The PhD Seminar Program:
The time for the seminar is 15:15-16:15 on fridays. The place is MVL:14.
Fall 2014
No talks so far... Which friday do you prefer for your talk?
Spring 2014
7th. february, 15:15-16, MV:L14
Speaker: Mahdi Hormozi
Title: A journey into singular integrals
Abstract: Singular integrals are among the most interesting and
important objects of study in analysis. This topic attracted several
leading mathematical innovators (e.g. Stein, Fefferman, etc). My talk
will cover some basic notions and definitions (Hilbert transform, the
space BMO, etc) and in the end of the talk I discuss briefly the very
important T(1)-theorem.
25th. april, 15.15-16, MV:L14
Speaker: Jacob Leander
Title: Understanding population variability using non-linear mixed effects models
Abstract: In
this talk I introduce you to the concept of mixed-effects models which
are very useful when samples are taken from a population of individuals
(e.g. in clinical trials or on a large collection of cells). We
consider the inverse problem of estimating model parameters from
measured data using the likelihood approach. In my current research I
investigate the possibility of combining stochastic differential
equations and mixed-effects models to allow for a more general model
specification.
23th. may, 15.15-16, MV:L14
Speaker: Elin Solberg
Title: On electro-optical modulators and electric field simulations
Abstract:
The Fraunhofer research project OptoScope, involving several
institutes, aims to develop an oscilloscope for high frequency electric
signals reaching up to 1THz. The principle relies on chirped pulses
being used in time-stretch analog-to-digital converters to stretch high
frequency electric signals, so that they can be measured by
conventional detectors. The task of Fraunhofer Chalmers Centre (FCC)
i to simulate one of the key components of the time-stretch
system, an electro-optical modulator (EOM). This comes down to solving
Maxwell's equations in an open, inhomogeneous, optically very long -
several thousand wavelengths - waveguide. In my talk I will describe
the principles of the time-stretch system and the EOM, and present our
current work in which we use the time-domain beam propagation method
for the EOM simulations.
Fall 2013
25th. october, 15:15-16, MV:L14
Speaker: Henrike Häbel
Title: Spatial modeling of micro-structures of materials
Abstract: In several
industrial areas mass transport of liquids in a material is crucial for its
properties and function. The aim
of my Ph.D. project is to construct and fit spatial models to given data on
biomaterial in order to understand and control mass transport properties such
as diffusion through these complex geometrical micro-structures. For example,
images from porous Ethyl cellulose / Hydroxypropyl cellulose
blended films used for controlled drug release have been studied. Their
micro-structure is mainly determined by the percentage of HPC which acts as a
pore former. After
having converted these images using statistical image analysis techniques, 2D
or 3D models are constructed and fitted to the given data applying methods from
stochastic geometry and spatial statistics. These
models are based on so called marked point processes. In particular, the
centers of the pores are modeled by random vectors of coordinates of points in
a study region. The pores themselves can be modeled by unions of overlapping
spheres. For this purpose, marks are assigned to each point representing the
radii of the spheres.
In my talk, I am going to introduce the concept of
marked point processes and how it can be applied to construct models of
micro-structures of materials using the example of porous polymer blended films.
8th. november, 15:15-16, MV:L14
Speaker: Zuzana Sabartova
Title: Surrogate
models for simulation based optimization
Abstract: The aim
of my Ph.D. project is to find the optimal set of tires for each truck and
operation cycle specification in order to reduce the fuel consumption of the
truck. The tire selection problem is very complex and requires models of
expensive simulation-based functions. Many optimization algorithms designed for
solving simulation-based optimization problems are based on creating a quickly
evaluable surrogate model of an expensive function. It
is not guaranteed by any existing interpolation or approximation method that
the final surrogate model meets a physical meaning or interpretation of
the original complex function, we refer to such properties as an expert
knowledge.
In my
talk, I am going to provide a framework how the standard interpolation methods
namely radial basis functions (RBFs) methods can be varied in order to fit the
expert expectations.
15th. november, 15:15-16, MV:L14
Speaker: Roza Maghsood
Title: Detection of the Curves based on Lateral Acceleration using Hidden Markov
Models
Abstract: In vehicle design it is desirable to model the loads by
describing the load environment, the customer usage and the vehicle dynamics.
In this study a method will be proposed for detection of curves using a lateral
acceleration signal. The method is based on Hidden Markov Models (HMMs) which
are probabilistic models that can be used to recognize patterns in time series
data. In an HMM, 'hidden' refers to a Markov chain where the states are not
observable, however what can be observed is a sequence of data where each
observation is a random variable whose distribution depends on the current
hidden state. The idea here is to consider the current driving event as the
hidden state and the lateral acceleration signal as the observed sequence.
Examples of curve detection are presented for both simulated and measured data.
The classification results indicate that the method can recognize left and right
turns with small misclassification errors.
Spring 2013
27th march, 15.15-16, MV:L14
Speaker: Anton Muratov
Title: Polya's urns, Dirichlet distributions, exchangeability and random Dirichlet
measures
Abstract: Random Dirichlet measure, also known as Ferguson process, is a random element on
a set of purely discrete measures on a general measurable space. Dirichlet
measures are widely used as priors in non-parametric models. They are
particularly good in that quality, because the posteriors have a simple
probabilistic interpretation. Dirichlet measures naturally arise as limits in
various processes. I will give a brief introduction on how to construct
Dirichlet measures, how to interpret something being Dirichlet-distributed, how
to manipulate the Dirichlet random vectors; as well as some not-so-complicated
urn model intuition. If time allows, I will mention the connection between the
Dirichlet measures and Gamma processes with independent increments.
12th april, 15.15-16.15, MV:L14
Speaker: Fredrik Boulund
Title: Bacteria, their genes and metagenomics, or: solving problems of
querying very large data sets
The diversity in bacterial communities
is immense and in most cases highly unknown. The collection of all DNA from
a bacterial community is called the metagenome and metagenomics is the tool
used to study these complex mixtures of bacterial DNA. By using modern DNA
sequencing technologies it is now possible to unlock the hidden interactions
within the bacterial communities to determine the function of organisms that
were previously out of reach using regular culture-based methods.In this
talk I will introduce the topic of metagenomic analysis. I will give an
examples from two of my research projects: one of a published method that
uses statistical models of genes (hidden Markov models) for detecting and
identifying fragments of specific genes in random DNA fragments from a
metagenomes. Along with this will be a brief discussion on the problem of
evaluating the accuracy of predictions in gene finding. The other project I
will mention is an analysis workflow and distribution framework for working
with terabyte-sized data sets on computer cluster systems that is currently
in development.
19th april
Speaker: Mariana Pereira
Title: Conditional Random Fields applied to Bioinformatics.
Abstract: Traditionally, Bioinformatics have
used hidden Markov models (HMM) to analyze biological sequences, i.e. DNA, RNA
and protein [1]. HMMs are models defined by two processes. One is a Markov
process, hidden from the observer. The other is the observed process that
depends on the hidden. The hidden process jumps between states in a state space,
and emits an observation in each jump. For instance, when applied to gene
finding, the hidden states are labels such as gene or non-gene, and the observed
variables are DNA bases.
HMMs are a particular case of
directed graphical models. In these models, edges have directions from a parent
to a child variable in such a way that edges have a clear probabilistic
interpretation: the child depends on the parent. Conditional Random Fields (CRF)
are undirected graphical models [2]. Thus, edges have no direction and no
probabilistic interpretation. This provides CRFs with more flexibility than
HMMs. While HMMs calculate the joint probability p(Y,X) of the hidden state
sequence Y and the observed sequence X, CRFs model the conditional probability
p(Y|X), which is sufficient to predict which sequence of labels is more likely
given the observed sequence. Thus, there is no need to calculate the marginal
probability p(X), making it computationally simpler. Also, CRFs require fewer
independence assumptions and it is easy to incorporate external
information.
[1] Axelson-Fisk M. Comparative Gene Findings: Models, Algorithms and Implementation. Springer, London, 2010.
[2] Lafferty J., McCallum A., Pereira F. Conditional random fields: Probabilistic models for segmenting and labeling sequence data. ICML, 2001.
3rd. may
Speaker: Viktor Jonsson
Title: Metagenomics, statistical modeling and Bayesian
statistics.
Abstract: Metagenomics is the field where entire communities of
microbes are studied on the genome level. The vast majority of bacteria cannot
be cultivated individually in the lab because they are highly adapted and rely
on the complex environment found in their particular habitat. This makes
metagenomics an important technique for studying the microbes that surround us
and govern our lives.
In this talk I will present my research on developing a
statistical method for comparative metagenomics. I will go through the important
experimental and computational steps behind such an analysis and focus on why
statistical modeling is useful. Markov Chain Monte Carlo sampling is needed
because the model becomes too complex to handle with standard frequentistic
methods and some of the background to MCMC will be covered. Finally I will show
some preliminary results comparing the new model to other standard methods,
results which sometimes are not what you expected them to
be…
15th. may, 15.15-16.15, MV:L14
Speaker: Jacob Hultgren
Title: Invitation to Toric Geometry
Abstract: This seminar is based
on a reading course about toric varieties I just finished.
A compactification of C^n is a way to add something
of dimension < n to C^n such that the resulting space is compact. A common
example is the Riemann sphere where a “point at infinity” has been added to the
complex plane to wrap it up into a sphere. These compactifications of C^n are
examples of a wider class of varieties called toric varieties. It turns out that
this type of varieties are, in some sense, completely determined by a set of
combinatorial data.
I will start out by explaining what a variety is and
then continue with toric varieties. The goal is to explain how to go from a
toric variety to its combinatorial data and, if there is time, show how to use
this data to glue together simple toric varieties into new toric varieties.
Spring 2012
Topic 1: Mathematics education
4th april
Speakers: Ida Säfström and Helena Johansson
Title: Different perspectives on research in mathematics education
Abstract: PhD students in Mathematics, specialising in Educational Sciences,
present some of their research.
Topic 2: Complex analysis
2nd. may
Speaker: Richard Lärkäng
Title: Cauchy's integral
formula and the division algorithm for polynomials
Abstract: In one
variable complex analysis, Cauchy's integral formula is a
fundamental tool. I
will try explain how, if things are properly
defined, it is an elementary
consequence of Green's formula (or the
divergence theorem) in 2-variable
calculus.
Then I will show how one could express the division algorithm
for
polynomials in one complex variable with the help of Cauchy's
integral
formula. This might be a rather complicated way to solve an
easy
problem, but it illustrates nicely what my research topic,
residue
currents in several complex variables, is and how it might show
up.
Topic 3: Stochastic Modeling in Biology (continuation)
23rd. may
Speaker: Krzysztof Bartoszek
Title: Conditioned Yule process and phylogenetic comparative methods
Abstract: The
majority of phylogenetic comparative methods assume that the underlying
phylogeny is known without error. Despite the increasing quantity and quality
of molecular data this is still a simplification as there are many possible
sources of error. Therefore we need somehow to connect models of tree growth
with models of phenotype evolution.
The framework of conditioned (on the
number of contemporary species) branching processes which has evolved in
the
past decade offers possibilities in this direction. In the talk we will
concentrate on the conditioned Yule process, characterize a Brownian motion
process evolving on it and discuss how this allows us to construct second order
phylogenetic confidence intervals for the ancestral state.
Fall 2011
Topic 1: Kinetic Theory
14th october:
Speaker: Svitlana Ruzhytska
Title : Boltzmann Equation. Introduction
Abstract : I
will give a short introduction to the Boltzmann equation describing 'delute
gas'. I will show, how to obtain macroscopic properties of the gas such as
pressure, temperature, density and others from the microscopic parameters
involved in the Boltzmann equation such as particle velocity, position,
distribution function. I will also show, that conservation laws of mass,
momentum, and energy at micro- and macro levels are satisfied, as well as law of
non-decreasing entropy, which allows one to relate Boltzmann equation to the
classical fluid dynamics.
20th october (Wednesday 15:15-16:15):
Speaker: Dawan Mustafa
Title: More on the Bolzmann
equation and its connection to the Kac model.
Abstract: We continue with
Svitlanas lecture and move on discussing celebrating mathematical results on the
Boltzmann equation. Another model which is less complicated but still governs
most properties as for the Boltzmann equation is called the Kac-model. The Kac
model is a probabilistic model. We will also discuss the connections between
the Boltzmann and Kac model.
Topic 2: Optimal Control Theory
26th october:
Speakers: Adam Andersson
Title: A short overview of optimal control theory.
Abstract: Consider a dynamical system governed by a differential
equation. The equation depends on some parameter u. The aim here is to
control the dynamics in an optimal way, balancing the cost of
controling and the cost of deviating from a certain desirable behaviour
of the solution. I will present examples of controled ODEs and PDEs.
Control of stochastic ODEs will also be considered. Solving such
problems mainly divides into two different approaches. The first one is
by solving a PDE, called the Hamilton-Jacobi-Bellman equation. From the
solution one can often compute the optimal control. The other one is by
using Lagrange methods and calculus of variations.
4th november:
Speaker: Peter Helgesson
Title: Some basic concepts of Mean Field Game theory
Abstract: Mean field game theory (MFG) is a new branch of game theory,
first described in a series of papers by P.L Lions and J.M Lasry in 2006,
describing certain game theoretic problems with a large number of interacting
players. By approximating the discrete N-player game by a continuum of “small”
players one arrives at a field theoretic model, much like the Boltzmann kinetic
theory or Hartree-Fock method in quantum physics, where a player is subjected to
a single "mean field" behavior of all the other players, rather than considering
every opponent individually. The general setting of the MFG problem turns out to
be a coupled PDE forward/backward system of the Hamilton-Jacobi-Bellman equation
and a Fokker-Planck type of equation. In this talk I will introduce the ideas
and the mathematical frame work of MFGs in a sketchy “casual Friday manner”, as
well as discuss some examples and applications.
11th november, 16:15-17:15:
Speaker: Emil Gustavsson:
Title: Discrete Dynamic Programming in Optimization
Abstract:
Dynamic programming is a method used in optimization for solving
multi-stage decision problems. I will talk about Bellmans principle of
optimality, and how the optimal solutions can be found by solving a
number of subproblems recursively. If there is time, I will also say
something about "the curses of dimensionality" that often appear in
dynamic programming settings, and present a approximative method for
solving the optimality equations.
Topic 3: Stochastic Modeling in Biology
25th november, 15:15-16:15:
Speaker: Martin Berglund
Title: Mixed-effects models for time series
data
Abstract: Mixed-effects models are often used to represent
clustered, and therefore dependent data. I will discuss how mixed-effects
modelling can be used to set up a model for a population of individuals. Some
parameters of the model are assumed to be identical for each individual in the
population, whereas others are individual-specific and introduced as random
effects in the population model.
I will consider the case of time series
data for each individual. The underlying individual-specific model that is used
to describe the data is based on differential equations. One goal with
mixed-effects modelling is to develop a population model that describes the
distribution of the parameters in the population.
Topic 4: Combinatorial games
9th december, 15:15-16:15:
Speaker: Urban Larsson,
Title: Combinatorial games, part 1
Abstract: We study 2 player combinatorial games with
alternating moves and normal winning condition: a player unable to move
loses. If the players have the same ruleset the game is impartial. Then the
positions are partitioned into P and N, the previous player or the next player
wins. In general, for partizan games, there is a ruleset for (player) Left and
another for Right and so, there are four outcome classes: P, N, Left or Right
wins. A disjunctive sum of games is a play in a finite number of games at the
same time. The player in turn chooses precisely one component and moves in it.
We study some particular games and their game trees. Then we discuss equivalence
classes (canonical forms) of games and thereby explain how to win in a sum of
games.
16th december, 15:15-16:15:
Speaker: Ragnar Freij,
Title: Combinatorial games, part 2
Abstract: In this talk, we will discuss different notions of equivalence of combinatorial
games, and operations on them. We obtain an algebraic theory of combinatorial
games, where a curious substructure is observed. This subclass of all
combinatorial games is a linearly ordered field into which every other linearly
ordered field embeds. Our excursion will lead us to the reals, the
infinitesimals, the ordinals and other number systems. Once we are hypnotized by
the beauty of the subject and the handwaving of the lecturer, this diversity
will be explained by the observation that "abstract combinatorial game theory is
only a set theory with decorations"