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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

Knot mosaic tabulation

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Involve 2018年第1期11卷 13-26页

作者： Lee, Hwa Jeong Ludwig, Lewis D. Paat, Joseph Peiffer, Amanda School of Undergraduate Studies College of Transdisciplinary Studies Daegu Gyeongbuk Institute of Science and Technology Daegu 42988 South Korea Department of Mathematics and Computer Science Denison University 100 West College Granville 43023 OH United States Department of Applied Mathematics and Statistics Johns Hopkins 211-E Whitehead Hall 3400 N. Charles St. Baltimore 21218-2682 MD United States Department of Math and Computer Science Denison University Granville 43020 OH United States

In 2008, Lomonaco and Kauffman introduced a knot mosaic system to define a quantum knot system. A quantum knot is used to describe a physical quantum system such as the topology or status of vortexing that occurs in liquid helium II for example. Kuriya and Shehab proved that knot mosaic type is a complete invariant of tame knots. In this article, we consider the mosaic number of a knot, which is a natural and fundamental knot invariant defined in the knot mosaic system. We determine the mosaic number for all eight-crossing or fewer prime knots. This work is written at an introductory level to encourage other undergraduates to understand and explore this topic. No prior knowledge of knot theory is assumed or required. © 2018, math.matical sciences Publishers. All rights reserved.

关键词： crossing number knot mosaic knots mosaic number

Building Sense Tagged Corpus Using Wikipedia for Supervised Word Sense Disambiguation

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Procedia computer science 2018年 123卷 403-412页

作者： Abdulgabbar Saif Nazlia Omar Ummi Zakiah Zainodin Mohd Juziaddin Ab Aziz Computer-Math Department Faculty of Applied Sciences Thamar University Yemen Center for Artificial Intelligence Technology Faculty of Information Science & Technology Universiti Kebangsaan Malaysia Malaysia

Building of sense-tagged data is a main challenge for supervised techniques that achieved promising results in word sense disambiguation. The manual building of sense-tagged data is a labor and a time-consuming task because each ambiguous word has to be labeled in collected contexts by linguistic experts. Therefore, this paper proposes a knowledge-based method for building the Arabic sense-tagged corpus from Wikipedia. The method starts with mapping Arabic WordNet and Wikipedia to select the Wikipedia article for the corresponding sense in WordNet. In this mapping step, the cross-lingual method is used to measure the similarity between features of a Wikipedia article and a WordNet sense separately. Then, the incoming-links of Wikipedia articles are exploited to extract instances for the sense of each ambiguous word in WordNet. For handling the lack of instances of some articles in Wikipedia, the multiword-based technique is proposed to increase a number of instances for each concept. Experimental results show that the cross-lingual method outperforms monolingual method that is based on Arabic features only. The sense-tagged corpus is created for 50 ambiguous words yielding 148 senses with 30,961 instances.

关键词： Word Sense Disambiguation Wikipedia Arabic WordNet Alignment Text Processing Similarity Measures

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

Caterpillars are Antimagic

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arXiv 2018年

作者： Lozano, Antoni Mora, Mercè Seara, Carlos Tey, Joaquín Computer Science Department Universitat Politècnica de Catalunya Spain Mathematics Department Universitat Politècnica de Catalunya Spain Math. Department Universidad Autónoma Metropolitana-Iztapalapa Mexico

An antimagic labeling of a graph G is a bijection from the set of edges E(G) to {1, 2, ..., |E(G)|} such that all vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of the labels assigned to the edges incident to u. A graph is called antimagic when it has an antimagic labeling. Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic and the conjecture remains open even for trees. Here we prove that caterpillars are antimagic by means of an O(n log n) *** Codes 05C78 Copyright © 2018, The Authors. All rights reserved.

关键词： Trees (math.matics)

POS-tags features for Protein-Protein Interaction Extraction from Biomedical Articles

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POS-tags features for Protein-Protein Interaction Extraction...

IEEE International Congress on Electronics, Electrical Engineering and Computing (INTERCON)

作者： Pedro Shiguihara-Juárez Nils Murrugarra-Llerena Alneu de Andrade Lopes Department of Computer Science Universidad Peruana de Ciencias Aplicadas Lima Peru Department of Computer Science Univesity of Pittsburgh Pittsburgh PA USA Institute of Math. Sciences and Comp. University of São Paulo São Carlos SP Brazil

ISBN: (纸本)9781538654927

Protein-Protein Interaction (PPI) extraction from biomedical articles consists on extracting sentences were two or more proteins interact. Traditional articles tackle this problem creating more sophisticated classifiers. In contrast to them, we focus on discriminative features that can be exploited by traditional classifiers. Our method exploits information from POS-tags features and are combined with a bag-of-words approach. We used five standard corpora of PPI: Aimed, Bioinfer, HPRD50, IEPA and LLL. Our method is simple and achieves high results compared with other approaches. We achieve an improvement of 11% with our best competitor.

关键词： Feature extraction Proteins Protein engineering Bayes methods Machine learning Task analysis Support vector machines

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

Building a Good Team: Secretary Problems and the Supermodular Degree 17

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Building a Good Team: Secretary Problems and the Supermodula...

Annual ACM-Society for Industrial and applied math.atics Symposium on Discrete Algorithms

作者： Moran Feldman Rani Izsak Department of Mathematics and Computer Science The Open University of Israel Department of Computer Science and Applied Math. Weizmann Institute of Science

ISBN: (纸本)9781510836358

In the (classical) SECRETARY PROBLEM, one has to hire the best among n candidates. The candidates are interviewed, one at a time, at a uniformly random order, and one has to decide on the spot, whether to hire a candidate or continue interviewing. It is well known that the best candidate can be hired with a probability of 1/e (Dynkin, 1963). Recent works extend this problem to settings in which multiple candidates can be hired, subject to some constraint. Here, one wishes to hire a set of candidates maximizing a given objective set function. Almost all extensions considered in the literature assume the objective set function is either linear or submodular. Unfortunately, real world functions might not have either of these properties. Consider, for example, a scenario where one hires researchers for a project. Indeed, it can be that some researchers can substitute others for that matter. However, it can also be that some combinations of researchers result in synergy (see, e.g., Woolley et al., science 2010, for a study on collective intelligence). The first phenomenon can be modeled by a submoudlar set function, while the latter cannot. In this work, we study the secretary problem with an arbitrary non-negative monotone valuation function, subject to a general matroid constraint. One can prove that, generally, only very poor results can be obtained for this class of objective functions. We tackle this hardness by combining the following: (1) Parametrizing our algorithms by the supermodular degree of the objective function (defined by Feige and Izsak, ITCS 2013), which, roughly speaking, measures the distance of a function from being submodular. (2) Suggesting an (arguably) natural model that permits approximation guarantees that are polynomial in the supermodular degree (as opposed to the standard model which allows only exponential guarantees). Our algorithms learn the input by running a non-trivial estimation algorithm on a portion of it whose size depends on the s

关键词： secretary Objective function algorithms Function solidification Matroid candidate species Standard model Researchers Nonnegative

Defining the C-ITS Reference Architecture

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Defining the C-ITS Reference Architecture

Software Architecture Companion (ICSA-C)

作者： Priyanka Karkhanis Mark G.J van den Brand Saurab Rajkarnikar Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven The Netherlands Dept. of Math. & Comput. Sci. Eindhoven Univ. of Technol. Eindhoven Netherlands

Cooperative-Intelligent Transport Systems (CITS) aims to facilitate cooperative, connected and automated mobility. The C-ITS domain comprises widely spread systems like traffic management systems, traffic light controllers, and vehicle on-board units. Such complex and heterogeneous systems have independent uses but demand a strategy to facilitate their convergence. C-ITS is currently demonstrated by projects such as C-MobILE, which is a large scale demonstration project spanning from 2017-2020. One of the main objectives of C-MobILE is to define a reference architecture for large scale C-ITS deployment and demonstration at the partner deployment sites across Europe. The C-MobILE C-ITS reference architecture is defined using the C-ITS architecture framework that is compatible with the ISO/IEC/IEEE 42010 international standard for architecture descriptions of systems. C-MobILE C-ITS reference architecture captures the needs of deployment sites and provides a guidance for future projects. In this paper, we present the context and the functional view of the C-MobILE C-ITS reference architecture and share the lessons learned.

关键词： computer architecture Roads Europe Architecture Standards Context modeling Sensors