# Department Seminars & Colloquia

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The driving passion of molecular cell biologists is to understand the molecular mechanisms that control important aspects of cell physiology, but this ambition is – paradoxically – limited by the very wealth of molecular details currently known about these mechanisms. Their complexity overwhelms our intuitive notions of how molecular regulatory networks might respond under normal and stressful conditions. To make progress we need a new paradigm for connecting molecular biology to cell physiology. I will outline an approach that uses precise mathematical methods to associate the qualitative features of dynamical systems, as conveyed by ‘bifurcation diagrams’, with ‘signal–response’ curves measured by cell biologists.

This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

Cell growth, DNA replication, mitosis and division are the fundamental processes by which life is passed on from one generation of eukaryotic cells to the next. The eukaryotic cell cycle is intrinsically a periodic process but not so much a ‘clock’ as a ‘copy machine’, making new daughter cells as warranted. Cells growing under ideal conditions divide with clock-like regularity; however, if they are challenged with DNA-damaging agents or mitotic spindle disruptors, they will not progress to the next stage of the cycle until the damage is repaired. These ‘decisions’ (to exit and re-enter the cell cycle) are essential to maintain the integrity of the genome from generation to generation. A crucial challenge for molecular cell biologists in the 1990s was to unravel the genetic and biochemical mechanisms of cell cycle control in eukaryotes. Central to this effort were biochemical studies of the clock-like regulation of ‘mitosis promoting factor’ during synchronous mitotic cycles of fertilized frog eggs and genetic studies of the switch-like regulation of ‘cyclin-dependent kinases’ in yeast cells. The complexity of these control systems demands a dynamical approach, as described in the first lecture. Using mathematical models of the control systems, I will uncover some of the secrets of cell cycle ‘clocks’ and ‘switches’.

This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

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Room B332, IBS (기초과학연구원)
Discrete Mathematics
Nika Salia (IBS Extremal Combinatorics and Probability Group)
Exact results for generalized extremal problems forbidding an even cycle

Room B332, IBS (기초과학연구원)

Discrete Mathematics

We determine the maximum number of copies of $K_{s,s}$ in a $C_{2s+2}$-free $n$-vertex graph for all integers $s \ge 2$ and sufficiently large $n$. Moreover, for $s\in\{2,3\}$ and any integer $n$ we obtain the maximum number of cycles of length $2s$ in an $n$-vertex $C_{2s+2}$-free bipartite graph.
This is joint work with Ervin Győri (Renyi Institute), Zhen He (Tsinghua University), Zequn Lv (Tsinghua University), Casey Tompkins (Renyi Institute), Kitti Varga (Technical University of Budapest BME), and Xiutao Zhu (Nanjing University).

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Room B332, IBS (기초과학연구원)
Discrete Mathematics
Florent Koechlin (LORIA, INRIA, Nancy, France)
Uniform random expressions lack expressivity

Room B332, IBS (기초과학연구원)

Discrete Mathematics

In computer science, random expressions are commonly used to analyze algorithms, either to study their average complexity, or to generate benchmarks to test them experimentally. In general, these approaches only consider the expressions as purely syntactic trees, and completely ignore their semantics — i.e. the mathematical object represented by the expression.
However, two different expressions can be equivalent (for example “0*(x+y)” and “0” represent the same expression, the null expression). Can these redundancies question the relevance of the analyses and tests that do not take into account the semantics of the expressions?
I will present how the uniform distribution over syntactic expression becomes completely degenerate when we start taking into account their semantics, in a very simple but common case where there is an absorbing element. If time permits it, I will briefly explain why the BST distribution offers more hope.
This is a joint work with Cyril Nicaud and Pablo Rotondo.

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ZOOM
Math Biology
David Anderson (University of Wisconsin – Madison)
Stationary distributions and positive recurrence of chemical reaction networks

ZOOM

Math Biology

Cellular, chemical, and population processes are all often represented via networks that describe the interactions between the different population types (typically called the “species”). If the counts of the species are low, then these systems are often modeled as continuous-time Markov chains on the d-dimensional integer lattice (with d being the number of species), with transition rates determined by stochastic mass-action kinetics. A natural (broad) mathematical question is: how do the qualitative properties of the dynamical system relate to the graph properties of the network? For example, it is of particular interest to know which graph properties imply that the stochastically modeled reaction network is positive recurrent, and therefore admits a stationary distribution. After a general introduction to the models of interest, I will discuss this problem, giving some of the known results. I will also discuss recent progress on the Chemical Recurrence Conjecture, which has been open for decades, which is the following: if each connected component of the network is strongly connected, then the associated stochastic model is positive recurrent.

This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

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ZOOM
Math Biology
Anne Skeldon (University of Surrey)
Mathematical modelling of the sleep-wake cycle: light, clocks and social rhythms

ZOOM

Math Biology

We’re all familiar with sleep, but how can we mathematically model it? And what determines how long and when we sleep? In this talk I’ll introduce the nonsmooth coupled oscillator systems that form the basis of current models of sleep-wake regulation and discuss their dynamical behaviour. I will describe how we are using models to unravel environmental, societal and physiological factors that determine sleep timing and outline how we are using models to inform the quantitative design of light interventions for mental health disorders and address contentious societal questions such as whether to move school start time for adolescents.

This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

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Room B332, IBS (기초과학연구원)
Discrete Mathematics
Giannos Stamoulis (LIRMM, Université de Montpellier)
Model-Checking for First-Order Logic with Disjoint Paths Predicates in Proper Minor-Closed Graph Classes

Room B332, IBS (기초과학연구원)

Discrete Mathematics

The disjoint paths logic, FOL+DP, is an extension of First Order Logic (FOL) with the extra atomic predicate $\mathsf{dp}_k(x_1,y_1,\ldots,x_k,y_k),$ expressing the existence of internally vertex-disjoint paths between $x_i$ and $y_i,$ for $i\in \{1,\ldots, k\}$. This logic can express a wide variety of problems that escape the expressibility potential of FOL. We prove that for every minor-closed graph class, model-checking for FOL+DP can be done in quadratic time. We also introduce an extension of FOL+DP, namely the scattered disjoint paths logic, FOL+SDP, where we further consider the atomic predicate $\mathsf{s-sdp}_k(x_1,y_1,\ldots,x_k,y_k),$ demanding that the disjoint paths are within distance bigger than some fixed value $s$. Using the same technique we prove that model-checking for FOL+SDP can be done in quadratic time on classes of graphs with bounded Euler genus.
Joint work with Petr A. Golovach and Dimitrios M. Thilikos.

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Room B332, IBS (기초과학연구원)
Discrete Mathematics
Zixiang Xu (IBS Extremal Combinatorics and Probability Group)
On the degenerate Turán problems

Room B332, IBS (기초과학연구원)

Discrete Mathematics

For a graph $F$, the Turán number is the maximum number of edges in an $n$-vertex simple graph not containing $F$. The celebrated Erdős-Stone-Simonovits Theorem gives that \[ \text{ex}(n,F)=\bigg(1-\frac{1}{\chi(F)-1}+o(1)\bigg)\binom{n}{2},\] where $\chi(F)$ is the chromatic number of $H$. This theorem asymptotically solves the problem when $\chi(F)\geqslant 3$. In case of bipartite graphs $F$, not even the order of magnitude is known in general. In this talk, I will introduce some recent progress on Turán numbers of bipartite graphs and related generalizations and discuss several methods developed in recent years. Finally, I will introduce some interesting open problems on this topic.