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Numerical equivalence between sph and probabilistic mass transfer methods for lagrangian simulation of dispersioni

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arXiv 2018年

作者： Sole-Mari, Guillem Schmidt, Michael J. Pankavich, Stephen D. Benson, David A. Universitat Politècnica de Catalunya Barcelona Spain UPC-CSIC Barcelona Spain 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

Several Lagrangian methodologies have been proposed in recent years to simulate advection-dispersion of solutes in fluids as a mass exchange between numerical particles carrying the fluid. In this paper, we unify these methodologies, showing that mass transfer particle tracking (MTPT) algorithms can be framed within the context of smoothed particle hydrodynamics (SPH), provided the choice of a Gaussian smoothing kernel whose bandwidth depends on the dispersion and the time discretization. Numerical simulations are performed for a simple dispersion problem, and they are compared to an analytical solution. Based on the results, we advocate for the use of a kernel bandwidth of the size of the characteristic dispersion length ` = √2D∆t, at least given a "dense enough" distribution of particles, for in this case the mass transfer operation is not just an approximation, but in fact the exact solution, of the solute’s displacement Copyright © 2018, The Authors. All rights reserved.

关键词： Mass transfer

Algorithmic (Semi-)Conjugacy via Koopman Operator Theory

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arXiv 2022年

作者： Redman, William T. Fonoberova, Maria Mohr, Ryan Kevrekidis, Ioannis G. Mezić, Igor The Interdepartmental Graduate Program in Dynamical Neuroscience University of California Santa Barbara United States AIMdyn Inc. Santa Barbara United States The Department of Chemical and Biomolecular Engineering and of Mathematics and Statistics The Johns Hopkins University United States The Department of Mechanical Engineering and of Mathematics University of California Santa Barbara United States

Iterative algorithms are of utmost importance in decision and control. With an ever growing number of algorithms being developed, distributed, and proprietarized, there is a similarly growing need for methods that can provide classification and comparison. By viewing iterative algorithms as discrete-time dynamical systems, we leverage Koopman operator theory to identify (semi-)conjugacies between algorithms using their spectral properties. This provides a general framework with which to classify and compare algorithms. © 2022, CC0.

关键词： Dynamical systems

High temperature structure detection in ferromagnets

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arXiv 2018年

作者： Cao, Yuan Neykov, Matey Liu, Han Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Statistics & Data Science Carnegie Mellon University PittsburghPA United States Department of Electrical Engineering and Computer Science Northwestern University EvanstonIL United States

This paper studies structure detection problems in high temperature ferromagnetic (positive interaction only) Ising models. The goal is to distinguish whether the underlying graph is empty, i.e., the model consists of independent Rademacher variables, versus the alternative that the underlying graph contains a subgraph of a certain structure. We give matching upper and lower minimax bounds under which testing this problem is possible/impossible respectively. Our results reveal that a key quantity called graph arboricity drives the testability of the problem. On the computational front, under a conjecture of the computational hardness of sparse principal component analysis, we prove that, unless the signal is strong enough, there are no polynomial time linear tests on the sample covariance matrix which are capable of testing this problem. Copyright © 2018, The Authors. All rights reserved.

关键词： Ferromagnetism

Clustering Analysis of a Spatiotemporal Dataset with a Novel Kernel Density Estimator

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Clustering Analysis of a Spatiotemporal Dataset with a Novel...

International Conference on Machine Learning and Cybernetics (ICMLC)

作者： Jen-Chien Yu Chun-Chieh Yang John Reuben Gilbert Rou-Jun Liu Yen-Jen Oyang Meng-Han Yang Department of Computer Science and Information Engineering National Kaohsiung University of Science and Technology Kaohsiung City Taiwan ROC Master Program in Statistics National Taiwan University Taipei Taiwan ROC Department of Computer Science & Information Engineering National Taiwan University Graduate Institute of Biomedical Electronics and Bioinformatics National Taiwan University

A vast number of spatiotemporal datasets collected from a wide range of sources has motivated scientists to develop effective approaches to identify interesting patterns hidden in these datasets. In this respect, kernel density estimators, which belong to a class of non-parametric estimators in statistics, have been widely exploited in recent years. With this background, we have developed a novel kernel density estimator aiming to provide accurate analysis results. According to the evaluation with a real spatiotemporal dataset, which collected emergency medical service records in a county in the United States, the proposed kernel density estimator can approximate the probability density function significantly more accurately than a conventional kernel density estimator. Furthermore, we have exploited the proposed kernel density estimator to identify interesting patterns hidden in the real spatiotemporal dataset.

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Correction: Thiazole-fused androstenone and ethisterone derivatives: potent β- and γ-actin cytoskeleton inhibitors to treat melanoma tumors

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RSC medicinal chemistry 2025年第4期16卷 2025 Apr 3页

作者： Sanjay Adhikary Subrata Roy Shailesh Budhathoki Siam Chowdhury Abbey Stillwell Alexei G Basnakian Alan Tackett Nathan Avaritt Mohamed Milad Mohammad Abrar Alam Department of Chemistry and Physics College of Sciences and Mathematics Arkansas State University Jonesboro Arkansas 72467 USA malam@astate.edu. Environmental Sciences Program College of Sciences and Mathematics Arkansas State University Jonesboro AR 72467 USA. Molecular Biosciences Program College of Sciences and Mathematics Arkansas State University Jonesboro AR 72467 USA. Computer Science The College of Engineering and Computer Science Arkansas State University Jonesboro AR 72468 USA. Department of Pharmacology and Toxicology University of Arkansas for Medical Sciences 4301 W. Markham St Little Rock AR 72205 USA. Central Arkansas Veterans Healthcare System W. 7th St Little Rock AR 72205 USA. Department of Biochemistry and Molecular Biology University of Arkansas for Medical Sciences Little Rock AR 72205 USA. The Department of Mathematics and Statistics Arkansas State University Jonesboro AR 72467 USA. Arkansas Biosciences Institute Arkansas State University Jonesboro AR 72467 USA.

[This corrects the article DOI: 10.1039/D4MD00719K.].

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Rainfall frequency analysis using event-maximum rainfalls – An event-based mixture distribution modeling approach

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Weather and Climate Extremes 2024年 43卷

作者： Cheng, Ke-Sheng Chen, Bo-Yu Lin, Teng-Wei Nakamura, Kimihito Ruangrassamee, Piyatida Chikamori, Hidetaka Department of Bioenvironmental Systems Engineering National Taiwan University Taipei Taiwan Master Program in Statistics National Taiwan University Taipei Taiwan Graduate School of Agriculture Kyoto University Kyoto Japan Department of Water Resources Engineering Faculty of Engineering Chulalongkorn University Bangkok Thailand Department of Environmental Management Engineering Okayama University Okayama Japan

Rainfall frequency analysis, an essential work for water resources management, is often conducted by using the annual maximum rainfall series. For rainfall stations with short record lengths and outliers presence, the use of annual maximum series for rainfall frequency analysis may yield design rainfall estimates of higher uncertainties. Moreover, for regions with cyclostationary climate patterns, the annual maximum rainfalls may be caused by different prevalent storm types, which differ in terms of their occurrence frequency and storm rainfall characteristics. In this study, we propose a novel event-maximum-rainfall-based mixture distribution modeling approach for rainfall frequency analysis. By considering the event-maximum rainfalls of individual storm events, the sample size for parameter estimation increases, and the uncertainty of design rainfall estimates reduces. Mixture distribution modeling enables a thorough investigation of the contributing probabilities of different storm types to the annual maximum rainfall. Through rigorous stochastic simulation, we demonstrated the superiority of the proposed approach over the conventional annual maximum rainfall approach. The proposed approach was applied to four representative rainfall stations in Taiwan, and the results revealed that the proposed approach is more robust than the conventional annual maximum rainfall approach. The results provide insights into the contributions of individual storm types to the annual maximum rainfall. © 2023 The Authors

关键词： Annual maxima Event-maximum rainfalls Frequency analysis Mixture distribution Negative binomial distribution Poisson distribution

On the Parameter Combinations that Matter and on Those that do Not

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arXiv 2021年

作者： Evangelou, Nikolaos Wichrowski, Noah J. Kevrekidis, George A. Dietrich, Felix Kooshkbaghi, Mahdi McFann, Sarah Kevrekidis, Ioannis G. Department of Chemical and Biomolecular Engineering Johns Hopkins University United States Department of Applied Mathematics and Statistics Johns Hopkins University United States Department of Mathematics and Statistics University of Massachusetts Amherst United States Department of Informatics Technical University of Munich Germany The Program in Applied and Computational Mathematics Princeton University United States Department of Chemical and Biological Engineering Princeton University United States Lewis-Sigler Institute for Integrative Genomics Princeton University United States

We present a data-driven approach to characterizing nonidentifiability of a model’s parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the output behavior of a chemical system: a set of effective parameters for the model. Furthermore, we introduce and use a Conformal Autoencoder Neural Network technique, as well as a kernel-based Jointly Smooth Function technique, to disentangle the redundant parameter combinations that do not affect the output behavior from the ones that do. We discuss the interpretability of our data-driven effective parameters, and demonstrate the utility of the approach both for behavior prediction and parameter estimation. In the latter task, it becomes important to describe level sets in parameter space that are consistent with a particular output behavior. We validate our approach on a model of multisite phosphorylation, where a reduced set of effective parameters (nonlinear combinations of the physical ones) has previously been established *** Codes 37E99 (Primary), 68T07 (Secondary) Copyright © 2021, The Authors. All rights reserved.

关键词： Parameter estimation

Emergent spaces for coupled oscillators

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arXiv 2020年

作者： Thiem, Thomas N. Kooshkbaghi, Mahdi Bertalan, Tom Laing, Carlo R. Kevrekidis, Ioannis G. Department of Chemical and Biological Engineering Princeton University United States Program in Applied and Computational Mathematics Princeton University United States Department of Mechanical Engineering Massachusetts Institute of Technology United States School of Natural and Computational Sciences Massey University New Zealand Department of Applied Mathematics and Statistics Johns Hopkins University United States

Systems of coupled dynamical units (e.g. oscillators or neurons) are known to exhibit complex, emergent behaviors that may be simplified through coarse-graining: a process in which one discovers coarse variables and derives equations for their evolution. Such coarse-graining procedures often require extensive experience and/or a deep understanding of the system dynamics. In this paper we present a systematic, data-driven approach to discovering "bespoke" coarse variables based on manifold learning algorithms. We illustrate this methodology with the classic Kuramoto phase oscillator model, and demonstrate how our manifold learning technique can successfully identify a coarse variable that is one-to-one with the established Kuramoto order parameter. We then introduce an extension of our coarse-graining methodology which enables us to learn evolution equations for the discovered coarse variables via an artificial neural network architecture templated on numerical time integrators (initial value solvers). This approach allows us to learn accurate approximations of time derivatives of state variables from sparse flow data, and hence discover useful approximate differential equation descriptions of their dynamic behavior. We demonstrate this capability by learning ODEs that agree with the known analytical expression for the Kuramoto order parameter dynamics at the continuum limit. We then show how this approach can also be used to learn the dynamics of coarse variables discovered through our manifold learning methodology. In both of these examples, we compare the results of our neural network based method to typical finite differences complemented with geometric harmonics. Finally, we present a series of computational examples illustrating how a variation of our manifold learning methodology can be used to discover sets of "effective" parameters, reduced parameter combinations, for multi-parameter models with complex coupling. We conclude with a discussion of possible ext

关键词： Neural networks

Functional Connectome-Based Predictive Modeling in Autism

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BIOLOGICAL PSYCHIATRY 2022年第8期92卷 626-642页

作者： Horien, Corey Floris, Dorothea L. Greene, Abigail S. Noble, Stephanie Rolison, Max Tejavibulya, Link O'Connor, David McPartland, James C. Scheinost, Dustin Chawarska, Katarzyna Lake, Evelyn M. R. Constable, R. Todd [a]Interdepartmental Neuroscience Program Yale School of Medicine New Haven Connecticut [b]MD-PhD Program Yale School of Medicine New Haven Connecticut [c]Department of Pediatrics Yale School of Medicine New Haven Connecticut [d]Department of Neurosurgery Yale School of Medicine New Haven Connecticut [e]Department of Radiology and Biomedical Imaging Yale School of Medicine New Haven Connecticut [f]Department of Biomedical Engineering Yale University New Haven Connecticut [g]Department of Psychology Yale University New Haven Connecticut [h]Department of Statistics and Data Science Yale University New Haven Connecticut [i]Yale Child Study Center New Haven Connecticut [j]Methods of Plasticity Research Department of Psychology University of Zürich Zurich Switzerland [k]Donders Center for Brain Cognition and Behavior Radboud University Nijmegen Nijmegen The Netherlands

Autism is a heterogeneous neurodevelopmental condition, and functional magnetic resonance imaging-based studies have helped advance our understanding of its effects on brain network activity. We review how predictive modeling, using measures of functional connectivity and symptoms, has helped reveal key insights into this condition. We discuss how different prediction frameworks can further our understanding of the brain-based features that underlie complex autism symptomatology and consider how predictive models may be used in clinical settings. Throughout, we highlight aspects of study interpretation, such as data decay and sampling biases, that require consideration within the context of this condition. We close by suggesting exciting future directions for predictive modeling in autism.

关键词： Clinical translation Development Fingerprinting Individual differences Machine learning Resting-state fMRI