Forschungsschwerpunkt Mathematische Modellierung (FSPM2)

Seminars (Colloquium)


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.

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.

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).

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 applying 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.

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

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.

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.

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.

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.

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 into 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).

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