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On a theta product of Jacobi and its applications to q-gamma products

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arXiv 2018年

We give a new proof for a product formula of Jacobi which turns out to be equivalent to a q-trigonometric product which was stated without proof by Gosper. We apply this formula to derive a q-analogue for the Gauss multiplication formula for the gamma function. Furthermore, we give explicit formulas for short products of q-gamma functions.33B15, 33E05 Copyright © 2018, The Authors. All rights reserved.

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Semi-smooth Newton methods for nonlinear complementarity formulation of compositional two-phase flow in porous media

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arXiv 2018年

作者： Bui, Quan M. Elman, Howard C. Applied Math Stats and Scientific Computation University of Maryland College ParkMD United States Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD United States

Simulating compositional multiphase flow in porous media is a challenging task, especially when phase transition is taken into account. The main problem with phase transition stems from the inconsistency of the primary variables such as phase pressure and phase saturation, i.e. they become ill-defined when a phase appears or disappears. Recently, a new approach for handling phase transition has been developed, whereby the system is formulated as a nonlinear complementarity problem (NCP). Unlike the widely used primary variable switching (PVS) method which requires a drastic reduction of the time step size when a phase appears or disappears, this approach is more robust and allows for larger time steps. One way to solve an NCP system is to reformulate the inequality constraints as a non-smooth equation using a complementary function (C-function). Because of the non-smoothness of the constraint equations, a semi-smooth Newton method needs to be developed. In this work, we consider two methods for solving NCP systems used to model multiphase flow: (1) a semi-smooth Newton method for two C-functions: the minimum and the Fischer-Burmeister functions, and (2) a new inexact Newton method based on the Jacobian smoothing method for a smooth version of the Fischer-Burmeister function. We show that the new method is robust and efficient for standard benchmark problems as well as for realistic examples with highly heterogeneous media such as the SPE10 benchmark.76S05, 76M25, 65Z05, 76T99 Copyright © 2018, The Authors. All rights reserved.

关键词： Porous materials

A robust minimal learning machine based on the m-estimator 25

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A robust minimal learning machine based on the m-estimator

25th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, ESANN 2017

作者： Gomes, Joao P.P. Mesquita, Diego P.P. Freire, Ananda L. Junior, Amauri H. Souza Karkkainen, Tommi Federal University of Ceará - UFC Department of Computer Science Fortaleza-CE Brazil Federal Institute of Ceará Department of Teleinformatics Fortaleza-CE Brazil University of Jyvaskyla Department of Math. Information Technology Finland

ISBN: (纸本)9782875870391

In this paper we propose a robust Minimal Learning Machine (R-RLM) for regression problems. The proposed method uses a robust M-estimator to generate a linear mapping between input and output distances matrices of MLM. The R-MLM was tested on one synthetic and three real world datasets that were contaminated with an increasing number of outliers. The method achieved a performance comparable to the robust Extreme Learning Machine (R-RLM) and thus can be seen as a valid alternative for regression tasks on datasets with outliers. © ESANN 2017 - Proceedings, 25th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning. All rights reserved.

关键词： Machine learning

Convergence rates for empirical estimation of binary classification bounds

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arXiv 2018年

作者： Sekeh, Salimeh Yasaei Noshad, Morteza Moon, Kevin R. Hero, Alfred O. Department of Electrical Engineering and Computer Science University of Michigan Ann ArborMI United States Departments of Genetics and Applied Math Yale University New HavenCT United States

Bounding the best achievable error probability for binary classification problems is relevant to many applications including machine learning, signal processing, and information theory. Many bounds on the Bayes binary classification error rate depend on information divergences between the pair of class distributions. Recently, the Henze-Penrose (HP) divergence has been proposed for bounding classification error probability. We consider the problem of empirically estimating the HP-divergence from random samples. We derive a bound on the convergence rate for the Friedman-Rafsky (FR) estimator of the HP-divergence, which is related to a multivariate runs statistic for testing between two distributions. The FR estimator is derived from a multicolored Euclidean minimal spanning tree (MST) that spans the merged samples. We obtain a concentration inequality for the Friedman-Rafsky estimator of the Henze-Penrose divergence. We validate our results experimentally and illustrate their application to real datasets. Copyright © 2018, The Authors. All rights reserved.

关键词： Classification (of information)

The extinction problem for a class of distylous plant populations

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arXiv 2018年

作者： Alsmeyer, Gerold Raschel, Kilian Inst. Math. Stochastics Department of Mathematics and Computer Science University of Münster Orleans-Ring 10 MunsterD-48149 Germany CNRS Institut Denis Poisson Universite de Tours Parc de Grandmont ToursF-37200 France

In this paper, the extinction problem for a class of distylous plant populations is considered within the framework of certain nonhomo-geneous nearest-neighbor random walks in the positive quadrant. For the latter, extinction means absorption at one of the axes. Despite connections with some classical probabilistic models (standard two-type Galton-Watson process, two-urn model), exact formulae for the probabilities of absorption seem to be difficult to come by and one must therefore resort to good approximations. In order to meet this task, we develop potential-theoretic tools and provide various sub- and super-harmonic functions which, for large initial populations, provide bounds which in particular improve those that have appeared earlier in the literature. Copyright © 2018, The Authors. All rights reserved.

关键词： Harmonic functions

The unintended consequences of inconsistent closure policies and mobility restrictions during epidemics

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BMC global and public health 2023年第1期1卷 28页

作者： Benjamin M Althouse Brendan Wallace B K M Case Samuel V Scarpino Antoine Allard Andrew M Berdahl Easton R White Laurent Hébert-Dufresne University of Washington Seattle 98105 WA USA. New Mexico State University Las Cruces 88003 NM USA. Department of Applied Mathematics University of Washington Seattle 98195 WA USA. Present Address: Quantitative Ecology and Resource Management University of Washington Seattle WA 98195 USA. School of Aquatic & Fishery Sciences University of Washington Seattle WA 98195 USA. Department of Computer Science University of Vermont Burlington 05405 VT USA. Vermont Complex Systems Center University of Vermont Burlington 05405 VT USA. Institute for Experiential AI Northeastern University Boston Massachusetts USA. Department of Health Sciences Northeastern University Boston MA USA. Khoury College of Computer Sciences Northeastern University Boston MA USA. Santa Fe Institute Santa Fe NM USA. Département de physique de génie physique et d'optique Université Laval Québec (Québec) G1V 0A6 Canada. Centre interdisciplinaire en modélisation mathématique Université Laval Québec (Québec) G1V 0A6 Canada. School of Aquatic & Fishery Sciences University of Washington Seattle 98195 WA USA. Department of Biological Sciences University of New Hampshire Durham 03824 NH USA. Gund Institute for Environment University of Vermont Burlington 05405 VT USA.

Background:Controlling the spread of infectious diseases-even when safe, transmission-blocking vaccines are available-may require the effective use of non-pharmaceutical interventions (NPIs), e.g., mask wearing, testing, limits on group sizes, venue closure. During the SARS-CoV-2 pandemic, many countries implemented NPIs inconsistently in space and time. This inconsistency was especially pronounced for policies in the United States of America (US) related to venue closure. Methods:Here, we investigate the impact of inconsistent policies associated with venue closure using math.matical modeling and high-resolution human mobility, Google search, and county-level SARS-CoV-2 incidence data from the USA. Specifically, we look at high-resolution location data and perform a US-county-level analysis of nearly 8 million SARS-CoV-2 cases and 150 million location visits, including 120 million church visitors across 184,677 churches, 14 million grocery visitors across 7662 grocery stores, and 13.5 million gym visitors across 5483 gyms. Results:Analyzing the interaction between venue closure and changing mobility using a math.matical model shows that, across a broad range of model parameters, inconsistent or partial closure can be worse in terms of disease transmission as compared to scenarios with no closures at all. Importantly, changes in mobility patterns due to epidemic control measures can lead to increase in the future number of cases. In the most severe cases, individuals traveling to neighboring jurisdictions with different closure policies can result in an outbreak that would otherwise have been contained. To motivate our math.matical models, we turn to mobility data and find that while stay-at-home orders and closures decreased contacts in most areas of the USA, some specific activities and venues saw an increase in attendance and an increase in the distance visitors traveled to attend. We support this finding using search query data, which clearly shows a shift in in

关键词： Adaptive behavior COVID-19 Disease modeling Metapopulation models Mobility data

Direct estimation of information divergence using nearest neighbor ratios

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Direct estimation of information divergence using nearest ne...

2017 IEEE International Symposium on Information Theory, ISIT 2017

作者： Noshad, Morteza Moon, Kevin R. Sekeh, Salimeh Yasaei Hero, Alfred O. University of Michigan Electrical Engineering and Computer Science Ann ArborMI United States Yale University Genetics and Applied Math Department New HavenCT United States

ISBN: (纸本)9781509040964

We propose a direct estimation method for Rényi and f-divergence measures based on a new graph theoretical interpretation. Suppose that we are given two sample sets X and Y, respectively with N and M samples, where η := M/N is a constant value. Considering the k-nearest neighbor (k-NN) graph of Y in the joint data set (X, Y), we show that the average powered ratio of the number of X points to the number of Y points among all k-NN points is proportional to Rényi divergence of X and Y densities. A similar method can also be used to estimate f-divergence measures. We derive bias and variance rates, and show that for the class of γ-Hölder smooth functions, the estimator achieves the MSE rate of O(N-2γ/(γ+d)). Furthermore, by using a weighted ensemble estimation technique, for density functions with continuous and bounded derivatives of up to the order d, and some extra conditions at the support set boundary, we derive an ensemble estimator that achieves the parametric MSE rate of O(1/N). Our estimator requires no boundary correction, and remarkably, the boundary issues do not show up. Our approach is also more computationally tractable than other competing estimators, which makes them appealing in many practical applications. © 2017 IEEE.

关键词： Nearest neighbor search

Foundations of e-Democracy

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arXiv 2017年

作者： Shapiro, Ehud Department of Computer Science & Applied Math Weizmann Institute of Science Rehovot Israel

The Internet revolution of democracy, which will transform earthly representative democracies by employing the communication and collaboration capabilities of the Internet, has yet to come. Here, we enlist the wisdom of our forefathers to lead the way. By consulting the 1789 Declaration of the Rights of Man and of the Citizen, we distill core values of democracy and derive from them requirements for the foundations of e-democracy. Building these foundations can usher the urgently-needed revolution of democracy. Copyright © 2017, The Authors. All rights reserved.

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Density functional theory-based modeling and calculations of a polyamide molecular unit for studying forward-osmosis-dewatering of microalgae 10

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Density functional theory-based modeling and calculations of...

10th IEEE International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment and Management, HNICEM 2018

作者： Itliong, Jester N. Rojas, Kurt Irvin M. Ubando, Aristotle T. Chen, Wei-Hsin Villagracia, Al Rey C. David, Melanie Y. Culaba, Alvin B. Ong, Hui Lin Moreno, Joaquin Lorenzo V. Manrique, Robby B. Chang, Jo-Shu Kasai, Hideaki Bernardo, Gian Paolo O. Padama, Allan Abraham B. Arboleda, Nelson B. Physics Department De la Salle University Applied Physics Department Eulogio 'Amang' Rodriguez Institute of Science and Technology Manila Philippines Mechanical Engineering Dept. De la Salle University Manila Philippines Institute of Math. Sci. Physics University University of the Philippines Los Baños Philippines Dept. of Chemical Engineering National Cheng Kung University Tainan Taiwan Dept. of Aeronautics Astronautics National Cheng Kung University Tainan Taiwan Taiwan School of Materials Engineering Universiti Malaysia Perlis Perlis Malaysia Akashi College National Institute of Technolgy Hyogo Japan

ISBN: (纸本)9781538677674

Both the preparation of a reliable all-atom model of a polyamide (PA) membrane and the determination of its electrostatic parameters are considered significant challenges in a proposal to study forward-osmosis-dewatering of microalgae using molecular dynamics (MD). Density functional theory (DFT)-based calculations can effectively calculate for optimized structure and electrostatic properties, thus, employed to model and characterize the PA membrane starting from its molecular unit. The performed structural optimization resulted to the most stable configuration of the PA unit with bond length values that showed strong stability in the molecule such as the amide bond length of 1.413 Å which was found to differ from that of a related study by 3%. The calculated charge density distributions, electrostatic potential isosurface, and Mulliken charges on the PA unit provided potential binding sites and insights on the formation of amide bonds on the PA molecule. The non-amidebonded nitrogen atom of m-phenylene diamine (MPD) was found to be the most active site in the molecule due to its highest magnitude of negative charge (positive Coulomb potential), suggesting that amide bond-formation with a carbon atom of a trimesoyl chloride (TMC) monomer is most likely to occur during polymerization. The calculated charges in the amide group and the zero-net sum of these charges also agreed reasonably well with another study. The results are of vital importance in parameterizing the interaction potentials of PA for use in the MD simulations. © 2018 IEEE.

关键词： Density functional theory