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Inverse scattering on the quantum graph for graphene

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arXiv 2021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 Professor Emeritus University of Tsukuba Tsukuba305-8571 Japan Department of Math. Analysis Saint-Petersburg State University Universitetskaya nab. 7/9 St. Petersburg199034 Russia National Research University Higher School of Economics St. Petersburg 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 and symmetric, we show that the S-matrix for all energies in any given open set in the continuous spectrum determines the *** Codes 81U40, 47A40 Copyright © 2021, The Authors. All rights reserved.

关键词： Inverse problems

On Biased Compression for Distributed Learning

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arXiv 2020年

作者： Beznosikov, Aleksandr Horváth, Samuel Richtárik, Peter Safaryan, Mher Computer Electrical and Math. Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia Skolkovo Institute of Science and Technology Moscow121205 Russia School of Applied Mathematics and Informatics Moscow Institute of Physics and Technology Moscow141701 Russia

In the last few years, various communication compression techniques have emerged as an indispensable tool helping to alleviate the communication bottleneck in distributed learning. However, despite the fact biased compressors often show superior performance in practice when compared to the much more studied and understood unbiased compressors, very little is known about them. In this work we study three classes of biased compression operators, two of which are new, and their performance when applied to (stochastic) gradient descent and distributed (stochastic) gradient descent. We show for the first time that biased compressors can lead to linear convergence rates both in the single node and distributed settings. We prove that distributed compressed SGD method, employed with error feedback mechanism, enjoys the ergodic rate O ( δLexp[−µKδL ] + (CKµ+δD) ) , where δ ≥ 1 is a compression parameter which grows when more compression is applied, L and µ are the smoothness and strong convexity constants, C captures stochastic gradient noise (C = 0 if full gradients are computed on each node) and D captures the variance of the gradients at the optimum (D = 0 for over-parameterized models). Further, via a theoretical study of several synthetic and empirical distributions of communicated gradients, we shed light on why and by how much biased compressors outperform their unbiased variants. Finally, we propose several new biased compressors with promising theoretical guarantees and practical performance. Copyright © 2020, The Authors. All rights reserved.

关键词： Stochastic systems

On the relationship between the centroid and the footprint of uncertainty of Interval Type-2 fuzzy numbers

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On the relationship between the centroid and the footprint o...

IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

作者： Juan Carlos Figueroa-García Roman Neruda Yurilev Chalco-Cano Heriberto Román-Flores Assistant Professor of the Engineering Dept. Universidad Distrital Distrital Francisco José de Caldas Bogotá Colombia Assistant Professor of the Institute of Computer Science of the Czech Academy of Sciences Prague Czech Republic professor of the Math. Dept. Universidad de Tarapacá Arica Chile professor of the Instituto de Alta Investigación of Universidad de Tarapacá Arica Chile

ISBN: (数字)9781728169323

ISBN: (纸本)9781728169330

This paper presents experimental results about the relationship between the Footprint Of Uncertainty (FOU) and the centroid of Interval Type-2 Fuzzy Numbers (IT2FN) which are a subclass of Type-2 fuzzy numbers. Four types of IT2FNs are analyzed: singleton-core triangular, interval-core triangular, singleton-core Gaussian and interval-core Gaussian IT2FNs. A quadratic relationship was detected, characterized, and their results are presented and discussed using numerical experiments.

关键词： Fuzzy sets Uncertainty Measurement uncertainty Electronic mail Indexes Fuzzy control Optimization

Classification of two-dimensional left(right) unital algebras over algebraically closed fields and

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Journal of Physics: Conference Series 2020年第1期1489卷

作者： H Ahmed U Bekbaev I Rakhimov Department of Math. Faculty of Science UPM Selangor Malaysia & Depart. of Math. Faculty of Science Taiz University Taiz Yemen Department of Science in Engineering Faculty of Engineering IIUM Malaysia Department of Mathematics Faculty of Computer and Mathematical Sciences UiTM Malaysia & Institute for Mathematical Research (INSPEM) UPM Serdang Selangor Malaysia

In this paper we describe all left, right unital and unital algebra structures on two-dimensional vector space over any algebraically closed field and . We tabulate the algebras and provide their unit elements.

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On classification of 2-dimensional evolution algebras and its applications

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Journal of Physics: Conference Series 2020年第1期1489卷

作者： H Ahmed U Bekbaev I Rakhimov Department of Math. Faculty of Science UPM Selangor Malaysia & Depart. of Math. Faculty of Science Taiz University Taiz Yemen Department of Mathematical and Natural Sciences TTPU Tashkent Uzbekistan & Department of Science in Engineering Faculty of Engineering IIUM Malaysia Department of Mathematics Faculty of Computer and Mathematical Sciences UiTM Malaysia & V.I.Romanovskiy Institute of Mathematics Uzbekistan Academy of Science

In the paper we give a complete classification of 2-dimensional evolution algebras over algebraically closed fields, we compare the list of representatives of the isomorphism classes with that of obtained earlier by t...

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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

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

New Convergence Aspects of Stochastic Gradient Algorithms

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arXiv 2018年

作者： Nguyen, Lam M. Nguyen, Phuong Ha Richtárik, Peter Scheinberg, Katya Takáč, Martin van Dijk, Marten IBM Research Thomas J. Watson Research Center Yorktown HeightsNY10598 United States Department of Electrical and Computer Engineering University of Connecticut StorrsCT06268 United States Computer Electrical and Math. Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal Kazakhstan School of Operations Research and Information Engineering Cornell University IthacaNY14850 United States Department of Industrial and Systems Engineering Lehigh University BethlehemPA18015 United States

The classical convergence analysis of SGD is carried out under the assumption that the norm of the stochastic gradient is uniformly bounded. While this might hold for some loss functions, it is violated for cases where the objective function is strongly convex. In Bottou et al. (2018), a new analysis of convergence of SGD is performed under the assumption that stochastic gradients are bounded with respect to the true gradient norm. We show that for stochastic problems arising in machine learning such bound always holds;and we also propose an alternative convergence analysis of SGD with diminishing learning rate regime. We then move on to the asynchronous parallel setting, and prove convergence of Hogwild! algorithm in the same regime in the case of diminished learning rate. It is well-known that SGD converges if a sequence of learning rates {ηt} satisfies P∞t=0 ηt → ∞ and P∞t=0 ηt2 t} is a diminishing sequence and P∞t=0 ηt → ∞. In other words, we extend the current state-of-the-art class of learning rates satisfying the convergence of SGD. Copyright © 2018, The Authors. All rights reserved.

关键词： Learning algorithms

Global Software engineering Experience through International Capstone Project Exchanges

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Global Software Engineering Experience through International...

International Conference on Global Software engineering (ICGSE)

作者： Dean Knudson Stavros Kalafatis Carsten Kleiner Stephen Zahos Barbara Seegebarth Jonas Deeterfelt Iman Avazpour Kristian Sandahl Peter Gorder Jeewani Ginige Alex Radermacher Hugo Caballero Humberto Gomez Mikael Roos Computer Science Dept. North Dakota State University Fargo ND USA ECE Department Texas A& M University College Station TX USA Computer Science Dept. Hannover University of Applied Sciences & Arts Hannover Germany Agricultural and Biological Eng. University of Illinois at Urbana-Champaign Urbana IL USA Institute of Marketing Technische Universitat Braunschweig Braunschweig Germany Linkopings universitet Linkoping SE School of IT Deakin University Burwood Australia Department of Computer and Information Science Linkoping University Linkoping SE Sweden Department of Mechanical and Aerospace Engineering Univ. of Colorado Colorado Springs CO USA Sch. of Comput. Eng. & Math. Western Sydney Univ. Sydney NSW Australia Departamento de Ingenieria Mecanica Universidad del Norte Barranquilla Colombia Department of Computer Science and Engineering Blekinge Institute of Technology (BTH) Karlskrona Sweden

Today it is very common for software systems to be built by teams located in more than one country. For example, a project team may be located in the US while the team lead resides in Sweden. How then should students be trained for this kind of work? Senior design or capstone projects offer students real-world hands-on experience but rarely while working internationally. One reason is that most instructors do not have international business contacts that allow them to find project sponsors in other countries. Another reason is the fear of having to invest a huge amount of time managing an international project. In this paper we present the general concepts related to "International Capstone Project Exchanges", the basic model behind the exchanges (student teams are led by an industry sponsor residing in a different country) and several alternate models that have been used in practice. We will give examples from projects in the US, Germany, Sweden, Australia, and Colombia. We have extended the model beyond software projects to include engineering projects as well as marketing, and journalism. We conclude with a description of an International Capstone Project Exchange website that we have developed to aid any university in establishing their own international project exchange.

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