Tue, 08 Oct 2019
14:00
L2

Traces of Class/Cross-Class Structure Pervade Deep Learning Spectra

Vardan Papyan
(Stanford University)
Abstract


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.

Mon, 07 Oct 2019
15:45
L6

Action rigidity for free products of hyperbolic manifold groups

Emily Stark
(University of Utah)
Abstract

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.

Tue, 24 Sep 2019
14:15
L4

Contravariant forms on Whittaker modules

Adam Brown
(IST Austria)
Abstract

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.

Tue, 24 Sep 2019

12:00 - 13:00
C1

A graph based approach for functional urban areas delineation

Lionel Houssou
(University of La Rochelle)
Abstract

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.
 

Mon, 23 Sep 2019 11:00 -
Wed, 25 Sep 2019 16:00
L3

EUROMECH: Fluid and solid mechanics for tissue engineering

Various Speakers
Further Information

In vitro tissue engineering (TE) aims to create functional tissue and organ samples external to the body to replace damaged or diseased tissues and organs. By using cells (e.g. autologous or allogenic) in combination with natural or synthetic biomaterial scaffolds and biochemical factors, tissueengineered products have many advantages over traditional approaches such as donor tissue and organ transplantation that can elicit an adverse immune response. The development of the growing tissue construct, the combination of scaffold, cells, extracellular matrix (ECM) and biochemical factors, often occurs within a bioreactor that enables precise control of the bio-mechanochemical environment experienced by the cells within the growing construct.


This is particularly important in the development of mechanosensitive tissues, such as bone. Successfully engineering tissues in vitro has required the development of new smart biomaterials, new tissue growth strategies involving defined biological cues, and novel and bespoke bioreactor environments for growing tissue under physiological mechanical conditions. To date, only simple avascular tissues have been successfully generated to a standard where they can be used in a clinical setting, and research into methods for improving tissue viability is essential.


In TE systems, fluid and solid mechanics are used to provide mechanical load (e.g. via fluid shear, elastic deformation) to mechanosensitive tissues such as bone and vasculature, and a key challenge is to recreate the mechanical environment within the bioreactor system that is unique to the tissue under consideration. The fluid flows and solid deformations are intricate, requiring an understanding of novel fluid-structure interactions between the fluid flows, the cells and their ECM, and the (often deformable) biomaterial.  Furthermore, successful tissue growth in bioreactor systems relies on appropriate solute delivery to and waste-product removal from the cells in the tissue construct. To promote transport (without recourse to agitation methods that can be damaging to cells in a tissue-engineering setting), fluid flows are exploited to enhance transport by advection. 

In this colloquium, we will present state-of-the-art theoretical and experimental fluid and solid mechanics for TE, and explore the transformative potential of combined quantitative theoretical and experimental approaches to inform in vitro TE protocols. The theoretical models will be validated via detailed comparison of the theoretical model predictions with quantitative data obtained from state-of-the art biomechanics experiments. The hybrid approach of combining the resulting insights from the validated theoretical models with in vitro TE experiments can then be used to inform bioreactor and smart biomaterial design for TE strategies, with the aim of improving tissue viability.

Delegates are drawn from the theoretical and experimental fluid and solid mechanics communities. To ensure the focus remains applicable to the TE challenges, we have invited leading figures from the TE community, which will also facilitate new opportunities for interdisciplinary collaboration.

Abstract

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

Wed, 18 Sep 2019

17:00 - 18:00
L1

David Sumpter - Soccermatics: could a Premier League team one day be managed by a mathematician? SOLD OUT

David Sumpter
(University of Uppsala)
Further Information

Former Barcelona, Bayern Munich and current Manchester City coach Pep Guardiola is considered by many to be a footballing genius. He has revolutionised the tactical approach to football and that revolution has come about through his careful study of the geometry of the game. But can abstract mathematics really help a team improve its performance?

David Sumpter thinks it can. Unlike the simple statistics applied to (lesser) sports, football is best understood through the patterns the players create together on the field. From the geometry of shooting, through the graph theory of passing, to the tessellations created by players as they find space to move in to, all of these patterns can be captured by mathematical models. As a result, football clubs are increasingly turning to mathematicians. 

David Sumpter is Professor of Applied Mathematics at the University of Uppsala, Sweden. His scientific research covers everything from the inner workings of fish schools and ant colonies, the analysis of the passing networks of football teams and segregation in society.

5.00pm-6.00pm, Mathematical Institute, Oxford

Please email @email to register

Watch live:
https://facebook.com/OxfordMathematics
https://livestream.com/oxuni/sumpter

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

Wed, 18 Sep 2019 09:00 -
Thu, 19 Sep 2019 17:00
L2

On growth and pattern formation: A celebration of Philip Maini's 60th birthday

Various Speakers
Further Information

The cost for registration is £80. This includes lunch and coffee both days of the workshop, and drinks at a reception following the public lecture on Wednesday 18th September. Registration should be completed through the University of Oxford Online stores: https://www.oxforduniversitystores.co.uk/product-catalogue/mathematical…

Deadline for registration: July 5th. Space is limited, so register early to avoid disappointment!

Abstract

 

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 SumpterUppsala University (Public lecture), Derek MoultonUniversity of Oxford, Hans OthmerMinnesota University, Jen Flegg, University of Melbourne, Jim MurrayUniversity of Washington, Jonathan SherrattHeriot-Watt University, Kevin PainterHeriot-Watt University, Linus Schumacher, University of Edinburgh, Lucy HutchinsonRoche, Mark ChaplainUniversity of St Andrews, Mark LewisUniversity of Alberta, Mary MyerscoughUniversity of Sydney, Natasha MartinUniversity of Bristol, Noemi Picco, Swansea University, Paul Kulesa, Stowers Institute for Medical Research, Ruth Baker, University of Oxford, Santiago SchnellUniversity 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)

Tue, 17 Sep 2019

12:00 - 13:00
C4

Gravity model on small spatial scales: mobility and congestion in supermarkets

Fabian Ying
(University of Oxford)
Abstract

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.

Fri, 13 Sep 2019

11:45 - 13:15
L3

InFoMM CDT Group Meeting

Alissa Kamilova, Oliver Whitehead, Zhen Shao
(Mathematical Institute)
Tue, 10 Sep 2019 09:30 -
Wed, 11 Sep 2019 18:30

ENIUS TRAINING SCHOOL, BERN | 15 BURSARIES AVAILABLE | APPLICATIONS NOW OPEN

(Swiss Institute for Translational and Entrepreneurial Medicine)
Further Information

The Training School will bring together a multi-disciplinary group of clinicians, biomedical engineers, biologists and physical scientists to present recent advances in mathematical, computational, in-vitro, and in-vivo approaches to further our understanding of fluid mechanics within the stented ureter and to identify current challenges in urinary stent design. Moreover, leading speakers from the world of industry and regulatory affairs will share their experiences of commercialisation in the medtech industry, and how they have addressed industrial and regulatory challenges when taking their “next-generation” products from bench-to-bedside.

Here is a preliminary program.

We would like to encourage Early Career Researchers (Master students, PhD students, and PostDocs) to apply as trainees, by sending their CV and a short statement (of no more than 250 words) to francesco.clavica@artorg.unibe.ch, explaining why they would like to attend the Training School. Participants are encouraged to present a poster about their work, and should send a title of their poster together with their application.

We will award 15 grants to fund accommodation, travel, and subsistence of trainees

Applications should be submitted by July 15th, and applicants will be notified by the end of July about the outcome of their application.

Mon, 09 Sep 2019 12:00 -
Wed, 11 Sep 2019 12:00
L5

Workshop on Higher-order Interaction Networks: Dynamics, Structure, Data

See below for speaker information
(Speakers from several universities)
Further Information

The goal of the research workshop "Higher-order interaction networks: dynamics, structure, data" is to bring together researchers from these different communities with distinct perspectives on network dynamics —- from network science, dynamical systems, and data science/machine learning -- to develop novel approaches to understand networked systems. By cutting across different mathematical communities, this will allow to develop new tools, for example by exploring links between data driven methods (such as machine learning) and dynamics. A particular focus of this workshop will be on the role of non-dyadic dynamical interactions (joint interactions between more than two nodes) whose importance for the modeling, analysis, and control of such networked systems have recently been highlighted.

Expressions of interest are now open with an initial deadline of June 1, 2019, with notification of acceptance no later than June 15, 2019.

Participation in the workshop will cost a nominal fee of £50 which will be used to cover catering during the workshop. Participants will also have the chance to attend the workshop dinner on Wednesday 10th September at the nearby Somerville College, the cost of which will be £30.  

Thanks to generous funding from EU and the London Mathematical Society, there is limited travel support for UK-based early career researchers available. Please indicate whether you wish to apply for support during registration.

For further information including registration please click here.

Confirmed Speakers:

Lou Pecora (Naval Research Labs)
Tanya Berger-Wolf (Illinois)
Santiago Segarra (Rice)
Tiago Pereira (USP Sao Carlos)
Marta Sales-Pardo (Barcelona)
Jacopo Grilli (Santa Fe Institute/ICTP Trieste)
Marya Bazzi (ATI)
Rebecca Hoyle (Southampton)
Ana Paula Dias (Porto)
Laetitia Gauvin (ISI Torino)
Heather Harrington (Oxford)
Rodolphe Sepulchre (Cambridge)
Jess Enright (Stirling)
Peter Ashwin (Exeter)
Pawel Dlotko (Swansea)

Tue, 27 Aug 2019
12:00
L4

Aspects of Scattering Amplitudes and Moduli Space Localization

Sebastian Mizera
(Perimeter/IAS Princeton)
Abstract

 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.

 

Tue, 20 Aug 2019

12:00 - 13:00
C4

Fitting In and Breaking Up: A Nonlinear Version of Coevolving Voter Models

Yacoub H. Kureh
(University of California Los Angeles)
Abstract

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).

Fri, 19 Jul 2019
12:00
L6

Mass, Kaehler Manifolds, and Symplectic Geometry

Prof Claude LeBrun
(Stonybrook)
Abstract

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.
 

Tue, 09 Jul 2019

12:00 - 13:00
N3.12

Predicting epidemic risk from contact and mobility data

Eugenio Valdano
(University of California Los Angeles)
Abstract

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.

Mon, 08 Jul 2019 11:30 -
Tue, 09 Jul 2019 14:00
L5

UK Fluids Network Special Interest Group: Fluid Mechanics of Cleaning and Decontamination

Various Speakers
(University of Oxford)
Further Information

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Please Register here

 

Mon, 08 Jul 2019 09:00 -
Wed, 10 Jul 2019 17:00
L2

NetMob 2019

NetMob 2019
(University of Oxford and others)
Further Information

NetMob is the primary conference in the analysis of mobile phone datasets in social, urban, societal and industrial problems. Previous editions in Boston and Milano brought together more than 250 researchers, practitioners and decision-makers from more than 140 institutions and 30 countries.

The 2019 edition of NetMob will take place at the Mathematical Institute of Oxford University in a conference format similar to that of the previous editions: one track of short contributed talks, a simplified submission procedure, no proceedings (except for a book of abstracts), and the possibility to present recent results or results submitted elsewhere.

For more information and how to join click here

Thu, 04 Jul 2019

14:00 - 15:30
C3

Mean flow instability of surface gravity waves propagating in a rotating frame: the Ekman-Stokes instability

Dr. Kannabiran Seshasayanan
(CEA Paris-Saclay)
Abstract

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.

Tue, 02 Jul 2019

12:00 - 13:00
C4

Functional module detection through integration of single-cell RNA sequencing data with protein interaction networks

Florian Klimm
(University of Oxford)
Abstract

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.

Mon, 01 Jul 2019

16:00 - 17:00
C6

Uniqueness of regular shock reflection

Wei Xiang
(City University of Hong Kong)
Abstract

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.

Mon, 01 Jul 2019

15:00 - 16:00
C6

The role of polyconvexity in dynamical problems of thermomechanics

Athanasios Tzavaras
(KAUST)
Abstract

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.

Fri, 28 Jun 2019

16:00 - 17:00
L4

Global solutions of the compressible Navier-Stokes equations

Professor Cheng Yu
(University of Florida)
Abstract

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.

Fri, 28 Jun 2019

11:45 - 13:15
L5

InFoMM CDT Group Meeting

Caoimhe Rooney, Attila Kovacs, Rahil Sachak-Patwa, Thomas Babb
(Mathematical Institute)