Stochastic models in Computer Science; Graph-theoretic and other applications
A simple yet fascinating continuous-time stochastic processes, known as Brownian motion marveled natural scientists over decades. The growth and evolution of Random methods of computation and experimentation from the context of physical sciences towards its ever expanding reach to the realms of modern computing is the topic of the tutorial. The lectures and demo strive to explain computers as stochastic processes and pose deterministic events, i.e the existence of events in a probabilistic manner. The idea is to explain/demonstrate the guiding principles in lucid language with the aid of several analytical examples and videos/demos and motivate the young students and researchers to explore this powerful and elegant paradigm.
Outline including a short summary of every section
- Discrete probability models in Computer Science- Randomness, Random variable, the real number line and the set of integers, Playing an ancient game of probability with simulation (Video demo-Web Application), Fair coin tossing game and implications in discrete sampling. Discrete distributions and applications in Computer Science (Demo using toolkit developed by the presenter), Fermi’s neutron experiment.
- Measures of central tendency and implications-Expectation of a discrete random variable, probability mass function, Variance and estimation- implications in randomized sort algorithms, Monte Carlo simulation and its application in Econometric modeling.
- Random Graphs-Posing a deterministic problem via the theory of uncertainty, Erdos-Renyi theorem, Probability of edge connectivity and existence of cycles/cliques/independent sets in undirected graphs
- Applications in Computer Modeling- Markov Birth-death process, M/M/1 and M/M/K queues and applications in facility management, system performance analysis, Bayesian classification and Risk bounds in identifying/marking vulnerability in application security( Original research by the presenter)
- Intended audience Post-graduate/Doctoral students and young faculty (less than two years in an academic position)
- Specific goals and objectives
- Help grow familiarity with a very active and crucial branch of Applied Mathematics and Computer Science
- Help develop the process of intuitive thought in Computer modeling
- Enunciate the broad areas of application such as System performance analysis, pattern classification, social network, Software Engineering, to name a few
- Help demystify large complex networks with the aid of stochastic modeling
- Present the theory in such a manner which helps clarify the veracity and versatility of a score of applications.
Snehanshu Saha has been awarded degrees in Mathematics and Computer Science. He earned his Masters in Mathematical Sciences at Clemson University and PhD from the Department of Mathematics at University of Texas at Arlington in 2008. After working briefly at his Alma matter, he moved to the University of Texas El Paso, where he taught differential equations, calculus and linear algebra. He is a Professor of Computer Science and Engineering at PESIT South since 2011 and heads the Center for Basic Initiatives in Mathematical Modeling. He has published 30 peer-reviewed articles in reputed International journals and conferences.