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arXiv 2022年

作者： Crossette, Nathan Carr, Lincoln D. Wilcox, Bethany R. Department of Physics University of Colorado Boulder BoulderCO80309 United States Quantum Engineering Program Colorado School of Mines GoldenCO80401 United States Department of Physics Colorado School of Mines GoldenCO80401 United States Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States

Social network analysis (SNA) has been gaining traction as a technique for quantitatively studying student collaboration. We analyze networks, constructed from student self-reports of collaboration on homework assignments, in two courses from the University of Colorado Boulder and one course from the Colorado School of Mines. All three courses occurred during the COVID-19 pandemic, which allows for a comparison between the course at the Colorado School of Mines (in a fully remote format) with results from a previous pre-pandemic study of student collaboration at the Colorado School of Mines (in a hybrid format). We compute nodal centrality measures and calculate the correlation between student centrality and performance. Results varied widely between each of the courses studied. The course at the Colorado School of Mines had strong correlations between many centrality measures and performance which matched the patterns seen in the pre-pandemic study. The courses at the University of Colorado Boulder showed weaker correlations, and one course showed nearly no correlations at all between students' connectivity to their classmates and their performance. Taken together, the results from the trio of courses indicate that the context and environment in which the course is situated play a more important role in fostering a correlation between student collaboration and course performance than the format (remote, hybrid, in-person) of the course. Additionally, we conducted a short study on the effect that missing nodes may have on the correlations calculated from the measured networks. This investigation showed that missing nodes tend to shift correlations towards zero, providing evidence that the statistically significant correlations measured in our networks are not spurious. © 2022, CC BY.

关键词： Students

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A class of dimension-free metrics for the convergence of empirical measures

arXiv

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arXiv 2021年

作者： Han, Jiequn Hu, Ruimeng Long, Jihao Department of Mathematics Princeton University PrincetonNJ08544-1000 United States Department of Mathematics Department of Statistics and Applied Probability University of California Santa BarbaraCA93106-3080 United States The Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544-1000 United States

This paper concerns the convergence of empirical measures in high dimensions. We propose a new class of probability metrics and show that under such metrics, the convergence is free of the curse of dimensionality (CoD). Such a feature is critical for high-dimensional analysis and stands in contrast to classical metrics (e.g., the Wasserstein metric). The proposed metrics fall into the category of integral probability metrics, for which we specify criteria of test function spaces to guarantee the property of being free of CoD. Examples of the selected test function spaces include the reproducing kernel Hilbert spaces, Barron space, and flow-induced function spaces. Three applications of the proposed metrics are presented: 1. The convergence of empirical measure in the case of random variables;2. The convergence of n-particle system to the solution to McKean-Vlasov stochastic differential equation;3. The construction of an Ε-Nash equilibrium for a homogeneous n-player game by its mean-field limit. As a byproduct, we prove that, given a distribution close to the target distribution measured by our metric and a certain representation of the target distribution, we can generate a distribution close to the target one in terms of the Wasserstein metric and relative entropy. Overall, we show that the proposed class of metrics is a powerful tool to analyze the convergence of empirical measures in high dimensions without *** Codes 60B10, 60E15, 60K35, 91A16, 60H10 © 2021, CC BY.

关键词： Stochastic systems

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Convergence of Mass Transfer Particle Tracking Schemes for the Simulation of Advection-Diffusion-Reaction Equations

SSRN

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SSRN 2024年

作者： Pankavich, Stephen D. Schauer, Lucas Schmidt, Michael J. Engdahl, Nicholas B. Bolster, Diogo Benson, David A. Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States Center for Computing Research Sandia National Laboratories AlbuquerqueNM87185 United States Department of Civil and Environmental Engineering Washington State University PullmanWA99164 United States Department of Civil and Environmental Engineering and Earth Sciences University of Notre Dame Notre DameIN46556 United States Hydrologic Science and Engineering Program Department of Geology and Geological Engineering Colorado School of Mines GoldenCO80401 United States

Since their introduction, multi-species mass-transfer particle tracking (or MTPT) algorithms have been used to accurately simulate advective and dispersive transport of solutes, even within systems that feature nonlinear chemical reactions. The MTPT methods were originally derived from a probabilistic or first-principles perspective and have previously lacked a more rigorous derivation arising directly from the underlying advection-diffusion-reaction equation (ADRE). Herein, we provide a fully rigorous derivation of the MTPT method as a Lagrangian approximation of solutions to the ADRE, complete with a description of the error and order of accuracy generated by this approximation. Numerical simulations further detail the fidelity of MTPT methods and display parameter regimes wherein the numerical error is independent of the chosen time step, and thereby dependent only upon the numerical discretization of the spatial domain via the number of particles within a simulation. Finally, different normalizations of the local Green's function are shown to generate similar approximations of the underlying solution for stationary particles. © 2024, The Authors. All rights reserved.

关键词： Lagrange multipliers

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Mutually beneficial confluence of structure-based modeling of protein dynamics and machine learning methods

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Current Opinion in Structural Biology 2023年 78卷 102517页

作者： Banerjee, Anupam Saha, Satyaki Tvedt, Nathan C. Yang, Lee-Wei Bahar, Ivet Computational and Systems Biology University of Pittsburgh School of Medicine Pittsburgh 15261 PA United States Computational and Applied Mathematics and Statistics The College of William and Mary Williamsburg 23185 VA United States Institute of Bioinformatics and Structural Biology and PhD Program in Biomedical Artificial Intelligence National Tsing Hua University Hsinchu 300044 Taiwan Physics Division National Center for Theoretical Sciences Taipei 106319 Taiwan

Proteins sample an ensemble of conformers under physiological conditions, having access to a spectrum of modes of motions, also called intrinsic dynamics. These motions ensure the adaptation to various interactions in the cell, and largely assist in, if not determine, viable mechanisms of biological function. In recent years, machine learning frameworks have proven uniquely useful in structural biology, and recent studies further provide evidence to the utility and/or necessity of considering intrinsic dynamics for increasing their predictive ability. Efficient quantification of dynamics-based attributes by recently developed physics-based theories and models such as elastic network models provides a unique opportunity to generate data on dynamics for training ML models towards inferring mechanisms of protein function, assessing pathogenicity, or estimating binding affinities. © 2022 The Authors

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Pediatric Dysphonia and the Access to Voice Therapy: A Study in Speech Therapy Services Available in a Capital City in the Northeast of Brazil

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Journal of Voice 2023年

作者： Sales, Neuza Josina Sampaio, Anne Thamires Santos Pimentel, Déborah de Oliveira, Eleonora Ramos Prado-Barreto, Valeria Maria Castaneda, Daniel Francisco Neyra de Carvalho Barreto, Ikaro Daniel Gurgel, Ricardo Queiroz Federal University of Sergipe UFS Sergipe Aracaju Brazil Municipal Secretary of Health Sergipe Aracaju Brazil Department of Medicine Federal University of Sergipe UFS Sergipe Aracaju Brazil Department of Medicine at the Federal University of Sergipe Sergipe Aracaju Brazil Department of Statistics and Actuarial Sciences Federal University of Sergipe UFS Sergipe São Cristóvão Brazil Biometrics and Applied Statistics Program Rural University of Pernambuco UFRPE Pernambuco Recife Brazil Department of Medicine Graduate in Health Sciences Federal University of Sergipe UFS Sergipe Aracaju Brazil

Objectives: Defining the laryngeal and vocal alterations in the pediatric group studied in private speech therapy facilities;and estimating the time period between the problem being identified by the parents and the access to the proper provided services. Methods: A cross-sectional analytical observational research with data collected from medical records by the speech therapist of each private facility. A written form was prepared and sent to the speech therapists of the 40 existing facilities. We received 124 of them from the pediatric group being assisted in 15 of the facilities. The form included questions about gender, age, vocal complaints;general degree of dysphonia;otorhinolaryngological diagnosis of vocal fold alterations;the age that the problem was identified by the parents and the beginning of speech therapy. The larynx was examined by videonasopharyngolaryngoscopy, and voice quality by auditory-perceptual assessment. Results: The time period between the identification of the participant's dysphonia by the parents and the start of speech therapy was considered long (3.5 years). The group showed variance in the proportion of nodule and cyst between genders. The highest prevalence of nodules occurred in boys;and the cyst in girls. Moderate general dysphonia occurred between 4 and 17 years old, average age of 7 years and 7 months, with greater distribution between 5 and 10 years of age. Conclusions: The average time delay until the start of speech therapy was 3.5 years, more frequently in the 5–10 years group and due to nodules in boys and cysts in girls. © 2023 The Voice Foundation

关键词： Childhood dysphonia Dysphonia Epidemiology Otolaryngology Speech therapy Voice disorders

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Modelling and forecasting daily average temperature in Bangkok, Thailand

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AIP Conference Proceedings 2024年第1期3123卷

作者： Kanyarat Thitiwatthanakan Manad Khamkong Ravi Lonkani Thanasak Mouktonglang Ph.D. Program in Applied Statistics Department of Statistics Faculty of Science Chiang Mai University 50200 Chiang Mai Thailand Department of Statistics Faculty of Science Chiang Mai University 50200 Chiang Mai Thailand Department of Finance Faculty of Business Administration Chiang Mai University 50200 Chiang Mai Thailand Department of Mathematics Faculty of Science Chiang Mai University 50200 Chiang Mai Thailand

In order to predict the occurrence of extreme climate events, forecasting and describing dynamic changes in temperature are essential. Understanding these events will allow action to be taken in order to minimize their associated effects. In this paper, we present a feasible model for estimating daily average temperatures in Bangkok, Thailand. The daily maximum and minimum temperature observations between 2006 and 2021 were collected from the Thai Meteorological Department for the study. The Fourier series was then applied to the average daily temperature as the mean function, and then the auto-regressive integrated moving average, ARIMA (4,1,1), was used to predict the residuals that occurred from the mean function to describe the evolution of the temperature. Analysis of the root mean square error (RMSE) value from the models, which is 0.9536, revealed that the methods fitted the data quite well.

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C^0DISCONTINUOUS GALERKIN METHODS FOR A PLATE FRICTIONAL CONTACT PROBLEM

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Journal of Computational Mathematics 2019年第2期37卷 184-200页

作者： Fei Wang Tianyi Zhang Weimin Han School of Mathematics and Statistics Xi 'an Jiaotong University Xi'an 710049 China Program in Applied Mathematical and Computational Sciences University of Iowa Iowa City IA 52242 USA School of Mathematics and Statistics Xi 'an Jiaotong University Xi'an 710049 China Departinent of Mathematics University of Iowa Iowa City. IA 52242 USA

Numerous C^0 discontinuous Galerkin (DG) schemes for the Kirchhoff plate bending problem are extended to solve a plate frictional contact problem, which is a fourth-order elliptic variational inequality of the second kind. This variational inequality contains a nondifferentiable term due to the frictional contact. We prove that these C^0 DG methods are consis tent and st able, and derive optimal order error estima tes for the quadratic element. A numerical example is presented to show the performance of the C^0 DG methods;and the numerical convergence orders confirm the theoretical prediction.

关键词： Variational inequality of fourth-order Discontinuous Galerkin method Plate frictional contact problem Optimal order error estimate

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Explaining heterogeneity in medial entorhinal cortex with task-driven neural networks 35

Explaining heterogeneity in medial entorhinal cortex with ta...

引用

35th Conference on Neural Information Processing Systems, NeurIPS 2021

作者： Nayebi, Aran Attinger, Alexander Campbell, Malcolm G. Hardcastle, Kiah Low, Isabel I.C. Mallory, Caitlin S. Mel, Gabriel C. Sorscher, Ben Williams, Alex H. Ganguli, Surya Giocomo, Lisa M. Yamins, Daniel L.K. Neurosciences Ph.D. Program Stanford University United States Department of Neurobiology Stanford University United States Department of Computer Science Stanford University United States Department of Applied Physics Stanford University United States Department of Psychology Stanford University United States Department of Statistics Stanford University United States Wu Tsai Neurosciences Institute Stanford University United States Facebook AI Research Facebook Inc. United States

ISBN: (纸本)9781713845393

Medial entorhinal cortex (MEC) supports a wide range of navigational and memory related behaviors. Well-known experimental results have revealed specialized cell types in MEC - e.g. grid, border, and head-direction cells - whose highly stereotypical response profiles are suggestive of the role they might play in supporting MEC functionality. However, the majority of MEC neurons do not exhibit stereotypical firing patterns. How should the response profiles of these more "heterogeneous" cells be described, and how do they contribute to behavior? In this work, we took a computational approach to addressing these questions. We first performed a statistical analysis that shows that heterogeneous MEC cells are just as reliable in their response patterns as the more stereotypical cell types, suggesting that they have a coherent functional role. Next, we evaluated a spectrum of candidate models in terms of their ability to describe the response profiles of both stereotypical and heterogeneous MEC cells. We found that recently developed task-optimized neural network models are substantially better than traditional grid cell-centric models at matching most MEC neuronal response profiles - including those of grid cells themselves - despite not being explicitly trained for this purpose. Specific choices of network architecture (such as gated nonlinearities and an explicit intermediate place cell representation) have an important effect on the ability of the model to generalize to novel scenarios, with the best of these models closely approaching the noise ceiling of the data itself. We then performed in silico experiments on this model to address questions involving the relative functional relevance of various cell types, finding that heterogeneous cells are likely to be just as involved in downstream functional outcomes (such as path integration) as grid and border cells. Finally, inspired by recent data showing that, going beyond their spatial response selectivity, MEC cells

关键词： Cells

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Wire Before You Walk

Wire Before You Walk

引用

Asilomar Conference on Signals, Systems & Computers

作者： Tesfa Asmara Dhananjay Bhaskar Ian Adelstein Smita Krishnaswamy Michael Perlmutter Department of Computer Science Pomona College Claremont CA USA Mathematics and Statistics Pomona College Claremont CA USA Department of Genetics Yale School of Medicine New Haven CT USA Department of Mathematics Yale University New Haven CT USA Department of Computer Science Yale University New Haven CT USA Program for Applied Mathematics Yale University New Haven CT USA Computational Biology and Bioinformatics Program Yale University New Haven CT USA Wu Tsai Institute Yale University New Haven CT USA Department of Mathematics Boise State University Boise ID USA

Node embeddings aim to associate a vector to every vertex of a graph which can then be used for downstream tasks such as clustering, classification, or link prediction. Many popular node embeddings such as no $d$ e2vec and DeepWalk are based upon counting which nodes frequently co-occur in random walks of the graph. In this paper, we show that the performance of such algorithms can be improved by rewiring the edges of the graph through a variety of network indices before running DeepWalk. These rewirings effectively give the random walker an inductive bias and increase the accuracy of a logistic regression classifier applied to the node embedding on several benchmark data sets.

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Recent Methodological Advances in Federated Learning for Healthcare

arXiv

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arXiv 2023年

作者： Zhang, Fan Kreuter, Daniel Chen, Yichen Dittmer, Sören Tull, Samuel Shadbahr, Tolou Preller, Jacobus Rudd, James H.F. Aston, John A.D. Schönlieb, Carola-Bibiane Gleadall, Nicholas Roberts, Michael Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom ZeTeM University of Bremen Bremen Germany Research Program in Systems Oncology Faculty of Medicine University of Helsinki Helsinki Finland Addenbrooke’s Hospital Cambridge University Hospitals NHS Trust Cambridge United Kingdom Department of Medicine University of Cambridge Cambridge United Kingdom Department of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge United Kingdom Department of Haematology University of Cambridge Cambridge United Kingdom

For healthcare datasets, it is often not possible to combine data samples from multiple sites due to ethical, privacy or logistical concerns. Federated learning allows for the utilisation of powerful machine learning algorithms without requiring the pooling of data. Healthcare data has many simultaneous challenges which require new methodologies to address, such as highly-siloed data, class imbalance, missing data, distribution shifts and non-standardised variables. Federated learning adds significant methodological complexity to conventional centralised machine learning, requiring distributed optimisation, communication between nodes, aggregation of models and redistribution of models. In this systematic review, we consider all papers on Scopus that were published between January 2015 and February 2023 and which describe new federated learning methodologies for addressing challenges with healthcare data. We performed a detailed review of the 89 papers which fulfilled these criteria. Significant systemic issues were identified throughout the literature which compromise the methodologies in many of the papers reviewed. We give detailed recommendations to help improve the quality of the methodology development for federated learning in healthcare. © 2023, CC BY.

关键词： Paper

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