Project:
Bayesian adaptation
using Gaussian priors; B. Szabo, PhD
In
recent years there has been a huge increase in the use of adaptive
Bayesian methods in high-dimensional or nonparametrical statistical
problems. The two most popular procedures are the empirical Bayes and
the hierarchical full Bayes methods. Our goal is to contribute in the
fundamental understanding of the asymptotic behavior of these methods.
We focused mainly on the empirical Bayes method, but the derived results
can be applied to the hierarchical Bayes method also. We were examining
the Gaussian sequence model and showed that by bad choice of the prior
distribution, the empirical Bayes method behaves sub-optimally, but with
careful choice we can get optimal, adaptive results.
Project:
Nematic phase transitions for hard-rod lattice models; S. Taati, PD
Nematic liquid
crystals flow like liquids but have anisotropic optical properties as in
most crystals. They are widely used in the liquid crystal displays (LCD).
The molecules of a liquid crystal material resemble long and thin rigid
rods. In the nematic phase, these rods tend to align, while their
relative positions remain disordered. In the lattice model, the
molecules are abstracted as n-by-1 rectangles that are placed on the
two-dimensional lattice, either horizontally or vertically, without
overlapping one another. In this project, we aim to prove the
occurrence of a nematic phase in this model within the framework of
statistical mechanics
Project: Random polymers; M. Heydenreich,
Assistent to Professor
The research of Markus
Heydenreich is centered around critical phenomena of random spatial
models. This includes models for porous media and (abstract) polymers.
In particular, the self-similar, fractal structures appearing at the
critical point are investigated. Special emphasis is on the study of
random walk on the incipient infinite cluster, a primary example of
random walk on a fractal like structure. This example exhibits anomalous
diffusion, which means that the random walk on the incipient infinite
cluster (like on many natural fractals) is significantly slower than on
Euclidean space.
Project:
Multilayered queueing systems;
J.P. Dorsman, PhD
The current
research project is placed within the domain of shared resource
possession in stochastic networks. Recent applications in engineering,
business and the public sector led to systems with much more complex,
often layered, service architectures, where entities that act as server
at one layer can act as customer at a higher layer. The performance
analysis and design of these new applications require the development of
sophisticated new stochastic network models. So far, such layered
systems have only been analysed approximately and through simulations,
and were limited to computer-science problems. However, the mathematical
analysis of such systems is extremely challenging and exciting.
In this project, contrary to previous approximation studies, we aim to
develop new mathematical tools that will allow for rigorous mathematical
insights into the quantitative and qualitative behaviour of layered
queueing systems. Up to now, we have studied a class of queueing systems
consisting of two layers, where the interaction between the two layers
leads to statistical dependence between the queue lengths of the queues
within the upper layer. We have derived accurate approximations for the
marginal queue length distributions of these queues by modelling the
interaction between the layers explicitly. In addition, through the use
of the Power-Series algorithm, we have studied the light-traffic
behaviour of the joint queue length for these queues. When the
heavy-traffic behaviour can be identified as well, a combination of the
two will lead to valuable insights in the joint queue length process for
the queues in the upper layer.
Project: Modeling brain
networks dynamics; B. Rós, PhD
My
research is in the area of stochastic modeling and statistical analysis
of brain network dynamics. In the project we consider the brain as a
system that consists of a set of interconnected specialized regions that
give rise to behavior through their mutual interactions. Changes in
behavior over time or differences in behavior under different conditions
can be due to specific changes or differences in this network. In this
project we use mathematical modeling and statistical analysis to
identify which regions in the brain cooperate in different situations
and under different conditions and how they do this. Our approach is to
build a network model consisting of appropriate brain regions as nodes
with the edges defined by the relationships between them. This model
will be inferred from simultaneously collected spatio-temporal fMRI and
EEG data.
Project: Stochastics models
for emergency care
(NOW/Defense PhD); S. Ding, PhD
My research falls into the
area of multi-skill call centers. The objective is to improve the
performance of a multi-skill call centers. To this end, a good and
accurate forecasting method is of interests. This requires investigation
of time-series analysis. Forecast of a call center plays a crucial role
in the performance of a call center. I am very interested in evaluating
and comparing different forecast methods, and develop a suitable method
for our data. When we obtain the call forecast, the next step is to make
stuffing for call centers. The number of agents per skill group is the
key point in reaching the service level of call centers. In order to
derive this number with cost minimization, simulation and approximation
will be useful. Besides the theoretical interests of call center problem,
it also has a practical usage in the industry.
Project:
Network Congestion; N.S. Walton, Ass.Prof
My
research is principally concerns congestion occurring in networks. Many
congested systems naturally converge to a certain mode of behavior,
whether that be equilibrium or non-equilibrium behavior. In a number of
circumstances, such behavior can be expressed as the solution to an
optimization problem. Although congestion may be unavoidable in a well
utilized network, by understanding the nature of such optimization
descriptions, we can hope to better understand how to redesign systems
to optimize what we want them to optimize.
The tools used in this analysis include to probability, queueing theory,
optimization and game theory, and application areas include Internet,
telephony and road traffic.
Project: Sandpile models on random graphs; Mrs. W. Ruszel, Ass.Prof.
We study two types of models. The first
model is a sandpile model on the complete graph with a uniformly bounded
critical height h. The simplest example occurs when this critical height
equals 2. Here, the dynamics consist of two types. At each time, if the
configuration is stable, then there is a new “particle” dropped into the
system at a uniform location, otherwise the unstable site picks h sites
at random and distributes the particles to those sites. One of the sites
is a sink, where the particle upon entering is lost. We want to study
the stationary state of the joint distribution of the number of sites
that need to be toppled as well as the number of topplings still to be
performed at each time step. Moreover, we aim to study the tail
behavior of the avalanche size, which is defined as the time the system
takes to return to a stable configuration after adding a new particle.
The
second model we consider is a sandpile model on a random binary tree
with branching parameter p. The dynamics is a composition of the
sandpile dynamics and the topology of the random graph itself, leading
to double randomness. We want to investigate the avalanche sizes in the
stationary state depending on p. For p=1 previous results show power-law
behavior for the avalanche sizes. We want to investigate weather this
happens already for some p smaller than 1. |