Forschungsschwerpunkt Mathematische Modellierung (FSPM2)

Seminars (Colloquium)


Freitag, 19.07.2024, 16:00 c.t., H9: Johannes Schmidt-Hieber, Twente
Statistical learning in biological neural networks

Compared to artificial neural networks (ANNs), the brain learns faster, generalizes better to new situations and consumes much less energy. ANNs are motivated by the functioning of the brain but differ in several crucial aspects. For instance, ANNs are deterministic while biological neural networks (BNNs) are stochastic. Moreover, it is biologically implausible that the learning of the brain is based on gradient descent. In this talk we look at biological neural networks as a statistical method for supervised learning. We relate the local updating rule of the connection parameters in BNNs to a zero-order optimization method and derive some first statistical risk bounds.

Freitag, 12.07.2024, 16:00 c.t., X-E0-200: Annika Hoyer, Bielefeld

Freitag, 21.06.2024, 16:00 c.t., X-E0-200: Mathias Trabs, Karlsruhe
Towards statistical guarantees for uncertainty quantification in deep learning

An essential feature in modern data science, especially in machine learning as well as high-dimensional statistics, are large sample sizes and large parameter space dimensions. As a consequence, the design of methods for uncertainty quantification is characterized by a tension between numerically feasible and efficient algorithms and approaches which satisfy theoretically justified statistical properties.
In this talk we discuss a Bayesian MCMC-based method with a stochastic Metropolis-Hastings as a potential solution. By calculating acceptance probabilities on batches, a stochastic Metropolis-Hastings step saves computational costs, but reduces the effective sample size. We show that this obstacle can be avoided by a simple correction term. We study statistical properties of the resulting stationary distribution of the chain if the corrected stochastic Metropolis-Hastings approach is applied to sample from a Gibbs posterior distribution in a nonparametric regression setting. Focusing on deep neural network regression, we prove a PAC-Bayes oracle inequality which yields optimal contraction rates and we analyze the diameter and show high coverage probability of the resulting credible sets.
The talk is based on joint work with Sebastian Bieringer, Gregor Kasieczka and Maximilian F. Steffen.

Freitag, 24.05.2024, 16:00 c.t., X-E0-200: Stefan Rotter, Freiburg
Associative remodeling and repair in self-organizing networks

Structural plasticity and other types of network remodeling are prominent and well-documented processes during brain development, maturation, learning, and aging. Stunningly high turnover rates of neuronal connectivity have been observed under baseline conditions, and even more so upon stimulation or perturbation. However, these findings raise questions about the underlying biological mechanisms and biological function of this drastic form of brain plasticity. Since direct experiments are notoriously difficult to perform and analyze, formal models are crucial for predicting and understanding the emergent properties of graphs or networks with highly dynamic structure. To this end, we consider ensembles of directed multi-graphs with constrained indegrees and outdegrees, the Directed Configuration Model, as this reflects well the limited material resources of brain networks. Similar to the law of mass action in chemistry, we outline a kinetic theory of random graph formation and structural self-organization. We study the equilibria of these networks and describe the transient effects of perturbation. We apply our theoretical findings to biological neural networks of the brain, where the vertices are neurons and the directed edges are chemical synapses between neurons. In this setting, stimulation leads to perturbation of the network structure, followed by dynamic reconfiguration and convergence to a new structural equilibrium that is different from the previous one, reminiscent of hysteresis in solid state physics. I will describe some emergent properties of this new model, including Hebb's rule (“neurons that fire together wire together”) and self-repair of networks under appropriate conditions. For certain perturbation strategies, this provides us with models for brain maturation during adolescence and for engram formation in learning and memory. I will also discuss possible links to psychological phenomena like classical conditioning and describe new machine learning strategies based on the self-organization of networks that can be derived from our biologically motivated theory.

Freitag, 03.05.2024, 16:00 c.t., D5-153: Jürgen Schnack, Bielefeld
The Unreasonable Effectiveness of the Finite Temperature Lanczos Method

I will explain an astonishingly accurate, yet pretty simple approximation to evaluate thermodynamic equilibrium functions in quantum mechanics. The method rests on the Lanczos procedure, thus can be understood with matrix-vector procedures. Although originally designed to approximate extreme eigenvalues it could be shown that the method can easily be extended to address problems at finite temperature. A mathematical as well as a physical interpretation will be offered.

Winter Semester 2023/2024 Freitag, 26.01.2024, 16:00 c.t., V2-213: Roland Langrock (Bielefeld)
Periodic variation in hidden Markov models

The class of hidden Markov models (HMMs) is a popular tool for mo- delling time series driven by underlying states. HMMs can be used for example to relate animal movement processes to underlying beha- vioural modes, to infer the disease state of a patient from biomarkers, or to predict extreme share returns as a function of the underlying ner- vousness of the financial market. After a general introduction to this versatile class of time series models, I will focus on one particular ex- tension of HMMs, namely model formulations that attempt to capture periodic variation in the state-switching dynamics (e.g. daily variation in animal behaviour, or seasonality in economic markets). Such peri- odic variation is commonly modelled using trigonometric functions, but can alternatively and more flexibly be incorporated using cyclic splines. I will showcase these modelling approaches in case studies, in which I will also illustrate a positive consequence of such periodic modelling, namely that for periodic HMMs the distributions of the dwell times in the different system states can deviate substantially from a geometric distribution as it would be implied by a homogeneous HMM.

Freitag, 12.01.2024, 16:00 c.t., V2-213: Vitali Wachtel (Bielefeld)
Probabilistic approach to risk processes with level-dependent premium rate

In this talk I shall discuss classical risk processes and risk processes with level dependent premium rate. I shall present a purely probabilistic approach to processes with level-dependent rate, which allows one to obtain upper and lower bounds for ruin probabilities.

Freitag, 08.12.2023, 16:00 c.t., V2-213: Carolin Herrmann (Berlin)
Statistically proven? - the role of a valid sample size calculation in clinical trials

Randomized clinical trials are the preferred study design for answering medical research questions in an evidence-based way. Apart from a research idea, different aspects have to be decided on when planning a clinical trial, e.g. the treatments to compare with, the endpoints and the sample size.
Clinical trials can only be deemed successful if they come along with a valid sample size planning. Sample sizes should be large enough to detect an existing relevant effect with a sufficient probability. At the same time, they are supposed to be as small as possible to keep possible study related risks low and to not postpone a potential market approval unnecessarily.
After a short introduction to clinical trials, we consider the basic concept of sample size planning as well as more advanced statistical methods for updating sample sizes during ongoing trials.

Dienstag, 28.11.2023, 16:00 c.t., X-E0-200: Alexander Schönhuth (Bielefeld)
Diffusion Models: A Tutorial

Diffusion models have been one of the fundamental building blocks of generative deep learning techniques such as "text-to-image" models. In essence, diffusion models reflect a novel, neural network guided sampling strategy. They apply for heavily complex probability distributions. They are based on the general idea that only artificial intelligence techniques can lead one the way from random number generation to, for example, random images showing beaches with palm trees. I will discuss the mathematical and computational foundations of these models. I will also point out why such models may have the potential in attempts to "generate random life".

Freitag, 10.11.2023, 16:00 c.t., D2-136: Arndt von Haeseler (Wien)
Single-cell RNA sequencing and phylogenetic inference

In the talk we will merge the emerging field of scRNA sequencing data with the established field of phylogenomics. We will show that a simple transformation of the complex and high-dimensional scRNA data and the subsequent phylogenetic analysis leads to surprisingly clear visualisations and can thus provide the basis for new biological insights. The talk will be rounded off with some illustrative examples.
This is joint work with Christiane Elgert and Julia Naas.

Sommer Semester 2023 Montag, 17.07.2023, 16:00 c.t., D2-136: Mike Steel (Christchurch, Neuseeland)
Phylogenetic theory in conservation biology

The current rapid extinction of species leads not only to their loss, but also to the disappearance of the pendant and interior branches in the underlying evolutionary tree, along with the unique features (e.g. traits) that have evolved along these branches. In this talk, I describe some recent and new results for quantifying different measures of phylogenetic diversity and for predicting its loss under simple extinction models.

Freitag, 14.07.2023, 16:00 c.t., D2-136: Kai-Uwe Bux, Bielefeld
The Greek way of saying "let epsilon be greater than zero"

Proving equality of areas, lengths or angles was an important aspect of ancient geometrical thought (that's what the word "metric" indicates). For polygonal areas, the standard method is "cut and rearrange". This method does not apply in all cases for volumes or areas of curved shapes like circles. Archimedes in particular was very fond of integrating curved areas and volumes. We now know that limits are unavoidable in this case. So, our colleagues from antiquity (and among them Archimedes) did run into this problem; and they solved it very much in the same way that Cauchy and Weierstrass did. There is but one difference: the Greeks did neither have the concept of a real number nor did they think about functions. I shall outline the way in which ancient mathematicians dealt with limit arguments in a purely geometric fashion where one only deals with quantities and ratios without identifying those with numbers.

Freitag, 21.04.2023, 16:00 c.t., D2-136: Martin Wahl (Universität Bielefeld)
Principal component analysis in infinite dimensions

In high-dimensional settings, principal component analysis (PCA) reveals some unexpected phenomena, ranging from eigenvector inconsistency to eigenvalue (upward) bias. While such high-dimensional phenomena are now well understood in the spiked covariance model, the goal of this talk is to present some extensions for the case of PCA in infinite dimensions. As applications, I will discuss the prediction error of principal component regression (PCR) in the overparametrized regime, as well as nonlinear dimensionality reduction methods such as Laplacian eigenmaps and diffusion maps.

Winter Semester 2022/2023 Freitag, 27.01.2023, 16:00 c.t., online: Susanne Ditlevsen (Kopenhagen)
Time scales in early warnings: how to predict the time of tipping?
Zoom Room, Meeting ID: 674 2419 1845, Passcode: 524697

In recent years there has been an increasing awareness of the risks of collapse or tipping points in a wide variety of complex systems, ranging from human medical conditions, pandemics, ecosystems to climate, finance and society. Though these are governed by very different dynamics, they are characterized by variations on multiple spatial and temporal scales. This leads to incomplete understanding or uncertainty in modelling of the dynamics. Even in systems where governing equations are known, such as the atmospheric flow, predictability is limited by the chaotic nature of the systems and by the limited resolution in observations and computer simulations. In order to progress in analyzing these complex systems, assuming unresolved scales and chaotic dynamics beyond the horizon of prediction as being stochastic has proven itself efficient and successful.
When complex systems undergo critical transitions by changing a control parameter through a critical value, a structural change in the dynamics happens, the previously statistically stable state ceases to exist and the system moves to a different statistcally stable state. In order to establish under which conditions an early warning for tipping can be given, we consider a simple stochastic model, which can be considered a generic representative of many complex two state systems. We show how this provides a robust statistical method for predicting the time of tipping. The medthod is used to give a warning of a forthcoming collapse of the Atlantic meridional overturning circulation.
Ditlevsen, P.D., Ditlevsen, S. (2022). Warning of a forthcoming collapse of the Atlantic meridional overturning circulation. Research Square

Freitag, 20.01.2023, 16:00 c.t., H11: Boris Hemkemeier (Commerzbank Frankfurt)
Zwanzig Jahre Cybercrime und was wir dagegen tun können

Anfang der 2000er schwappte Phishing aus den USA nach Europa rüber. Inzwischen sind die Betriebssysteme sicherer, die Kunden aufgeklärter und die technischen Verfahren im Onlinebanking in der Praxis kaum zu überwinden. Trotzdem ist der Cybercrime eine Wachstumsbranche, denn Angriffe haben sich von der Technik auf den Trickbetrug verlagert. Phishing, Techniker-Support und WhatsApp-Betrug, Enkeltrick 2.0. Aber auch CFO-Fraud und selbst die Ransomware leben allein vom Storrytelling. Wir diskutieren, welche Gegenmaßnahmen jenseits sicherer Technik effektiv sind und welche Herausforderungen in der Modellierung von  Cyberrisiken stecken.

Freitag, 16.12.2022, 16:00 c.t., X-E0-203,
Marie Doumic (Paris)
What triggers bacterial division? Mathematical modelling and inference for bacterial population dynamics

What triggers the bacterial division? To answer this question, several types of mathematical models have been built, studied, and more recently compared to experimental data on growing and dividing bacterial population. This is the field of structured population equations and stochastic processes, which knows a long-lasting interest for more than sixty years, leading to much progress in their mathematical understanding. They have been developed to describe a population dynamics in terms of well-chosen traits, assumed to characterize well the individual behaviour. More recently, thanks to the huge progress in experimental measurements, the question of estimating the parameters from population measurements also attracts a growing interest, since it finally allows to compare model and data, and thus to validate - or invalidate - the "structuring" character of the variable.
However, the so-called structuring variable may be quite abstract ("maturity", "satiety"...), and/or not directly measurable, whereas the quantities effectively measured may be linked to the structuring one in an unknown or intricate manner. We can thus formulate a general question: is it possible to estimate the dependence of a population on a given variable, which is not experimentally measurable, by taking advantage of the measurement of the dependence of the population on another - experimentally quantified - variable?
In this talk, we give first hints to answer this question, addressing it first in a specific setting, namely the growth and division of bacteria, and focus on a specific recently introduced model, the so-called "increment of size"-structured equation, where the division depends on the increment of size between birth and division.

Sommer Semester 2022
Dienstag, 12.04.2022, 16:00 c.t., online und in Y-1-201: Thomas Hillen (Universität Alberta)
Non-local Models for Cellular Adhesion
Zoom Room Meeting ID: 945 6235 5050, Passcode: 246256

Cellular adhesion is one of the most important interaction forces between cells and other tissue components. In 2006, Armstrong, Painter and Sherratt introduced a non-local PDE model for cellular adhesion, which was able to describe known experimental results on cell sorting and cancer growth. Since then, this model has been the focus of applications and analysis. The analysis becomes challenging through non-local cell-cell interaction and interactions with boundaries. In this talk I will present theoretical results of the adhesion model, such as a random walk derivation, biologically realistic boundary conditions, pattern formation and results on local and global existence of solutions.
(joint work with A. Buttenschoen, K. Painter, A. Gerisch, M. Winkler).

Winter Semester 2021/2022 Freitag, 26.11.2021, 16:00 c.t., online und in V2-210/216,
Peter Bühlmann (ETH Zurich)
Statistical Learning: Causal-oriented and Robust
Zoom Room, Meeting ID: 930 2011 6784, Passcode: 462251

Reliable, robust and interpretable machine learning is a big emerging theme in data science and artificial intelligence, complementing the development of pure black box prediction algorithms. Looking through the lens of statistical causality and exploiting a probabilistic invariance property opens up new paths and opportunities for enhanced interpretation, robustness and external validity, with wide-ranging prospects for various applications.

Freitag, 19.11.2021, 16:00 c.t., Online: Claudia Neuhauser (University of Houston)
Mathematical Models of Host-Symbiont Interactions
Zoom Room, Meeting ID: 973 1183 7014, Passcode: 367914

Host-symbiont interactions are ubiquitous in nature. They can involve pathogens and mutualists and have different levels of specificity. We will first introduce some general models before a pplying the modeling framework to virotherapy of cancer. Virotherapy of cancer relies on engineered viruses that selectively attack and kill cancer cells but leave healthy cells unaffected. The success of this therapy relies on the successful establishment of an infection that results in the death of cancer cells. We used spatially explicit, stochastic models of multi-species interactions to map out under what conditions the symbiont (virus) effectively eliminates the host (cancer cells). I will present rigorous results and conjectures based on simulations. I will report on an experimental system (in vitro and in vivo) that was developed by Dr. David Dingli (Mayo Clinic) and uses this mathematical framework to predict the effectiveness of virotherapy in cancer.

Sommer Semester 2021 Freitag, 25.06.2021, 16:00 c.t., Online: Arndt von Haeseler (Universität Wien)
Evolution of taboo free sequences
Zoom Room, Meeting ID: 961 4237 2382, Passcode: 970387

Models of sequence evolution typically assume that all DNA-sequences are possible. However, restriction enzymes that cut DNA at specific recognition sites provide an example where carrying a recognition site can be evolutionary disadvantageous. Motivated by this observation, we studied the set of DNA sequences with \textbf{taboos}, that is, with prohibited $k$-mers. The taboo-set is referred to as $\mathbb{T}$ and any allowed DNA as a taboo-free DNA. We consider the so-called Hamming graph $\Gamma_n(\mathbb{T})$, with taboo-free DNA of length $n$ as vertex set and whose edges connect two taboo-free DNA if their Hamming distance equals one. Any (random) walk on this graph describes the evolution of a DNA sequence that avoids taboos. We describe the construction of the vertex set of $\Gamma_n(\mathbb{T})$. Then we state conditions under which $\Gamma_n(\mathbb{T})$ and its suffix subgraphs are connected. Moreover, we provide an algorithm that determines if all these graphs are connected for an arbitrary $\mathbb{T}$. Finally, we give some illustrative examples how taboo sequence influence distance estimation. Moreover we discuss more general aspects of taboo sequences, when discussing evolution. This is joint work with Cassius Manuel, Dominic Földvari, Stephan Pfannerer (lexicographical order by the first name) Ref: C. Manuel, A von Haeseler (2020) J. Math. Biology 81:1029-1057

Winter Semester 2020/2021 Freitag, 19.03.2021, 16:00 c.t., Online: Alexander Schoenhuth (Universität Bielefeld)
Capsule Networks - a brief tutorial and applications in biology
Zoom Room, Meeting ID: 926 4815 6073, Passcode: 042902

I will provide a brief tutorial about capsule networks (CAPNs), and explain in particular what distinguishes them from convolutional neural networks (CNNs). Although suggested as a useful concept already earlier, CAPNs enjoyed their first successful application in 2017, eventually. The motivation that underlies the design of CAPNs is to overcome technical challenges that affected CNNs, in particular when dealing with distorted or overlapping images. Key to success is to have neurons, the fundamental units of neural networks, being modeled as vectors (in CAPNs) instead of just scalars (as in CNNs). One major advantage of CAPNs was found to be the interpretability of the capsules, as fundamental building blocks. Time allowing, I will present two applications in biology, where interpretability of predictions is a crucial concern.

Freitag, 19.02.2021, 16:00 c.t., Online: Adam Mielke (Universität Bielefeld)
Territorial behaviour of birds of prey versus random matrix spacing distributions
Zoom Room, Meeting ID: 954 2522 3899, Passcode: 367638

We investigate the territorial behaviour of buzzards in the Teutoburger Forest by performing a large-scale analysis of nest positions gathered over the last 20 years. We use comparison of the nearest and next-to-nearest neighbour distributions to those of a Coulomb gas as a measure of the territorial behaviour by quantifying the strength and range of repulsion between the points. A one-parameter fit is made to a moving time average, using the charge of the particles as the fitting parameter. It reveals a significant increase in repulsion over the observed period of time that coincides with an increase in population. This effect is seen for both nearest and next-to-nearest neighbours, though the effect is smaller for the next-to-nearest neighbour, which indicates short-range interaction. Our results correlate well with concepts of population ecology. This is joint work with Gernot Akemann, Michael Baake, Nayden Chakarov, Oliver Krüger, Meinolf Ottensmann, and Rebecca Werdehausen

Freitag, 12.02.2021, 16:00 c.t., Online: David Kikuchi (Universität Bielefeld)
Signals, true and false: evolutionary and ecological consequences of decision-making under risk
Zoom Room, Meeting ID: 920 8144 5044, Passcode: 036718

Exact analytical solutions for population genetic models are rarely possible because of the complex interplay between recombination and other processes. Simulation is therefore a fundamental tool in population genetics, as it allows us to explore the models that we are interested in, evaluate analytical approximations, and to fit parameters for these models to data. We show how a recently introduced data structure, the "succinct tree sequence", allows us to simulate these ancestral processes exactly for millions of samples, a speed increase of several orders of magnitude over the previous state-of-the-art.

Freitag, 20.11.2020, 16:00 c.t., Online: Jerome Kelleher (Big Data Institute, Oxford University)
Simulating ancestral processes for large samples
Zoom Room, Meeting ID: 998 4232 9998, Passcode: 640513

Exact analytical solutions for population genetic models are rarely possible because of the complex interplay between recombination and other processes. Simulation is therefore a fundamental tool in population genetics, as it allows us to explore the models that we are interested in, evaluate analytical approximations, and to fit parameters for these models to data. We show how a recently introduced data structure, the "succinct tree sequence", allows us to simulate these ancestral processes exactly for millions of samples, a speed increase of several orders of magnitude over the previous state-of-the-art.

Freitag, 13.11.2020, 16:00 c.t., Online: Ulrike Schlägel (Universität Potsdam)
Movement-mediated community assembly and coexistence
Zoom Room, Meeting ID: 973 7063 5015, Passcode: 184489

Biodiversity trends due to anthropogenic environmental change are varied. While we experience an overall loss of species, individual communities and metacommunities may increase or decrease in diversity, depending on spatial and environmental factors as well as the intricacies of species' interactions within their environments. Many of the processes that shape community composition and allow species coexistence are mediated by organismal movements. Yet, bridging from movement processes at the small scale of individuals to species interactions at the community scale is challenging. In this talk, I will present some of my work on integrating movement ecology and biodiversity research by means of synthesis as well as conceptual and statistical developments.

Sommer Semester 2020 Freitag, 08.05.2020, 16:00 c.t., Online: Lorenzo Sadun (University of Texas, USA)
The problem of latency in estimating the Covid-19 replication number R0.

Figuring out how to restart the world's economy without a resurgence of disease depends on understanding how contagious Covid-19 really is. However, estimates of the basic replication number $R_0$ vary greatly, with well-respected groups publishing estimates whose 95% confidence intervals don't even overlap. In this talk I'll go over the basic SIR and SEIR models of disease spread and present several different ways to treat the latency period between being exposed and becoming infectious. Simple SEIR models are unstable; working with a fixed set of data, small changes to the model can result in large changes to the estimated value of $R_0$. More realistic models are more complicated and are even less stable. The upshot is that we know much less about $R_0$ than is generally believed, and the error bars on the high side are particularly large. Containing the outbreak for an extended period may be a lot harder than our leaders think.

Winter Semester 2019/2020 Mittwoch, 19.02.2020, 10:00 s.t., CITEC 1.204: Marc Alexa (TU Berlin)
Representing Frames as Möbius Transformations — Complementing Quaternions with a Measure for Deformations

Let us say that a frame is given by three ‘sticks’ (of equal lengths) meeting in one common point. We are interested in representing the orientation and the ‘shape’ of the frame. Orientation is the rotation relative to a reference frame; and ‘shape’ is the deformation relative to a reference frame. It turns out that any frame can be turned into any other frame by a Möbius transformation. This viewpoint reveals that rotations are points on a 3-sphere, the so-called unit quaternions. Unit quaternions are well-known and quite useful as a representation for rotations in space — they are continuous in the variables, minimal in the sense that at least four coordinates are necessary for a continuous representation, and they come with a natural metric that allows us to measure the ‘amount’ of rotation, i.e. the angle. The viewpoint of Möbius transformations also reveals, and this is the new aspect of this work, that deformations are points on a hyperboloid. So ‘shape’ can be described as a point in hyperbolic space. This is a representation that, just like unit quaternions, is continuous, small, and comes with a natural metric that allows measuring the amount of deformation.

Freitag, 08.11.2019, 16ct, V3-204: Jochen Röndigs (Bielefeld)
Following manifolds in equivariant evolution equations - a generalisation of the freezing method to infinite-dimensional symmetry

Equivariant evolution equations possess a symmetry described by a Lie group that acts on the phase space. The freezing method separates the dynamics of such an equation into dynamics within the symmetry group and within the phase space. The method has successfully been used to 'freeze' wave patterns in PDEs. However so far only finite-dimensional Lie groups have been considered. This talk presents a generalisaton of the freezing method to infinite-dimensional symmetry. To do so manifolds are studied and the symmetry group employed is the group of diffeomorphisms. The application of the freezing method is developed for this case introducing additional free variables which provide extra degrees of freedom within the group. Special attention is paid to the control of these variables as they determine the dynamics within the group which carries out the true feature of the freezing method. New control techniques had to be designed for the infinite-dimensional setting since the free variables satisfy a differential equation themselves. A numerical approach is described as well to illustrate the results by following close curves and tori in dynamical systems over time. Especially invariant sets, level curves and attractors, were considered to demonstrate various splittings of dynamics.

Sommer Semester 2019 Dienstag, 11.06.2019, 14ct, U10-146: Mike Steel (Christchurch, New Zealand)
Birth-death models in phylogenetics: symmetries, shapes, and the loss of biodiversity

The role of birth-death processes in modelling speciation and extinction in macro-evolution has a long history, with a classic paper by Yule in the 1920s. In this talk, I describe how such models can predict the ‘shape’ of evolutionary trees, as well as the expected loss of phylogenetic diversity under rapid extinction at the present.I also describe some recent work revealing certain symmetries in these processes, which has implications for the inference of speciation and extinction rates from phylogenies.

Freitag, 24.05.2019, 16ct, V3-204: Elisabeth Georgii (München)
Data-driven plant science: from multi-omics analysis to phenotype modeling

High-throughput omics technologies provide comprehensive measurements of tens of thousands of molecular features at different levels of cellular organization. Integrating such high-dimensional and heterogeneous data to facilitate discovery of biological relationships poses various computational challenges, starting from appropriate data management and automated analysis workflows up to advanced machine learning, data mining and visualization techniques. This talk highlights examples of data-driven hypothesis generation regarding biological mechanisms of combined drought and heat stress responses in plants, which are increasingly important under predicted climate change scenarios. In particular, both correlated and contrasting regulation patterns between the transcriptome and the metabolome are put into biological context. Even after stress relief and during extended recovery periods, plants maintain a molecular memory that increases their tolerance to subsequent stress events. Our data suggest that this memory differs with stress frequency or intensity, exists across tissues, involves specific genes and is consistent with phenotypic observations. Finally, recent developments in plant phenotyping and approaches toward integrative phenotype modeling are presented.

Freitag, 10.05.2019, 16ct, V3-204: Michael Baake (Bielefeld)
The Markov embedding problem revisited - from an algebraic perspective

The Markov embedding problem, namely whether a given Markov matrix can occur within a continuous time Markov semigroup, is still unsolved even for 4x4 matrices. It became quite famous in the 1960s through an influential paper by Sir John Kingman and led to some interesting equivalent reformulations, but defied a practically effective solution already for 3x3 matrices for a long time, and still does beyond. In this contribution, the problem will be reviewed and some extensions will be presented, which were triggered by the recent need in phylogeny that has put the problem again on the table.

Winter Semester 2018/2019 Freitag, 11.01.2019, 16ct, V3-204: Christiane Fuchs (Universität Bielefeld)
Stochastic Modelling and Inference of Cellular Processes

The molecular biology of life seems inaccessibly complex, and gene expression is an essential part of it. It is subject to random variation and not exactly predictable. Still, mathematical models and statistical inference pave the way towards the identification of underlying gene regulatory processes. In contrast to deterministic models, stochastic processes capture the randomness of natural phenomena and result in more reliable predictions of cellular dynamics. Stochastic models and their parameter estimation have to take i nto account the nature of molecular-biological data, including experimental techniques and measurement error. This talk presents according modelling and estimation techniques and their applications: the derivation of mRNA contents in single cells; the identification of differently regulated cells from heterogeneous populations using mixed models; and parameter estimation for stochastic differential equations to understand translation kinetics after mRNA transfection.

Freitag, 19.10.2018, 16ct, V3-204: Philip Gerrish, Atlanta/Bielefeld
Is there sex on other planets?

We ask the question: if an alien system of self-replicating entities were discovered, should we expect sex and/or recombination to be features of this system? Put differently, is there something about mutation and natural selection that inherently promotes the evolution of sex and recombination? Current theory finds many special circumstances in which sex and recombination might be expected to evolve, but this “patchwork of special cases” (with many holes) does not seem to fit the observations: in nature, sex and recombination are everywhere — spanning all environments and all levels of organismal size and complexity. Increasingly, even species traditionally thought to be asexual have been caught “having sex on the sly”. The observations, therefore, seem to call for an encompassing feature common to living things in general that promotes the evolution of sex and recombination. And we think we may have a candidate! We think this general feature might be none other than natural selection itself. I will show you what we’re thinking and how it works, will go through the case of structured populations which has a nice intuitive “visual proof” as well as a presentable “simplest case” proof, and will show you how far we’ve gotten with the full problem, with hopes for some nice feedback. This is joint work with Ben Sprung (Philadelphia), Julien Chevallier (Grenoble), and Bernard Ycart (Grenoble).
Sommer Semester 2018 Mittwoch, 30.05.2018, 16ct, U10-146: Carsten Wiuf (Copenhagen)
Stochastic modelling and analysis of DNA sequence data from Follicular Lymphoma

An cancer evolution model is proposed at the level of the individual cells, similar to other models that are used in population genetics to model the evolution of populations. The focus is on a particular form of cancer, called Follicular Lymphoma. A population of tumor cells initiates from a single cell harboring a t(14,18)-translocation which is considered a precursor step to Follicular Lymphoma. From there on the tumor evolves by accumulation of other driver and passenger mutations. A mathematical model is derived akin to coalescent models and various properties of the model are discussed in relation to statistical inference from DNA sequence data. DNA sequence data from primary and relapse tumors from (approx) 15 individuals are subsequently analyzed using the model, and parameters and the time of origin of the tumors are estimated.

Freitag, 15.06.2018, 16ct, U10-146: Mike Steel (Christchurch, New Zealand)
The combinatorics of ‘capturing’ a phylogenetic tree from discrete characters or distances

We consider two versions of the following question: What is the smallest amount of ‘data’ required to uniquely determine a phylogenetic (evolutionary) tree?In the first version, the ‘data’ consists of discrete characteristics observed at the leaves of a tree, and these characteristics are assumed to have evolved from an unknown ancestral state without homoplasy. For the second version, the data consists of leaf-to-leaf distances between certain pairs of leaves in the tree. Both questions give rise to interesting combinatorial subtleties, and lead to two recent mathematical results.

Freitag, 27.04.2018, 16ct, V3-204: Jens Stoye (Bielefeld University)
On Indexing for Jumbled Pattern Matching

Jumbled pattern matching is a variant of string matching where the order of characters in the matched region is ignored. It has applications in various areas of bioinformatics and beyond. Like in ordinary string matching, indexing allows to speed-up the search of multiple patterns in the same text. Recently, the problem of indexing binary strings for jumbled pattern matching has received quite some attention. While it seems unlikely to develop faster algorithms in terms of input size, we can still make progress on the problem by considering other natural parameters. One such parameter is the number of runs of 1s in the input, i.e. the length of the run length encoding (RLE) of the input string. We present a new and very simple algorithm matching the best known running times. This algorithm can be extended, either so that the index returns the position of a match (if there is one), or so that the algorithm uses only \$n\$ bits of space instead of \$n\$ words. To better understand the behaviour of the latter variant, we also study some combinatorial problems arising from comparing the RLE of the input string to the RLE of the binary output string. Some of these problems are still open, and any idea from the audience will be highly appreciated. This is joint work with Luis Kowada, Luís Felipe Cunha, Roland Wittler, Travis Gagie, Szymon Grabowski and maybe others.

Mittwoch, 02.05.2018, 16ct, T2-204: Scott Balchin (Warwick/Sheffield)
Introduction to topological methods in data analysis

Persistent homology is a method of analyzing features of point-cloud style data which persist across multiple scales. This exciting new method of data analysis is being found increasingly applicable in the study of 'big data'. For example, applications are being explored in the study of directed networks, image compression, and the analysis of recombination, reassortment and horizontal gene transfer in phylogenetics. As the method is purely topological, it works on data of any dimension, and is actually coordinate free. The goal of this talk is to describe the steps required to compute the PH of some data-set, including the algorithms involved, and to discuss how one should interpret the results. I will then go on to explain the limitations of the method, as well as variations such as applications to different data types, and multi-dimensional persistence.

Winter Semester 2017/2018 Friday, 12.01.2018, 16ct, V3-204: Roland Langrock (Bielefeld University)
Spline-based nonparametric inference in general state-switching models

Hidden Markov models (HMMs) and their various extensions have been successfully applied in various disciplines, including biology, speech recognition, economics/finance, climatology, psychology and medicine. They combine immense flexibility with relative mathematical simplicity and computational tractability, and as a consequence have become increasingly popular as general-purpose models for time series data. In this talk, I will demonstrate how the HMM machinery can be combined with penalised splines to allow for flexible nonparametric inference in HMM-type classes of models. The focus of the presentation will lie on practical aspects of nonparametric modelling in these frameworks, with the methods being illustrated in ecological and economic real data examples.

Friday, 27.10.2017, 16ct, V3-204: Meike Wittmann (Bielefeld University)
Fluctuating balancing selection and its effects on neutral genetic diversity

For organisms with several generations per year, seasonally fluctuating selection can be a powerful mechanism to maintain genetic polymorphism. For example, an allele favored during summer may stably coexist with an allele favored during winter, a form of balancing selection. Despite intense debate over decades, it is still unclear how much of the variation observed in the genomes of natural populations is due to balancing selection. In recent years, evolutionary biologists have started scanning genomes for genetic footprints of balancing selection (e.g. regions of increased diversity). However, these scans have generally assumed the simplest form of balancing selection where alleles are maintained at constant frequencies over time. There is currently insufficient theory to tell us what genetic footprint to expect under seasonally fluctuating selection, and how to distinguish it from neutrality but also from other forms of balancing selection. In this talk I will present results from coalescent models and stochastic simulations to characterize the impact of fluctuating balancing selection on neutral genetic diversity at various scales: at closely linked sites, at the scale of the chromosome, and at the genomic scale.

Sommer Semester 2017 Tuesday, 13.06.2017, 16ct, V3-201: Mike Steel (University of Canterbury, New Zealand)
Phylogenetic questions inspired by the theorems of Arrow and Dilworth

Biologists frequently need to reconcile conflicting estimates of the evolutionary relationships between species by taking a ‘consensus’ of a set of phylogenetic trees. This is because different data and/or different methods can produce different trees. If we think of each tree as providing a ‘vote’ for the unknown true phylogeny, then we can view consensus methods as a type of voting procedure. Kenneth Arrow’s celebrated ‘impossibility theorem’ (1950) shows that no voting procedure can simultaneously satisfy seemingly innocent and desirable properties. We adopt a similar axiomatic approach to consensus and asks what desirable properties can be jointly achieved.
In the second part of the talk, we consider phylogenetic networks (which are more general than trees as they allow for reticulate evolution).The question ‘when is a phylogenetic network merely a tree with additional links between its edges?’ is relevant to biology and interesting mathematically. Such ‘tree-based’ networks can be efficiently characterized.We describe these along with new characterization results related to Dilworth’s theorem for posets (1950), and matching theory on bipartite graphs.In this way, one can obtain fast algorithms for determining when a network is tree-based and, if not, to calculate how ‘close’ to tree-based it is.

Monday, 10.04.2017, 16 ct, U10-146: Reinhard Bürger (Vienna)
Two-locus clines on the real line

A population-genetic migration-selection model will be investigated which is continuous in space and time. The model assumes that two diallelic, recombining loci are under selection caused by an abrupt environmental change. The habitat is linear and unbounded, and dispersal occurs by diffusion. Selection is modeled by step functions such that in one region one allele at each locus is advantageous and in the other deleterious. Environmentally independent, intermediate dominance at both loci is admitted. The nonconstant stationary solutions of the resulting system of PDEs are called clines. First, an explicit expression for the single-locus cline with dominance is derived, thus generalizing classical results by Haldane and others. Interestingly, the slope of the cline in the center turns out to be independent of dominance. Second, under the assumption of strong recombination, the first-order approximation of the allele-frequency cline at each of the loci is derived, as is the linkage disequilibrium. Therefore, we obtain the quasi-linkage-equilibrium approximation of the two-locus cline. Its asymptotic properties are characterized explicitly. The consequences of dominance and linkage for the shape of the two-locus cline are explored for arbitrary recombination rates. Analogous models on a bounded habitat will be discussed briefly.

Winter Semester 2016/2017 Friday, 18.11.2016, 16 ct, V3-201: Bernd Sturmfels (Berkeley / Leipzig)
Does Antibiotic Resistance Evolve in Hospitals?

Nosocomial outbreaks of bacteria are well-documented. Based on these incidents, and the heavy usage of antibiotics, it has been assumed that antibiotic resistance evolves in hospital environments. To test this assumption, we studied resistance phenotypes of bacteria collected from patient isolates at a community hospital. A graphical model analysis shows no association between resistance and patient information other than time of arrival. This allows us to focus on time course data. We introduce a Hospital Transmission Model, based on negative binomial delay. Our main contribution is a statistical hypothesis test called the Nosocomial Evolution of Resistance Detector (NERD). It calculates the significance of resistance trends occurring in a hospital. It can help detect clonal outbreaks, and is available as an R-package. We applied the NERD method to each of the 16 antibiotics in the study via 16 hypothesis test. For 13 of the antibiotics, we found that the hospital environment had no significant effect upon the evolution of resistance; the p-values obtained for the other three antibiotics indicate that care should be taken in hospital practices with these antibiotics. This is joint work with Anna Seigal, Portia Mira and Miriam Barlow.

Friday, 28.10.2016, 16 ct, V3-204: Andreas Richter (Bielefeld University)
Evolvability as a quality criterion for linear deformation representations in evolutionary design optimization

Industrial product design is characterized by increasing complexity due to the high number of involved parameters, objectives, and boundary conditions, all typically changing over time. Population-based evolutionary design optimization targets to solve these kinds of application problems, offering efficient algorithms striving for high-quality solutions. An important factor in the optimization setup is the representation, which defines the encoding of the design and the mapping from parameter space to design space. Being able to numerically quantify the quality of different representation settings would strengthen the optimal choice of encoding. Motivated by the biological concept of evolvability, we propose three criteria, namely variability, regularity, and improvement potential, to evaluate linear deformation representations for their use in shape optimization problems. The first aspect characterizes the exploration potential of the design space, the second measures the expected convergence speed, and the third determines the expected improvement of the quality of a design. We propose and experimentally analyze mathematical definitions for each of the three criteria. We demonstrate the successful application of our model to two evolutionary optimization scenarios: fitting of 1D height fields and fitting of 3D face scans, both based on RBF deformations. Furthermore, we analyze the construction of optimal RBF deformation setups towards the three quality criteria.

Sommer Semester 2016 Monday (!) , 05.09.2016, 16 ct, V3-204 : Markus Nebel (Universität Bielefeld)
Analytic Combinatorics in Biology and Chemistry

At the latest with the computerization of many branches of their research discrete models became of increased importance to biologists and chemists. With the application of those models various quantitative questions were posed, most of which could be answered by methods from analytic combinatorics. Often, a special feature in this domain is the use of formal languages instead of directly applying the so-called symbolic method. In this talk we will discuss some representative examples showing the elegance of the method together with some of its enhancements in the context of biology and chemistry.

Friday, 15.07.2016, 16 ct, V3-204: Martin Möhle (Universität Tübingen)
On hitting probabilities of some Markov chains arising in mathematical population genetics - oscillation versus convergence

We derive some properties of the Greenwood epidemic Galton--Watson branching model. Formulas for the probability \$h(n,m)\$ that the associated Markov chain \$X\$ hits state \$m\$ when started from state \$n\ge m\$ are obtained. For \$m\ge 1\$ it follows that \$h(n,m)\$ slightly oscillates with varying \$n\$ and has infinitely many accumulation points. In particular, \$h(n,m)\$ does not converge as \$n\to\infty\$. It is shown that there exists a Markov chain \$Y\$ which is Siegmund dual to \$X\$. The hitting probabilities of the dual chain \$Y\$ are investigated. The second part of the talk addresses similar questions for the block counting process \$X\$ of the Bolthausen--Sznitman coalescent or more generally of the \$\beta(2-\alpha,\alpha)\$-coalescent with parameter \$0 \alpha 2\$. In this case the hitting probabilities \$h(n,m)\$ converge as the sample size \$n\$ tends to infinity. Formulas for the asymptotic hitting probabilities \$h(m):=\lim_{n\to\infty}h(n,m)\$ are provided.

Freitag, 10.06.2016, 16 ct, V3-204: Barbara Hammer (Universität Bielefeld)
Prototype-based machine learning models - some advances and open problems

Prototype-based machine learning techniques offer efficient nearest neighbor-based models for data classification: they represent a classification model in terms of typical prototypes in data space. Given a novel data point, its class is predicted as the class of its nearest prototype. There do exist intuitive learning schemes, which can infer suitable prototypes automatically from a given set of training data; further, the generalisation ability of prototype-based classifiers can be accompanied by distribution-independent large-margin generalization bounds, i.e. they provably display good generalization ability for novel data points for i.i.d. training data.

These facts have contributed to an increasing popularity of such models in the domain of biomedical data analysis or life-long learning, among others. Within the talk, we will address two advances for prototype-based models, discussing the basic concepts as well as open problems: (1) Metric learning - as distance based classifiers, prototype-based models fail whenever the used distance is not suitable for the observed data. This can be cured by so-called metric learning from data. We present basic concepts of metric learning and a recent application in the context of transfer learning for the adjustment of a classifier due to misplaced sensors. We also discuss the validity (and problems) of an interpretation of metric parameters as relevance terms. (2) Reject option for classification - in the domain of safety-critical systems or life-long learning, it becomes crucial to reject a classification for insecure regions of the classifier. We discuss the question how to enhance a prototype-based classifier by optimum reject options for the given training data.

Winter Semester 2015/2016 Freitag, 18.03.2016, 16 ct, U10-146: Oliver Krüger (Universität Bielefeld)
Models in ethology

The talk will illustrate the role of mathematical models in ethology in the context of population modelling, time series analysis and optimality modelling. The talk will demonstrate the importance of modelling for the evaluation of data from current long-term studies. The population ecology of birds of prey and the host-parasite coevolution of cuckoos will serve as empirical examples.

Freitag, 11.03.2016, 16 ct, V3-204 U10-146: Robert Giegerich (Universität Bielefeld)
Love over Gold? Mind over Matter? Pareto Optimization in Biosequence Analysis

Pareto Optimization is a technique to solve optimization problems under multiple objectives, while avoiding a mathematically questionable amalgamation of the objectives. Pareto optimization returns all solutions from the search space that are optimal in the sense that their score cannot be improved in one objective without decreasing it in some other objective. Pareto optimzation has some convenient and interesting mathematical properties - preservation of Bellman's Principle, scale-freeness, and the existence of ghost solutions. This makes it an attractive alternative to study biosequence analysis problems that have previously been tackled with pseudoscore approaches. Pareto optimization is available at keystroke in the Bellman's GAP dynamic programming system. The talk will shed some light on how this is achieved, and what we can do with it, using examples from comparative RNA structure prediction and the intergation of chemical probing data in RNA folding.

Freitag, 29.01.2016, 16ct, V3-204: Ulrike Schlägel (Universität Potsdam)
Models on the move: memory and temporal discretization in animal movement

Animal movement is an important ecological process. Many animals move to meet their daily and lifetime needs related to maintenance, survival, and reproduction. Movement of individuals scales up to population patterns, affecting populations’ abundances and distributions as well as community structures. Additionally, mobile animals provide important services to ecosystems, transporting seeds, pollen or smaller organisms, redistributing resources, or inducing disturbance regimes. During the last decades, studies of animal movement have benefitted from major advances in tracking technology that opened new dimensions for data collection and analysis. In this talk, I present two lines of research that address mathematical-statistical challenges of movement data analysis. First, I present an approach to detect cognition-based movement strategies in which animals consider their travel history for movement decisions. Second, I discuss a fundamental problem that arises when discrete-time movement data, e.g. GPS data, is analyzed by means of discrete-time models such as random walks and their extensions.

Sommer Semester 2015 Donnerstag, 25.06.2015, 14ct, U10-146: Mike Steel (University of Canterbury)
Combinatorial aspects of phylogenetic networks

Phylogenetic networks are directed graphs that display evolutionary relationships between species, and which can accommodate reticulate processes (e.g. the formation of hybrid species, or lateral gene transfer). In this talk, I will describe some recent combinatorial results on phylogenetic networks, aimed at addressing three questions: When is a network merely a tree with arcs between its branches? When can distances between taxa in a network appear perfectly tree-like? Which networks remain the same when they are ‘unfolded’ and then ‘refolded’? I will also report briefly on a curious combinatorial property that applies to binary planar networks, and which is algorithmically useful.

Freitag, 12.06.2015, 16ct, U10-146: Stefan Rotter (Universität Freiburg)
Spike Train Correlations Induced by Anatomical Microstructure

Correlations in neuronal spike trains reflect the structure of the underlying network. Pairwise correlations are caused, for instance, by direct synaptic interaction and by shared input. The contributions of more indirect, multi-synaptic pathways, however, are also very important and can be described by accounting for the connectivity motifs that arise in recurrent networks of arbitrary topology. Higher-order correlations can be dealt with in an analogous way, and new results will be presented on how one can manage the associated combinatorial problems. In recent work we were also able to demonstrate that the inverse problem of inferring (directed) connectivity from (undirected) pairwise correlations can be approximately solved by a method based on L1-optimization, provided that the networks are sparsely coupled but the level of sparsity is not too low. Applications of such methods to neuronal populations that are observed through mass signals (e.g. ECoG or MREG) are now pursued, using improved versions of the algorithm that exploit its specific algebraic structure.

Freitag, 22.05.2015, 16ct, V3-204: Dr. Silvia Gruhn (Universität zu Köln)
Mathematical modeling of the neural control of insect locomotion

The mechanism underlying the generation of stepping has been the object of intensive studies. Stepping involves the coordinated movement of different leg joints and is, in the case of insects, produced by antagonistic muscle pairs.\\ In the stick insect, the coordinated actions of three such antagonistic muscle pairs produce leg movements and determine the stepping pattern of the limb. The activity of the muscles is controlled by the nervous system as a whole and more specifically by local neuronal networks for each muscle pair. While many basic properties of these control mechanisms have been uncovered, some important details of their interactions in various physiological conditions have so far remained unknown. We have created a neuro-mechanical model of the coupled three joint control system of the stick insect's middle leg to unravel details of the neuronal and mechanical mechanisms driving a stepping single leg in situations other than forward walking. The model can generate forward, backward, or sideward stepping as well as searching movements. Using the model, it is, because of it's detailed biological description, possible to make detailed suggestions as to how rhythmic stepping might be generated by the central pattern generators of the local neuronal networks, how this activity might be transmitted to the corresponding motoneurons, and how the latter might control the activity of the related muscles. The entirety of these processes yields the coordinated interaction between neuronal and mechanical parts of the system. Moreover, based on experimental findings which state that only the activity of the muscles which move the leg forward and backward is reversed during backwards walking, we hypothesize and verify a mechanism by which motoneuron activity is modified by a premotor network and therefore suggest that this mechanism might serve as a basis for fast adaptive behaviour, like switches between forward and backward stepping, which occur, for example, during curve walking, and especially sharp turning, of insects.

Dienstag, 19.05.2015, 16ct, U10-146: Susanne Schindler (University of Oxford)
The reproductive value in two-sex models of age- and size-structured populations

The reproductive value (RV) of an individual describes the fraction of a future population that descended from it and is thus an important fitness measure. Estimating the RV from two-sex models is challenging as standard approaches to estimate the RV for one-sex models do not extend to the two-sex case. Furthermore, the age and size structure of a population renders a straightforward generalisation of Fisher's formula for the RV impossible, because the size-trajectory of an individual has to be taken into account. I demonstrate how to take individual size-trajectories with their consequences for offspring production into account and will present a way to calculate the RV in two-sex age-and-size structured models.

Winter Semester 2014/2015 Fr 06.02.2015, 16 Uhr c.t.: Mario Botsch (Universität Bielefeld),
Flexible Simulation Techniques for Topological Changes of Elastic Bodies
Fr 23.01.2015, 16 Uhr c.t.: Philipp Lampe (Bielefeld),
Computational methods in cluster theory
Fr 28.11.2014, 16 Uhr c.t.: Thorsten Hüls (Bielefeld),
Global bifurcations in a noninvertible model of asset pricing and a new approach for computing stable fibers
Fr 14.11.2014, 16 Uhr c.t.: Majid Salamat (Bielefeld),
Coupling from the past and perfect simulation>
Sommer Semester 2014 Freitag, 11.07.2014, 17ct, U10-146
Mike Steel, University of Canterbury

Autocatalytic sets and models of early life

A key step in the emergence of early life was the formation of a set of reactions that is (i) self-sustaining (all reactions involve reactants that are either produced by other reactions or are available in the environment) and (ii) autocatalytic (each reaction is catalyzed by some molecule produced by the system). Mathematical, algorithmic and stochastic techniques can help define, analyse, classify and search for these self-sustaining autocatalytic system in large chemical reaction networks. It is also possible to compute the probability of such systems forming in simple polymer models, as a function of the catalysis rate, and to determine their size when they first arise. In this talk, I will provide an overview of some of our earlier and more recent results in this area. This is joint work with Wim Hordijk, Elchanan Mossel and others.

Freitag, 11.07.2014, 16ct, U10-146
Arndt von Haeseler, Universität Wien

Modelling Coverage Patterns from High Throughput Sequencing Technologies

High throughput sequencing of transcriptomes enables high depth of coverage in transcriptome profiling. However, the resulting gene coverage pattern is far away from a uniform distribution. This uneven coverage is partly explained by biases inherent in the experimental protocols. The term 'uniform coverage' has been loosely used, without evidence that an unbiased sequencing experiment results in a uniform coverage pattern in the mathematical sense. Therefore we ask: What is a null hypothesis for the distribution of reads under perfect conditions? We will present a simple but realistic model that is computationally tractable. Moreover, we will present a preliminary analyses of real data to check if predicted patterns do occur. Finally, we will discuss further applications of the model. This is joint work with Celine Prakash and Stefanie Tauber.

Freitag, 20.06.2014, 16ct, V3-204
Holger Schielzeth, Universität Bielefeld, Fakultät für Biologie

Animal personality and the predictability of behaviour: mixed effects models that allow an estimation of between-individual variation in the variability

Many aspects of animal behaviour differ consistently between individuals, but while between-individual variation in average trait values has long been of interest to biologists, the role of within-individual variation has received much less attention. I will briefly review the concepts of behavioural plasticity, flexibility, consistency and predictability and the different indices that have been used for their quantification. I will then outline hierarchical generalized linear models (HGLM) and double-hierarchical generalized linear models (DHGLM) that have been developed in other contexts (in particular quantitative genetics), but can be adapted to the study of animal behaviour. A particular aim will be the presentation of an estimator predictability (the coefficient of variation in predictability) that can be used for comparisons across studies and study systems and might thus sever as a comment effect size estimator for meta-analyses.

Friday, 09.05.2014, 16ct, V3-204
Marc Steinbach, Uni Hannover

Mathematische Optimierung im Gastransport

Mit der Regulierung des europäischen Gasmarktes sind fundamentale strukturelle Änderungen verbunden, die für Gastransportunternehmen eine Fülle neuer und hochkomplexer Planungs- und Entscheidungsaufgaben mit sich bringen. Der Vortrag geht ein auf Anforderungen aus der Praxis, konkrete Herausforderungen der mathematischen Formalisierung und Modellierung sowie auf Optimierungsmodelle und Lösungsansätze, die aus einem Verbundprojekt mit einem großen Netzbetreiber hervorgegangen sind.

Winter Semester 2013/2014
  • Friday, 21.03.2014, 14 ct, U10-146
    David Bryant, University of Otago, New Zealand

    Phylogenetic analysis of species radiations using SNPs and AFLPs

    Technological wonders such as next generation sequencing mean that we can now, in principle, obtain SNP (single nucleotide polymorphism) data from multiple individuals in multiple species. This promises enormous benefits for population genetic and phylogenetic analysis, particularly of closely related or poorly resolved species. My interest is in how to analyse these data effectively and responsibly. We have developed an algorithm which estimates species trees, divergence times, and population sizes from independent (binary) makers such as well spaced SNPs. The method is based on coalescent theory (like the BEAST software), though it uses mathematical trickery to avoid having to consider all the possible gene trees. As a `full likelihood' method, it should be more accurate than alternative FST based approaches. I'll talk about our experiences applying this method to AFLP data from alpine plants, and some recent discoveries about the usefulness (or uselessness) of SNP data for estimating population sizes.

  • Monday, 02.12.2013, 16 ct, V5-148
    L’ubomír Baňas, Bielefeld University

    Phase field models for multiphase flow: modelling, numerics and applications

    Understanding and accurate prediction of multiphase multicomponent flows is of essential interest for a large number of scientific and engineering applications. Despite intensive past and present research efforts, it is still not clear how to accurately and efficiently simulate multiphase fluid flow for the full range of physical parameters and regimes such as, e.g., densities, viscosities, capillary relations, number of fluid phases, interface geometry, dynamic or static contact angles, etc. We review of a promising strategy for the modelling of incompressible multiphase flow based on the phase-field approach. We discuss advantages of the approach from the modelling and computational point of view. We also present a framework for multiscale flow simulations and discuss applications to multiphase flow in porous media.

  • Tuesday, 19.11.2013, 16ct, H4
    D. Shechtman, Technion, Haifa, Israel and ISU, Ames, Iowa, USA

    Quasi-periodic materials — crystal redefined

    Crystallography has been one of the mature sciences. Over the years, the modern science of crystallography that started by experimenting with x-ray diffraction from crystals in 1912, has developed a major paradigm — that all crystals are ordered and periodic. Indeed, this was the basis for the definition of crystal in textbooks of crystallography and x-ray diffraction. Based upon a vast number of experimental data, constantly improving research tools, and deepening theoretical understanding of the structure of crystalline materials, no revolution was anticipated in our understanding the atomic order of solids.

    However, such a revolution did happen with the discovery of the icosahedral phase, the first quasi-periodic crystal (QC) in 1982, and its announcement in 1984 [1, 2]. QCs are ordered materials, but their atomic order is quasiperiodic rather than periodic, enabling formation of crystal symmetries, such as icosahedral symmetry, which cannot exist in periodic materials. The discovery created deep cracks in this paradigm, but the acceptance by the crystallographers' community of the new class of ordered crystals did not happen in one day. In fact, it took almost a decade for QC order to be accepted by most crystallographers. The official stamp of approval came in a form of a new definition of Crystal by the International Union of Crystallographers. The paradigm that all crystals are periodic has thus been changed. It is clear now that although most crystals are ordered and periodic, a good number of them are ordered and quasi-periodic.

    While believers and nonbelievers were debating, a large volume of experimental and theoretical studies was published, a result of a relentless effort of many groups around the world. Quasi-periodic materials have developed into an exciting interdisciplinary science.

    This talk will outline the discovery of QCs and describe the important role of electron microscopy as an enabling discovery tool.

    [1] D. Shechtman, I. Blech, Met. Trans. 16A (June 1985) 1005-1012.
    [2] D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Phys. Rev. Letters, Vol 53, No. 20 (1984) 1951-1953.

  • Friday, 15.11.2013, 16ct, V3-204
    D. Frettloeh, University Bielefeld

    Tilings, pinwheels and quasicrystals

    The discovery of quasicrystals by Daniel Shechtman in 1982 kindled a demand for good models of such solids. An obvious choice are tilings (tesselations) in 2 and 3 dimensions. Understanding phenomena occurring in tilings may help to understand phenomena occurring in quasicrystals or related solids. One interesting such phenomenon is the ocuurrence of tiles in infinitely many different orientations in simple deterministic tilings. This talk gives a survey of this phenomenon, accompanied by several appealing images.

Sommer Semester 2013
  • Friday, 20.09.2013, 14ct, U10-146
    Ulrike Lampe, University Bielefeld

    Staying tuned: Developmental plasticity contributes to grasshopper signal adjustment in response to road noise

    Rising levels of anthropogenic noise all over the world lead to degradation and masking of acoustic communication signals, thereby making successful signal transmission in acoustically communicating species increasingly difficult. It is well-known that man-made noise affects signal production in different vertebrate taxa. In our earlier work we demonstrated that male Chorthippus biguttulus grasshoppers from roadside habitats produced courtship signals with elevated frequency components compared to their conspecifics from rural habitats. Here, we used a common garden design to study the evolutionary mechanisms behind this effect. We collected grasshopper nymphs from roadside and rural habitats and transferred them to the laboratory to rear half of them in a noisy environment (mimicking roadside conditions), whereas the other half was confronted with a control treatment. Males from roadside habitats produced signals with higher frequency components compared to males from rural habitats, thus supporting our previous result. More interestingly, males from the noisy treatment group produced courtship signals with higher frequencies compared to males from the control treatment, indicating noise-induced developmental plasticity. Moreover, grasshopper from roadside habitats produced signals with an increased syllable to pause ratio, possibly suggesting another strategy to avoid degradation by high background noise levels.

  • Monday, 02.09.2013, 14ct, U10-146
    Mike Steel,University of Canterbury

    Ancestral reconstruction, lateral gene transfer, and the joys of leaping between trees

    In part 1, I will present some recent results with Olivier Gascuel on how accurately we can expect to predict ancestral states at the interior nodes of a phylogenetic tree from discrete character data at the extant leaves.
    In part 2, I will describe a second project on species tree reconstruction when genes have evolved under a simple model of random lateral gene transfer (LGT). The aim is to answer questions such as: could we reconstruct a species tree on (say) 200 species from a large number of gene trees, if each gene has been laterally transferred into other lineages, on average, ten times? And can LGT lead to inconsistent tree estimation? Our analysis involves a curious connection to random walks on cyclic graphs.

  • Friday, 12.07.2013, 16 ct, in V3-204
    Odile Sauzet, University Bielefeld
    So einfach ist das! Eine Notwendigkeit in der Medizinische Statistik? Abstract:
    In randomisierten kontrollierten Studien werden meistens zwei (oder mehr) Gruppen verglichen, und die statistischen Methoden hierfür sind unkompliziert. Aber was kann man tun, wenn die „beste“ Methode nicht hilft, um die Studienergebnisse richtig zu verstehen? Man kann eine andere, neue Methode entwickeln, die genau diese Fragestellung beantwortet. Aber dann kommen die Herausforderungen: die Methode muss die „Wahrheit“ (es gibt einen Unterschied) zeigen, aber muss verständlich (für einen Nichtstatistiker) und anerkannt (von Zeitschriftengutachtern) sein. Es ist alles nicht so einfach! Anhand des Beispiels von Dichotomisierung einer normalverteilten Variable werden wir zeigen, wie man eine einfache und (fast) genau „beste“ Methode entwickeln kann, um zwei Gruppen zu vergleichen. Damit werden wir die obengenannten Herausforderungen beantworten.

  • Friday, 28.06.2013, 16 ct, in V3-204
    Alan Rendall, University Mainz

    Chemical reaction network theory and immunological signalling pathways

    Modelling of biological systems often leads to large systems of ordinary differential equations containing many parameters which are poorly known. One approach to understanding the global dynamics of solutions of these systems is chemical reaction network theory (CRNT). When the results of this theory apply they give powerful results but it is not clear how widely they can be expected to be relevant for biological models. After giving an introduction to CRNT I will discuss an example (the NFAT signalling pathway) where I was able to use the theory to show that all solutions of the system converge to steady states at late times. I will also describe an earlier result of Eduardo Sontag on the kinetic proofreading model of T cell activation which inspired this work.

  • Friday, 14.06.2013, 16 ct, in V3-204
    Noemi Kurt, Technical University of Berlin

    Duality of Markov processes: Theory and some population biological applications

    Duality is a powerful tool in the analysis of Markov processes, which allows to understand certain aspects of one process (X_t) by analyzing another process $(Y_t)$ which is dual, meaning that E_x[H(X_t, y)]=E^y[H(x,Y_t)] for a suitably large class of duality functions H. Duality has been applied in a wide range of applications, such as interacting particle systems, superprocesses, queueing theory, SPDEs and many more, and is intrinsically connected to concepts like time reversal, stochastic monotonicity, symmetries and conserved quantities. In this talk, we present the notion of duality as well as some aspects of existence and uniqueness of dual processes. We will then turn our attention to monotone and non-monotone interacting particle systems and their connections via duality, and explain how such dualities are conserved under rescalings. Some of the rescaled processes can be understood as population dynamical models involving various types of selection, and our methods give an insight on their monotonicity properties.
    This is joint work with Sabine Jansen.

  • Friday, 24.05.2013, 16 ct, in G2-104
    Wolf-Juergen Beyn, Uni Bielefeld

    Mathematische Modellbildung, Analyse und Simulation zellulärer Prozesse

    Im Vortrag werden einige Grundprinzipien mathematischer Modellbildung diskutiert, die zum Verständnis des Zusammenwirkens zellulärer Einzelprozesse beitragen können. Zunächst wird auf die verschiedenen Modelltypen eingegangen, die sich durch Begriffspaare wie diskret-kontinuierlich, stationär-zeitabhängig, räumlich homogen-inhomogen, linear-nichtlinear und zufällig-deterministisch unterscheiden lassen. Speziell werden dann einfache Modellgleichungen für enzymatisch ablaufende Stoffwechselprozesse analysiert und Möglichkeiten aufgezeigt, um diese Modelle auf Transportprozesse und genetische regulierte Netzwerke zu erweitern. Dabei entstehen oft große Systeme nichtlinearer Differentialgleichungen, die eine Vielzahl von Parametern enthalten und deren Lösungsverhalten nicht einfach zu überblicken ist. Einerseits werden solche Systeme auf dem Computer simuliert und mit experimentellen Daten verglichen, andererseits versucht man die Modelle so zu reduzieren (Hauptkomponentenanalyse, Pseudostationarität), dass Einsichten in biochemisch relevantes Verhalten gewonnen werden können.

  • Friday, 26.04.2013, 16 ct, in V3-204
    Stefanie Tauber, Uni Wien

    Exploring the sampling universe of RNA-seq

    How deep is deep enough? While RNA-sequencing represents a well- established technology, the required sequencing depth for detecting all ex- pressed genes is not known. If we leave the entire biological overhead and meta-information behind we are dealing with a classical sampling process. Such sampling processes are well known from population genetics and thor- oughly investigated. Here we use the Pitman Sampling Formula to model the sampling process of RNA-sequencing. By doing so we characterize the sampling by means of two parameters which grasp the conglomerate of differ- ent sequencing technologies, protocols and their associated biases. We differ between two levels of sampling: number of reads per gene and respectively, number of reads starting at each position of a specific gene. The latter ap- proach allows us to evaluate the theoretical expectation of uniform coverage and the performance of sequencing protocols in that respect. Most impor- tantly, given a pilot sequencing experiment we provide an estimate for the size of the underlying sampling universe and, based on these findings, eval- uate an estimator for the number of newly detected genes when sequencing an additional sample of arbitrary size.
    This is joint work with Arndt von Haeseler.
Winter Semester 2012/2013
  • Tuesday, 05.02.2013, 11:15 in U10-146
    Andreas Richter,Graphics & Geometry Group,University of Bielefeld

    Discrete knot optimization

    The topic of this talk is the optimization or unfolding of knots — arbitrary simple closed curves — toward an as-simple-as-possible and esthetically pleasing shape. Applications can be found in, e.g., robotics, protein folding, and curve classification. The curve optimization is performed by numerically minimizing a suitable knot energy, which typically is formulated on continuous curves and discretized in a second step. In contrast, I present a geometrically intuitive energy for polygons that is discrete from the beginning. The resulting optimization is simple to implement, efficient and robust to compute, and yields results of comparable or even superior quality. In this talk I will discuss general requirements on knot energies, compare several optimization techniques, and present numerical and (cool) visual results.

  • Sommer Semester 2012
    • Friday, June 29th 2012, 16:15 in V3-204
      Mike Steel,University of Canterbury, Neuseeland

      'Lassoing' a tree: Phylogenetic theory for sparse patterns of taxon coverage

      Phylogenomic data often exhibit partial taxon coverage, whereby each loci is present or sequenced only for some corresponding subset of the species under study. This leads to some interesting mathematical and statistical questions as to whether a fully resolved underlying evolutionary tree for all the taxa can be reconstructed, given perfect phylogenetic estimates from each locus. We first describe the extent to which a pattern of taxon coverage can be 'phylogenetically decisive' in various senses, and provide some applications to data (joint work with Sanderson and McMahon). We then consider tree reconstruction from distance data, in settings where accurate estimates of evolutionary distance exist between only certain pairs of taxa: Does this partial information suffice to pin down -- or, as we say, 'lasso' -- the underlying phylogenetic tree? We describe a number of new combinatorial results concerning lassos (joint work with Dress and Huber), and conclude with some open problems.

      17:15 in V3-204
      Jan Manuch, University of British Columbia

      Linearization of ancestral chromosomal genomes

      Recovering the structure of ancestral genomes can be formalized in terms of the Consecutive-Ones Property (C1P) of binary matrices. The corresponding optimization problem asks to extract, from a given binary matrix, a maximum subset of rows that satisfy the C1P. This problem is in general intractable, in particular if the ancestral genome is expected to contain only linear chromosomes or a unique circular chromosome. In the present work, we consider a relaxation of these problems, which consists in allowing genomes that can contain several chromosomes, each either linear or circular. We show that, when restricted to binary matrices of degree two (every row has at most two non zero entries), used in most ancestral genome reconstruction frameworks, the problem of recovering an ancestral genome with several circular or linear chromosomes is polynomially solvable using a reduction to a matching problem. We also prove that for degree 3 matrices the problem is NP-complete, thus tracing sharp tractability boundaries.

    • Friday, April 27th 2012, 16:15 in V3-204
      Volker Dürr, Bielefeld

      What changes when animals change their movements?

      Animals adapt their behaviour to the prevalent requirements posed by their environment. Quite often, such adaptation of behaviour involves a change in movement. For example, animals may change gait when accelerating, or they may engage in distinct movement sequences as their behavioural goal changes. From a neuroscience point of view, it is interesting to understand HOW these changes in movement are being brought about by the nervous system. A prerequisite for answering this question is the understanding of WHAT actually changes in the movement, i.e., which parameters are being modified, or when and how often certain movement motifs occurred before and after the observed change. In my talk, I will give an introduction to the scientific approach of natural movement analysis and explain why I believe that the answer to the WHAT question is necessary (and not trivial) for the answer of the HOW question in motor control. For this, I will present examples from at least three kinds of changes in the movement of insect limbs. First there are apparent changes that may be explained by properties of the dynamic system without any trigger for the observed transition in movement. This includes apparently distinct movement sequences of single legs, for example during searching or cleaning. Second, there are changes in coupling strength between adjacent joints. This includes changes in tactile sampling during near-range exploration. Third, there are changes in likelihood of certain movement components. This includes distinct kinds of steps that occur at different times and at different places during natural, unrestrained walking and climbing.
    Winter Semester 2011/2012
    • Friday, January 20th 2012, 16:15 in V3-204
      Leif Engqvist, Bielefeld

      Theoretical approaches to understanding male fertility evolution

      When females mate with more than one male, a male reproductive success will to a large extent be determined by the fertilization success of his sperm. In this highly competitive situation, sperm with reduced capacity will only have minute chances to fertilize an egg cell. Genetic changes causing a decrease in semen quality should therefore be rapidly swept away by selection. At odds with this view are many studies demonstrating variation in sperm viability traits in natural populations. Why do males not manufacture sperm of the highest possible viability? One reason might be that producing highly viable sperm is costly. Thus, decreased sperm viability may be advantageous if males can afford to gain some other benefit. Furthermore, sperm cells key position in gene transfer between generations makes them the midpoint of a number of important genetic conflicts. Therefore, the evolution of optimal fertility might be highly constrained. Here I will present three recent theoretical models that take these considerations into account and aim to answer the following questions regarding male fertility evolution: (1) How is sperm ageing predicted to be influenced by female mating rate? (2) How does variation in fertility traits influence male investment in sperm competition? (3) When does selection lead to variation in fertility and evolution of alternative reproductive strategies? These analyses reveal some highly interesting and counterintuitive results that also show that male strategic investment in sperm traits are often in strong conflict with female fertility.

    • Friday, December 9th 2011, 16:15 in V3-204
      Sebastian Steinfartz, Bielefeld

      Ökologisch-bedingte adaptive Diversifizierung bei Feuersalamandern (Salamandra salamandra): eine Herausforderung für "maßgeschneiderte"Simulationsmodelle

      Die Entstehung biologischer Vielfalt auf ganz unterschiedlichen taxonomischen Niveaus ist ein zentrales Forschungsgebiet moderner Evolutionsforschung. Vor allem die Frage, auf welche Weise und mit welcher Geschwindigkeit neue Arten entstehen, hat Biologen seit jeher im besonderen Maße fasziniert und interessiert. Mitteleuropäische, nacheiszeitlich wiederbesiedelte Lebensraumgemeinschaften eignen sich besonders gut dafür, mögliche Artbildungsprozesse und deren zugrunde liegenden Mechanismen zu untersuchen, da viele der Populationen in diesen Gebieten sich erst vor vergleichsweise kurzer Zeit (ca. 6000-8000 Jahren) etabliert haben und Anpassungs- und Diversifizierungsprozesse noch nicht abgeschlossen sind und quasi in situ beobachtet und untersucht werden können. Die Arbeitsgruppe von Sebastian Steinfartz untersucht seit etwa 10 Jahren die ökologisch-bedingte Diversifizierung von Feuersalamander-Populationen im Rheinland mit besonderem Fokus auf den Kottenforst bei Bonn. Ökologische sowie populationsgenetische Studien konnten zeigen, dass sich die Feuersalamander in dieser Population aufgrund der Adaptation an unterschiedliche Larvalgewässer in zwei genetisch differenzierte Gruppen aufgespalten haben, und dass dieser Prozess der adaptiven Diversifizierung noch nicht abgeschlossen ist und eventuell zur Bildung neuer Arten führen könnte. Im Rahmen des Vortrages soll eine aktuelle Momentaufnahme des Wissenstandes dieses ökologisch-bedingten Differenzierungsprozesses gezeichnet werden. Gleichzeitig soll diskutiert werden inwieweit auf diese Population maßgeschneiderte Simulationsmodelle zum einen die festgestellte Diversität und Differenzierung erklären können und ob die ökologisch unterschiedlich angepassten Typen den Artbildungsprozess in Zukunft abschließen werden oder nicht.

  • Monday, November 28th 2011, 17:15 in H6
    Prof. Dr. Walter Steurer, ETH Zuerich

    Why are quasicrystals quasiperiodic?

    To answer this question we have to distinguish between metallic quasicrystals and quasiperiodic self-assembled colloidal structures. In the latter case special pair potentials with two different length scales and three-body interactions seem to be the main driving factors besides entropy. In case of metallic quasicrystals, the underlying mechanism is quite different. Here, the packing of low-energy clusters with non-crystallographic symmetry seems to be the decisive factor. The way of overlapping of these clusters and some other factors lead to a much higher structural order than in the case of soft quasicrystals. The focus of the talk will be on the ordering principles of metallic quasicrystals.

  • Friday, November 4th 2011, 16:15 in V3-204
    Mathias Staudigl, IMW, Bielefeld

    Stochastic Stability: Approximation, Convergence and Optimal Control (joint with William H. Sandholm, University of Wisconsin-Maddison)

    In this talk we will discuss some ongoing research on evolutionary equilibrium selection in games using stochastic methods which are frequently used in economics. Since the seminal papers of Kandori, Mailath and Rob (Econometrica, 1993) and Young (Econometrica, 1993) the Freidlin-Wentzell method to assess the stability of attractors has been frequently applied in game theoretic models. However, up to now a satisfactory analysis of these models was restricted to either very simple strategic situations (i.e. games), or very simple perturbations of the dynamics. In this talk we will present some new tools how to overcome these two obstacles by using ideas from stochastic and deterministic optimal control theory. We will conclude by pointing out that our methods are not only useful in the study of stochastic evolutionary game dynamics, but also can be applied to classical optimization problems, such as Markov decision processes. This is joint work with William H. Sandholm, University of Wisconsin-Maddison.
  • Sommer Semester 2011 $texte["10"] = '
    • Friday, July 22nd 2011, 14:15 in U10-146
      Michael Kopp, University of Vienna

      Adaptation of a quantitative trait to a moving optimum

      Biological population can adapt to new environments if established gene variants are substituted by beneficial mutations, but surprisingly little is known about the nature of these mutations. Recent modeling efforts have focused on predicting the distribution of phenotypic effect sizes of individual substitution events. While the majority of these models considers adaptation after an abrupt change in the environment, I will present results for adaptation to gradual environmental change. I will show that the rate of environmental change can have a strong impact on the statistical patterns of adaptive substitutions. These results may help our understanding of evolutionary responses to global change.

    • Thursday, July 14th 2011, 10:15 in U10-146
      Mareike Fischer, Center for Integrative Bioinformatics, Vienna

      Reconstructing evolutionary trees - Chances and pitfalls in modern phylogenetics

      Ever since Darwin published his first sketch of an evolutionary tree in 1859, scientists have been trying to reconstruct the Tree of Life. Such reconstructions are nowadays usually based on DNA data, which is interpreted with the help of tree inference methods. Maximum Parsimony (MP), Maximum Likelihood (ML) and distance-based methods (DB) are three such methods which are frequently used. In the first part of my talk, I will introduce MP and DB and I will show that even for the best possible DNA data, these methods can give contradictory results. In the second part of my talk, I will focus on the relationship between MP and ML, which has been widely discussed. For instance, it is well known that under a simple model of substitution, MP and ML always choose the same set of trees for DNA sequences. But some surprising properties of MP and ML have only recently been discovered: I will present examples for MP and ML favoring different trees when the underlying model is changed slightly - for example, when substitution probabilities are subject to an upper bound or when a molecular clock condition is imposed. Finally, I will show that, even though the two parts of my talk may seem unrelated at first glance, the same construction idea can be used to establish both results. This talk is based on joint work with Bhalchandra Thatte and Hans-Jürgen Bandelt.

    • Friday, June 24th 2011, 16:15 in V3-204
      Kristan Schneider, University of Vienna

      Genetic Hitchhiking and the Evolution of Anti-Malarial Drug Resistance

      Malaria is among the most devastating human diseases, and it is still a threat to the public health in large areas of the developing world. Malaria control is highly dependent on the use of drugs, which clear out parasites in infected hosts. However, many important drugs have been rendered useless because parasites evolved resistance against them. Understanding the evolutionary history of the spread of drug resistance is the key to extend the lifespan of affordable and reliable anti-malarial drugs, and hence to guarantee successful malaria control. However, reconstructing the evolutionary history of drug resistance in the absence of reliable clinical and epidemiological data is difficult. Hence, theoretical models that predict the dynamics of the spread of resistance are urgently needed. While it is difficult to build mathematical models that consider the full complexity of malaria, we might be able to reconstruct the dynamics of drug resistance by analyzing empirical data. We introduce a model for the spread of drug resistance among human malaria parasites, which is designed to study genetic hitchhiking. It incorporates all characteristics of the complex malaria-transmission cycle and accounts for the fact that only a fraction of infected hosts receive drug treatment. It also incorporates that hosts can be co-infected by differently many parasites. The number of parasites co-infecting a host is either a constant or, more generally, follows a given frequency distribution. We show that the hitchhiking effect is similar but different from standard hitchhiking, and explain why standard hitchhiking theory cannot be applied to drug resistance in malaria. Furthermore, we show that a genome-wide reduction in relative heterozygosity occurs provided drug pressures are sufficiently high and sufficiently many hosts are infected by single haplotype strains.

    • Friday, June 17th 2011, 16:15 in V3-204
      Jan de Ruiter, Faculty of Linguistics and Literary Studies, Bielefeld University

      Modeling inter-channel dependencies using conditional entropy -- chasing the illusion of causality.

      An intriguing problem in the field of human interaction is the mutual relationship between multiple signal "channels". An example is social eye-gaze ("Blickkontakt) and turn-taking. In order to get a formal handle on this problem, I have captured my empirical data in a state transition table of a Markov Model, combining turn-taking and eye-gaze states. This gives us a representation of a) how much time the communicating dyads spend in each state, and b) what the transitional probabilities are between different states. This representation turns out to be surprisingly useful to nail down and test vague and verbal theories about turn-taking and eye-gaze. A deeper and more challenging problem is to establish which channel determines ("dominates") the behavior of the other. It could be that turn-taking states cause certain patterns in eye-gaze states (as in Adam Kendon´s 1967 standard theory), but it could also be that eye-gaze states have an effect on turn-taking states. This leads us to the more general, but very fishy problem of establishing causality from existing (historical) data sets, which is impossible for two reasons: first, as Bertrand Russell and others have convincingly argued, causality does not exist (except in our minds), and second, it is always possible that what looks like causality from A to B is actually a correlation between A and B caused by a third (unknown) factor C. Nevertheless, I am experimenting with conditional entropy used on partitionings of the transition probabilities of the Markov model, in an attempt to approximate the unattainable goal of establishing causality. Please note that this is work in progress, and not a completed thesis. I invite everyone to join and contribute to the discussion.
    Winter Semester 2010/2011
    • Thursday, February 3rd 2011, 14:15 in U10-146
      Lorens Imhof, Bonn University

      Phenotype Switching and Mutations in Random Environments

      Cell populations can benefit from changing phenotype when the environment changes. One mechanism for generating these changes is stochastic phenotype switching, whereby cells switch stochastically from one phenotype to another according to genetically determined rates, irrespective of the current environment, with the matching of phenotype to environment then determined by selective pressure. This mechanism has been observed in numerous contexts, but identifying the precise connection between switching rates and environmental changes remains an open problem. Here we introduce a simple model to study the evolution of phenotype switching in a finite population subject to random environmental shocks. We compare the successes of competing genotypes with different switching rates and obtain a characterization of how the optimal switching rates depend on the frequency of environmental changes in a symmetric setting. Our results explain why the optimum is relatively insensitive to fitness in each environment. This is joint work with Drew Fudenberg.

    • Thursday, December 9th 2010, 14:15 in U10-146
      Evelyn Herrholz, Hochschule Neubrandenburg

      Parsimonious histograms

      In the context of one-dimensional density estimation we are faced with the construction of histograms for given real-valued data. Even if a histogram is a rather simple density its construction is quite difficult. The number and width of the bins have to be specified in a satisfactory manner for a wide range of data sets. Therefore we consider tubes of functions with piecewise constant boundaries around the empirical cumulative distribution function. It is already known that the taut string minimizes typical smoothness functionals as well as the number of modes in such tubes. The latter provides an histogram with minimal number of local extremes. A related optimization problem is to obtain a histogram with the smallest number of (unequal length) bins. Its solution is subject of this talk.

    • Thursday, October 21st 2010, 15:00 in U10-146
      Marc Hellmuth, Leipzig University

      Approximate Graph Products

      This talk is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected graphs is derived.

      Moreover, since most graphs are prime although they can have a product-like structure, also known as approximate graph products, the practical application of the well-known "classical" prime factorization algorithm is strictly limited. This new PFD algorithm is based on a local approach that covers a graph by small factorizable subgraphs and then utilizes this information to derive the global factors. Therefore, we can take advantage of this approach and derive in addition a method for the recognition of approximate graph products.

    • Thursday, October 21st 2010, 14:15 in U10-146
      Atheer Matroud, Massey University, Neuseeland

      Nested tandem repeats- computation and analysis

      Nested tandem repeat (NTR) is a complex repetitive structure, also referred to as Variable Length Tandem Repeats by [Hauth and Joseph, 2002]. NTRs structure contains two motifs repeated and interspersed with each other. In this presentation I will focus on illustrating some computation and analysis work I have done on this fascinating repetitive structure, highlighting the NTR that exists in the Taro plant and its possible use as a marker for intra-specific population study.

    • Thursday, October 14th 2010, 14:15 in U10-146
      Arndt Telschow, Helmholtz-Zentrum für Infektionsforschung, Braunschweig

      The role of Wolbachia and other reproductive parasites in eukaryotic evolution

      Reproductive parasites are cytoplasmically inherited endosymbionts that manipulate the host reproductive system to their own advantage but to the disadvantage of their host. Common forms of reproductive parasitism are cytoplasmic incompatibility, male-killing, feminization, and parthenogenesis induction. Well-studied reproductive parasites belong to the bacterial groups Wolbachia, Rickettsia, Spiroplasma, and Cardinia. The wide distribution of these bacteria among arthropods, with Wolbachia estimated to infect 20-70% of all insect species, make the study of reproductive parasitism an important topic in evolution and ecology. In the first part of the presentation, it is discussed how reproduction parasites modify host gene flow and promote speciation. A mathematical modelling approach is used and analytical results for gene flow modification are presented. The results support the view that Wolbachia can promote host speciation, and, further, suggest strong impact of reproductive parasites on host gene flow. In the second part, results from the Nasonia genome project are presented which suggest horizontal gene transfer between Wolbachia, Nasonia, and pox viruses. These results suggest an important role of reproductive parasites in eukaryotic evolution.
    Sommer Semester 2010
    • Thursday, June 10th, 2010, 14:15 in V3-204
      Volker Böhm, Bielefeld

      On the Dynamics of Asset Prices under Autoregressive Forecasting and Noise

      The talk studies the impact of the interaction of two groups of heterogeneous investors (so called fundamentalists and chartists) on the dynamics of asset prices in the capital asset pricing model (CAPM). Members of both groups apply so called mean reverting autoregressive forecasting rules.

      Forecasts by chartists are made according to an adaptive mean reverting principle for the first two conditional moments using past asset price data. Fundamentalists\acute; forecasts also use a mean reverting process, however, relative to a perceived so called fundamental value of asset price assumed to follow a stationary random walk. Different degrees of mean reversion have a strong impact on the dynamics of asset prices and returns showing the occurrence of a Neimark-Sacker bifurcation after a period doubling.

      An extensive numerical analysis shows that under these bifurcations highly cyclical time series of prices and returns occur which show the three typical features of empirically observed series of asset prices and returns, insignificant autocorrelation patterns of prices and returns for high order lags, which are non decaying for absolute and squared returns, as well as heavy tailed and skewed distributions. These results provide evidence that the non linearities induced by adaptive/autoregressive expectations are the major cause for overshooting features and fluctuating asset prices.

      The talk extends the analysis to study the impact of different random influences on aggregate asset supply, asset dividends, and on the fundamental asset price using numerical methods. For small enough noise, the period doubling and the Neimark-Sacker bifurcations are preserved inducing similar persistent autocorrelations. However, with larger perturbations and/or group switching, the bifurcations and autocorrelations disappear showing convergence to stationary solutions (random fixed points) without significant autocorrelations.

    • Thursday, May 27th, 2010, 14:15 in V3-204
      Reinhard Bürger, University of Vienna

      Multilocus migration-selection models

      Most natural populations are geographically structured and experience spatially varying selection. We present a general population-genetic model that incorporates migration between local populations (demes) and selection acting within demes on multiple gene loci, each with an arbitrary number of alleles. The model is formulated in terms of a system of difference equations and describes the evolution of gamete frequencies in the demes. In the absence of selection, we prove global convergence to linkage equilibrium and to spatial homogeneity. This result is used to derive the weak-selection limit and to prove generic global convergence of trajectories if selection is weak relative to migration and recombination. Analogous results can be proved for the weak-migration limit and the Levene model.

    • Thursday, May 20th, 2010, 14:15 in V3-204
      Richard Gardner, Western Washington University

      Reconstruction in Geometric Tomography

      Geometric tomography is the area of mathematics concerned with the retrieval of information about a geometric object from data about its orthogonal projections onto lines or planes or its intersections with lines or planes. In recent years, a number of algorithms have been developed for the purpose of reconstructing convex bodies from data of this sort. Examples are parallel and point X-rays, width or brightness functions, and support functions. In each case the algorithm takes as input a finite number of noisy (that is, corrupted by error) measurements and outputs a convex polytope that approximates the unknown convex body. The algorithms have all been proved to be strongly consistent, meaning that under suitable conditions, the Hausdorff distance from the output convex polytope to the unknown body converges, almost surely, to zero as the number of measurements increases. In some cases rates of convergence have also been obtained by applying the theory of empirical processes.
      The talk will survey these results, and briefly mention also a very recent one concerning reconstruction from covariograms, functions giving the volume of the intersection of a convex body with its translates. This reconstruction problem is closely related to the Phase Retrieval Problem for characteristic functions of convex bodies.
      The earliest algorithm to be discussed was proposed by electrical engineers in 1990, without proof of convergence. The mathematical methods involve convex geometry and probability, but the talk is intended to be accessible to a general audience. The algorithms have been implemented and pictures of typical computer reconstructions will be presented.

    • Part 1: Thursday, April 29th, 2010, 14:15 in V3-204
      Part 2: Thursday, May 6th, 2010, 14:15 in V3-204
      Michael Baake, Bielefeld

      Diffraction theory of deterministic and stochastic structures

      Mathematical diffraction theory is concerned with the determination of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra has improved considerably. Moreover, the phenomenon of homometry shows various unexpected new facets. This is particularly so when systems with stochastic components are taken into account.
      This talk reviews some of the recent results, with focus on concrete examples, and is mainly based on joint work with U. Grimm and R.V. Moody. In particular, after giving a short introduction, we will discuss classic deterministic examples with singular continuous and with absolutely continuous spectra, and compare the latter with random systems. A systematic approach is proposed via the theory of stochastic processes.
    Winter Semester 2009/2010
    • Friday, March 12th, 2010, 10:15 in V3-204
      Götz Gelbrich, Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig

      Herzinsuffizienz und Depression: Henne und Ei, oder interagierende Leiden?

      Depression hat unter herzinsuffizienten Patienten eine deutlich erhöhte Prävalenz, ist mit erhöhter Mortalität verbunden und hat mit der Schwere der Herzinsuffizienz eine Reihe klinischer Korrelate. Es wird der Frage nachgegangen, ob die Depression nur ein Marker für die Progression der Herzinsuffizienz ist, oder ob zwischen beiden Erkrankungen durch diverse Pathomechanismen vermittelte Wechselwirkungen bestehen. Dazu werden anhand eines Strukturgleichungsmodells längsschnittliche wechselseitige Beziehungen der Herzinsuffizienz und der Depression untersucht.

    • Thursday, February 4th, 2010, 14:15 in V3-204
      Thomas Wiehe, University of Cologne

      Testing for genomic signatures of adaptive events

      Identifying genome sites which underwent recent adaptive evolution - and distinguishing these genetic from demographic signals - is still a major challenge in computational population genomics. Here, I will discuss two approaches, one based on microsatellite variability and one based on haplotype structure, to address this question. Furthermore, I will present a method of alignment-free genome comparison and applications.

    • Thursday, January 28th, 2010, 14:15 in V3-204
      Eva Buchkremer, Bielefeld

      Should I stay or should I go? Foraging decisions under uncertainty

      Experiments testing for variance-sensitivity (also called risk-sensitivity) usually offer two options delivering identical expected payoffs, with one option providing a constant and the other one a variable reward or delay. Animals often show a preference for the constant option when variance is in amount (variance-aversion) and a preference for the variable option when variance is in delay (variance-proneness). Variance-sensitivity is a taxonomically widespread phenomenon. Variance-sensitive foraging preferences contradict predictions derived from evolutionarily-motivated models that emphasize long-term energetic benefits. We discuss a new approach of explaining variance-sensitive preferences. We hypothesize that decision mechanisms are primarily supposed to ensure optimal responses to the environment in which the animal forages. This paper demonstrates that simple decision rules ensure long-term rate maximization and exhibit variance-sensitive behavior when tested in a classical risk-sensitivity situation. We also show that behavioral patterns observed in experiments like preferences for constant reward amounts and variable time delays are produced by the decision rules. The decision rules presented here are a first step towards a decision mechanism that is psychologically plausible, is advantageous in natural foraging situations and explains irrational behavior like variance-sensitivity.

    • Thursday, January 14th, 2010, 14:15 in V3-204
      Jens Stoye, Bielefeld

      Rearrangement Models and Single-Cut Operations

      At an abstract level, genomes can be compared based on their gene order, yielding a number of interesting combinatorial and algorithmical problems. These include the calculation of the minimum number of rearrangements that are necessary to transform one genome into another one, where different rearrangement models have been considered in the past, such as reversals (REV), Hannenhalli-Pevzner (HP), and Double-Cut and Join (DCJ). Though each one can be precisely defined, the general notion of a model so far remained undefined. In this talk, we give a formal set-theoretic definition, which allows us to investigate and prove relationships between distances under various existing and new models. Somewhat surprisingly, we observe an asymmetry within the space of models we study, that might be due to an underlying combinatorial structure that still needs to be elucidated.

      This is joint work with Anne Bergeron (Montreal) and Paul Medvedev (Toronto).

    • New date soon...
      Reinhard Bürger, University of Vienna

      Multilocus migragtion-selection models

      Most natural populations are geographically structured and experience spatially varying selection. We present a general population-genetic model that incorporates migration between local populations (demes) and selection acting within demes on multiple gene loci, each with an arbitrary number of alleles. The model is formulated in terms of a system of difference equations and describes the evolution of gamete frequencies in the demes. In the absence of selection, we prove global convergence to linkage equilibrium and to spatial homogeneity. This result is used to derive the weak-selection limit and to prove generic global convergence of trajectories if selection is weak relative to migration and recombination. Analogous results can be proved for the weak-migration limit and the Levene model.

    • Thursday, November 12th, 2009, 14:15 in V3-204
      Arndt von Haeseler, University of Vienna

      A different view of sequence evolution

      Models to describe the evolution of biological sequences abound. With the increased number of models statistical procedures have been suggested to select the "best" model from a large class of typically nested models. While these procedures are widely used, the Litmus test, whether the best model really describes the observed data, is typically not carried out. We will present a method to do exactly this. Moreover, we will suggest an algorithm that gives a biologically interpretation to explain the difference between observed data and predicted data by the model. Several examples will illustrate the strategy.

      This is joint work with Tanja Gesell, Steffen Klaere, and Minh Anh Thi Nguyen.

    • Wednesday, November 4th, 2009, 16:15 in V3-201
      Dieter Joseph, Infineon, Munich

      Entwicklungen der Patentwelt in Industrie und Forschung

      Ein Erfahrungsbericht aus der Praxis.
    Sommer Semester 2009
    • Thursday, August 27th, 2009, 14:15 in V3-204
      Peter Pfaffelhuber, University of Freiburg

      Bacterial population genomics

      The genome of bacteria is less stable than the genome of eucariotes. In particular, it is an empirical observation that bacteria from the same population carry different genes. We study a model where new genes are introduced from the environment and can be lost along ancestral lines. By randomizing the genealogy according to a Kingman coalescent this mutation model, which appears to be new in the population genetic literature, can be analyzed. Moreover, empirical data fit well with our theoretical results. This is joint work with Franz Baumdicker, Wolfgang Hess, University of Freiburg.

    • Thursday, July 2nd, 2009, 14:15 in V3-204
      Mike Steel, University of Canterbury, Christchurch, New Zealand

      Mixed up trees: The geometry of phylogenetic mixtures

      Increasingly complex (and "realistic") models of sequence evolution carry with them a risk. Namely, as models become more parameter rich, the ability to accurately infer evolutionary history from sequence data can decrease unless the additional parameters can somehow be independently estimated. In extreme cases two quite different scenarios (e.g. different trees, or the same tree with quite different branch lengths) can quite perfectly describe the same data if the background parameters are adjusted suitably. This talk will describe some fundamental mathematical limitations in some recent approaches to inferring evolutionary history, and discuss their relevance for molecular systematics.

    • Thursday, June 25th, 2009, 14:15 in V3-204
      Arne Traulsen, MPI for evolutionary biology in Plön

      From Game Theory to Populations Genetics (and back?)

      In the past five years, evolutionary game dynamics has made significant advances by considering finite populations. Many unexpected and novel results have been obtained that are not compatible with the usual deterministic framework of evolutionary game dynamics. The new dynamics is intimately connected to population genetics, but adds a new perspective that stresses frequency dependent selection. An important problem of game theory is the evolution of costly cooperation among selfish individuals. In population genetics, this is often described by inclusive fitness methods. It turns out, however, that the underlying assumptions are in general very different from the approach of evolutionary game theory.

    • Tuesday, June 16th, 2009, 18:15 in W9-109
      Yeneng Sun, National University of Singapore

      Modeling large societies with uncertainty

      No abstract available.

    • Thursday, May 7th, 2009, 12:30 in V3-201
      H.-G. Purwins, Münster

      Lokalisierte Lösungen der erweiterten FitzHugh-Nagumo Gleichungen

      Selbstorganisierte dissipative Strukturen sind in Natur und Technik weit verbreitet und nicht wenige Wissenschaftler sind der Ansicht, dass deren Verständnis und Anwendung eine der ganz großen Herausforderungen der modernen Naturwissenschaften darstellen. Der vorliegende Vortrag beschäftigt sich mit derartigen Strukturen in der Form von solitären lokalisierten Spots, die auch "Dissipative Solitonen" (DSen) genannt werden. Diese Objekte zeigen in vieler Hinsicht teilchenhaftes Verhalten und werden sowohl experimentell als auch als Lösungen von Reaktions-Diffusions-Systemen vom FitzHugh-Nagumo-Typ beobachtet. Im ersten Teil des Vortrags wird an Hand von experimentellen elektrischen Transportsystemen dargelegt, dass DSen z.B. als stationäre und laufende isolierte Pulse, als stationäre, laufende und rotierende "Moleküle" und als "kristalline", "flüssige" und "gasförmige" Vielteilchensysteme auftreten. Die dabei entdeckten Wechselwirkungsphänomen umfassen sowohl Streunung und Clusterbildung als auch Generation und Annihilation. Numerische Untersuchungen zeigen, dass sich alle experimentellen Beobachtungen qualitativ durch die verallgemeinerte FitzHugh-Nagumo-Gleichung beschreiben lassen. Es erweist sich, dass diese Gleichung als eine Art "Normalform" für eine größere Universalitätsklasse DSen tragender Systeme betrachtet werden kann.
      Im zweiten Teil des Vortrags wird besprochen, wie sich unter bestimmten Voraussetzungen aus der verallgemeinerte FitzHugh-Nagumo-Gleichung Teilchengleichungen ableiten lassen, die das dynamische Verhalten schwach wechselwirkender DSen sehr gut beschreiben.
    Winter Semester 2008/2009
    • Thursday, February 5th, 2009, 14ct in V3-204
      Wilfried Gabriel, LMU Muenchen

      When is reversible phenotypic plasticity advantageous?

      The ability of a genotype to express different phenotypes in variable environments often leads to a fitness advantage. Such adaptive phenotypic plasticity occurs in traits ranging from morphology to physiology and behavior and can be observed in nearly all classes of organisms. Understanding the selective advantage and the limits of plasticity is crucial to numerous issues in evolution and ecology. Environmental tolerance functions describe how fitness of an organism depends on the environmental state. Mode and variance of tolerance functions can be treated as quantitative genetic traits and its values may be altered if an organism performs phenotypic plastic changes induced by environmental cues. Non-plastic, irreversible plastic or reversible plastic genotypes are favored depending on time pattern and variance of environmental changes, on the reliability of the environmental cues, on the time spans needed to perform plastic shifts and on the costs of plasticity.

    • December 12th, 2008 14ct in V3-204
      Aernoud van Enter, Uni Groningen

      First-order transitions for nonlinear n-vector models

      I discuss the occurrence of first-order transitions in temperature in various short-range lattice models with a rotation symmetry in d at least 2. Such transitions turn out to be widespread under the condition that the interaction potentials are sufficiently nonlinear. Some extensions to annealed models, and to the phenomenon of chaotic temperature dependence will be also discussed.

    • November 6th, 2008 14ct in V3-204
      Lars Koch, IMW, Bielefeld

      Persistent Ideologies in an Evolutionary Setting

      We analyse finite two player games in which agents are unable to verify payoffs. Agents believe in ideologies that specify virtual payoff matrices of the game. We may, but do not need to assume the presence of ideologies that are equivalent to the true payoffs. There may be infinitely many different ideologies present at the same time. Given ideologies, agents maximize and choose actions. We define an equilibrium concept and prove existence. We assume equilibrium play at each point in time, however we refrain from assuming a particular equilibrium selection. Based on this setup, we define an evolutionary dynamic on the distribution of ideologies within the population. In this meta game agents adapt new ideologies. We assume a monotonic imitation dynamic, i.e. ideologies that lead to actions which are relatively successful in terms of true payoffs spread faster in the population than ideologies that recommend relatively unsuccessful actions. We characterize the set of stable distributions on the space of ideologies. For any finite 2 player normal form game we show that there is an open set of ideologies being not equivalent to the true payoffs that is not selected against by evolutionary monotonic dynamics based on the true payoffs of the game. If the game has a strict equilibrium set, we show stability of non-equivalent ideologies. We illustrate these results for generic 2X2-games.

    • SPECIAL: Lecture series in context of "Jahr der Mathematik"
      Mathematik ist überall: Mathematische Modellbildung

      • December 17th, 2008, 18:00 in H13
        Klaus Reinhold, Bielefeld
        Wie variabel ist die Variabilität biologischer Merkmale?

      • December 8th, 2008, 18:00 in H15(!)
        Karl Sigmund, Wien
        Zwischen Zwang und Freiwilligkeit: Die Spieltheorie der Kooperation

      • November 26th, 2008, 18:00 in H13
        Ellen Baake, Bielefeld
        Sind Mutationen spontan oder gerichtet?
        Das Luria-Delbrück-Experiment

      • November 12th, 2008, 18:00 in H13
        Frank Riedel, Bielefeld
        Total smart und auch noch reich - hohe Mathematik in der Wirtschaft

      • October 29th, 2008, 18:00 in H13
        Philippe Blanchard, Bielefeld
        Komplexe Netzwerke und zufällige Graphen in und jenseits der Physik

        (For abstracts visit "Jahr der Mathematik")
    Sommer Semester 2008
    • July 2nd, 2008
      Werner Kirsch, Hagen

      Mathematik und Politik: Von Macht, Ministern und Quadratwurzeln

      Die Frage nach einer angemessenen Vertretung aller Beteiligten am demokratischen Entscheidungsprozess ist eine der Grundfragen der Demokratie. So haben zum Beispiel im Ministerrat der Europäischen Union die Mitgliedsstaaten - je nach ihrer Bevölkerungsgröße - unterschiedlich viele Stimmen. Immer wieder gibt es bei Gipfeltreffen der EU Streit und Gezerre um diese Stimmgewichte; erst im vergangenen Jahr überraschte die polnische Regierung die Öffentlichkeit mit ihrer Forderung nach der "Quadratwurzel-Verteilung" der Stimmen. Ähnliche Probleme ergeben sich bei anderen internationalen Organisationen (Weltbank, UNO), bei Länderkammern, wie dem Bundesrat, oder bei der Machtverteilung in großen Wirtschaftsunternehmen (z.B. VW).
      Kann man solche Machtverteilungen mit Hilfe der Mathematik analysieren? Ist es möglich, mit mathematischen Methoden eine Stimmverteilung als besonders "gerecht" auszuzeichnen? Der Vortrag wird versuchen, diese Fragen zu beantworten und Denkanstöße für die politische Praxis zu liefern.
      Dieser Vortrag ist der Auftakt zu einer Veranstaltungsreihe im Rahmen des Jahres der Mathematik mit dem Titel "Mathematik ist überall: Mathematische Modellbildung". Diese Reihe wird im Wintersemester fortgesetzt.

    • July 1st, 2008
      Mike Steel, Christchurch, New Zealand

      The Joys of Being Mean: Tricks for (Evolutionary) Trees

      I describe how one can sometimes obtain useful insights into the properties of phylogenetic models -- both old and new -- that at first seem quite complex, by exploiting standard properties of expectation (the "mean" of an appropriate random variable).

    • April 24th, 2008
      Tanja Gernhard, TU Munich

      A statistic for detecting lineage-specific bursts in a tree

      In this talk I discuss tree statistics. First, the most common tree statistics are reviewed. We will see that lineage-specific speciation bursts cannot be detected with those statistics. I present a new statistic summarizing the timing of branching events, the runs statistic, which detects lineage-specific bursts. The statistic is applied to two example applications: we show that the evolution of the Hepatitis C virus appears to proceed in a lineage-specific bursting fashion; the ant phylogeny shows a speciation burst, but there is no evidence for lineage-specific bursting.
    Winter Semester 2007/2008
    • January 31st, 2008
      Joachim Krug, University of Cologne

      Adaptation dynamics in smooth and rugged fitness landscapes

      The talk will begin by briefly introducing key concepts of population genetics such as fitness landscapes, sequence space and fixation in the context of the Wright-Fisher model for the asexual evolution of finite populations, which provides a basic description of evolution experiments with bacteria and viruses. I then identify the parameters which allow for a broad classification of evolutionary regimes in rugged fitness landscapes with many peaks [1], and provide a detailed analysis of the phenomenon of clonal interference in a smooth (non-epistatic) landscape [2]. Finally, I will describe recent work on the house-of-cards model in finite populations [3], which is the simplest realization of a fitness landscape with strong epistasis. The talk is based on joint work with Kavita Jain and Su-Chan Park.

      [1] K. Jain, JK, Genetics 175, 1275 (2007)
      [2] S.C. Park, JK, PNAS 104, 18135 (2007)
      [3] S.C. Park, JK, submitted to JSTAT (arXiv:0711.1989)

    • December 13th, 2007
      Eva Maria Griebeler, University of Mainz

      Effekte der globalen Temperaturerhöhung auf die Populationsdynamik von Arten am Beispiel der Westlichen Beißschrecke (Platycleis albopunctata) und der Dreikantmuschel (Dreissena polymorpha)

      Die globale Klimaveränderung wird die Habitate vieler Arten dramatisch verändern. Falls es ihnen nicht gelingt sich an die geänderten Umweltbedingungen anzupassen, werden sie möglicherweise langfristig aussterben. In meinem Vortrag möchte ich den Effekt von Temperaturerhöhung auf die Populationsdynamik exemplarisch für eine terrestrische und eine aquatisch lebende Art analysieren. Freilandstudien haben gezeigt, dass sowohl die Westliche Beißschrecke (Platycleis albopunctata) als auch die Dreikantmuschel (Dreissena polymorpha) in Habitaten mit sehr unterschiedlichen Temperaturbedingungen überleben können. Man kann daher vermuten, dass die beiden Arten auch unter der zukünftig zu erwartenden Temperaturerhöhung überleben werden. Diese Hypothese habe ich mit Hilfe von zwei Simulationsmodellen überprüft.

    • December 4th, 2007
      Achim Klenke, University of Mainz

      Infinite Rate Mutually Catalytic Branching

      In 1998 Dawson and Perkins introduced a model of continuous state mutually catalytic branching on some countable Abelian group $S$ as site space. At each colony $k$ at time $t$ there is a continuous amount $X_t^i(k)$ of particles of type $i=1,2$. Time evolution is governed by
      • migration on $S$ according to some symmetric random walk kernel $a$,
      • random fluctuations of each type that are modelled locally by Feller´s branching diffusion but at a rate proportional to the mass of the respective other type.
      Formally, the evolution can be described by a system of stochastic differential equations,
      $$ dX^i_t(k)=\sum_{l\in
		 +\sqrt{\gamma X1_t(k)X2_t(k)\,}dW^i_t(k),$$

      where $i=1,2$, $k\in S$, $\gamma>0$ is a parameter, and $(W^i(k))_{i=1,2,\;k\in S}$ is an independent family of Brownian motions.
      For the investigation of the longtime behaviour of this model it is useful to understand the limit model of $\gamma=\infty$. In a first step we construct this limit model via a martingale problem involving a Lévy-type jump measure on the state space $[0,\infty)2\setminus(0,\infty)2$ of each colony. In a second step we derive a sufficient condition for global coexistence of both types when started from a finite initial state. We show that it is sufficient that
      1. $$G_{\log}(k,l):=\int_0^\infty
			  <\infty\quad\mbox{for} k,l\in S,
        where $a_t$ is the continuous time kernel of the $a$-random walk, and

      2. the initial masses of type 1 and 2 are placed at sites $k_1$ and $k_2$ such that $G_{\log}(k_1,k_2)$ is small.

      In contrast, for the $\gamma<\infty$ model, Dawson and Perkins showed that for coexistence of types the weaker condition that $a$ is transient is necessary and sufficient.

      This is joint work with Leonid Mytnik.

    • October 25th, 2007
      Joachim Krug, University of Cologne

      Adaption dynamics in smooth and rugged fitness landscapes

      The talk will begin by briefly introducing key concepts of population genetics such as fitness landscapes, sequence space and fixation in the context of the Wright-Fisher model for the asexual evolution of finite populations, which provides a basic description of evolution experiments with bacteria and viruses. I then identify the parameters which allow for a broad classification of evolutionary regimes in rugged fitness landscapes with many peaks [1], and provide a detailed analysis of the phenomenon of "clonal interference" in a smooth (non-epistatic) landscape [2]. The talk is based on joint work with Kavita Jain and Su-Chan Park.

      [1] K. Jain, JK, Genetics 175, 1275 (2007)
      [2] S.C. Park, JK, PNAS (in press)
    Sommer Semester 2007
    • June 18th, 2007
      Marc Steinbach, University of Hannover

      Nonlinear Optimization on Scenario Trees

      Multistage stochastic programming models are becoming vital in decision support for planning under uncertainty in various areas. While linear scenario tree models are widely used, well understood, and tractable by (almost) mature large scale optimization codes, comparably well developed solvers for nonlinear models do not yet exist. We present an approach that combines a suitable interior point method (handling nonlinearity and nonconvexity) with a "tree-sparse KKT solver" for the expensive linear-indefinite Newton step subproblems (handling the excessive size of multistage models by exploiting their rich structure). The approach is motivated and illustrated with examples from portfolio optimization, robust process control, and electricity trading, for which computational results will be presented.

    • June 14th, 2007
      Iwan Jensen, Melbourne University

      Exact solutions for models of punctured staircase polygons

      In many cases real life phenomena are modelled by simplified solvable models, which despite the simplifications can give us great insight into the behaviour of the more complicated fully-fledged problem. A well-known long standing problem in statistical mechanics is to find the perimeter generating function for self-avoiding polygons on two-dimensional lattices. Several simplifications of this problem are solvable, but all the simpler models impose an effective directedness or other constraint that reduces the problem, in essence, to a one-dimensional problem. A very important and interesting insight gained from these simple models (staircase polygons in particular) is a conjecture for the limit distribution of area and scaling function for self-avoiding polygons. Here we report on the discovery of the exact perimeter generating function for two models of punctured staircase polygons. We started by counting the exact number of punctured polygons. Using this series we found that all the terms in the generating function can be reproduced from a linear Fuchsian differential equation. In one case we managed to solve the ODE and find a closed form expression for the generating function. We have since been able to prove this results exactly using combinatorial arguments. This solution allows a generalisation to a model with any fixed number of nested punctures as well as to other types of polygons. This is joint work with Andrew Rechnitzer (University of British Columbia), Mike Zabrocki (York University) and Anthony Guttmann (Melbourne University) and contains significant results from work with Christoph Richard.

    • May 24th, 2007
      Frank Riedel, Bielefeld University

      Evolutionary Game Theory - Theory and Applications for Continuum Strategy Models

      We give an overview of evolutionary reasoning in Game Theory, with a special emphasis on games with a continuum of strategies. Whereas traditional game theory relies on the concepts of rationality, common knowledge and Nash equilibrium, evolutionary models use only the forces of selection and mutation to decsribe long run outcomes in games. Interestingly, the "folk theorem of evolutionary game theory" shows that stable states of such dynamics frequently are (very robust) Nash equilibria. In this sense, evolution leads to rationality. The talk discusses in which sense this can be rationalized to games with a continuum of strategies.

    • May 10th, 2007
      Carmen Molina-Paris, University of Leeds

      Peripheral T cell repertoire maintenance -- the quasi-stationary distribution

      A healthy immune system requires a T cell population that responds promptly to foreign antigen. This is achieved by using a variety of self-peptides to (i) select a receptor repertoire in the thymus and (ii) keep naive T cells alive and ready for action in the periphery. In this talk I will present a stochastic mathematical model to study T cell repertoire diversity maintenance. The model incorporates the concept of survival stimuli emanating from self antigen presenting cells. I will show that in the mean field approximation clonotype extinction is guaranteed and compute extinction times of T cell clonotypes without thymic input. I will introduce the concept of the mean niche overlap and make use of the quasi-stationary distribution to compute average clonotype numbers for different values of the niche overlap.

    • April 5th, 2007
      Bernd Kugelmann, University of Greifswald

      Optimale Steuerung am Beispiel von Fischfangquoten

      Im Vortrag wird ein Modell für die zeitliche Entwicklung von einer oder mehrerer Fischpopulationen in der Ostsee unter dem Einfluss von Erntemaßnahmen vorgestellt. Diese Fangbemühungen sollen so gesteuert werden, dass ein rein ökonomisches Zielkriterium optimiert wird. Mit steigender Komplexität des Modells wird die analytische Lösung des Problems immer schwieriger. Im Vortrag wird eine Methode zur numerischen Lösung dieses Optimalsteuerungsproblems erläutert und die Ergebnisse werden diskutiert.
    Winter Semester 2006/2007
    • January 23rd, 2007
      Erwin Frey, Ludwig-Maximilians-Universität Munich

      Soft Materials and Collective Phenomena in Cellular Systems

      Rapid developments in molecular biology and single molecule methods have provided evidence that soft interactions and fluctuation phenomena play a vital role in biology, in particular on the level of the very fundamental processes such as cytoskeletal organization, force generation by molecular motors, and cell motility.
      In this talk I will review our understanding of fibrous materials that are ubiquitious in nature, and collective phenomena which may arise in intracellular transport processes. The elastic properties of fibrous biomaterials result from a subtle interplay between the architecture of the network and the elastic properties of its building blocks. A description of these systems requires novel concepts in polymer physics. Brownian motion governs the transport along molecular multi-lane highways in cells. Exploring these systems´ behavior, we find that it can be tuned by controlling particle fluxes at the boundaries and the bulk of the track. In addition to their biological relevance these systems may also be viewed as novel nonequilibrium devices.

    • January 18th, 2007
      Marc Timme, Max Planck Institute for Dynamics and Self-Organization and Bernstein Center for Computational Neuroscience Göttingen

      Speed Limits in Spiking Neural Networks Explained by Random Matrix Theory

      Precisely coordinated spatio-temporal spiking dynamics have been observed experimentally in different neuronal systems and are discussed to be an essential part of computation in the brain. Their dynamical origin, however, remains unknown.
      Here we study the dynamics of neural network models and reveal basic mechanisms underlying the neurons´ precise temporal coordination. We focus on the synchronization dynamics of neural networks exhibiting a complicated connection topology. In such networks, an irregular, balanced state coexists with a synchronous state of regular activity. Using a random matrix approach we predict the speed of synchronization in such networks in dependence of properties of individual neurons and their interaction network. We find that the speed of synchronization is limited by the network connectivity and remains finite, even if the coupling strengths between neurons become infinitely large. We offer an intuitive explanation of this phenomenon.

    • January 15th, 2007
      Hans-Otto Georgii, University of Munich

      The two-dimensional Ising model: What can we learn from its typical configurations?

      The Ising model on the square lattice Z^2 is a primary example of a statistical mechanics model showing phase transition. The interplay between its local and global behaviour is clearly displayed by the random geometry of clusters appearing in its typical configurations. In conjunction with the attractiveness and nearest-neigbour character of the interaction, this geometry allows a detailed analysis of the possible equilibrium states. In particular, it follows that - at any temperature - there exist either one or two extremal equilibrium states. The talk will give an introduction to the model and describe some central results and techniques.

    • December 7th, 2006
      Sven Wiesinger, Bielefeld University

      Two mathematical models for stochastic resonance in an asymmetric double-well potential

      After an introduction to the concept of stochastic resonance and some notes about applications, the talk will concentrate on an overview of two mathematical approaches to stochastic resonance in an asymmetric double-well potential: The classical approach, based on the Freidlin-Wentzell theory for random perturbations of dynamical systems, and a newer approach based on research results by N. Berglund and B. Gentz.
    Sommer Semester 2006
    • August 21st, 2006
      Ulrich Gerland, LMU Munich

      Physical, functional, and evolutionary aspects of transcription factor-DNA interaction

      To regulate the transcription of a gene, one or more transcription factors bind to closeby sites on the DNA, which they recognize through their specific sequences. The aim of this talk is to illustrate how the physical process of target site location and discrimination from the genomic background is entangled with the biological function. This interplay of physics and function can also shed some light on the evolutionary aspects of these interactions.

    • August 3rd, 2006
      Jay Taylor, Oxford University, U.K.

      The common ancestor process via diffusion theory

      One strategy for incorporating population genetic processes into a phylogenetic framework is through the common ancestor process, which describes the sequence of mutations along the unique lineage from which all extant individuals are descended. Although the common ancestor process in a population evolving according to a multitype branching process has been studied in some depth (e.g., Georgii and Baake (2003)), analysis of the CAP for a population of constant size is complicated by the lack of independence between individuals. In particular, if there are fitness differences between individuals, then the CAP fails to satisfy the Markov property. Fearnhead (2002) was able to characterize the CAP for a population with two fitness classes using the ancestral selection graph, obtaining a Markov process by introducing a family of virtual lineages representing those necessarily out-competed by the common ancestor (which is guaranteed to survive for all time).
      In this talk we will describe an alternative characterization of the common ancestor process using the coupled allele frequency-coalescent process introduced by Kaplan, Darden and Hudson (1988). Here we obtain a Markov process by keeping track not only of the type of the common ancestor but also of the frequencies of the types segregating in the population. We show that our results complement those obtained by Fearnhead in the case of constant fitnesses. In addition, the diffusion theoretic approach readily extends to other one-dimensional population genetic models and we use it to study the common ancestor process in populations subject to frequency-dependent selection, fluctuating selection, and bottlenecks.

    • July 18th, 2006
      Mike Steel, University of Canterbury, Christchurch, New Zealand

      Combinatorial approaches in phylogenetics

      Phylogenetics is the reconstruction and analysis of "evolutionary" trees and graphs in biology (and related areas of classification, such as linguistics). Discrete mathematics plays an important role in the underlying theory. We will describe some of the ways in which concepts from combinatorics (e.g. poset theory, greedoids, cyclic permutations, Menger´s theorem, closure operators, chordal graphs) play a central role. As well as providing an overview, we also describe some recent and new results, and outline some open problems.

    • July 6th, 2006
      Ellen Baake, Bielefeld University

      Der Gordische DNA-Knoten: Enzymscheren und Geometrie

      Im Laufe des Lebens einer Zelle wird ihre DNA mehrfach verknäult und wieder entwirrt. Dafür verantwortlich sind gewisse Enzyme, sogenannte Topoisomerasen, die, wie der Name schon sagt, bestimmte topologische Operationen an DNA-Molekülen durchführen. Ihre Funktionsweise wurde in enger Kooperation zwischen Biochemikern und Mathematikern aufgeklärt; wesentliches Werkzeug war dabei der Satz von White zur Geometrie von Bändern.
      Der Vortrag gibt einen Überblick über diesen "Klassiker" der mathematischen Biologie.

    • June 27th, 2006
      Gaby Schneider, University of Frankfurt

      A stochastic model for near-synchronous neuronal firing activity

      The precise timing of the firing of cortical neurons may be central for information processing in the brain. Recently, very small delays have been discovered between pairs of neurons, invisible in the raw processes but detectable in their cross correlation function. A stochastic model for the parallel firing activity of multiple neurons is presented which offers a possible explanation for the mechanism of the observed delays.

    • June 22nd, 2006
      Jochen Blath, TU Berlin

      Lambda-Coalescents as stochastic models in population genetics: Are they really out there?

      Stochastic processes form a cornerstone of quantitative population genetics. Of particular interest in this talk are so-called coalescent processes, which can be used to model the genealogical tree of a population.
      Since their introduction in 1999, the structure of so-called Lambda-Coalescents and of their corresponding population models, the generalised Fleming-Viot (super-)processes, has been thoroughly studied. Special cases, e.g. Beta-coalescents with Beta strictly between 1 and 2, allowing multiple genealogical mergers, can be considered as models for the genealogy of populations with rather extreme reproductive behaviour, in so far as, e.g., single individuals are able, within a single reproductive step, to produce a number of offspring potentially of the same order of magnitude as the size of the original population.
      However, for the genealogy of many populations (in the domain of attraction of the so-called classical Fleming-Viot process), the reasonable (and very succesful) standard model in population genetics is KingmanŽs Coalescent, which allows binary genealogical mergers only. Methods developed on the basis of this model admit, e.g. via importance sampling or MCMC methods, efficient likelyhood-based inference of evolutionary parameters from relatively large samples in population genetics.
      Recently, Eldon and Wakely provided evidence that the Kingman Coalescent as traditional null-model, in certain situations (e.g. for some marine species), might need to be replaced by more general models, since such species do exhibit the extreme reproductive behaviour described above.
      In a joint project with Matthias Birkner (WIAS Berlin), we address the question whether, how and which Lambda Coalescents can provide better models as basis for fully likelihood based inference in such situations.