European Institute for Statistics, Probability, Stochastic Operations Research and its Applications

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Adding randomness to the complete graph can dramatically change its apparent structure, from a highly connected and symmetric graph to one that is inhomogeneous and tree-like. I will describe a way to couple processes on the complete graph with corresponding processes on an infinite tree, and explain how we can extract scaling behaviour when the size of the complete graph is large.

The linear complementarity problem (LCP) is as follows: Given a square matrix M and a vector q, find non-negative vectors z and w such that w-Mz=q and w'z=0. Linear programming and quadratic programming (optimization problems) are special cases. LCP also appears in game theory and the study of stochastic queueing networks.
In this talk I will introduce the LCP, outline and give insight on some basic results and show the connection to overflow queuing networks (current joint work with Erjen Lefeber). Since this is an EPPS talk, I will also try to give it a personal touch. Also, since I already gave one EPPS talk where I showed pictures and talked about my past, this time I will try to concentrate more on the future....

Coming from Berlin, I shall devote the first (personal) part of my talk to speaking about the Berlin WALL. Following the fall of the WALL, I shall change focus to (probabilistic) two-type interacting particle systems. In particular, I introduce the voter model and the contact process and give a graphical representation for both of them. With the help of this representation I shall give examples for two techniques commonly used in this area, namely, coupling and duality.

Analytic problem solving for Eurandom

In this presentation I briefly introduce myself by saying something about my math education, scientific career, competences and research expertises. Furthermore, I try to indicate in what way I could be helpful for your research by showing a number of examples where my problem solving capabilities gave rise to (semi-) analytic solutions.

t.b.a.

Will give an overview of the different limit theorems that arise in the setting of Galton-Watson processes. The talk will be based on spine decomposition techniques due to Russell Lyons. 

Lihu Xu (EURANDOM)

An introduction to Malliavin calculus

I will try to give an immature review on the Malliavin calculus based on my very limited knowledge in this subject. We shall study Malliavin derivatives, integration by part formula, Clark-Ocone formula, Malliavin matrix, regularity of probability law and the application to degenerate diffusions. We shall not give any rigorous proof of theorems, but give some formal derivation (for instance integration by part formula) or some heuristic interpretation (for instance the application part). If the time is permitted, I would like to talk a little about Stein method or Wiener chaos decomposition. One of nice materials for Milliavin calculus is http://www.statslab.cam.ac.uk/~peter/mystuff/papers.html by Friz.

As with good EPPS tradition, I will open this talk by discussing my life, showing family pictures and trying to be a little bit funny. I'll then move onto show pictures of colleagues that have been edited using Photoshop, or actually maybe I WILL NOT DO THAT since it is not so funny. I'll then move onto the real fun subject: Interactive Demonstrations with MATHEMATICA.

MATHEMATICA has a nice feature (since version 6) that allows to create simple interactive calculations: Manipulate[f[x],{x,0,1}] opens a window that displays the results of f[x], with a slider for x in the range [0,1] and re-evaluates f[x] in "real time" based on the position of the slider (which the user moves). This simple (almost trivial) feature allows one to create simple (and not so simple) demonstrations of mathematical phenomena which often give a-lot of insight. It is actually also a good research tool - I'll show a case or two where it helped me.

I'll then present some of the content of an undergraduate course that I taught in Israel: http://stat.haifa.ac.il/~yonin/interactive_demos_course_winter_09/int_demos.html  The purpose of that course was 3 fold: 1) To teach the students the basics of MATHEMATICA 2) To strengthen understanding (and give some intuition) for basic concepts of probability, statistics and queuing theory 3) To try to use the students for creating demonstrations for the so-called "Queuing Science Exploratorium": http://stat.haifa.ac.il/~yonin/qsm/main.html , a project I've been trying to build for hosting interactive demonstrations of queuing theory on the web

We show that in the stationary M/G/1 queue, if the service time distribution is IFR , then (a) The distribution of the number of customers in the system is also IFR (DFR), (b) The conditional distribution of the remaining service time given the number of customers in the system is also IFR  and (c) The conditional distribution of the remaining service time given the number of customers in the system, is stochastically decreasing with the number of customers in the system. In the DFR case, items a and b are change to DFR as well, while in item c, “decreasing” should be changed to “increasing”.

I will a give a talk about my current research topic the next day. So I want to take the opportunity to talk about something that (hopefully) most of you find interesting. I want to give a not too technical insight into the mathematical fundamental and idea of finance mathematics. 

In this talk I define invasion percolation cluster and state some recent results about its geometry.

We propose a probabilistic method for detection of signals and reconstruction of images in presence of random noise. The method uses results from percolation and random graph theories. We are able to detect and estimate not only regular images, but also weak signals, as well as fine structures such as curves. We describe a randomized algorithm that detects objects in noisy images very quickly. The algorithm works substantially faster than, say, wavelets-based algorithms. Moreover, a slightly modified version of this algorithm also produces reasonable estimates of images. Consistency and computational complexity of our algorithms will be discussed. It is expected that the algorithms are quick enough to be used in real-time systems. Some funny pictures will be also shown.

Alexander Ledovskikh has been graduated in National Technical University (Kiev Polytechnical Institute, Kiev, Ukraine), and then he has got his PhD in Institute For Sorption and Problems of Endoecology National Academy of Science of Ukraine, Kiev. After he has been appointed as a post-doc in TU/e his research activity is devoted to modelling of hydrogen storage in hydride-forming materials. Based on first principles chemical reaction kinetics and statistical thermodynamics, the model is able to describe the complex processes occurring in hydrogen storage systems, including phase transitions. A complete set of equations, governing pressure-composition isotherms and equilibrium potential in both solid-solution and two-phase coexistence regions has been obtained. The combination of thermodynamic and formal chemical kinetic descriptions is a good advantage of proposed model. The model has been tested on various hydride-forming materials. Good agreement between experimental and theoretical results has been found in all cases. The research results of Alexander have been published in famous scientific journals.

We will show how our transient interpretations of Little’s law and the ASTA (Arrivals See Time Averages) property can be used to provide new insight into the transient behavior of queueing systems that behave in a preemptive manner.  In particular, we will first show how our transient interpretations of Little’s law can be used to derive nice probabilistic expressions for all moments of $Q(t)$, which represents the number of customers at time $t$ in an M/G/1 queue that behaves in a preemptive Last-Come-First-Served manner (can be preemptive-resume, preemptive-repeat, or any random mixture of these disciplines), for any initial condition $Q(0)$.  As a consequence, by properly rescaling time and space and taking appropriate limits, these moments can also be used to derive analogous moment expressions for a regulated Brownian motion.  Next, we will show how the main ideas behind ASTA can be used to derive the Laplace-Stieltjes transform of the probability mass function (pmf) of $Q(t)$, for preemptive systems with state-dependent Poisson arrivals and services, and multiple deletions.  An interesting special case of our preemptive-queueing model is a birth-death process, and we will show how to use our results to quickly rediscover a probabilistic interpretation of the pmf of Q(t) for the M/M/1 model, which was previously derived in a work of Abate, Kijima and Whitt through the use of different methods.

Last modified: 14-10-11
Maintained by JM

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