Winona State University, USA
By Prof. Joyati Debnath, Winona State University, USA.
We see the existence of complex networks in all aspects of our lives, they include communication networks, neural network, circuit network, spread of infection network, Facebook friends’ network, transportation network, trading network, just to name a few. The sizes of the complex networks are increasing by the minute as we progress towards the next century. It is apparent that we need to rely on available spanning tree analysis and the integration of multimedia tools and other studies for understanding the networks. The number of spanning trees is an important invariant of a network. The spanning trees entropy of a complex network provides a useful insight about its robustness. The increase of this number provides the reliability and availability of the complex networks, whereas effective integration of multimedia tools can provide specific events for the network simulation. The effective complexity analysis and network reliability is important aspects of complex networks. This keynote presentation will focus on the fundamental techniques on complexity analysis of the topology of Small-World, Flower, and Mosaic Networks, a recent collaborated research work. Two combinatorial approaches, namely bipartition and the reduction methods that facilitate the calculation of the complexity of complex and large networks will be discussed and highlight the potential of these approaches.
Biography
Professor Joyati Debnath is currently a Full Professor of the Department of Mathematics and Statistics at Winona State University (WSU), Minnesota. She received M. S. degree in Pure Mathematics and Ph. D. degree in Applied Mathematics from Iowa State University, Ames, Iowa. She has been a faculty at Winona State University for over 27 years and teaching a wide range of undergraduate courses in Mathematics. She received numerous Honors and Awards including the Best Teaching Award from Iowa State University, the Outstanding Woman of Education Award, and Who’s Who Among American Teachers. Her research interests include Integral Transform Theory, Partial Differential Equations and Boundary Value Problem, Associations of Variables, Discrete Mathematics, Software Engineering Metrics and Tools, Forensic Science, Complex Network Theory, and Topological Graph Theory.
Professor Joyati Debnath has always been actively involved in research projects and has supervised many undergraduate students and graduate students in mathematics. Her students received recognition for best paper presentations at the national and international conferences. She is an author or co-author of over 70 publications in numerous refereed journals and conference proceedings in Mathematics, and Computer Science.
She has made numerous teaching and research presentations and served as the technical session chair at national and international conferences in Mathematics, and Computer Science including the Annual Meeting of the American Mathematical Society (AMS), Annual Meeting of the Society of Industrial and Applied Mathematics (SIAM), International Conference in Industrial and Applied Mathematics (ICIAM), International Congress of Mathematicians (ICM), International Conference on Computers and Their Applications, International Conference on Computer Applications in Industry and Engineering, and IEEE International Symposium in Signal Processing and Information Technology. She taught courses in lower level and advanced level courses in mathematics at universities in India, Taiwan, China, Tanzania and Sudan.
