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Previous Seminars

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Numerical Analysis Group Seminar:

Thursday 22nd August, 2.00-3.00p.m. in LT908

Professor Marco Cuturi

School of Informatics, Kyoto University

Sinkhorn Distances - Lightspeed Computation of Optimal Transportation Distances

Abstract:

Optimal transportation distances are a fundamental family of parameterized distances for probability distributions. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation involves -- when comparing finite dimensional histograms -- the resolution of a linear program whose cost is prohibitive whenever the histograms' dimension exceeds a few hundreds. We propose in this work a new family of optimal transportation distances that look at transportation problems from a maximum-entropy perspective. We smooth the classical optimal transportation problem with an entropic regularization term, and show that the resulting optimum is also a distance which can be computed through Sinkhorn-Knopp's matrix scaling algorithm at a speed that is several orders of magnitude faster than that of transportation solvers. Contrary to traditional network simplex solvers, we show how this algorithm can be vectorized and efficiently parallelized using GPGPUs. We also report improved performance over classical optimal transportation distances on the MNIST benchmark problem.

The talk will be self contained and I will spend the first half of the talk introducing the family of optimal transportation distances.

 

CMIM Group Seminar

Wednesday 21st August 2013, 3.00-4.00p.m. in LT908

Joao Luiz Azevedo - Instituto de Aeronáutica e Espaço, Brazil

High-Order Reconstruction Scheme Formulations for Compressible Flows

Abstract:

To come.

PME Scientific Seminar

Tuesday, 20th August 2013, 1.00p.m., LT907

Dr Karen Lamb

Clinical Epidemiology and Biostatistics Unit at the Murdoch Children's Research Institute in Australia

Neighbourhood and health: does place matter?

  

Applied Analysis Seminar

Friday 5th July 2013, 2.00pm in LT907

Professor Jerzy Filar

Strategic Professor of Mathematics and Statistics, Flinders University, Australia

The Hamiltonian cycle problem and Markov decision processes

Abstract:

We consider the famous Hamiltonian cycle problem (HCP) embedded in a Markov decision process (MDP).  More specifically, we consider a moving object on a graph G where, at each vertex, a controller may select an arc emanating from that vertex according to a probabilistic decision rule.  A stationary policy is smply a control where these decision rules are time invariant.  Such a policy induces a Markov chain on the vertices of the graph.  Therefore, HCP is equivalent to a search for a stationary policy that induces a 0 - 1 probability transition matrix whose non-zero entries trace out a Hamiltonian cycle in the graph.  A consequence of this embedding is that we may consider the problem over a number of, alternative, convex - rather than discrete - domains.  These include: (a) the space of stationary policies, (b) the more restricted but, very natural, space of doubly stochastic matrices induced by the graph, and (c) the associated spaces of so-called "occupational measures".

This approach to the HCP has led to both theoretical and algorithmic approaches to the underlying HCP problem.  In this presentation, we outline a selection of results generated by this line of research.

CMIM Group Extraordinary Seminar

Friday 21st June 2013, 3.00-4.00p.m. in LT907

Professor Chuck Gartland 

Electric-Field-Induced Instabilities in Liquid-crystal Films

Abstract:

The orientational properties of materials in the liquid-crystal phase (characterized by the "director field", a unit vector field, in the simplest macroscopic continuum models) are strongly influenced by applied electric fields, which provide a common switching control mechanism in liquid crystal based technologies.  In turn, the liquid crystal medium, by virtue of its anisotropic and generally inhomogeneous nature, also influences the local electric field; so the equilibrium director field and electric field must be computed in a coupled, self-consistent way.

Equilibria correspond to stationary points of the "free energy" (an integral functional of the director field and the electrostatic potential field), which fails to be coercive, in typical applications, due to both the negative-definite nature of the director/electric-field coupling term and the pointwise unit-vector constraints on the director field.  We will discuss characterizations of local stability of equilibrium fields in such settings and anomalous behavior that can result even in simple geometries, such as those of classic Freedericksz transitions.

Numerical Analysis Group Extraordinary Seminar:

Thursday 20th June, 12noon in LT907

Professor Theodoros Katsaounis

University of Crete, Greece

Error control and adaptivity for the linear Schrödinger equation in the semiclassical regime

Abstract:

We derive optimal order a posteriori error bounds for fully discrete Crank-Nicolson finite element scheme for linear Schrödinger equations.  The derivation of the estimators is based on the reconstruction technique;  in particular, we introduce a novel elliptic reconstruction that leads to estimates which reflect the physical properties of the equation.  Our analysis also includes rough potentials.  Using the obtained a posteriori error estimators, we further develop and analyze an existing time-space adaptive alogorithm, and we apply it to the one-dimensional Schrödinger equation in the semiclassical regime.  The adaptive algorithm reduces the computational cost drastically and provides efficient error control for the solution and the observables of the problem, especially for small values of the Planck constant.

 

 

Numerical Analysis Group Extraordinary Seminar:

Monday 17th June, 12noon in LT907

Professor Klaus Bohmer

Magburg, Germany

A Convergence Theory for Mesh-free Methods for a Nonlinear Second Order Elliptic Equation

Abstract:

This lecture is an appetizer for my two books in OUP: Numerical Methods for Nonlinear Elliptic Differential Equations, A Synopsis, Numerical Methods for Bifurcation and Center Manifolds in Nonlinear Elliptic and Parabolic Differential Equations, 2010 and 2014. We extend for the first time the linear discretization theory of Schaback, developed for meshfree methods, to nonlinear operator equations, relying heavily on methods of Bohmer, Vol I. There is no restriction to elliptic problems nor to symmetric numerical methods like Galerkin techniques. Trial spaces can be arbitrary, but have to approximate the solution well, and testing can be weak or strong. We present Galerkin techniques as an example. On the downside, stability is not easy to prove for special applications, and numerical methods have to be formulated as optimization problems. Results of this discretization theory cover error bounds and convergence rates. As an example we present the meshless method for some nonlinear elliptic problems of second order. Numerical examples are added for illustration.

 

International Workshop on Stochastic Differential Delay Equations and Their Applications

Monday-Tuesday, 10-11th June 2013, 10.00 a.m. in LT908

10 June 2013

10:00–10:28 Registration/Tea and Coffee

Chair: Professor Xuerong Mao, University of Strathclyde

10:28–10:30 Welcome address

10:30–11:20 Professor Tomas Caraballo, University of Sevilla

Asymptotic behaviour of Multi-valued Random Dynamical Systems

with delays

11:20–12:10 Dr John Appleby, City University of Dublin

Dependence and independence of generalised growth rates on initial

functions in solutions of functional differential equations

12:10–13:10 Lunch break and posters

Chair: Dr John Appleby, Dublin City University

13:10–14:00 Dr. Yi Ming Lai, University of Strathclyde

Synchronization of Stochastic Oscillators

14:00–14:50 Dr Riedle Markus, King College London

Stochastic delay equations and the Cauchy problem driven by

cylindrical Levy processes

14:50–15:20 Tea and Coffee

Chair: Professor Tomas Caraballo, University of Sevilla

15:20–16:10 Dr Lihu Xu, Brunel University London

Ergodicity of SPDEs forced by highly degenerate \alpha stable

noises

16:10–17:00 Dr. Sotirios Sabanis, University of Edinburgh

Euler approximations with varying coefficient

17:00-17:50 Prof Alexandra Rodkina, University of the West Indies

On discretization of of SDDEs

17:50–18:30 Discussions and posters

----- 

11 June 2013

Chair: Prof Neville Ford, University of Chester

10:00–10:50 Prof Uwe Kuechler, Humboldt Universitat zu Berlin

Sequential parameter estimators with guaranteed accuracy for delay

differential equations

10:50–11:40 Mr Wei Liu, University of Strathclyde

Almost sure stability of the Euler--Maruyama method with random

variable stepsize

11:40–12:30 Dr Kai Liu, University of Liverpool

A large deviation principle of retarded Ornstein-Uhlenbeck

processes driven by Levy noise

12:30–13:30 Lunch break and posters

Chair: Dr Changgui Yuan, University of Swansea

13:30–14:20 Prof Neville Ford, University of Chester

Modelling and analysis for mixed type (stochastic) functional

differential equations

14:20–15:10 Dr Wei Yang, University of Strathclyde

Sensitivity analysis for HJB equations with an application to a

coupled backward-forward system

15:10–15:40 Tea and Coffee

Chair: Prof Uwe Kuchler, Hamboldt Universitat Zu Berlin

15:40–16:30 Dr Lukas Szpruch, University of Edinburgh

Multilevel Monte Carlo method

16:30–17:20 Dr Changgui Yuan, University of Swansea

Bismut Formulae for Functional SDEs

17:20–18:00 Cheese, wine, discussions and posters

Universities of Strathclyde and Glasgow, Centre for Mathematics Applied to the Life Sciences. Summer Research Symposium 2013

Wednesday 5th June 2013, 12.00-6.00p.m., in Room LT908

Cardiovascular Disease and Treatment: Mathematical Modelling and Clinical Insights

CMALS is holding an afternoon symposium which will bring together mathematicians, clinicians and industrialists involved in research under the above theme.  Our expert speakers include Professor Keith Oldroyd and Dr Julian Gunn who will share some of the current challenges in the treatment of heart disease and highlight some of the technologies currently being used clinically. Professor Nick Hill and Dr Martin Meere will discuss the role that mathematics can play in furthering our understanding of disease progression and in the development of drug delivery devices.  We will also have four short presentations from early career researchers.

The meeting will commence with a buffet lunch and end with a wine reception, providing an excellent opportunity to network, to share ideas and to set up collaborations.

PME Scientific Seminar: Stochastic Oscillators in Ecology and Neuroscience

Wednesday, 15th May 2013, 1.00, LT907

Yi Ming Lai

To prepare for his PhD vivia, Yi Ming Lai will be presenting his research.  Everyone is welcome to attend and some rolls and sofr drinks will be available.

  

Colloquia: PDEs for fishing and conservation of marine ecosystems

Wednesday, 8th May 2013, 3.30-4.30, LT908

Professor Richard Law

University of York

Abstract:

This talk describes the use of dynamical models of marine size spectra to learn how exploitation and conservation of marine ecosystems might be reconciled.  The approach is based on a modelling framework, new in the context of fisheries management, involving systems of partial differential equations that keep track of biomass flow as fish eat one another and grow.  The results suggest that the goals of sustainable exploitation and conservation are not as irreconcilable as has previously been thought, if exploitation is moved towards matching the natural productivity of components of marine ecosystems (balanced harvesting).

SIAM Student Chapter Event

Monday, 29th April 2013, 2.00p.m. LT908

The speakers are:

Martin Burns who is a former Strathclyde PhD student, will provide a background and introduction.

Cecilia MacIntyre, A statistician for the Scottish Government working on Census Quality Assurance

and

Nick Trefethen, Oxford Professor of Numerical Analysis

There will be a short coffee break between talks with refreshments afterwards at 4.30p.m.

 All welcome

Colloquia: Multi-Scale Mechanics and Evolving Discontinuities

Wednesday, 24th April 2013, 3.30-4.30 LT908

Professor René de Borst, Regius Professor of Civil Engineering and Mechanics

University of Glasgow

Abstract:

Multi-scale methods are a new paradigm in many branches of engineering science. When resolving smaller and smaller scale evolving discontinuities become more important. We will start by a concise classification of multi-scale computational mechanics, and we will concentrate on computational methods that allow for concurrent computing at multiple scales. Difficulties that relate to the efficient and accurate coupling between the various  subdomains will be highlighted, with an emphasis on the coupling of domains that aremodelled by dissimilar field equations. Next, we will focus on evolving discontinuities that arise at different scales, including fracture, and discuss various methods forresolving them, such as level sets, phase-field approaches, partition-of-unity methods,and isogeometric analysis. Finally, approaches will be outlined for multi-scale analyses that include coupling of evolving discontinuities with non-mechanical effects.

PME Scientific Seminar: Sufficiency, Order Statistics and the Demon Problem: They're Now...They're Wow

Wednesday 24th April, 1.00p.m. in LT907

Professor John Quigley

University of Strathclyde, Department of Management Science

Abstract:

Monitoring energy consumption of consumers by utility companies is prohibitively expensive at the household level, so aggregate measures are taken for clusters of households.  This creates a challenge for assessing the level of energy stored in each household, for which we may require a minimum level is available.  From a statistical modelling perspective we seek an understanding of the order statistics from a sample given their arithmetic mean. This talk describes a simple approach to determining the probability that a sample average will be between any two order statistics for the case where the parent distribution is Normal or Exponential.  The problem relates to the assessment of outliers and was initially discussed in 1953 by Youden, who named it the Demon Problem.  While progress has been made on the problem with asymptotic results available for the case of the Normal distribution and an exact solution for the case of the Exponential distribution, this talk proposes a much simpler derivation through noting that the sample average is a sufficient statistic for the parent population and explicitly modelling the dependency in the subsequent conditional probability distribution.  This reduces the problem to one of finding orthant probabilities for which procedures are well known.  The results are then applied to our case.

 

CMIM Group Seminars: Modelling drug release from arterial stents

Tuesday 23rd April, 3.00-4.00p.m. in LT907

Dr Sean McGinty

University of Strathclyde

Presentation

Tuesday, 23rd April 2013, 11.00, LT908

Professor Paulo de Veiga

University of São Paulo, São Carlos, Brazil

Professor Paulo will present on current research at the University of Sao Paulo in the areas of Computer Science and Pure and Applied Mathematics and Statistics.

PME Scientific Seminar: Issues in studies of vaccine effect

Wednesday 10th April, 1.00p.m. in LT907

Mr Alan Yeung

Department of Mathematics, University of Strathclyde

 

 

Stochastic Analysis Group Seminar: Mathematics in Insurance

Thursday, 28th March 2013, 4.00-5.00p.m., LT907

Mr. Graeme Lawson

Prudential plc

 

 

PME Scientific Seminar: Are farmed fish safe to eat, or is it all horses for courses?

Wednesday 27th March, 1.00p.m. in LT907

Dr David Morris

Department of Mathematics, University of Strathclyde

Numerical Analysis Group Seminar:

Tuesday 26th March, 4.00p.m. in LT907

Des Higham : Algorithms in Stochastic Simulation and Network Science

 

Phil Knight : Bistochastic Clustering

Abstract : We exploit properties of the SVD of a bistochastic matrix to form natural clusters amongst the rows. By turning a general square matrix into one that's bistochastic we motivate a preconditioning strategy.

 

Alison Ramage : Iterative Solution of Large Linear Systems

 

Gabriel Barrenechea : An unexpected rounding error problem

 

Oleg Davydov : Current Research Interests

 

Penny Davies : "Convolution splines" for time dependent boundary integral equations (TDBIEs)

Abstract:  This is a new method for approximating TDBIEs in time which combines attractive features of convolution quadrature (good stability properties, ease of implementation) and space-time Galerkin (sparse system matrices).

 

John Mackenzie : Scientific Computing -- From Cells to Daz

Abstract : I will present details of novel computational methods being developed  to tackle a range of scientific and industrial problems ranging from cell migration and chemotaxis to the manufacture of household detergents. In particular I will focus of the solution of problems on evolving domains and surfaces and the use of adaptive moving mesh methods. 

 

Iain Stewart : Computational challenges in liquid crystals'

Abstract: The modification of numerical techniques that are particular to non-Newtonian fluids (e.g., Oldroyd-B fluids) have recently been adapted so that they can be applied to nonlinear Ericksen-Leslie equations in 2D and 3D geometries [1,2]. Further modifications are presently underway for a recently formulated nonlinear smectic liquid crystal dynamic theory [3].

[1] Cruz, Tome, Stewart and McKee, J. Non-Newtonian Fluid Mech., 165, 143--157  (2010).

[2] Cruz, Tome, Stewart and McKee. To appear in J. Comput. Phys. (2013).

[3] Stewart,  Continuum Mech. Thermodyn., 18, 343-360 (2007).

Colloquia: Smectics, Metrics and All That

Wednesday, 20th March 2013, 3.30-4.30, LT908

Professor Randall Kamien

University of Pennsylvania

Abstract: I will discuss the homotopic classification of topological defects in liquid crystals with special attention to systems with broken translational symmetry.  In the simplest case of smectics, we can see that this classification breaks down and needs repair or reformulation.  I will discuss the latter and show how it leads to a surprising, underlying symmetry in smectic ground states.

PME Scientific Seminar To be announced

Wednesday 13th March, 1.00p.m. in LT907

Dr Angus Cameron

Department of Mathematics, University of Strathclyde

PME Scientific Seminar Some problems of experiment analysis in molecular biology

Wednesday 27th February, 1.00p.m. in LT907

Dr Michael Grinfeld

Department of Mathematics, University of Strathclyde

Numerical Analysis: Convolution quadrature and FEM/BEM coupling in time-domain

Tuesday, 26th February 2013, 4.00-5.00 LT907

Dr Lehel Banjai

Abstract:  

In this talk we will consider numerical discretization of convolutions of a given operator kernel with known or to-be-computed data.  The discretization of choice for this talk will be convolution quadrature.  We will describe how this type of quadrature preserves a number of useful properties of the continuous convolution and how these lead to excellent stability properties of the discrete scheme.

As an application we will consider wave scattering problems on unbounded domains.  In particular we will consider the coupling of finite element and boundary element methods in the time domain.   Here, on a bounded domain the wave equation will be discretized in time by the standard (explicit) leapfrog scheme, whereas the problem in the unbounded complement will be formulated as a time-domain boundary integral equation and discretized by (an implicit) convolution quadrature.  The properties of convolution quadrature will help us show the stability of the resulting scheme.  The talk will end with some numerical results.

CMIM Group Seminars: Multiscale problems in dislocation theory

Tuesday 26th February, 3.00-4.00p.m. in LT907

Dr Lucia Scardia

University of Glasgow

Colloquia: Existence and concentration for nonlinear Schrödinger equations with fast decaying potentials

Wednesday, 20th February 2013, 3.30-4.30 LT908

Dr Vitaly Moroz

Swansea University

Abstract:  

We discuss the existence of positive stationary solutions for a class of nonlinear Schrödinger equations. Amongst other results, we prove the existence of semi-classical solutions which concentrate around a positive local minimum of the potential. The novelty is that no restriction is imposed on the rate of decay of the potential at infinity. In particular, we cover the case where the potential is compactly supported. This is joint work with Jean Van Schaftingen (Louvain-la-Neuve, Belgium)



Numerical Analysis: Quasi-Interpolation with Radial Basis Functions

Tuesday, 19th February 2013, 4.00-5.00, LT907

Professor Martin Buhmann

Giessen University, Germany

Abstract:  

Quasi-interpolation is a very useful alternative to the usual interpolation ansatz with radial basis functions as an approximation method in multiple dimensions. Like interpolation, for many standard kernels, the quasi-interpolants exist and recover polynomials for equally spaced and for scattered data. Due to this and their localness, they turn out to be highly appropriate in many applications for smoothing purposes. In this talk, we give an overview of the idea of quasi-interpolation, and we extend the approximation order results for quasi-interpolation using Sobolev spaces. All typical radial functions such  as (inverse) multiquadrics and polyharmonic splines are considered. Among other results, we give error estimates to approximands which are less smooth than usually required in the native spaces. We also consider more general approximations from radial basis function spaces including the idea of compression.

CMIM Group Seminars: Freezing colloidal suspensions: ice segregation and pattern formation

Tuesday 19th February, 3.00-4.00p.m. in LT907

Dr Anthony Anderson

University of Cambridge

Abstract:

Colloidal suspensions do not freeze uniformly; rather, the frozen phase (e.g. ice) becomes segregated, trapping bulk regions of the colloid within, which leads to a fascinating variety of patterns that are of both practical and mathematical interest. Yet, despite the central importance of ice segregation in several applications, its physics are still poorly understood. In this talk, I will review previous work on the micro-scale physics that govern the interaction of a single inert particle with a solid-liquid interface where phase change is occurring. I will also touch on the fundamental particle-particle interactions in colloidal suspensions. From this foundation, I will discuss some attempts to formulate homogenized continuum theories to model the freezing behaviour of concentrated suspensions. These continuum theories provide insight into the possible mechanisms of pattern formation caused by ice segregation; however, we've recently conducted directional solidification experiments that reveal some key inadequacies of these theories. I will discuss these experimental observations and present a case study of periodic ice-lensing using a 1D dynamical model. This model reproduces several of the experimental observations and has some important implications in frost heave.

CMIM Group Seminars: The Ericksen–Leslie theory for liquid crystals and its developments

Tuesday 12th February, 2.00-3.00p.m. in LT907

Professor Iain Stewart

University of Strathclyde

Abstract:

A review of the Ericksen-Leslie theory for the dynamics of nematic liquid crystals will be presented. Its developments related to smectic and other liquid crystals phases will also be discussed.

Applications to 'switching phenomena' in liquid crystals will be highlighted. Developments to cover coagulation processes with non-Newtonian flow behaviour will also be mentioned if time permits.

 

Workshop on Stochastic Differential Equations and Their Applications

Friday 1st February 2013, 2.30-6.30p.m. in LT907 and Common Room

2:30-3:10
Alexei Kulik:
Regularity and stability of laws of solutions to Levy driven SDE's

3:10-3:50
Svetlana Anulova:
On stability and convergence for degenerate diffusion with switching /or with jumps

3:50-4:10
Tea/Coffee

4:10-4:50
Alexander Veretennikov:
On Poisson equations with a potential in the whole space

4:50-5:30
Oleg Butkovsky:
Convergence of Markov processes in the Wasserstein metric
with applications to stochastic functional differential equations

5:30-6:30
Cheese and wine

Every one is welcome, though the members of stochastic analysis group
are required to attend.

Colloquia: Sizing up marine ecosystems: understanding, tracking and predicting change

Wednesday 30th January 2013, 3.30-4.30, LT908

 Dr Julia Blanchard

Department of Animal & Plant Sciences, University of Sheffield, Sheffield, UK 

Abstract:

Marine ecosystems are dynamic and complex. Understanding the consequences of change from multiple human and environmental pressures can be challenging, but this knowledge is needed to assess the ecosystem effects of human activities, track progress towards meeting global biodiversity objectives and to develop an ecosystem approach to fisheries management. Many ecological indicators and models have been developed to address these goals and size-based methods are emerging as a powerful approach due to their simplicity and well-established theory. I will give an overview of recent work showing how size-based methods can be used to help us understand the structure of marine ecosystems, establish abundance baselines of marine communities and their resilience to multiple top-down and bottom-up pressures. 

 

Numerical Analysis Seminar "How to climb a billion dimensional hill using a coin and a compass and count the steps before departure" : Parallel coordinate descent methods for big data optimization [In the numerical PDE community coordinate descent methods are known under the name multiplicative/additive Schwarz methods; see [3]]

Tuesday 11th December 2012 at 4.00p.m. in LT907.

Dr. Peter Richtarik - Edinburgh

Abstract:

With growing digitization of the world it is increasingly easier to collect mammoth-size amounts of data. Often, this data is analyzed using an optimization algorithm, and leads to difficult huge-scale optimization problems with millions or billions of variables.

 Existing optimization algorithms, which are perfectly suited for solving problems of medium size, such as polynomial-time interior-point methods, are often not useful in this new setting due to the bad dependence of their complexity on the problem dimension.

Hence, there is a pressing need to devise and analyze new methods, or adapt classical methods, that would be capable of working in the big data setting. An entirely different approach to the scale problem is via acceleration of existing methods on parallel computing architectures such as many-core computers and clusters thereof, or systems based on graphical processing units (GPUs).

 In this talk we describe a new method that combines the two approaches outlined above. Our method has both i) a good dependence on the problem dimension and b) is parallel in nature, and hence is well-suited for solving certain structured big data optimization problems. In particular, we show that randomized block coordinate descent methods, such as those developed in [2], can be accelerated by parallelization when applied to the problem of minimizing the sum of a partially block separable smooth convex function and a simple block separable convex function.

 Many problems of current interest in diverse communities (statistics, optimal experimental design, machine learning, mechanical engineering), can be cast in this form, including least-squares, L1 regularized least-squares (LASSO), group and sparse group LASSO , computing c and A-optimal designs of statistical experiments, training (sparse) linear support vector machines (SVM) and truss topology design (TTD).

 We describe a generic parallel randomized block coordinate descent algorithm (PR-BCD) and several variants thereof based on the way parallelization is performed. In all cases we prove iteration complexity results, i.e., we give bounds on the number of iterations sufficient to approximately solve the problem with high probability.

Our results generalize the intuitive observation that in the separable case the theoretical speedup caused by parallelization should be equal to the number of processors. We show that the speedup increases with the number of processors and with the degree of partial separability of the smooth component of the objective function. Our analysis also works in the mode when the number of blocks being updated at each iteration is random, which allows for modelling situations with variable (busy or unreliable) number of processors.

 We conclude with some encouraging computational results applied to a LASSO instance involving a matrix with 20 billion nonzeros.

 All results are based on joint work with Martin Takac (Edinburgh).

 [1] Peter Richtarik and Martin Takac. Parallel coordinate descent methods for big data optimization. November 2012.

 http://www.optimization-online.org/DB_HTML/2012/11/3688.html

 [2] Peter Richtarik and Martin Takac. Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function. To appear in  Mathematical Programming, April 2011.

 http://arxiv.org/abs/1107.2848

 [3] M. Griebel, P. Oswald. Greedy and randomized versions of the multiplicative Schwarz method. June 2011.

 http://wissrech.ins.uni-bonn.de/research/pub/griebel/GSASsubmissionLAA_preprint.pdf

Colloquia: Schrödinger's green cat: Why do species distribution models fail in being predictive?

Wednesday, 5 December 2012, 14:00-15:00 LT908

Professor Jason Matthiopoulos

Institute of Biodiversity, Animal Health and Comparative Medicine, College of Medicine, Veterinary & Life Sciences, Graham Kerr Building, University of Glasgow, Glasgow

http://www.gla.ac.uk/researchinstitutes/bahcm/staff/jasonmatthiopoulos/

Abstract:

 Spatial ecology aims to understand where organisms are, why they are there, and where else they might be. This latter objective requires us to extrapolate species distributions to regions we have never observed, or forecast change in the future. Such predictive capabilities can only be attained given rich field data, constant environments, a deep understanding of the study species and suitable theoretical models. It is certainly frustrating (if not entirely unexpected) that despite the frequent violation of most of these requirements, the scientific literature is teeming with publications that attempt such predictions for important issues in conservation and wildlife resource management.

I will present a brief review of existing theoretical approaches to the analysis of species distribution data and of the reasons why their predictions regularly fail. I will present recent work that successfully extends the predictive reach of these models and illustrate their application with both synthetic and real data, using telemetry from grey wolves (Canislupus).

Beyond these developments, I will examine the underlying reason why spatial ecology has yet to fulfill its original promise: Its inadvertent de-coupling from the other two cornerstones of ecology – population dynamics and evolution. I therefore propose a synthetic approach to these three fundamental areas and outline ways in which it can be achieved mathematically and estimated statistically.

An interesting by-product of this approach is that it offers the potential to quantify from field data such chimaeric concepts as the fundamental niche, the critical habitat and the carrying capacity.



Numerical Analysis: A New Multiscale Method for (Semi-)Linear Elliptic Problems

Tuesday, 27th November 2012, 16:00-17:00, LT907

Speaker: Dr Daniel Peterseim

Humboldt Universität zu Berlin

Abstract: This talk summarizes some recent results on (semi-)linear elliptic multiscale problems with rough coefficients.  I will propose and analyze a new Multiscale Method which is based on a generalized finite element basis that spans a low dimensional macroscopic approximation space based on some coarse mesh.  The basis is assembled by performing parallel localized microscopic computations in small patches that have a diameter of order H log(1/H) where H is the coarse mesh size.  The energy (resp. L2) error of the method converges linearly (resp. quadratically) with respect to the coarse mesh size without any pre-asymptotic effects.  As further applications of this theory, I will comment on eigenvalue problems and the fast iterative solution of the corresponding linear systems of algebraic equations.

 

Applied Analysis: Interval orders and related structures

Tuesday, 20th November 2012, 16:00-17:00, LT907

Speaker: Sergey Kitaev

University of Strathclyde, Department of Computer and Information Sciences

Abstract: A partially ordered set (poset) is an interval order if it is isomorphic to some set of intervals on the real line, partially ordered by left-to-right precedence. Interval orders are important in mathematics, computer science, engineering and the social sciences. For example, complex manufacturing processes are often broken into a series of tasks, each with a specified starting and ending time. Some of the tasks are not time-overlapping, so at the completion of the first task, all resources associated with that task can be used for the following task. On the other hand, if two tasks have overlapping time periods, they compete for resources and thus can be viewed as conflicting tasks. A poset is said to be (2+2)-free if no two disjoint 2-element chains have comparable elements (a chain is a pair of comparable elements). In 1970, Fishburn proved that (2+2)-free posets are precisely interval orders. Recently, Bousquet-Mélou, Claesson, Dukes, and Kitaev introduced ascent sequences, which not only allowed us to enumerate interval orders, but also to connect them to other combinatorial objects, namely to Stoimenow's diagrams (used to study the space of Vassiliev's knot invariants), to certain upper triangular matrices, and to certain pattern avoiding permutations (a very active area of research these days). A host of papers by various authors has followed this initial paper, studying various aspects of the structures involved, the interplay between them and enumerative aspects.

 

Edinburgh Mathematical Society: Vignettes in Mathematics

Friday, 16th November 2012, 16:00-17:00, LT908

Speaker: Prof. Richard Craster

Imperial College, London

http://www3.imperial.ac.uk/people/r.craster

Abstract: An argument one occasionally hears runs as follows: In an age of symbolic/computer algebra and high speed computing surely everything can now be done semi-automatically? The algebra being done symbolically using Maxima, Reduce, Mathematica or Maple, to mention but a few, and the resulting equations solved numerically by, say, Matlab or put into large scale finite element packages such as Abacus or Comsol. This surely renders the bespoke Mathematician obsolete in this brave new world? Indeed one barely needs to be able to even code - apparently.

This talk will present a series of vignettes based on real-world problems from the interface between Mathematics and Physics (Metamaterials), Mechanical Engineering (Waves) and Chemical Engineering (coating flows) and Geophysics (lava and wrinkling) that will be discussed as exemplars where the judicious use of asymptotically small or large terms, or the pattern recognition and manipulations well-known to Mathematicians have a real role to play in explaining phenomena in many areas of modern science. Indeed, as a species the Mathematician may be evolving, but, to steal a well known phrase - reports of their death have been greatly exaggerated!

 

Stochastic Seminar: The white noise effects the threshold of a stochastic SIRS epidemic model in a population with varying size

Wednesday, 14th November 2012, 14:00-15:00, LT907

Professor Daqing Jiang from China Northeast Normal University will give a talk on:

The white noise effects the threshold of a stochastic SIRS epidemic model in a population with varying size.

Abstract. In this paper, a stochastic SIRS epidemic model in a population with varying size is discussed. A new threshold R0 is identified which determines the outcome of the disease. When the noise is small, if R0<1, the infection fraction of the population disappears, so the disease dies out. While if R0>1, the infected fraction persists in the mean and we derive the disease is endemic. Furthermore, we derive that the disease will prevail, which is measured through the difference between the solution and the endemic proportion equilibrium of the deterministic model in time average and the sufficient condition is obtained. On the other hand, when the noise is large, we obtain that the large noise will suppress the epidemic to prevail. These results are illustrated by computer simulations.

All are welcome.

 

Numerical Analysis: Stabilized finite element methods for convection-diffusion-reaction equations

Tuesday, 13th November 2012, 16:00-17:00, LT907

Speaker: Dr. Petr Knobloch

Abstract:This presentation is devoted to the numerical solution of steady scalar convection--diffusion--reaction equations by means of the finite element method. If convection dominates diffusion, the solution of the continuous problem typically possesses interior and boundary layers which cannot be resolved properly unless the mesh is extremely fine. This often leads to spurious oscillations in the numerical solution. In particular, the solutions of the classical Galerkin finite element discretization are typically globally polluted by spurious oscillations. Therefore, various stabilization techniques have been developed during the last four decades to remove or, at least, to diminish these oscillations. We shall review some of these approaches and compare them by means of numerical tests.

We shall also discuss the choice of stabilization parameters which may significantly influence the accuracy of the discrete solution. In particular, we shall show how the stabilization parameters can be computed a posteriori by means of the minimization of an appropriate target functional.

 

Colloquia: Instabilities in internal two-phase flows

Wednesday, 31st October 2012, 15:30-16:30, LT908

Dr Andrew Hazel

University of Manchester

http://www.maths.manchester.ac.uk/~ahazel

Abstract: TBA

 

Colloquia: Wrinkling of a stretched thin sheet

24th October 2012, 15:30-16:30, LT908

Joint with NBDES

Prof Eliot Fried

McGill University

http://people.mcgill.ca/eliot.fried/

Abstract: When a thin rectangular sheet is clamped along two opposing edges and stretched, its inability to accommodate the Poisson contraction near the clamps may lead to the formation of wrinkles with crests and troughs parallel to the axis of stretch. A variational model for this phenomenon is proposed. The underlying energy functional includes bending and membranal contributions. Motivated by work of Cerda, Ravi-Chandar & Mahadevan, the functional is minimized subject to a global constraint on the area of the mid-surface of the sheet. Analysis of a boundary-value problem for the ensuing Euler–Lagrange equation shows that wrinkled solutions exist only above a threshold of the applied stretch. A sequence of critical values of the applied stretch, each element of which corresponds to a discrete number of wrinkles, is determined. Whenever the applied stretch is sufficiently large to induce more than one wrinkle, previously proposed scaling relations for the wrinkle wavelength and root-mean-square amplitude are confirmed. Comparisons with experimental measurements and numerical results indicate that the analytical results are remarkably robust.


Reference
E. Cerda, K. Ravi-Chandar & L. Mahadevan. Thin films: Wrinkling of an elastic sheet
under tension. Nature 419 (2002), 579–580.


Continuum Mechanics and Industrial Mathematics: Slender body theory via dimensional reduction and hyperviscous regularization

Tues, 23rd October 2012, 15:00-16:00, LT907

Prof Eliot Fried

McGill University

http://people.mcgill.ca/eliot.fried/

Abstract:

The classical slender body theory for viscous flows was initiated by Burgers and was developed in the seventies with the primary objective of obtaining the drag force and torque required to sustain the rigid motion of slender bodies in viscous fluids. The ultimate goal of this effort was to provide estimates for parameters such as the effective viscosity of suspensions of solid particles in fluids. Despite the success in describing the viscous flow generated by a single particle of general shape, the treatment of a more realistic number of suspended particles represents a formidable computational challenge. Our approach to slender body theory aims at a reduction of the computational complexity of the problem, replacing slender three-dimensional particles with lower-dimensional objects, and replacing the surrounding Newtonian fluid by a quasi-Newtonian second-gradient fluid. In such a fluid, an additional parameter, namely the product of the viscosity and a characteristic length (called the gradient length) enters the flow equation, which resembles the well-known hyperviscous regularization of the Navier-Stokes equation. The central idea underlying our approach is that the aforementioned gradient length represents the effective thickness of the lower-dimensional objects, in the sense that the drag force and torque required to sustain their rigid motion in a hyperviscous fluid are the same as those required to sustain the corresponding motion of a particle whose thickness corresponds to the gradient length in a Newtonian fluid. Rigorous proofs of this assertion have been constructed for simple geometries of the slender body. A proof of its general validity and an analysis of the computational advantages of our approach are in progress.

Reference

J.M. Burgers. On the motion of small particles of elongated form suspended in a viscous liquid (in Chapter III of Second Report on Viscosity and Plasticity). Verhandelingen der Koninklijke Nederlandse Akademie van Wetenschappen 16 (1938), 113.

 



Numerical Analysis: Combination Preconditioning of Saddle Point Systems for Positive Definiteness

16th October 2012, 16:00-17:00, LT907

Jennifer Pestana

Abstract: Saddle point systems arise in a variety of applications, including fluid dynamics and PDE-constrained optimization.  For solving such systems, preSaddle point systems arise in a variety of applications, including fluid dynamics and PDE-constrained optimization.  For solving such systems, preconditioned Krylov subspace methods are popular.  In recent years, several preconditioners have been proposed for which the preconditioned system is nonsymmetric but self-adjoint with respect to an inner product.  In this talk we show how certain of these preconditioners can be combined in a systematic way to form new self-adjoint preconditioned saddle point systems.  We also show that we can combine two preconditioners, for each of which the preconditioned saddle point system is indefinite, to obtain a positive definite combination.  To this positive definite preconditioned saddle point system a conjugate gradient method in a nonstandard inner product can be applied that converges rapidly.conditioned Krylov subspace methods are popular.  In recent years, several preconditioners have been proposed for which the preconditioned system is nonsymmetric but self-adjoint with respect to an inner product.  In this talk we show how certain of these preconditioners can be combined in a systematic way to form new self-adjoint preconditioned saddle point systems.  We also show that we can combine two preconditioners, for each of which the preconditioned saddle point system is indefinite, to obtain a positive definite combination.  To this positive definite preconditioned saddle point system a conjugate gradient method in a nonstandard inner product can be applied that converges rapidly.

 

Colloquia: Core-periphery structure in networks

3rd October 2012, 15:30-16:30, LT908

Dr Mason Porter

University of Oxford

http://people.maths.ox.ac.uk/porterm

Intermediate-scale (or 'meso-scale') structures in networks have received considerable attention, as the algorithmic detection of such structures makes it possible to discover network features that are not apparent either at the local scale of nodes and edges or at the global scale of summary statistics. Numerous types of meso-scale structures can occur in networks, but investigations of meso-scale network features have focused predominantly on the identification and study of community structure. In this talk, I discuss a new method to investigate the meso-scale feature known as core-periphery structure, which consists of an identification of a network's nodes into a densely connected core and a sparsely connected periphery. In contrast to traditional network communities, the nodes in a core are also reasonably well-connected to those in the periphery. This new method of computing core-periphery structure can identify multiple cores in a network and takes different possible cores into account, thereby enabling a detailed description of
core-periphery structure. I illustrate the differences between this method and existing methods for identifying which nodes belong to a core, and I use it to classify the most important nodes using
examples of friendship, collaboration, transportation, and voting networks. I will also briefly discuss the relationship between core-periphery structure and dynamics in functional brain networks.