University of Oxford

Cells adapt their metabolic state in response to changes in the environment.  I will present a systematic framework for the construction of flux graphs to represent organism-wide metabolic networks.  These graphs encode the directionality of metabolic fluxes via links that represent the flow of metabolites from source to target reactions.  The weights of the links have a precise interpretation in terms of probabilities or metabolite flow per unit time. The methodology can be applied both in the absence of a specific biological context, or tailored to different environmental conditions by incorporating flux distributions computed from constraint-based modelling (e.g., Flux-Balance Analysis). I will illustrate the approach on the central carbon metabolism of Escherichia coli, revealing drastic changes in the topological and community structure of the metabolic graphs, which capture the re-routing of metabolic fluxes under each growth condition.

By integrating Flux Balance Analysis and tools from network science, our framework allows for the interrogation of environment-specific metabolic responses beyond fixed, standard pathway descriptions.

The immune system finds very rare amounts of pathogens and responds against them in a timely and efficient manner. The time to find and respond against pathogens does not vary appreciably with the size of the host animal (scale invariant search and response). This is surprising since the search and response against pathogens is harder in larger animals.

The first part of the talk will focus on using techniques from computer science to solve problems in immunology, specifically how the immune system achieves scale invariant search and response. I use machine learning techniques, ordinary differential equation models and spatially explicit agent based models to understand the dynamics of the immune system. I will talk about Hierarchical Bayesian non-linear mixed effects models to simulate immune response in different species.

The second part of the talk will focus on taking inspiration from the immune system to solve problems in computer science. I will talk about a model that describes the optimal architecture of the immune system and then show how architectures and strategies inspired by the immune system can be used to create distributed systems with faster search and response characteristics.

I argue that techniques from computer science can be applied to the immune system and that the immune system can provide valuable inspiration for robust computing in human engineered distributed systems.

The non-local Fisher KPP equation is used to model non-local interaction and competition in a population. I will discuss recent work on solutions of this equation with a compactly supported initial condition, which strengthens results on the spreading speed obtained by Hamel and Ryzhik in 2013. The proofs are probabilistic, using a Feynman-Kac formula and some ideas from Bramson's 1983 work on the (local) Fisher KPP equation.

Patlak-Keller-Segel equations 
\[
\begin{aligned}
u_t - L u &= - \mathop{\text{div}\,} (u \nabla v) \\
v_t - \Delta v &= u,
\end{aligned}
\]
where L is a dissipative operator, stem from mathematical chemistry and mathematical biology.
Their variants describe, among others, behaviour of chemotactic populations, including feeding strategies of zooplankton or of certain insects. Analytically, Patlak-Keller-Segel equations reveal quite rich dynamics and a delicate global smoothness vs. blowup dichotomy. 
We will discuss smoothness/blowup results for popular variants of the equations, focusing on the critical cases, where dissipative and aggregative forces seem to be in a balance. A part of this talk is based on joint results with Rafael Granero-Belinchon (Lyon).

Abstract: Triangulations of surfaces serve as important examples for cluster theory, with the natural operation of “diagonal flips” encoding mutation in cluster algebras and categories. In this talk we will focus on the combinatorics of mutation on marked surfaces with infinitely many marked points, which have gained importance recently with the rising interest in cluster algebras and categories of infinite rank. In this setting, it is no longer possible to reach any triangulation from any other triangulation in finitely many steps. We introduce the notion of mutation along infinite admissible sequences and show that this induces a preorder on the set of triangulations of a fixed infinitely marked surface. Finally, in the example of the completed infinity-gon we define transfinite mutations and show that any triangulation of the completed infinity-gon can be reached from any other of its triangulations via a transfinite mutation. The content of this talk is joint work with Karin Baur.

We consider the classic problem of establishing a statistical ranking of a set of n items given a set of inconsistent and incomplete pairwise comparisons between such items. Instantiations of this problem occur in numerous applications in data analysis (e.g., ranking teams in sports data), computer vision, and machine learning. We formulate the above problem of ranking with incomplete noisy information as an instance of the group synchronization problem over the group SO(2) of planar rotations, whose usefulness has been demonstrated in numerous applications in recent years. Its least squares solution can be approximated by either a spectral or a semidefinite programming (SDP) relaxation, followed by a rounding procedure. We perform extensive numerical simulations on both synthetic and real-world data sets (Premier League soccer games, a Halo 2 game tournament and NCAA College Basketball games) showing that our proposed method compares favorably to other algorithms from the recent literature.

We propose a similar synchronization-based algorithm for the rank-aggregation problem, which integrates in a globally consistent ranking pairwise comparisons given by different rating systems on the same set of items. We also discuss the problem of semi-supervised ranking when there is available information on the ground truth rank of a subset of players, and propose an algorithm based on SDP which recovers the ranks of the remaining players. Finally, synchronization-based ranking, combined with a spectral technique for the densest subgraph problem, allows one to extract locally-consistent partial rankings, in other words, to identify the rank of a small subset of players whose pairwise comparisons are less noisy than the rest of the data, which other methods are not able to identify. 
 

Bubble Dynamics

We shall discuss certain generalisations of the Rayleigh Plesset equation for bubble dynamics

Self-assembly of a filament by curvature-inducing proteins

We explore a simplified macroscopic model of membrane shaping by means of curvature-sensing proteins. Equations describing the interplay between the shape of a freely floating filament in a fluid and the adhesion kinetics of proteins are derived from mechanical principles. The constant curvature solutions that arise from this system are studied using weakly nonlinear analysis. We show that the stability of the filament’s shape is completely characterized by the parameters associated with protein recruitment and establish that in the bistable regime, proteins aggregate on the filament forming regions of high and low curvatures. This pattern formation is then followed by phase-coarsening that resolves on a time-scale dependent on protein diffusion and drift across the filament, which contend to smooth and maintain the pattern respectively. The model is generalized for multiple species of proteins and we show that the stability of the assembled shape is determined by a competition between proteins attaching on opposing sides.

I will compare features of (classical) cohomology theory of groups to the rather exotic features of bounded (or continuous bounded) cohomology of groups.
Besides giving concrete examples I will state classical cohomological tools/features and see how (if) they survive in the case of bounded cohomology. Such will include the Mayer-Vietoris sequence, the transfer map, resolutions, classifying spaces, the universal coefficient theorem, the cup product, vanishing results, cohomological dimension and relation to extensions. 
Finally I will discuss their connection to each other via the comparison map.