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Inverse scattering on the quantum graph - Edge model for graphen

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arXiv 2019年

作者： Ando, Kazunori Isozaki, Hiroshi Korotyaev, Evgeny Morioka, Hisashi Department of Electrical and Electronic Engineering and Computer Science Ehime University Matsuyama790-8577 Japan Graduate School of Pure and Applied Sciences Emeritus University of Tsukuba Tsukuba305-8571 Japan Department of Math. Analysis Saint-Petersburg State University Universitetskaya nab. 7/9 St. Petersburg199034 Russia

We consider the inverse scattering on the quantum graph associated with the hexagonal lattice. Assuming that the potentials on the edges are compactly supported, we show that the S-matrix for all energies in any open set in the continous spectrum determines the *** Codes 81U40, 47A40 Copyright © 2019, The Authors. All rights reserved.

关键词： Inverse problems

Optimal tests for elliptical symmetry: Specified and unspecified location

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arXiv 2019年

作者： Babić, Slađana Gelbgras, Laetitia Hallin, Marc Ley, Christophe Department of Applied Mathematics Computer Science and Statistics Ghent University Krijgslaan 281 GentS9 B-9000 Belgium Vlerick Business School Département de Mathématique Université libre de Bruxelles Campus de la Plaine CP210 BruxellesB-1050 Belgium ECARES Département de Mathématique Université libre de Bruxelles CP114/4 Ave. F.D. Roosevelt Bruxelles50 B-1050 Belgium Department of Applied Mathematics Computer Science and Statistics Ghent University Krijgslaan 281 GentS9 B-9000 Belgium

Although the assumption of elliptical symmetry is quite common in multivariate analysis and widespread in a number of applications, the problem of testing the null hypothesis of ellipticity so far has not been addressed in a fully satisfactory way. Most of the literature in the area indeed addresses the null hypothesis of elliptical symmetry with specified location and actually addresses location rather than non-elliptical alternatives. In this paper, we are proposing new classes of testing procedures, both for specified and unspecified location. The backbone of our construction is Le Cam's asymptotic theory of statistical experiments, and optimality is to be understood locally and asymptotically within the family of generalized skew-elliptical distributions. The tests we are proposing are meeting all the desired properties of a"good" test of elliptical symmetry: they have a simple asymptotic distribution under the entire null hypothesis of elliptical symmetry with unspecified radial density and shape parameter;they are affine-invariant, computationally fast, intuitively understandable, and not too demanding in terms of moments. While achieving optimality against generalized skew-elliptical alternatives, they remain quite powerful under a much broader class of non-elliptical distributions and significantly outperform the available competitors. Copyright © 2019, The Authors. All rights reserved.

关键词： Asymptotic analysis

The representation theory of seam algebras

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arXiv 2019年

作者： Langlois-Rémillard, Alexis Saint-Aubin, Yvan DEPARTMENT OF APPLIED MATHEMATICS COMPUTER SCIENCE AND STATISTICS FACULTY OF SCIENCES GHENT UNIVERSITY KRIJGSLAAN 281-S9 9000 GENT Belgium DÉPARTEMENT DE MATHÉMATIQUES ET DE STATISTIQUE UNIVERSITÉ DE MONTRÉAL QUÉBECH3C 3J7 Canada

The boundary seam algebras bn,k(β = q+ q−1) were introduced by Morin-Duchesne, Ridout and Rasmussen to formulate algebraically a large class of boundary conditions for two-dimensional statistical loop models. The representation theory of these algebras bn,k(β = q+q−1) is given: their irreducible, standard (cellular) and principal modules are constructed and their structure explicited in terms of their composition factors and of non-split short exact sequences. The dimensions of the irreducible modules and of the radicals of standard ones are also given. The methods proposed here might be applicable to a large family of algebras, for example to those introduced recently by Flores and Peltola, and Crampé and Poulain d’Andecy. Copyright © 2019, The Authors. All rights reserved.

关键词： Algebra

The covariance of chiral fermions theory

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arXiv 2018年

作者： Andrzejewski, K. Brihaye, Y. Gonera, C. Gonera, J. Nski, P. Kosi Slanka, P. Ma Department of Computer Science Faculty of Physics and Applied Informatics University of Lodz Poland Physique-Mathématique Université de Mons-Hainaut Mons Belgium

The quasiclassical theory of massless chiral fermions is considered. The effective action is derived using time-dependent variational principle which provides a clear interpretation of relevant canonical variables. As a result their transformation properties under the action of Lorentz group are derived from first principles. 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

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 master stability function for synchronization in simplicial complexes

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arXiv 2020年

作者： Gambuzza, L.V. Di Patti, F. Gallo, L. Lepri, S. Romance, M. Criado, R. Frasca, Mattia Latora, V. Boccaletti, S. Department of Electrical Electronics and Computer Science Engineering University of Catania Catania95125 Italy CNR-Institute of Complex Systems Via Madonna del Piano Sesto Fiorentino Florence50019 Italy Department of Physics and Astronomy University of Catania Catania95125 Italy Department of Applied Math. and Data Complex Networks and Cybersecurity Research Institute University Rey Juan Carlos C/Tulipn s/n Mstoles Madrid28933 Spain Department of Physics and Astronomy University of Catania INFN Catania95125 Italy School of Mathematical Sciences Queen Mary University of London LondonE1 4NS United Kingdom The Alan Turing Institute The British Library LondonNW1 2DB United Kingdom Unmanned Systems Research Institute Northwestern Polytechnical University Xi'an710072 China Moscow Institute of Physics and Technology Dolgoprudny Moscow Region141701 Russia

All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as networks of coupled dynamical systems, where the graph links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework that allows to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We consider the most general ensemble of identical dynamical systems, organized on the nodes of a simplicial complex, and interacting through synchronization-non-invasive coupling function. The simplicial complex can be of any dimension, meaning that it can account, at the same time, for pairwise interactions, three-body interactions and so on. In such a broad context, we show that complete synchronization, a circumstance where all the dynamical units arrange their evolution in unison, exists as an invariant solution, and we give the necessary condition for it to be observed as a stable state in terms of a Master Stability Function. This generalizes the existing results valid for pairwise interactions (i.e. graphs) to the case of complex systems with the most general possible architecture. Moreover, we show how the approach can be simplified for specific, yet frequently occurring, instances, and we verify all our theoretical predictions in synthetic and real-world systems. Given the completely general character of the method proposed, our results contribute to the theory of dynamical systems with many-body interactions and can find applications in an extremely wide range of practical cases. Copyright © 2020, The Auth

关键词： Dynamical systems

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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