Past

The uniformly degenerate elliptic equation is a special class of degenerate elliptic equations. It appears frequently in many important geometric problems. For example, the Beltrami-Laplace operator on conformally compact manifolds is uniformly degenerate elliptic, and the minimal surface equation in the hyperbolic space is also uniformly degenerate elliptic. In this talk, we discuss the global regularity for this class of equations in the classical Holder spaces. We also discuss some applications.

The restricted isometry property is arguably the most prominent tool in the theory of compressive sensing. In its classical version, it features l_2 norms as inner and outer norms. The modified version considered in this talk features the l_1 norm as the inner norm, while the outer norm depends a priori on the distribution of the random entries populating the measurement matrix.  The modified version holds for a wider class of random matrices and still accounts for the success of sparse recovery via basis pursuit and via iterative hard thresholding. In the special case of Gaussian matrices, the outer norm actually reduces to an l_2 norm. This fact allows one to retrieve results from the theory of one-bit compressive sensing in a very simple way. Extensions to one-bit matrix recovery are then straightforward.
 

The 5th Oxford Neuron and Brain Mechanics Workshop will take place on 22 and 23 March 2018, in St Hugh’s College, Oxford. The event includes international and UK speakers from a wide variety of disciplines, collectively working on Traumatic Brain Injury, Brain Mechanics and Trauma, and Neurons research.

The aim is to foster new collaborative partnerships and facilitate the dissemination of ideas from researchers in different fields related to the study of brain mechanics, including pathology, injury and healing.

Focussing on a multi-disciplinary and collaborative approach to aspects of brain mechanics research, the workshop will present topics from areas including Medical, Neuroimaging, Neuromechanics and mechanics, Neuroscience, Neurobiology and commercial applications within medicine.

This workshop is the latest in a series of events established by the members of the International Brain Mechanics and Trauma Lab (IBMTL) initiative *(www.brainmech.ox.ac.uk) in collaboration with St Hugh’s College, Oxford.

Speakers

Professor Lee Goldstein MD, Boston University
Professor David Sharp, Imperial College London
Dr Ari Ercole, University of Cambridge
Professor Jochen Guck, BIOTEC Dresden
Dr Elisa Figallo, Finceramica SPA
Dr Mike Jones, Cardiff University
Professor Ellen Kuhl, Stanford University
Mr Tim Lawrence, University of Oxford
Professor Zoltan Molnar, University of Oxford
Dr Fatiha Nothias, University Pierre & Marie Curie
Professor Stam Sotiropoulos, University of Nottingham
Professor Michael Sutcliffe, University of Cambridge
Professor Alain Goriely, University of Oxford
Professor Antoine Jérusalem, University of Oxford

Everybody is welcome to attend but (free) registration is required.

https://www.eventbrite.co.uk/e/5th-oxford-international-workshop-on-neu…

Students and postdocs are invited to exhibit a poster.

For further information on the workshop, or exhibiting a poster, please contact: @email

The workshop is generously supported by the ERC’s ‘Computational Multiscale Neuron Mechanics’ grant (COMUNEM, grant # 306587) and St Hugh’s College, Oxford.

The International Brain Mechanics and Trauma Lab, based in Oxford, is an international collaboration on projects related to brain mechanics and trauma. This multidisciplinary team is motivated by the need to study brain cell and tissue mechanics and its relation with brain functions, diseases or trauma.

The BSHM meeting on “The history of computing beyond the computer” looks at the people and the science underpinning modern software and programming, from Charles Babbage’s design notation to forgotten female pioneers.

Registration will be £32.50 for standard tickets, £22.00 for BSHM members and Oxford University staff, and £6.50 for students. This will include tea/coffee and biscuits at break times, but not lunch, as we wanted to keep the registration fee to a minimum. A sandwich lunch or a vegetarian sandwich lunch can be ordered separately on the Eventbrite page. If you have other dietary requirements, please use the contact button at the bottom of this page. There is also a café in the Mathematical Institute that sells hot food at lunchtime, alongside sandwiches and snacks, and there are numerous places to eat within easy walking distance.

https://www.eventbrite.co.uk/e/the-history-of-computing-beyond-the-comp…

Programme

21 March 2018

17:00 Andrew Hodges, University of Oxford, author of "Alan Turing: The Enigma” on 'Alan Turing: soft machine in a hard world.’
http://www.turing.org.uk/index.html

22 March 2018

9:00 Registration

9:30 Adrian Johnstone, Royal Holloway University of London, on Charles Babbage's design notation
http://blog.plan28.org/2014/11/babbages-language-of-thought.html

10:15 Reinhard Siegmund-Schultze, Universitetet i Agder, on early numerical methods in the analysis of the Northern Lights
https://www.uia.no/kk/profil/reinhars

11:00 Tea/Coffee

11:30 Julianne Nyhan, University College London, on Father Busa and humanities data
https://archelogos.hypotheses.org/135

12:15 Cliff Jones, University of Newcastle, on the history of programming language semantics
http://homepages.cs.ncl.ac.uk/cliff.jones/

13:00 Lunch

14:00 Mark Priestley, author of "ENIAC in Action, Making and Remaking the Modern Computer"
http://www.markpriestley.net

14:45 Marie Hicks, University of Wisconsin-Madison, author of "Programmed Inequality: How Britain Discarded Women Technologists and Lost Its Edge In Computing"
http://mariehicks.net

15:30 Tea/Coffee

16:00 Panel discussion to include Martin Campbell-Kelly (Warwick), Andrew Herbert (TNMOC), and Ursula Martin (Oxford)

17:00 End of conference

Co-located event

23 March, in Mathematical Institute, University of Oxford, Symposium for the History and Philosophy of Programming, HaPoP 2018, Call for extended abstracts
http://www.hapoc.org/node/241

Andrew Hodges, University of Oxford, author of "Alan Turing: The Enigma” on 'Alan Turing: soft machine in a hard world.’

http://www.turing.org.uk/index.html

This event is free but you need to register:

https://www.eventbrite.co.uk/e/the-history-of-computing-beyond-the-comp… 2018

There is a conjecture by Colliot-Thelene (about 2005) that under specific hypotheses, a morphism of Q-varieties f : X --> Y has the property that for almost all prime numbers p, the corresponding map X(Q_p) --> Y(Q_p) is surjective. A sharpening of the conjecture was solved by Denef (2016), and later, "if and only if" conditions on f were given by Skorobogatov et al. The plan for the talk is to explain in detail the conjecture and the results mentioned above, and to report on work in progress on a different method to attack the conjecture under quite relaxed hypotheses.

Breakthroughs in machine learning have led to impressive results in numerous fields in recent years. I will review some of the best-known results on the computer science side, provide simple ways to think about the associated techniques, discuss possible applications in string theory, and present some applications in string theory where they already exist. One promising direction is using machine learning to generate conjectures that are then proven by humans as theorems. This method, sometimes referred to as intelligible AI, will be exemplified in an enormous ensemble of F-theory geometries that will be featured throughout the talk.

Speaker: Radu Cimpeanu
Title: Crash testing mathematical models in fluid dynamics

Abstract: In the past decades, the broad area of multi-fluid flows (systems in which at least two fluids, be they liquids or mixtures of liquid and gas, co-exist) has benefited from simultaneous innovations in experimental equipment, concentrated efforts on analytical approaches, as well as the rise of high performance computing tools. This provides a wonderful wealth of techniques to approach a given challenge, however it also introduces questions as to which path(s) to take. In this talk I will explore the symbiotic relationship between reduced order modelling and fully nonlinear direct computations, each of their strengths and weaknesses and ultimately how to use a hybrid strategy in order to gain an understanding over larger subsets of often vast solution spaces. The discussion will take us through a number of interesting topics in fluid mechanics on a wide range of scales, from electrohydrodynamic control in microfluidics, to nonlinear waves in channel flows and violent drop impact scenarios.

Speaker: Liana Yepremyan
Title: Turan-type problems for hypergraphs

Abstract: One of the earliest results in extremal graph theory is Mantel's Theorem  from 1907, which says that for given number of vertices, the largest triangle-free graph on these vertices is the complete bipartite graph with (almost) equal sizes. Turan's Theorem from 1941 generalizes this result to all complete graphs. In general, the Tur'\an number of a graph G (or more generally, of  a hypergraph) is the largest number of edges in a graph (hypergraph) on given number of vertices containing no copy of G as a subgraph. For graphs a lot is known about these numbers,  a result by Erd\Hos, Stone and Simonovits determines the correct order of magnitude of Tur\'an numbers  for all non-bipartite graphs. However, these numbers are known only for few  hypergraphs. We don't even know what is the Tur\'an number of the complete 3-uniform hypergraph on 4 vertices. In this talk I will give some  introduction  to these problems and brielfly describe some of the methods used, such as the stability method and the Lagrangian  function, which are interesting on their own.
 

Through laboratory experiments, we examine the transport, settling and resuspension of sediments as well as the influence of floating particles upon damping wave motion.   Salt water is shown to enhance flocculation of clay and hence increase their settling rate.   In studies modelling sediment-bearing (hypopycnal) river plumes, experiments show that the particles that eventually settle through uniform-density fluid toward a sloping bottom form a turbidity current.  Meanwhile, even though the removal of particles should increase the buoyancy and hence speed of the surface current, in reality the surface current stops.  This reveals that the removal of fresh water carried by the viscous boundary layers surrounding the settling particles drains the current even when their concentration by volume is less than 5%. The microscopic effect of boundary layer transport by particles upon the large scale evolution is dramatically evident in the circumstance of a mesopycnal particle-bearing current that advances along the interface of a two-layer fluid.  As the fresh water rises and particles fall, the current itself stops and reverses direction.  As a final example, the periodic separation and consolidation of particles floating on a surface perturbed by surface waves is shown to damp faster than exponentially to attain a finite-time arrest as a result of efficiently damped flows through interstitial spaces between particles - a phenomenon that may be important for understanding the damping of surface waves by sea ice in the Arctic Ocean (and which is well-known to anyone drinking a pint with a proper head or a margarita with rocks or slush).

Many symptoms of Parkinson’s disease are connected with abnormally high levels of synchrony in neural activity. A successful and established treatment for a drug-resistant form of the disease involves electrical stimulation of brain areas affected by the disease, which has been shown to desynchronize neural activity. Recently, a closed-loop deep brain stimulation has been developed, in which the provided stimulation depends on the amplitude or phase of oscillations that are monitored in patient’s brain. The aim of this work was to develop a mathematical model that can capture experimentally observed effects of closed-loop deep brain stimulation, and suggest how the stimulation should be delivered on the basis of the ongoing activity to best desynchronize the neurons. We studied a simple model, in which individual neurons were described as coupled oscillators. Analysis of the model reveals how the therapeutic effect of the stimulation should depend on the current level of synchrony in the network. Predictions of the model are compared with experimental data.

Topological data analysis (TDA) is a robust field of mathematical data science specializing in complex, noisy, and high-dimensional data.  While the elements of modern TDA have existed since the mid-1980’s, applications over the past decade have seen a dramatic increase in systems analysis, engineering, medicine, and the sciences.  Two of the primary challenges in this field regard modeling and computation: what do topological features mean, and are they computable?  While these questions remain open for some of the simplest structures considered in TDA — homological persistence modules and their indecomposable submodules — in the past two decades researchers have made great progress in algorithms, modeling, and mathematical foundations through diverse connections with other fields of mathematics.  This talk will give a first perspective on the idea of matroid theory as a framework for unifying and relating some of these seemingly disparate connections (e.g. with quiver theory, classification, and algebraic stability), and some questions that the fields of matroid theory and TDA may mutually pose to one another.  No expertise in homological persistence or general matroid theory will be assumed, though prior exposure to the definition of a matroid and/or persistence module may be helpful.

An important and relevant topic at Thales is 1-3 composite modelling capability. In particular, sensitivity enhancement through design.

A simplistic model developed by Smith and Auld1 has grouped the polycrystalline active and filler materials into an effective homogenous medium by using the rule of weighted averages in order to generate “effective” elastic, electric and piezoelectric properties. This method had been further improved by Avellaneda & Swart2. However, these models fail to provide all of the terms necessary to populate a full elasto-electric matrix – such that the remaining terms need to be estimated by some heuristic approach. The derivation of an approach which allowed all of the terms in the elasto-electric matrix to be calculated would allow much more thorough and powerful predictions – for example allowing lateral modes etc. to be traced and allow a more detailed design of a closely-packed array of 1-3 sensors to be conducted with much higher confidence, accounting for inter-elements coupling which partly governs the key field-of-view of the overall array. In addition, the ability to populate the matrix for single crystal material – which features more independent terms in the elasto-electric matrix than conventional polycrystalline material- would complement the increasing interest in single crystals for practical SONAR devices.

1.“Modelling 1-3 Composite Piezoelectrics: Hydrostatic Response” – IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 40(1):41-

2.“Calculating the performance of 1-3 piezoelectric composites for hydrophone applications: An effective medium approach” The Journal of the Acoustical Society of America 103, 1449, 1998

Oxford Mathematics Public Lectures

Can Mathematics Understand the Brain?' - Alain Goriely

The human brain is the object of the ultimate intellectual egocentrism. It is also a source of endless scientific problems and an organ of such complexity that it is not clear that a mathematical approach is even possible, despite many attempts. 

In this talk Alain will use the brain to showcase how applied mathematics thrives on such challenges. Through mathematical modelling, we will see how we can gain insight into how the brain acquires its convoluted shape and what happens during trauma. We will also consider the dramatic but fascinating progression of neuro-degenerative diseases, and, eventually, hope to learn a bit about who we are before it is too late. 

Alain Goriely is Professor of Mathematical Modelling, University of Oxford and author of 'Applied Mathematics: A Very Short Introduction.'

March 8th, 5.15 pm-6.15pm, Mathematical Institute, Oxford

Please email @email to register

The construction of permutation functions of a finite field is a task of great interest in cryptography and coding theory. In this talk we describe a method which combines Chebotarev density theorem with elementary group theory to produce permutation rational functions over a finite field F_q. Our method is entirely constructive and as a corollary we get the classification of permutation polynomials up to degree 4 over any finite field of odd characteristic.

This is a joint work with Andrea Ferraguti.
 

The talk originates from two studies on the dynamic properties of one-dimensional elastic quasicrystalline solids. The first one refers to a detailed investigation of scaling and self-similarity of the spectrum of an axial waveguide composed of repeated elementary cells designed by adopting the family of generalised Fibonacci substitution rules corresponding to the so-called precious means. For those, an invariant function of the circular frequency, the Kohmoto's invariant, governs self-similarity and scaling of the stop/pass band layout within defined ranges of frequencies at increasing generation index. The Kohmoto's invariant also explains the existence of particular frequencies, named canonical frequencies, associated with closed orbits on the geometrical three-dimensional representation of the invariant. The second part shows the negative refraction properties of a Fibonacci-generated quasicrystalline laminate and how the tuning of this phenomenon can be controlled by selecting the generation index of the sequence.

We consider calculation of VaR/TVaR capital requirements when the underlying economic scenarios are determined by simulatable risk factors. This problem involves computationally expensive nested simulation, since evaluating expected portfolio losses of an outer scenario (aka computing a conditional expectation) requires inner-level Monte Carlo. We introduce several inter-related machine learning techniques to speed up this computation, in particular by properly accounting for the simulation noise. Our main workhorse is an advanced Gaussian Process (GP) regression approach which uses nonparametric spatial modeling to efficiently learn the relationship between the stochastic factors defining scenarios and corresponding portfolio value. Leveraging this emulator, we develop sequential algorithms that adaptively allocate inner simulation budgets to target the quantile region. The GP framework also yields better uncertainty quantification for the resulting VaR/\TVaR estimators that reduces bias and variance compared to existing methods.  Time permitting, I will highlight further related applications of statistical emulation in risk management.
This is joint work with Jimmy Risk (Cal Poly Pomona). 
 

In this talk I will review recent results on the analysis of shock-capturing-type methods applied to convection-dominated problems. The method of choice is a variant of the Algebraic Flux-Correction (AFC) scheme. This scheme has received some attention over the last two decades due to its very satisfactory numerical performance. Despite this attention, until very recently there was no stability and convergence analysis for it. Thus, the purpose of the works reviewed in this talk was to bridge that gap. The first step towards the full analysis of the method is a rewriting of it as a nonlinear edge-based diffusion method. This writing makes it possible to present a unified analysis of the different variants of it. So, minimal assumptions on the components of the method are stated in such a way that the resulting scheme satisfies the Discrete Maximum Principle (DMP) and is convergence. One property that will be discussed in detail is the linearity preservation. This property has been linked to the good performance of methods of this kind. We will discuss in detail its role and the impact of it in the overall convergence of the method. Time permitting, some results on a posteriori error estimation will also be presented. 
This talk will gather contributions with A. Allendes (UTFSM, Chile), E. Burman (UCL, UK), V. John (WIAS, Berlin), F. Karakatsani (Chester, UK), P. Knobloch (Prague, Czech Republic), and 
R. Rankin (U. of Nottingham, China).

We consider the  symbiotic branching model, which describes a spatial population consisting of two types in terms of a coupled system of stochastic PDEs. One particularly important special case is Kimura's stepping stone model in evolutionary biology. Our main focus is a description of the interfaces between the types in the large scale limit of the system. As a new tool we will introduce a moment duality, which also holds for the limiting model. This also has implications for a classification of entrance laws of annihilating Brownian motions.

 The $n$-stranded pure surface braid group of a genus g surface can be described as the subgroup of the pure mapping class group of a surface of genus $g$ with $n$-punctures which becomes trivial on the closed surface. I am interested in the least dilatation of pseudo-Anosov pure surface braids. For the $n=1$ case, upper and lower bounds on the least dilatation were proved by Dowdall and Aougab—Taylor, respectively.  In this talk, I will describe the upper and lower bounds I have proved as a function of $g$ and $n$.

For energy functionals composed of competing short- and long-range interactions, minimizers are often conjectured to form essentially periodic patterns on some intermediate lengthscale. However,  not many detailed structural results or proofs of periodicity are known in dimensions larger than 1. We study a functional composed of  the attractive, local interfacial energy of charges concentrated on a hyperplane and the energy of the electric field generated by these charges in the full space, which can be interpreted as a repulsive, non-local functional of the charges. We follow the approach of Alberti-Choksi-Otto and prove that the energy of minimizers of this functional is uniformly distributed  on cubes intersecting the hyperplane, which are sufficiently large with respect to the intrinsic lengthscale.

This is a joint work with A. Julia and F. Otto.

Side channel leakage is no longer just a concern for industries that
traditionally have a high degree of awareness and expertise in
(implementing) cryptography. With the rapid growth of security
sensitive applications in other areas, e.g. smartphones, homes, etc.
there is a clear need for developers with little to no crypto
expertise to implement and instantiate cryptography securely on
embedded devices. In this talk, I explain what makes finding side
channel leaks challenging (in theory and in practice) and give an
update on our latest work to develop methods and tools to enable
non-domain experts to ‘get a grip’ on leakage in their
implementations.

Hall algebras of categories of quiver representations and coherent sheaves

on smooth projective curves over F_q recover interesting

representation-theoretic objects such as quantum groups and their

generalizations. I will define and describe the structure of the Hall

algebra of coherent sheaves on a projective variety over F_1, with P^2 as

the main example. Examples suggest that it should be viewed as a degenerate

q->1 limit of its counterpart over F_q.