Past

Numerous researchers recently applied empirical spectral analysis to the study of modern deep learning classifiers. We identify and discuss an important formal class/cross-class structure and show how it lies at the origin of the many visually striking features observed in deepnet spectra, some of which were reported in recent articles and others unveiled here for the first time. These include spectral outliers and small but distinct bumps often seen beyond the edge of a "main bulk". The structure we identify organizes the coordinates of deepnet features and back-propagated errors, indexing them as an NxC or NxCxC array. Such arrays can be indexed by a two-tuple (i,c) or a three-tuple (i,c,c'), where i runs across the indices of the train set; c runs across the class indices and c' runs across the cross-class indices. This indexing naturally induces C class means, each obtained by averaging over the indices i and c' for a fixed class c. The same indexing also naturally defines C^2 cross-class means, each obtained by averaging over the index i for a fixed class c and a cross-class c'. We develop a formal process of spectral attribution, which is used to show the outliers are attributable to the C class means; the small bump next to the "main bulk" is attributable to between-cross-class covariance; and the "main bulk" is attributable to within-cross-class covariance. Formal theoretical results validate our attribution methodology.
We show how the effects of the class/cross-class structure permeate not only the spectra of deepnet features and backpropagated errors, but also the gradients, Fisher Information matrix and Hessian, whether these are considered in the context of an individual layer or the concatenation of them all. The Kronecker or Khatri-Rao product of the class means in the features and the class/cross-class means in the backpropagated errors approximates the class/cross-class means in the gradients. These means of gradients then create C and C^2 outliers in the spectrum of the Fisher Information matrix, which is the second moment of these gradients. The outliers in the Fisher Information matrix spectrum then create outliers in the Hessian spectrum. We explain the significance of this insight by proposing a correction to KFAC, a well known second-order optimization algorithm for training deepnets.

The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.

In 1985, McDowell introduced a family of parabolically induced Whittaker modules over a complex semisimple Lie algebra, which includes both Verma modules and the nondegenerate Whittaker modules studied by Kostant. Many classical results for Verma modules and the Bernstein--Gelfand--Gelfand category O have been generalized to the category of Whittaker modules introduced by Milicic--Soergel, including the classification of irreducible objects and the Kazhdan--Lusztig conjectures. Contravariant forms on Verma modules are unique up to scaling and play a key role in the definition of the Jantzen filtration. In this talk I will discuss a classification of contravariant forms on parabolically induced Whittaker modules. In a recent result, joint with Anna Romanov, we show that the dimension of the space of contravariant forms on a parabolically induced Whittaker module is given by the cardinality of a Weyl group. This result illustrates a divergence from classical results for Verma modules, and gives insight to two significant open problems in the theory of Whittaker modules: the Jantzen conjecture and the absence of an algebraic definition of duality.

In an increasingly urbanized world, where cities are changing continuously, it is essential for policy makers to have access to regularly updated decision-making tools for an effective management of urban areas. An example of these tools is the delineation of cities into functional areas which provides knowledge on high spatial interaction zones and their socioeconomic composition. In this paper, we presented a method for the structural analysis of a city, specifically for the determination of its functional areas, based on communities detection in graphs. The nodes of the graph correspond to geographical units resulting from a cartographic division of the city according to the road network. The edges are weighted using a Gaussian distance-decay function and the amount of spatial interactions between nodes. Our approach optimize the modularity to ensure that the functional areas detected have strong interactions within their borders but lower interactions outside. Moreover, it leverages on POIs' entropy to maintain a good socioeconomic heterogeneity in the detected areas. We conducted experiments using taxi trips and POIs datasets from the city of Porto, as a study case. Trough those experiments, we demonstrate the ability of our method to portray functional areas while including spatial and socioeconomic dynamics.
 

Here is the scientific program.

Keynote speakers:

Roger Kamm, Cecil and Ida Green Distinguished Professor of Biological and Mechanical Engineering, MIT

Alicia El Haj,  Interdisciplinary Chair of Cell Engineering, Healthcare Technology Institute, University of Birmingham

Invited speakers (confirmed to date):

Davide Ambrosi, Politecnico di Torino, Italy

Anthony Callanan, University of Edinburgh, UK

Ruth Cameron, University of Cambridge, UK

Sonia Contera, University of Oxford, UK

Linda Cummings, New Jersey Institute of Technology, USA

Mohit Dalwadi, University of Oxford, UK

John Dunlop, University of Salzburg, Austria

John King, Nottingham, UK

Nati Korin, Technion, Israel

Catriona Lally, Trinity College Dublin, Ireland

Sandra Loerakker, TU Eindhoven, Netherlands

Ivan Martin, University of Basel, Switzerland

Scott McCue, Queensland University of Technology, Australia

Pierre-Alexis Mouthuy, University of Oxford, UK

Tom Mullin,  University of Oxford, UK

Ramin Nasehi, Politecnico di Milano, Italy

Reuben O'Dea, University of Nottingham, UK

James Oliver, University of Oxford, UK

Ioannis Papantoniou, KU Leuven, Belgium

Ansgar Petersen, Julius Wolf Institute Berlin, Germany

Luigi Preziosi, Politecnico di Torino, Italy

Rebecca Shipley, University College London, UK

Barbara Wagner, Weierstrass Institute for Applied Analysis and Stochastics, Berlin

Cathy Ye, Oxford University, UK

Feihu Zhao, TU Eindhoven, Netherlands

This meeting is being held in celebration of Prof Philip Maini's 60th birthday. Prof Maini has been an internationally leading researcher in mathematical biology for decades. He is currently the Director of the Wolfson Centre for Mathematical Biology, a position he has held since 1998. In the past 20 years he has grown the group significantly. He has established countless interdisciplinary collaborations, has over 400 publications in numerous areas of mathematical biology, with major contributions in mathematical modelling of tumours, wound healing and embryonic pattern formation. He has been elected Fellow of the Royal Society (FRS), Fellow of the Academy of Medical Sciences (FMedSci), and Foreign Fellow of the Indian National Science Academy (FNA). He has served or is serving on editorial board of a large number of journals, and was Editor-in-Chief of the Bulletin of Mathematical Biology [2002-15]. And yet his service to the community cannot be captured just by numbers and titles. Anyone who has met him and worked with him cannot but notice and be touched by his unfailing generosity and the many sacrifices he has made and continues to make day in and day out to help students, early career researchers, and fellow faculty alike.

This meeting provides an opportunity to celebrate Prof Maini's many accomplishments; to thank him for all of his sacrifices; and to bring together the large number of researchers – mathematicians, biologists, physiologists, and clinicians – that he has worked with and interacted with over the years. More broadly, the meeting provides a unique opportunity to reflect on mathematical biology, to provide perspectives on the trajectory of a field that was scarcely recognised and had very few dedicated researchers in the days of Prof Maini's own DPhil; yet a field that has grown tremendously since then. Much of this growth is attributable to the work of Prof Maini, so that today the value of mathematics in biology is increasingly recognized by biologists and clinicians, and with theoretical predictions of mathematical models having cemented a role in advancing biological understanding. 

Speakers

David Sumpter, Uppsala University (Public lecture), Derek Moulton, University of Oxford, Hans Othmer, Minnesota University, Jen Flegg, University of Melbourne, Jim Murray, University of Washington, Jonathan Sherratt, Heriot-Watt University, Kevin Painter, Heriot-Watt University, Linus Schumacher, University of Edinburgh, Lucy Hutchinson, Roche, Mark Chaplain, University of St Andrews, Mark Lewis, University of Alberta, Mary Myerscough, University of Sydney, Natasha Martin, University of Bristol, Noemi Picco, Swansea University, Paul Kulesa, Stowers Institute for Medical Research, Ruth Baker, University of Oxford, Santiago Schnell, University of Michigan, Tim Pedley, University of Cambridge

Organising committee

Ruth Baker (University of Oxford)

Derek Moulton (University of Oxford)

Helen Byrne (University of Oxford)

Santiago Schnell (University of Michigan)

Mark Chaplain (University of St Andrews)

The analysis and characterization of human mobility using population-level mobility models is important for numerous applications, ranging from the estimation of commuter flows to modeling trade flows. However, almost all of these applications have focused on large spatial scales, typically from intra-city level to inter-country level. In this paper, we investigate population-level human mobility models on a much smaller spatial scale by using them to estimate customer mobility flow between supermarket zones. We use anonymized mobility data of customers in supermarkets to calibrate our models and apply variants of the gravity and intervening-opportunities models to fit this mobility flow and estimate the flow on unseen data. We find that a doubly-constrained gravity model can successfully estimate 65-70% of the flow inside supermarkets. We then investigate how to reduce congestion in supermarkets by combining mobility models with queueing networks. We use a simulated-annealing algorithm to find store layouts with lower congestion than the original layout. Our research gives insight both into how customers move in supermarkets and into how retailers can arrange stores to reduce congestion. It also provides a case study of human mobility on small spatial scales.

Please register at:

https://sites.google.com/view/geometryandstrings2019/home

 It has been long known that intersection theory on the moduli space of punctured Riemann surfaces encodes observables in two-dimensional quantum gravity. It is natural to ask whether interacting theories could also admit a similar description. In the genus-zero case we put forward a twisted version of intersection theory on the moduli space and propose that it computes tree-level scattering amplitudes in a range of quantum field theories with a finite spectrum of particles. The resulting intersection numbers exhibit two alternative kinds of localization formulae. The first one receives contributions only from boundaries of the moduli space, thus leading to a Feynman diagram expansion, while the second one localizes on critical points of a certain Morse function.

We investigate a nonlinear version of coevolving voter models, in which both node states and network structure update as a coupled stochastic dynamical process. Most prior work on coevolving voter models has focused on linear update rules with fixed rewiring and adopting probabilities. By contrast, in our nonlinear version, the probability that a node rewires or adopts is a function of how well it "fits in" within its neighborhood. To explore this idea, we incorporate a parameter σ that represents the fraction of neighbors of an updating node that share its opinion state. In an update, with probability σq (for some nonlinearity parameter q), the updating node rewires; with complementary probability 1−σq, the updating node adopts a new opinion state. We study this mechanism using three rewiring schemes: after an updating node deletes a discordant edge, it then either (1) "rewires-to-random" by choosing a new neighbor in a random process; (2) "rewires-to-same" by choosing a new neighbor in a random process from nodes that share its state; or (3) "rewires-to-none" by not rewiring at all (akin to "unfriending" on social media). We compare our nonlinear coevolving model to several existing linear models, and we find in our model that initial network topology can play a larger role in the dynamics, whereas the choice of rewiring mechanism plays a smaller role. A particularly interesting feature of our model is that, under certain conditions, the opinion state that is initially held by a minority of nodes can effectively spread to almost every node in a network if the minority nodes views themselves as the majority. In light of this observation, we relate our results to recent work on the majority illusion in social networks.

Reference: 

Kureh, Yacoub H., and Mason A. Porter. "Fitting In and Breaking Up: A Nonlinear Version of Coevolving Voter Models." arXiv preprint arXiv:1907.11608 (2019).

In the speaker's previous joint work with Hans-Joachim Hein, a mass formula for asymptotically locally Euclidean (ALE) Kaehler manifolds was proved, assuming only relatively weak fall-off conditions on the metric. However, the case of real dimension four presented technical difficulties that led us to require fall-off conditions in this special dimension that are stronger than the Chrusciel fall-off conditions that sufficed in higher dimensions. This talk will explain how a new proof of the 4-dimensional case, using ideas from symplectic geometry, shows that Chrusciel fall-off suffices to imply all our main results in any dimension. In particular, I will explain why our Penrose-type inequality for the mass of an asymptotically Euclidean Kaehler manifold always still holds, given only this very weak metric fall-off hypothesis.
 

The vulnerability of a host population to a specific disease measures how likely pathogen introduction will lead to an epidemic outbreak, and how hard it is to contain or eliminate an ongoing one. Predicting vulnerability is thus key to designing risk-reduction strategies that limit disease burden on public health and economic development. To do that, highly-resolved data tracking contacts and mobility of the host population need to integrate into detailed models of disease dynamics. This represents a twofold challenge. Firstly, we need theoretical frameworks that turn data feeds into predictors of epidemic risk, and can identify which of the structural features of the host population drive its vulnerability. Secondly, we need new ways to access, analyze, and share the relevant contact and mobility data: a necessary step to make our predictions realistic and reliable. In my talk, I will address both issues. I will show how to analytically derive the conditions that discriminate between epidemic regime and quick pathogen extinction, by representing empirically measured contacts as time-evolving complex networks. The analytical core of this theory leads to a broad range of applications. At the same time, its data-driven nature prompts context-specific predictions that can inform policymaking, as I will show in two case studies: reorganizing nurse scheduling to reduce the risk of spread of healthcare-associated infections; linking the features of livestock trade movements to the spatial spread of cattle diseases. The latter application is also an example of how limited access and incomplete data collection represent a big hurdle to predictive vulnerability analysis. To overcome this, I will present a collaborative platform for analyzing and comparing trade networks coming from several European countries. Using a bring code to the data approach, our platform surmounts the strict regulations preventing data sharing, and builds an algorithm that predicts vulnerability even in situations when limited data on cattle trade are available. The ultimate goal of all these theoretical and numerical developments is to inform strategies that reduce the vulnerability of the host population by restructuring its contacts. However, such restructuring may entail a feedback effect, acting as selective pressure on the pathogen itself. In the last part of my talk, I will extend the developed formalism to modeling evolutionary pathways that maximize the invasion potential of the pathogen, given the observed host population structure. Specifically, I will link the emergence of exotic replication behaviors in plant-infecting viruses to historical changes in plant distribution patterns.

We study the stability properties of the Eulerian mean flow generated by monochromatic surface-gravity waves propagating in a rotating frame. The wave averaged equations, also known as the Craik-Leibovich equations, govern the evolution of the mean flow. For propagating waves in a rotating frame these equations admit a steady depth-dependent base flow sometimes called the Ekman-Stokes spiral, because of its resemblance to the standard Ekman spiral. This base flow profile is controlled by two non-dimensional numbers, the Ekman number Ek and the Rossby number Ro. We show that this steady laminar velocity profile is linearly unstable above a critical Rossby number Roc(Ek). We determine the threshold Rossby number as a function of Ek using a numerical eigenvalue solver, before confirming the numerical results through asymptotic expansions in the large/low Ek limit. These were also confirmed by nonlinear simulations of the Craik-Leibovich equations. When the system is well above the linear instability threshold, Ro >> Roc, the resulting flow fluctuates chaotically. We will discuss the possible implications in an oceanographic context, as well as for laboratory experiments.

In recent years, much attention has been given to single-cell RNA sequencing techniques as they allow researchers to examine the functions and relationships of single cells inside a tissue. In this study, we combine single-cell RNA sequencing data with protein–protein interaction networks (PPINs) to detect active modules in cells of different transcriptional states. We achieve this by clustering single-cell RNA sequencing data, constructing node-weighted PPINs, and identifying the maximum-weight connected subgraphs with an exact Steiner-Tree approach. As a case study, we investigate RNA sequencing data from human liver spheroids but the techniques described here are applicable to other organisms and tissues. The benefits of our novel method are two-fold: First, it allows us to identify important proteins (e.g., receptors) which are not detected from a differential gene-expression analysis as they only interact with proteins that are transcribed in higher levels. Second, we find that different transcriptional states have different subnetworks of the PPIN significantly overexpressed. These subnetworks often reflect known biological pathways (e.g., lipid metabolism and stress response) and we obtain a nuanced picture of cellular function as we can associate them with a subset of all analysed cells.

We will talk about our recent results on the uniqueness of regular reflection solutions for the potential flow equation in a natural class of self-similar solutions. The approach is based on a nonlinear version of method of continuity. An important property of solutions for the proof of uniqueness is the convexity of the free boundary.

The stabilization of thermo-mechanical systems is a classical problem in thermodynamics and well

understood in a context of gases. The objective of this talk is to indicate the role of null-Lagrangians and

certain transport/stretching identities in stabilizing thermomechanical systems associated with general

thermoelastic free energies. This allows to prove various convergence results among thermomechan-

ical theories, and suggests a variational scheme for the approximation of the equations of adiabatic

thermoelasticity.

In this talk, I will talk about the existence of global weak solutions for the compressible Navier-Stokes equations, in particular, the viscosity coefficients depend on the density. Our main contribution is to further develop renormalized techniques so that the Mellet-Vasseur type inequality is not necessary for the compactness.  This provides existence of global solutions in time, for the barotropic compressible Navier-Stokes equations, for any $\gamma>1$, in three dimensional space, with large initial data, possibly vanishing on the vacuum. This is a joint work with D. Bresch, A. Vasseur.