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Journal of mathematics Teacher Education 2021年第6期24卷 701-701页

作者： Marchant, Carlos Nicolas Gomez Park, Hyejin Zhuang, Yuling Foster, Jonathan Conner, AnnaMarie Department of Curriculum and Instruction The University of Texas at Austin Austin USA Department of Mathematics and Statistics James Madison University Harrisonburg USA College of Engineering University of Georgia Athens USA Department of Mathematics and Science Education University of Georgia Athens USA

Operator-based uncertainty quantification of stochastic fractional partial differential equations

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Journal of Verification, Validation and Uncertainty Quantification 2019年第4期4卷 041006页

作者： Kharazmi, Ehsan Zayernouri, Mohsen Department of Mechanical Engineering Michigan State University 428 S. Shaw Lane East LansingMI48824 United States Department of Computational Mathematics Science and Engineering Michigan State University 428 S. Shaw Lane East LansingMI48824 United States Department of Statistics and Probability Michigan State University 619 Red Cedar Road East LansingMI48824 United States

Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional orders as uncertain variables, we develop an operator-based uncertainty quantification framework in the context of stochastic fractional partial differential equations (SFPDEs), subject to additive random noise. We characterize different sources of uncertainty and then, propagate their associated randomness to the system response by employing a probabilistic collocation method (PCM). We develop a fast, stable, and convergent Petrov-Galerkin spectral method in the physical domain in order to formulate the forward solver in simulating each realization of random variables in the sampling procedure. Copyright © 2019 by ASME

关键词： Random processes

A review of face expression recognition system recommendation for psychiatric disease

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AIP Conference Proceedings 2023年第1期2683卷

作者： Ahmad Ilham Suryono Suryono Catur Edi Widodo Doctoral Program of Information System School of Postgraduate Studies Diponegoro University 50241 Semarang-Central Java Indonesia Department of Informatics Faculty of Engineering Universitas Muhammadiyah Semarang 50273 Semarang-Central Java Indonesia Department of Physics Faculty of Science and Mathematics Diponegoro University 50275 Semarang – Central Java Indonesia

Research on human mental disorders has started exploring the relationship between human facial expression recognition (FER) and symptoms of mental disorders because cases in FER are similar to symptoms in psychiatric disease. With the tremendous success of machine learning and deep learning, various models and architecture of these techniques are being leveraged to achieve better performance. The purpose of this work is to undertake a review of the most recent work on automatic facial emotion recognition (FER) using deep learning. We emphasize these contributions from the deep learning architecture and facial databases and the researchers’ progress by comparing the recommended technique with the findings produced. The study found that facial expression recognition based on cognitive internet of things (CIoT) in psychiatry disease did not yet exist, so it became a big opportunity to develop this research in the future. It can be concluded that this research can assist scholars by examining previous works and providing insights to improve this field and can be used as recommendations for psychiatric disease.

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A UNIFIED APPROACH TO LEAVITT PATH ALGEBRAS

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arXiv 2019年

作者： Mohan, R. Suhas, B.N. Statistics and Mathematics Unit Indian Statistical Institute Bangalore India Department of Mathematics Amrita School of Engineering Amrita Vishwa Vidyapeetham Bangalore India

We define Cohn-Leavitt path algebras AKpEq of a new class of graphs called A-graphs E9 , which generalize the constructions of Leavitt path algebras of various types of graphs. We compute Gröber-Shirshov basis of these algebras, characterize the algebras which are domains in terms of A-graph theoretic properties, and compute their Gelfand-Kirillov dimension. We then define the category of pre-Bergman A-graphs which are characterized as direct limits of finite complete sub-A-graphs. Finally, we define Bergman A-graphs, investigate their K-theory and also show that the lattice of order-ideals of V-monoids of Cohn-Leavitt path algebras of Bergman A-graphs is determined by A-graph theoretic data. Copyright © 2019, The Authors. All rights reserved.

关键词： Graphic methods

The number of closed ideals of L(p ⊕ q)

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arXiv 2020年

作者： Freeman, D. Schlumprecht, T.H. Zsák, A. Department of Mathematics and Statistics St Louis University St LouisMO63103 United States Department of Mathematics Texas A&M University College StationTX77843 United States Faculty of Electrical Engineering Czech Technical University in Prague Zikova 4 Prague166 27 Cambridge CB2 1RD United Kingdom

关键词： Mathematical operators

Qini-based uplift regression

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arXiv 2019年

作者： Belbahri, Mouloud Murua, Alejandro Gandouet, Olivier Nia, Vahid Partovi Department of Mathematics and Statistics University of Montreal Advanced Analytics Research and Development TD Insurance Department of Mathematics and Industrial Engineering École Polytechnique de Montréal

Uplift models provide a solution to the problem of isolating the marketing effect of a campaign. For customer churn reduction, uplift models are used to identify the customers who are likely to respond positively to a retention activity only if targeted, and to avoid wasting resources on customers that are very likely to switch to another company. We introduce a Qini-based uplift regression model to analyze a large insurance company's retention marketing campaign. Our approach is based on logistic regression models. We show that a Qini-optimized uplift model acts as a regularizing factor for uplift, much as a penalized likelihood model does for regression. This results in interpretable parsimonious models with few relevant explanatory variables. Our results show that performing Qini-based variable selection significantly improves the uplift models performance. Copyright © 2019, The Authors. All rights reserved.

关键词： Insurance

Multivariate distributionally robust convex regression under absolute error loss

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arXiv 2019年

作者： Blanchet, Jose Glynn, Peter W. Yan, Jun Zhou, Zhengqing Department of Management Science & Engineering Stanford University Department of Statistics Stanford University Department of Mathematics Stanford University

This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein perturbations of the empirical measure) of the absolute regression errors. The inner maximization is solved in closed form resulting in a regularization penalty involves the norm of the gradient. We show consistency of our estimator and a rate of convergence of order Õ(n-/d), matching the bounds of alternative estimators based on square-loss minimization. Contrary to all of the existing results, our convergence rates hold without imposing compactness on the underlying domain and with no a priori bounds on the underlying convex function or its gradient *** Codes 62H12, 62G20, 62G05 Copyright © 2019, The Authors. All rights reserved.

关键词： Functions

ESTIMATING CUSTOMER IMPATIENCE IN A SERVICE SYSTEM WITH UNOBSERVED BALKING

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arXiv 2020年

作者： Inoue, Yoshiaki Ravner, Liron Mandjes, Michel Department of Information and Communications Technology Graduate School of Engineering Osaka University 2-1 Yamadaoka Osaka Suita565-0871 Japan The Department of Statistics University of Haifa Israel Korteweg-de Vries Institute for Mathematics University of Amsterdam Netherlands Korteweg-de Vries Institute for Mathematics University of Amsterdam Science Park 904 Amsterdam1098 XH Netherlands

This paper studies a service system in which arriving customers are provided with information about the delay they will experience. Based on this information they decide to wait for service or to leave the system. Specifically, every customer has a patience threshold and they balk if the observed delay is above the threshold. The main objective is to estimate the parameters of the customers’ patience-level distribution and the corresponding potential arrival rate, using knowledge of the actual queue-length process only. The main complication, and distinguishing feature of our setup, lies in the fact that customers who decide not to join are not observed, remarkably, we manage to devise a procedure to estimate the underlying patience and arrival rate parameters. The model is a multi-server queue with a Poisson stream of customers, enabling evaluation of the corresponding likelihood function of the state-dependent effective arrival process. We establish strong consistency of the MLE and derive the asymptotic distribution of the estimation error. Several applications and extensions of the method are discussed. The performance is further assessed through a series of numerical experiments. By fitting parameters of hyperexponential and generalized-hyperexponential distributions our method provides a robust estimation framework for any continuous patience-level distribution. Copyright © 2020, The Authors. All rights reserved.

关键词： Information services

Modeling network populations via graph distances ∗

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arXiv 2019年

作者： Lunagómez, Simón Olhede, Sofia C. Wolfe, Patrick J. Department of Mathematics and Statistics Lancaster University Institute of Mathematics Ecole polytechnique fédérale de Lausanne Departments of Statistics Computer Science and Electrical & Computer Engineering Purdue University

This article introduces a new class of models for multiple networks. The core idea is to parametrize a distribution on labelled graphs in terms of a Fréchet mean graph (which depends on a user-specified choice of metric or graph distance) and a parameter that controls the concentration of this distribution about its mean. Entropy is the natural parameter for such control, varying from a point mass concentrated on the Fréchet mean itself to a uniform distribution over all graphs on a given vertex set. We provide a hierarchical Bayesian approach for exploiting this construction, along with straightforward strategies for sampling from the resultant posterior distribution. We conclude by demonstrating the efficacy of our approach via simulation studies and two multiple-network data analysis examples: one drawn from systems biology and the other from neuroscience. Copyright © 2019, The Authors. All rights reserved.

关键词： Population statistics

Asymptotic density of graphs excluding disconnected minors

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arXiv 2019年

作者： Kapadia, Rohan Norin, Sergey Qian, Yingjie Department of Computer Science and Software Engineering Concordia University MontrealQC Canada Department of Mathematics and Statistics McGill University School of Mathematics Georgia Institute of Technology

For a graph H, let c1(H) = lim n!1 max E(G) n , where the maximum is taken over all graphs G on n vertices not containing H as a minor. Thus c1(H) is the asymptotic maximum density of graphs not containing H as a minor. Employing a structural lemma due to Eppstein, we prove new upper bounds on c1(H) for disconnected graphs H. In particular, we determine c1(H) whenever H is union of cycles. Finally, we investigate the behaviour of c1(sKr) for fixed r, where sKr denotes the union of s disjoint copies of the complete graph on r vertices. Improving on a result of Thomason, we show that c1(sKr) = s(r-1)-1 for s = log r log log r , and c1(sKr) s(r-1)-1 for s = o log r log log r. Copyright © 2019, The Authors. All rights reserved.

关键词： Graphic methods