing Research Center King Abdullah University of Science and Technology Thuwal Saudi Arabia Department of Mathematics The University of Houston Houston Texas USA

ISBN: (数字)9798350387117

ISBN: (纸本)9798350387124

Addressing the statistical challenge of computing the multivariate normal (MVN) probability in high dimensions holds significant potential for enhancing various applications. For example, the critical task of detecting confidence regions where a process probability surpasses a specific threshold is essential in diverse applications, such as pinpointing tumor locations in magnetic resonance imaging (MRI) scan images, determining hydraulic parameters in groundwater flow issues, and forecasting regional wind power to optimize wind turbine placement, among numerous others. One common way to compute high-dimensional MVN probabilities is the Separation-of-Variables (SOV) algorithm. This algorithm is known for its high computational complexity of O(n 3 ) and space complexity of O(n 2 ), mainly due to a Cholesky factorization operation for an n×n covariance matrix, where n represents the dimensionality of the MVN problem. This work proposes a high-performance computing framework that allows scaling the SOV algorithm and, subsequently, the confidence region detection algorithm. The framework leverages parallel linear algebra algorithms with a task-based programming model to achieve performance scalability in computing process probabilities, especially on large-scale systems. In addition, we enhance our implementation by incorporating Tile Low-Rank (TLR) approximation techniques to reduce algorithmic complexity without compromising the necessary accuracy. To evaluate the performance and accuracy of our framework, we conduct assessments using simulated data and a wind speed dataset. Our proposed implementation effectively handles high-dimensional multivariate normal (MVN) probability computations on shared and distributed-memory systems using finite precision arithmetics and TLR approximation computation. Performance results show a significant speedup of up to 20X in solving the MVN problem using TLR approximation compared to the reference dense solution without sacrificin

关键词： Accuracy Tensors Wind speed Magnetic resonance imaging Linear algebra Wind power generation Approximation algorithms

A hybrid spherical fuzzy logarithmic decomposition of criteria importance and alternative ranking technique based on Adaptive Standardized Intervals model with application

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Decision Analytics Journal 2024年 11卷

作者： Yalçın, Galip Cihan Kara, Karahan Senapati, Tapan Mathematics Program Kırıkkale University Yahşihan/Kırıkkale 71450 Turkey Logistics Program Artvin Çoruh University Artvin 08300 Turkey School of Mathematics and Statistics Southwest University Beibei Chongqing 400715 China Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Thandalam Tamilnadu Chennai 602105 India

This study presents a hybrid fuzzy Multi-Attribute Group Decision Making (MAGDM) model with application to commercial insurance selection. The proposed hybrid model uses Spherical Fuzzy (SF) sets using Yager t-norm and t-conorm operations. The Logarithmic Decomposition of Criteria Importance (LODECI) method is used for criterion weighting due to its efficacy in stabilizing scenarios that may challenge other weighting techniques. For alternative ranking, the study employs the Alternative Ranking Technique based on Adaptive Standardized Intervals (ARTASI), offering enhanced flexibility in handling uncertainties inherent in expert evaluations. The combination of these methods and the utilization of SF sets gives rise to the proposed SF-LODECI-ARTASI hybrid model. The paper systematically delineates the procedural steps involving SF sets, Yager t-norm and t-conorm operations, SF-LODECI, and SF-ARTASI methods. Subsequently, the developed hybrid model is applied to a case study of commercial insurance selection, supported by a numerical example. The research application results emphasize the consistency of these findings with other alternative methods. Additionally, sensitivity scenarios are constructed to scrutinize the robustness of the proposed hybrid model. The study concludes by elucidating implications and contributions to the existing literature. © 2024 The Author(s)

关键词： Alternative ranking technique based on adaptive standardized intervals Insurance selection Logarithmic decomposition of criteria importance Multi-attribute group decision making Spherical fuzzy sets Yager t-norm and t-conorm