Affiliation: LIRMM, Université de Montpellier, CNRS, France & Department of Mathematics, NKUA, Greece
Title: Graph Degeneracy Measures: Algorithms and Applications
A complete tutorial on degeneracy parameters and applications can be found here
Abstract: A -core in a graph is a maximal subgraph with minimum degree at least . The degeneracy of a graph is the maximum for which contains a non-empty -core. This is a classic concept in Graph Theory that can be seen as a density measure on graphs and has been used as a theoretic model in several applications related to graph mining on large scale networks. This is due to the fact that -cores are providing a scalable graph hierarchization, called core decomposition, that partitions the graph to territories of increasing density. This facilitates the data analysis on several problems where the "densest parts" of the graph are of particular interest. We survey several applications of degeneracy and core decompositions in measures of collaboration as well as in problems of community detection in graphs emerging from real word networks. Depending on the semantics of the graph-represented relations, we present several variants of degeneracy on diverse combinatorial structures such as hypergraphs, directed graphs, and signed graphs.
Short CV: Prof. Dimitrios M. Thilikos received his PhD from the Department of Computer Engineering and Informatics of the University of Patras in 1996. He is a member of the AlGCo project-team, CNRS, LIRMM and Professor at the Dept. of Mathematics of NKUA. His research spans several fields of Theoretical Computer Science and Discrete Mathematics with contributions in Parameterized Computation and Graph Theory. His has published more than 160 papers in international conferences and journals related to Structural Graph Theory, Graph Decompositions, Approximation Algorithms, Probabilistic Methods, Graph Searching Games, and Graph Homomorphisms. He has contributions to applied areas such as Distributed Computing, Bioinformatics, and Data Mining. He taught several graduate and undergraduate courses at universities or research centers in Spain, Canada, France, Belgium, Greece, and Norway. He gave courses on Complexity Theory, Recursion Theory, Automata Theory, Algorithms, Combinatorics, Graph Theory, and Programming, including several mini-courses and tutorials at seasonal schools. He has supervised 6 PhD-thesis and 24 MSc Theses. He has has organized 11 conferences/workshops and has been 34 times a PC member of conferences/workshops – chairing three of them. In total, he has given 10 invited talks in conferences/workshops. Finally, he has been the editor or thee LNCS volumes and four volumes of international journals. In 2015 he received the EATCS Nerode Prize for his contribution to Parameterized Computation.
Affiliation: University of Hamburg
Title: Matheuristics: State-of-the-Art and a Text Mining Approach to a Matheuristics Survey
Abstract: In the last decades, one of the most interesting developments in the field of metaheuristics has been concerned with the development of hybrid algorithms, i.e., approaches that combine different components and methods. One of the most promising classes of hybrid algorithms is known under the name of "matheuristics," which are algorithms that combine techniques borrowed from mathematical programming with metaheuristic methods. The goal of this keynote is to survey and analyze the contributions emerged in the field of matheuristic, with a special focus on identifying the underlying patterns across the different methods.
We depart from the general approach adopted in survey papers in that we focus on conducting a text mining-based analysis. We use a skip-gram model to create a vector-space model which maps each paper into a continuous-valued vector. After converting each paper into a vector, we apply classical text mining techniques, i.e., clustering and topic modeling, to identify the central contributions within the realm of matheuristics. We then focus on these prominent papers and thoroughly review them. The presentation concludes by presenting a two-dimensional map of the extant matheuristics based on the text mining analysis.
Short CV: Stefan Voß is professor and director of the Institute of Information Systems at the University of Hamburg. Previous positions include full professor and head of the department of Business Administration, Information Systems and Information Management at the University of Technology Braunschweig (Germany) from 1995 up to 2002. He holds degrees in Mathematics (diploma) and Economics from the University of Hamburg and a Ph.D. and the habilitation from the University of Technology Darmstadt. His current research interests are in quantitative / information systems approaches to supply chain management and logistics including public mass transit and telecommunications. He is author and co-author of several books and several hundred papers in various journals. In the German Handelsblatt ranking he is continuously within the top 20 professors in business administration within the German speaking countries. The most recent Wirtschaftswoche ranking lists him among the top 10. Stefan Voß serves on the editorial board of some journals including being Editor of Netnomics and Editor of Public Transport. He is frequently organizing workshops and conferences. Furthermore, he is consulting with several companies.
Affiliation: Embry-Riddle Aeronautical University, Florida, USA
Title: Fast Algorithms and Applications of Delay Vandermonde Matrices
Abstract: Many problems in applied mathematics and electrical engineering cannot be solved by using standard techniques due large system solving problems. Thus, one can explore the structure to derive fast and stable algorithms. The delay Vandermonde matrix (DVM) is a Vandermonde matrix having nodes as wideband delays. The discrete Fourier transform (DFT) is also a Vandermonde matrix having nodes as the primitive roots of unity. Although the DVM is also a complex Vandermonde-structured matrix, unlike the DFT, DVM is lacking of unitary, periodicity, symmetry, or circular shift properties.
In this talk, we first introduce a factorization for the DVM leading to low-complexity analog realizations. Afterwards a DVM algorithm will be obtained to efficiently generate analog true-time-delay beams that have no beam squint. Next, we present a self-contained factorization for the Vandermonde-type matrices associated with true-time delay based wideband analog multi-beam beamforming using antenna arrays. We show that the proposed algorithm attain O(NlogN) delay-amplifier circuit counts. Finally, the language of signal flow graph representation of digital structures is used to describe potential for real-world circuit implementation.
Short CV: Sirani Perera is an assistant professor in Mathematics at Embry-Riddle Aeronautical University (ERAU), USA working in the field of Numerical Linear Algebra. Her research interests include: Scientific Computing, Structured Matrices (e.g. Vandermonde, Quasiseparable, Semiseparable, Bezoutian, and Banded), Matrices with Displacement Structure, DCT, DST, FFT, Algorithms for Computer Arithmetic, Complexity and Performance of Algorithms, Signal Processing, and Image Processing. As an early career female mathematician, she has addressed solutions for problems in applied mathematics and electrical engineering through her publications. Perera is working as the Co-PI of an NSF grant for the project entitled "Collaborative Research: Wideband Multi-Beam Antenna Arrays Low-Complexity Algorithms and Analog-CMOS Implementations", 2017-2020. The algorithms that she derives through the NSF grant can be utilized to solve the longstanding beam squint problem. In 2017, she has filed a provisional patent application entitled "System and Method for Performing Self-Recursive Discrete Cosine Transform and Inverse Discrete Cosine Transform". She has received grants, fellowships, and scholarships including: Faculty Innovative Research in Science and Technology Grants and Faculty Research Development Awards by ERAU; Early Career Travel Grant by the International Linear Algebra Society Conference, Belgium; Advanced Doctoral Fellowship, Doctoral Dissertation Fellowship, Predoctoral Fellowship by the University of Connecticut, USA; Industrial Research Scholarship by City University London, UK, and Shell Centenary Scholarship by the Cambridge Commonwealth Trust, University of Cambridge, UK. In 2016, she has served as the co-chair of the International Industrial Mathematics Conference in Sri Lanka, which was funded through NSF IPSAT grant 2016/05, and was co-editor of the proceeding booklet entitled "Present Status and the way Forward for Public Universities in Sri Lanka". She has guided research students to derive fast and stable algorithms to solve problems in applied mathematics and electrical engineering. These researches have enabled her students not only to obtain the first place at the Discovery Day and Internal Students Research Awards at ERAU but also to obtain several external travel funds. Perera received a PhD in Mathematics from the University of Connecticut, USA in 2012. She was the first Sri Lankan to attend the Center for Mathematical Sciences at the University of Cambridge, UK with full Shell Centenary Scholarship, and obtained Part III Tripos (Hons.) in Mathematics in 2006. Perera has received BSc (Hons.) in Mathematics from the University Sri Jayewardenepura, Sri Lanka in 2004.
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