Applied Mathematics Seminars

Dr Rachel Bennett

School of Mathematics, University of Bristol

Abstract

Dr Stuart Hawkins

Macquarie University, Sydney (presently visiting the Isaac Institute at Cambridge)

Abstract

Dr Alex Frangi

University of Leeds

Abstract

Dr Benjamin Walker

Department of Mathematics, University College London

Abstract

Dr Xiaohao Cai 

University of Southampton

Abstract

Professor Sergey Sorokin

Department of Materials and Production, Aalborg University, Denmark

Abstract

Dr David Bourne

Associate Professor, Heriot-Watt University, Edinburgh

Abstract

Gregory J. Rodin

Professor Emeritus, Department of Aerospace Engineering and Engineering Mechanics and Oden Institute for Computational and Engineering Sciences, The University of Texas at Austin

Abstract

Mechanical behavior of thin constrained layers is analyzed in an asymptotic setting which allows one to examine various singular perturbations. Of particular interest are the following topics:

1. Compressible, incompressible, and nearly incompressible layers.
2. Identification of mechanical properties of interphases in glass-epoxy composites.
3. Poro-elastic layers and connections with Terzaghi’s tests.
4. Squeezing of power-law fluid layers between flat and curved surfaces.

Speaker: Dr. Bei Peng (University of Liverpool, Computer Science)

13:00 via Zoom

Meeting ID: 976 1568 3533
Passcode: m1LJJ$nU

Abstract - Many real-world learning problems involve multiple agents acting and interacting in the same environment to achieve some common goal, which can be naturally modeled as cooperative multi-agent systems. In this talk I will first overview some of the key challenges in cooperative multi-agent reinforcement learning. I will then describe the problem setting we focus on and the training paradigm we usually use to learn in such settings. One critical challenge in this setting is how to represent and learn the complex joint value functions. I will talk about two deep multi-agent reinforcement learning algorithms we developed recently to address this challenge. Finally, I will present Multi-Agent MuJoCo, a new comprehensive benchmark suite that we developed, based on the popular single-agent MuJoCo benchmark, to allow the study of decentralised continuous control. We believe it can potentially stimulate more progress in continuous multi-agent reinforcement learning.

Centre for Mathematical Imaging Techniques (CMIT)

Speaker: Prof. Ulugbek S. Kamilov (Washington University in St. Louis)

15:00 via Zoom

Abstract

Computational imaging is a rapidly growing area that seeks to enhance the capabilities of imaging instruments by viewing imaging as an inverse problem. Recently, model-based deep learning (MBDL) has emerged as a popular paradigm for solving inverse problems by jointly leveraging physical forward models and deep neural networks (DNNs) trained to represent imaging priors. This talk presents Regularization by Artifact Removal (RARE) and Continuous Neural Inversion (CONI) as two complementary paradigms for providing a “deep learning” extension to the classical theory. RARE uses pre-trained artifact-removing DNNs for infusing a learned prior knowledge into an inverse problem. On the other hand, CONI uses coordinate-based DNNs for continuously representing the unknown image at any spatial location. We present the latest theoretical insights and applications of both frameworks in biomedical imaging.

Biography

Ulugbek S. Kamilov is Assistant Professor and Director of Computational Imaging Group (CIG) at Washington University in St. Louis. He obtained the BSc/MSc degree in Communication Systems and the PhD degree in Electrical Engineering from EPFL, Switzerland, in 2011 and 2015, respectively. From 2015 to 2017, he was a Research Scientist at MERL, Cambridge, MA, USA. He is a recipient of the NSF CAREER Award in 2021 and the IEEE Signal Processing Society’s 2017 Best Paper Award. He was among 55 early-career researchers in the USA selected as a Fellow for the Scialog initiative on “Advancing Bioimaging" in 2021. His PhD thesis was selected as a finalist for the EPFL Doctorate Award in 2016. He has served as an Associate Editor of IEEE Transactions on Computational Imaging (2019-present), Biological Imaging (2020-present), and on IEEE Signal Processing Society’s Computational Imaging Technical Committee (2016-2021). He was a plenary speaker at iTWIST 2018 and is a program co-chair for BASP 2023.He has co-organized several large workshops in the area, including IMA Special Workshop on Computational Imaging in 2019, Learning for Computational Imaging (LCI) Workshop at ICCV 2021, IEEE International Workshop on Computational Cameras and Displays (CCD) at CVPR 2022.

This talk will be based on the following references

J. Liu, Y. Sun, C. Eldeniz, W. Gan, H. An, and U. S. Kamilov, “RARE: Image Reconstruction using Deep Priors Learned without Ground Truth,” IEEE J Sel Topics Signal Process, vol. 14, no. 6, pp. 1088-1099, October 2020.

J. Liu, S. Asif, B. Wohlberg, and U. S. Kamilov, “Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition,” Proc Ann Conf Neural Information Processing Systems (NeurIPS), (December 6-14), 2021.

Y. Sun, J. Liu, M. Xie, B. Wohlberg, and U. S. Kamilov, “CoIL: Coordinate-based Internal Learning for Tomographic Imaging,” IEEE Trans. Comput. Imag., vol. 7, pp. 1400-1412, November 2021.

R. Liu, Y. Sun, J. Zhu, L. Tian, and U. S. Kamilov, “Zero-Shot Learning of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements,” arXiv:2112.00002.

Research Centre in Mathematics and Modelling - Wave scattering and Solid Mechanics

Speaker: Artur Gower, University of Sheffield

16:00 via Zoom

Details and registration at https://www.icms.org.uk/V_WavScatSolMech.php

Liverpool Centre for Mathematics in Healthcare (LCMH) seminar

Speakers: Xiang-Yue Wang and Jun Liu  (Beijing Normal University)

09:00 via Zoom

Abstract: Convolutional Neural Networks (CNN) can well extract the features from natural images. However, the classification functions in the existing network architecture of CNNs are always simple and lack capabilities to handle important spatial information in a way that have been done for many well-known traditional variational models. Priors such as spatial regularization, volume, object shapes, topology priors cannot be well handled by existing CNN architectures. We propose a novel Soft Threshold Dynamics (STD) based framework which can easily integrate many priors such as local and nonlocal image edges information, star/convexity shapes of the classic variational models into the DCNNs for image segmentation. The novelty of our method is to interpret the activation functions (including softmax, sigmoid, ReLU) as primal-dual variational problem, and thus many priors can be imposed in the dual space. By unrolling method, we can build several STD based network architectures which can enable the outputs of CNN to have many special priors. The proposed method is a general framework and it can be applied to any image segmentation CNNs. We will give some applications to show the efficiency of our method.

Liverpool Centre for Mathematics in Healthcare (LCMH) seminar

Speaker: Dr Victoria Kearns (University of Liverpool)

14:00 via Zoom

Abstract: Delivery of drugs to the eye is a key treatment for a number of sight-threatening diseases. For diseases of the back of the eye, such as diabetic retinopathy and age-related macular degeneration, the most effective route for drug delivery to the vitreous cavity is by injection into the eye, which has several drawbacks. Implantable devices that can achieve controlled, sustained drug release could provide an improved approach to drug treatment in the posterior segment of the eye. We have been developing novel, biomaterial-based technology to meet this unmet clinical need.

The outer blood-retinal barrier (OBRB) is important in controlling drug clearance from the posterior segment of the eye. Complementary in vitro and computational models of this tissue could provide a fast, inexpensive method of understanding release profiles of drug delivery devices. In this talk, I will give an overview of the clinical problems and our attempts to solve them, and discuss our work on development of a computational model to evaluate drug release from a silicone oil-based delivery system and validation of this model using in vitro tools.

Liverpool Centre for Mathematics in Healthcare (LCMH)

Speaker: Dr Tom McDonald (University of Liverpool)

Abstract: Treating patients with chronic diseases represents a staggering 70% of the NHS’ costs, and is likely to present a significantly increasing burden on healthcare systems in the future. Although chronic disease represents a vast range of conditions, the success of therapeutic treatment for these conditions faces a common challenge: global patient adherence to treatment regimens is typically poor, resulting in increased morbidity and mortality. In this work we seek to use a novel in situ forming drug delivery system to form injectable implants that provide long-term drug release. This long-acting drug delivery would address the issue of poor adherence and improve patient outcomes for chronic disease.

Mathematical Biology

Speaker: Carl Whitfield (University of Manchester)

13:00 via Zoom

Abstract: The airways in human lungs form a complex tree network that branches in a dyadic manner repeatedly to transport gas to and from the microscopic alveoli. In healthy lungs this elaborate branching structure acts to maximise the surface area available for gas exchange in the limited 3D space. However, in many obstructive lung conditions the airways can become blocked or constricted, causing uneven delivery of gas or ventilation heterogeneity (VH). In this talk I will discuss some simple models that we have used to model VH using real patient data and Bayesian inference. Second, I will talk about some of our work in dimensionality reduction and uncertainty quantification in models of ventilation and gas transport on the whole airway network. In particular I will introduce some techniques in spectral graph theory that can be used to reduce and characterise simulations in image-based airway models.

Speaker: Chris Overton (Liverpool, Manchester)

13:00 via Zoom

Abstract: As part of the ongoing response to the COVID-19 outbreak in the UK,  we have developed a compartmental model for the flow of cases through hospitals. This provides a tool for monitoring the burden on hospitals, enabling informed management and planning. Some of the underlying parameters can be obtained through patient-level data, using maximum likelihood estimation. The remaining parameters are estimated by fitting the model to four hospital-level data streams. This model provides insight into these parameters (that are challenging to estimate directly from data) and can be used to obtain accurate short-term forecasts

Liverpool Centre for Mathematics in Healthcare (LCMH)

Speaker: Professor Antonio Cricenti: Istituto di Struttura della Materia - Consiglio Nazionale delle Ricerche, Roma

13:00 MATH-103

Biography: Professor Antonio Cricenti is Research Director at the Istituto di Struttura della Materia (ISM), Rome.  Under the umbrella of the Consiglio Nazionale delle Ricerche (CNR), the Institute performs cutting-edge interdisciplinary research in the fields of physics, chemistry, and materials science, with activities ranging from theoretical modelling to development of prototypal devices. 

Professor Cricenti has undertaken collaborative research on the early diagnosis of cancer by infrared SNOM, in partnership with the University of Liverpool.  His active interests include semiconductor and metal-semiconductor surfaces, biological cells, photoemission, optical reflectivity, and scanning probe microscopy.

Abstract: Carcinomas are complex biochemical systems and in the past their diagnosis was based on morphological differences between malignant cells and their benign counterpart. Recently the paradigm has changed and great interest is focused now on the biochemical profile of tumours, in view of the availability of new drugs that specifically target neoplastic cells. This new paradigm requires biochemical analysis of each tumour in order to establish the correct personalized oncological “target therapy”. Understanding the mechanism of molecular alterations of a specific tumour is a critical issue to predict the response to personalized therapy. This is important not only for discrimination between healthy and pathological tissues, but also for pre-cancerous tissue state earlier detection and understanding.

The potential of infrared and Raman spectroscopy to characterise cancerous tissues has long been recognised, and studies of various cancers by many groups have established that regions of malignant tissue can be easily identified on the basis of its optical spectrum. Early diagnosis of cancer requires an instrument providing specific chemical images at sub-cellular level and the development of diagnostic imaging. Infrared Scanning Near-field Optical Microscopy (IR-SNOM) and micro-Raman set-up meet these requirements provided that SNOM can been coupled with an appropriate infrared light source, that can be based on Free Electron Laser, femtosecond laser or quantum cascade laser.

We present IR-SNOM and micro-Raman in their spectroscopic mode, that is related to the local chemical composition and, thus, to the biological properties of the sample, for tissue imaging and early cancer diagnostics. Applications in the case of Oesophagous and Cervical Cancer as well as in the progression of Amyotrophic Lateral Sclerosis (ALS) will be presented.

Liverpool Centre for Mathematics in Healthcare

Speaker: Professor Peter Gritzmann (Technische Universität, München)

14:00 MATH-027

Abstract: Based on a discrete convex maximization model we give an efficient algorithm for computing feasible generalized power diagrams with near-optimal separation properties. Further, we show how this approach can be used to generalize the classical k-means algorithms from data analysis so that it becomes capable of handling weighted point sets and prescribed lower and upper bounds on the cluster sizes; the above discussion being based on joint work with S. Borgwardt and A. Brieden.

We also indicate how to handle the discrete inverse problem from material science to compute grain maps, i.e., representations of polycrystals, based only on measured data on the volume, center and, possibly, moments of their grains; this part of the discussion being work jointly undertaken with A. Alpers, A. Brieden, A. Lyckegaard and H. Poulsen.

Biography: Professor Peter Gritzmann is a distinguished German mathematician whose interest lies in the areas of discrete mathematics, optimisation and applied geometry. He is currently a professor of Mathematics at the Technical University of Munich, where he has served as Vice President for Administration and was director of the Carl Linde Academy. He has held visiting positions at the University of Washington (Seattle), the University of Minnesota (Minneapolis) and the University of Paris VII.

From 1974 to 1978 he was a fellow of the Studienstiftung des Deutschen Volkes and 1986/87 he had a Fedor Lynen Research Fellowship from the Alexander von Humboldt Foundation. He has also presided over the Alexander von Humboldt Foundation committee for scholarships.

In 1992 he was awarded the Max Planck Research Award; in 2000, the Karl Max von Bauernfeind Medal; and in 2013 the Euro Excellence in Practice Award. In 2002 and 2003 he served as president of the German Mathematical Society.

Liverpool Centre for Mathematics in Healthcare (LCMH)

Speaker: Dr Jinming Duan (University of Birmingham)

13:00 Teaching Hub 502 - Teaching Room 4

Dr Duan lectures in Computer Science at the University of Birmingham, having previously been a Research Associate at Imperial College London where he worked jointly within the Department of Computing and the Institute of Clinical Sciences to develop cutting-edge machine learning methods for different cardiovascular imaging problems.

His research includes deep neural nets, variational methods, partial/ordinary differential equations, numerical optimisation, and finite difference/element methods, with applications to image processing, computer vision and medical imaging analysis.

Speaker: Dr Domenico Tallarico (EMPA, EMPA Laboratory for Acoustics & Noise Control, Switzerland)

13:00 MATH-303

Abstract: Spatially-resolved finite-element models of large collections of unit-cells inevitably call for mathematical approximations and accurate reduction schemes. In this talk, we review well-known finite-element model order reduction techniques: an exact superelement, an eigenmode based superelement  and an asymptotic based superelement. We show how the latter two can be obtained from the exact superelement.  In the context of design of structured solids, we highlight their benefits in terms of reduced computational time and size with respect to standard full-size finite-element solutions.  Specifically, we define the superelements starting from unit cells of three-dimensional metastructures and use those to solve mathematical problems of general interest: (i) polynomial Bloch-Floquet eigenvalue problems associated with complex dispersion diagrams (i.e. complex Bloch vector as a function of frequency), and (ii) time-harmonic response of finite assemblies of unit cells.

Speaker: Dr Julien de Rosny (Director of Research, CNRS, L’Institut Langevin, Paris, France)

13:45 MATH-303

Abstract: When ambient noise propagates in a medium, it is strongly fingerprinted by this last. When the noise is sufficiently diffuse, one can show that the acoustic transient response between two positions can be passively estimated just by cross-correlating signals recorded at these two positions. For almost 20 years, this passive estimation of the Green’s functions by ambient noise correlation has grown significantly in many areas of acoustics. One active subject of study concerns elastic waves in solids. In this presentation, I focus on the emergence of Green's functions in thin plates where the bending mode (A0 mode) dominates. The presentation is made up of two parts. The first one relates to a fundamental work on the reconstruction of Green's functions not only by noise correlation, but by correlation of the "coda", that is to say multiply reverberated signals. The effect of the number of sources and the width of the correlation window on the quality of the reconstruction is directly related to the properties of spectral and spatial correlations of the eigen modes of the plate. The parallel with the time reversal allows an intuitive interpretation of the results. The degradation induced by the presence of additive noise is also discussed.

In the second part of the presentation, the application of this principle to integrated health control is presented. The method makes it possible to passively locate the appearance of faults on a plate. The detection remains effective even in the case where the sources of noise do not generate an evenly distributed field. The robustness of the method is explained in terms of the spatial stationarity of the source distribution. Different model faults have been tested. To compensate for the possible absence of noise in the frequency range useful for detection, secondary sources of noise based on the non-linear coupling of 2 mechanical resonators have been developed and validated.

Maths Biology Seminar Series

Speaker: Dr Ivan Olier (Liverpool John Moores University)

13:00 MATH-103

Abstract: Nowadays, vast amount of data is being collected as the result of rather increasingly large-scale experiments aimed at supporting development in medicine. Machine learning, a field originated from artificial intelligence, aims at extracting knowledge from data and making predictions without making strong assumptions about data nature and with minimum human intervention. Despite of being widely adopted in fields such as drug discovery and bioinformatics, the use of machine learning in healthcare remains lukewarm. Therefore, should we question ourselves whether we are providing the methods the healthcare research community needs? Or whether our findings are properly communicated to them?

With this talk, Dr Olier will offer his insight into these questions and present some examples of succeeding in modelling healthcare research problems using machine learning methods.

Dr Ivan Olier is Senior Lecturer in Data Science of the Department of Applied Mathematics of the Liverpool John Moores University (LJMU). He holds a PhD in Artificial Intelligence from the Technical University of Catalonia, Spain, in 2008. Before joining LJMU, he worked as Data Science researcher at the Autonomous University of Barcelona and at the University of Manchester, followed by a lectureship in Health Informatics at the University of Keele. Dr Olier's expertise is in machine learning and data science, with a particular focus on applications for healthcare. His research work has been published in more than 60 peer-reviewed manuscripts in areas such as machine learning, biostatistics, bioinformatics, biomedicine, and databases.

Liverpool Centre for Mathematics in Healthcare (LCMH)

Speaker: Dr Chantelle Mason (AstraZeneca)

11:00 MATH-104

Biography: Dr Chantelle Mason is a Senior Scientist (Modelling and Simulation Specialist) at AstraZeneca, based in Cambridge in the UK. Her research interests are primarily focused on applying mathematical modelling and statistical approaches to Toxicology and Pharmacology; her particular aims are to improve knowledge and reliability of predictions of drug toxicity, whilst at the same time reducing reliability on animal-testing through the creation of in-silico models.  More information on Dr Mason’s research and publications, can be found here.

Liverpool Centre for Mathematics in Healthcare (LCMH)

Speaker:  Professor Carole Le-Guyader, Laboratoire de Mathématiques de l’INSA (Université de Rouen)

13:00 MATH-117

Biography: Professor Le-Guyader is an Associate Professor (Laboratoire de Mathématiques) at the National Institute of Applied Sciences, Université de Rouen. Her research interests include: PDE, analysis and numerical simulation, image and signal processing, biomedical imaging, and HPC and its applications including those within medicine. She has authored or co-authored many papers on analysis and simulation, digital imaging mathematics and applications, and parallel computing.  Her book, Variational Methods in Image Processing, is also available here.

Liverpool Centre for Mathematics in Healthcare (LCMH)

Speaker: Di Qiu (The Chinese University of Hong Kong)

13:00 Central Teaching Hub: FLEX Room 1 (G17)

Abstract: We propose a novel way of computing surface folding maps via solving a linear PDE. This framework is a generalization to the existing quasi-conformal methods and allows manipulation of the geometry of folding. Moreover, the crucial quantity that characterizes the geometry occurs as the coefficient of the equation, namely the Beltrami coefficient. This allows us to solve an inverse problem of parametrizing the folded surface given only partial data but with known folding topology. Various interesting applications such as fold sculpting on 3D models and self-occlusion reasoning are demonstrated to show the effectiveness of our method.

RCMM Seminar

Speaker: Professor Sonia Mogilevskaya (University of Minnesota, USA)

14:00 MATH-303

Abstract: Thin coatings are key elements of virtually all composite materials; they are typically used for prevention of damage and increase in durability of the composite structures and products. Recent advances in surface chemistry made it possible to create nanoscale-sized high-performance coatings with tailor-made properties. Therefore, there exists tremendous interest in better understanding the processes that occur in composite structures with thin coatings layers. Numerical modeling of such structures is a challenging task, as accurate resolution of thin layers with standard continuum-based numerical methods, e.g. FEM or BEM, would require prohibitively fine mesh sizes. To avoid this, it has been proposed in the literature to replace a finite-thickness coating layer by an interface of zero thickness and model the associated jump conditions in the relevant fields. The existing models, however, are low order accurate with respect to the thickness of the layer. Important reasons for this considerable limitation are related to theoretical difficulties in constructing accurate higher-order interface models and to computational difficulties in integrating these models into standard -continuous FE formulations characterized by low regularity conditions for the involved fields and geometry. This talk presents a) a new approach in developing arbitrary order interface models for two-dimensional potential and elasticity problems involving thin isotropic interphase layers and b) a new variationally consistent two-dimensional FE discretization framework to naturally deal with higher-order derivatives on complex surfaces. Theoretical and computational benefits of the proposed approach and its extension to three-dimensional problems will be discussed.

All are welcome. Tea, coffee and biscuits will be served in room 303 prior to the lecture. Skype connection can be provided for colleagues who would like to participate in the event but not able to attend in person.

Maths Biology Seminar Series

Speaker: Johann Bauer (City University)

13:00 MATH-103

Abstract: The multi-population replicator dynamics (RD) is a dynamic approach to the study of multi-player games and to co-evolving populations, and it is related to simple reinforcement learning (Cross-learning). However, not all of its equilibria are Nash equilibria (NE) of the underlying game, and convergence in general is not guaranteed. Indeed, interior equilibria can never be asymptotically stable in RD.

We introduce the concept of mutation limits as the limits of the equilibria of mutation-perturbed versions of RD for vanishing mutation, and we prove the general existence of such mutation limits for a large range of games. We further define attracting mutation limits as being approximated by asymptotically stable equilibria of the mutation-perturbed RD. Hence, arbitrarily small mutation levels stabilize an attracting mutation limit. We give an example case for attracting mutation limits. In contrast to mutation limits, attracting mutation limits need not exist in all games, and the conditions for their existence are an open question.

RCMM Seminar

Speaker: Professor Yuri Antipov (Louisiana State University, USA)

14:00 MATH-303

Abstract: Acoustic and electromagnetic diffraction by a wedge is modeled by one and two Helmholtz equations coupled by boundary conditions. When the wedge walls are membranes or elastic plates, the impedance boundary conditions have derivatives of the third or fifth order, respectively. A new method of integral transforms is proposed. It requires mapping the wedge domain into a right-angled structure and applying two Laplace transforms. The main feature of the method is that the second parameter is a specific root of the characteristic polynomial of the ordinary differential operator resulting from the transformed PDE. For convex domains (concave obstacles), the problems reduce to scalar and order-2 vector Riemann-Hilbert problems. When the wedge is concave (a convex obstacle), the acoustic problem is transformed into an order-3 Riemann-Hilbert problem. The order-2 and 3 vector Riemann-Hilbert problems are solved by recasting them as scalar Riemann-Hilbert problems on Riemann surfaces. Exact solutions of the problems are determined. Existence and uniqueness issues are discussed.

EPSRC Liverpool Centre for Mathematics in Healthcare (LCMH)

Speaker: Professor Hongkai Zhao (University of California)

10:30 MATH-106

Abstract: Point clouds are the most natural and ubiquitous way of representing geometry and data in 3D and higher. Unlike images, which typically have a canonical form of representation as functions defined on a uniform grid in a rectangular domain, surfaces and manifolds in 3D and higher have more complicated geometrical structures and do not have a canonical or natural form of representation or global parametrization. Moreover, their embeddings in the ambient space are not intrinsic. In these lectures, intrinsic geometry and PDE based models and numerical algorithms for point clouds will be presented for geometric understanding, processing and shape analysis. Part of a five-part series running from Tuesday 17^th to Friday 20^th September.

EPSRC Liverpool Centre for Mathematics in Healthcare (LCMH)

Speaker: Professor Zhenkuan Pan

14:00 Stephenson Institute Seminar Room

Abstract: In this talk, I’ll give an overview briefly of the classical and state of the art mathematical models and algorithms for image processing, analysis and geometry related problems under the variational framework. The models cover image denoising, dehazing, blind deconvolution, inpainting, enhancement, decomposition, registration, segmentation, geometry processing, image processing on surfaces, optical flow computation. The algorithms cover time marching method, fixed point iterative method, dual method, ADMM method and some accelerated methods. Then, I’ll present some works of our group in texture image inpainting, texture image processing on surfaces, depth segmentation, and data classification on a graph.

Mathematical Biology

Speaker: Philip Murray (University of Dundee)

13:00 MATH-105

Abstract: Somitogenesis is a process that occurs during the development of the vertebrate embryo. At regular intervals in space and time, a pair of segments is formed, one on either side of the future spinal chord. Underlying the oscillatory pattern formation is a multicellular, genetic oscillator known as the somitogenesis clock that has a period of the order of hours. Mathematical models of spatiotemporal dynamics of gene expression, often formulated using  partial differential equations,  have a played a crucial role in understanding key features of pattern formation.

In this talk I will describe experiments undertaken at the University of Dundee in which the spatio-temporal dynamics of gene expression are measured in a piece of embryonic tissue. After showing that the experimental data are noisy and non-stationary, we will explore the following questions: (i) how do we extract variables from the experimental data that allow mathematical models to be validated?; and (ii) can current models explain the spatiotemporal dynamics observed in the experiments?

EPSRC Liverpool Centre for Mathematics in Healthcare (LCMH)

Speaker: Alexander Plakhov, Center for R&D in Mathematics and Applications, Department of Mathematics, University of Aveiro, Portugal

13:00 MATH-104

Abstract: Isaac Newton posed this problem nearly 330 years ago in his Mathematical Principles of Natural Philosophy. It is as follows. A body moves in a highly rarefied medium of point particles at rest, and the particles reflect elastically when colliding with the body’s surface. It is required to find the shape of the body that minimizes the force of aerodynamic resistance of the medium. Starting from 1993, new interest in mathematical community to Newton’s problem has been raised. The problem proved to be highly interdisciplinary, and various aspects of it were studied using methods borrowed from multidimensional variational analysis, theory of billiards, optimal mass transport, Kakeya needle problem, and theory of convex bodies. A review of the state of art in this area, with the emphasis on convex geometry, will be given.  

Speakers: Dr Alessio Trevisan (ENGINSOFT, Padova Italy) and Prof Michele Brun (University of Cagliari, Italy)

14:30 MATH-303

Abstracts: 

Numerical Approach and Simulation in the Multi-Physics Model of a Roller Coaster (Trevisan)

The lecture presents a three-dimensional FEM model of a dynamic response of a full-scale roller coaster. The model is based on a multi-physics variational formulation, and it has been used in the roller coaster design and optimisation.  The roller coaster represents a multi-scale elongated multi-structure, and  multi-scale effects are shown to be important in the analysis of its dynamic response.

Flexural Waves in Thin Structures.  Perfectly Matched Layers in Beams and Plates and a Platonic Crystal with Low-Frequency Locally-Resonant Spiral Structures (Brun)

In this talk, I will present some of the recent research directions on wave propagation in micro-structured media. Applications will be considered in the low frequency regime associated to flexural waves in thin structures.

The first part of the talk will be devoted to the design of non-reflecting absorbing layers for flexural waves. These perfectly matched layers are implemented in order to limit the computational domain in numerical applications concerning wave propagation. While in problems governed by second-order pde’s (Helmholtz and vector elasticity) these are well-known, surprisingly the problem of flexural waves has not been fully solved. Exact and approximate models will be presented based on coordinate transformation techniques together with a measure of the error.

In the second part of the talk a novel platonic crystal with low frequency locally resonant systems will be presented. The dynamic properties of the metamaterial will be shown and analytical formulae for the preliminary design of the microstructure will be given following an asymptotic approach. Applications of the micro-structured medium in terms of localization, wave trapping, surface waves, transmission amplification and shielding will be presented. The talk will conclude with the first demonstration of surface waves (Konenkov-Rayleigh waves) in thin plate structures for all types of classical boundary conditions

Mathematical Biology

Speaker: Dr Joanne Turner (University of Liverpool)

13:00 MATH-105

Abstract: In 2006, bluetongue (BT), a disease of ruminants, was introduced into northern Europe for the first time and more than two thousand farms across five countries were affected. In 2007, BT affected more than 35,000 farms in France and Germany alone. By contrast, the UK outbreak beginning in 2007 was relatively small, with only 135 farms in southeast England affected. We used a model to investigate the effects of three factors on the scale of simulated BT outbreaks in the UK: (1) place of introduction; (2) temperature; and (3) animal movement restrictions. Our results suggest that the UK outbreak could have been much larger had the infection been introduced into the west of England either directly or as a result of the movement of infected animals from southeast England before the first case was detected. The fact that air temperatures in the UK in 2007 were marginally lower than average probably contributed to the UK outbreak being relatively small. Finally, our results indicate that BT movement restrictions are effective at controlling the spread of infection. However, foot-and-mouth disease restrictions in place before the detection and control of BT in 2007 almost certainly helped to limit BT spread prior to its detection.

Mathematical Biology Seminar

Speaker: Fabian Spill (University of Birmingham)

13:00 MATH-105

Abstract: Cancer mostly kills through metastasis - the process where cancer cells leave the primary tumour and colonialize distant organs. Such movement of cells naturally requires forces. How cells generate forces through molecular pathways is thus an intense field of study. Moreover, it is becoming increasingly appreciated that forces not only arise from intracellular pathways, but can also affect pathways, for instance, through cellular mechanosensors. This way, forces can also affect cell behaviour directly. I will present a number of mathematical models that are used to understand the complex interplay of mechanical and chemical regulation of cells.

First, I will introduce a model of an endothelial cell monolayer that can predict the dynamic formation of gaps in the layer. These gaps arise due to forces that change the chemical binding rates of cell-cell adhesions. Experiments show that these gaps can be exploited by cancer cells when transmigrating through the endothelium - a crucial process during metastasis.

I will then show some work on modelling mechano-chemical pathways in cells. These pathways sense properties such as extracellular stiffness, but also cellular geometry, and can reprogram cells. Consequently, a physically altered tumour environment can activate such pathways and, independent or complementary to genetic changes, alter tumour cells towards more aggressive behaviour.

EPSRC Liverpool Centre for Mathematics in Healthcare (LCMH)

Speaker: Professor Weihong Guo (Case Western Reserve University, USA)

13:00 MATH-211

Abstract: Hyperspectral images provide rich spectral information that could be used in industry, medicine and remote sensing etc. Hyperspectral sensors achieve high resolution along spectral direction with the price of very low spatial resolution.  We provide a hyperspectral image (HIS) super resolution algorithm to increase its spatial resolution by fusing it with a multispectral image (MSI) which is usually available simultaneously during the data collection. Multispectral images have less spectral bands but higher spatial resolution compared with the hyperspectral counter part.  We propose a novel non-negative tensor dictionary learning based HSI super-resolution model using non-local spatial similarity and group-block-sparsity. It aims to preserve the high dimensional data structure while achieving nonlocal regularity. The computation is done on clusters obtained by tensor cube classification. Numerical experiments demonstrate that the proposed model outperforms many state-of-the-art HSI super-resolution methods.

Mathematical Biology Seminar

Speaker: Ivo Siekmann (Liverpool John Moores University)

13:00 MATH-105

Abstract: The dynamics of calcium concentrations in living cells has strong similarities with the electrical activity in the brain. Whereas local calcium spikes that vanish as quickly as they appear resemble the firing of neurons, the regular oscillations of calcium concentration across the whole cell remind us of the patterns seen in electroencephalograms (EEGs).

Similar to how neurons communicate with each other and broadcast signals across our body using electrical currents, signals within cells are transmitted via calcium signals. Calcium signals are generated by ion channels which, by opening and closing stochastically, release calcium from internal stores into the cell. Although each individual ion channel is stochastic, cells nevertheless behave deterministically – one of the most striking examples is the heartbeat which is reliably generated approximately every second for a whole lifetime. However, as difficult as it has been to relate the stochastic firing of individual neurons to the global electrical activity of the brain, it remains challenging to understand how calcium signals across the whole cell depend on the properties of individual ion channels.

In my talk I will explain how calcium dynamics can be modelled mathematically and how models can be parameterised with experimental data. I will also tell you of some of the discoveries that my collaborators and I made along the way.

EPSRC Liverpool Centre for Mathematics in Healthcare (LCMH)

Speaker: Rachel Tribbick (University of Lancaster)

13:00 MATH-104

Abstract: Modern studies of biological systems increasingly collect high-dimensional longitudinal data: repeated measurements of data on large numbers of outcomes over time. We can often assume correlation between observations from a single patient, both across time and outcomes. This correlation itself may be of scientific interest, but even when it is not, properly accounting for it can improve the parameter estimates of interest. Methods for jointly modelling multiple outcomes exist, but current literature demonstrating the application of this family of models to more than three outcomes is sparse.

In this talk I will describe an approach for modelling an unbalanced longitudinal data set with 12 outcomes: bone mineral density (BMD) measurements at different sites across the skeleton. This data has been collected on over 4000 patients as part of routine NHS scans for diagnosis osteoporosis. In order to be able to model the latent processes underlying the measurements, I developed a hierarchical mixed model in which both fixed and random effects are shared among measurements through a layer of latent variables. This layer is then linked to the observations at each site through a link matrix, the elements of which are also estimated. The observations are conditionally independent (both across time and sites) given the latent layer.

I will share the results and limitations of applying this model to the BMD data, aiming to answer the following questions of scientific interest:
(1) Do significant relationships exist between covariates and BMD/BMD loss at the femoral neck? 
(2) What is the relationship among BMD measurements across sites? 
(3) Do covariates have the same relationships with BMD/BMD loss across all sites?

EPSRC Liverpool Centre for Mathematics in Healthcare (LCMH)

Speaker: Peter Stewart (University of Glasgow)

13:00 MATH-105

Abstract: The optic nerve is a collection of nerve fibres which connect the photoreceptors in the retina to the brain. This nerve is surrounded by a sheath, which contains a thin layer of cerebrospinal fluid (CSF) at the intracranial pressure. The central retinal artery and vein, which supply the retinal circulation, pass through the centre of the optic nerve as they enter the eye, but about half way back from the globe they deviate and pass through the nerve sheath into the surrounding fatty tissue. Hence, these blood vessels form an interesting point of coupling between the eye and the brain. In this talk I will show how modelling of the flow of CSF along the nerve sheath and the flow of blood in the central retinal artery and vein can provide a route to abrupt pressure changes in the retinal circulation. In particular, I will demonstrate how a large increase in CSF pressure is transmitted into the retinal artery and vein, leading to a spreading shock wave through the retinal circulation and the possible rupture of retinal blood vessels (ie retinal haemorrhages).

Mathematical Biology Seminar

Speaker: Bärbel Finkenstädt and Måns Unosson (University of Warwick)

13:00 MATH-211

Abstract: Organisms have evolved an internal biological clock which allows them to temporally regulate and organize their physiological and behavioral responses to cope in an optimal way with the fundamentally periodic nature of the environment. It is now well established that the molecular genetics of such rhythms within the cell consist of interwoven transcriptional-translational feedback loops (TTFLs) involving about 15 clock genes, which generate circa 24-h oscillations in many cellular functions at cell population or whole organism levels. We will present statistical methods and modelling approaches  that address newly emerging large circadian data sets, namely spatio-temporal gene expression in SCN neurons and rest-activity actigraph data obtained from non-invasive e-monitoring, both of which provide unique opportunities for furthering progress in understanding the synchronicity of circadian pacemaking and address implications for monitoring patients in chronotherapeutic healthcare.

Mathematical Biology Seminar

Speaker: Alex Fletcher (University of Sheffield)

13:00 MATH-105

Abstract: The study of tissue patterning and morphogenesis promises to shed light on a wide range of developmental defects and inform strategies for the artificial growth of organs. Recently, the experimental study of patterning and morphogenesis has thrived due to a rise in quantitative methods. The resulting avalanche of data motivates the use of quantitative mathematical models to interpret and predict experimental observations. In this talk, I describe our recent work on the application of different mathematical modelling approaches to patterning and morphogenesis in epithelia, one of the major tissue types in animals. I illustrate how such models can be used to help gain mechanistic insights into, and generate quantitative predictions on, developmental processes such as planar polarity, tissue size control and axis extension.

Speaker: Dr Mike Smith (University of Manchester)

15:00 MATH-303

Abstract: When combining materials together to form an inhomogeneous composite material, the resulting properties (such as the optical, acoustic, or thermal properties) are typically given by some weighted average of the constituent values. I show that this is not the case for the opto-acoustic properties, namely, for the photoelastic response of a composite, which describes how the optical properties of a medium change under mechanical deformation (for most materials). I will show that a composite made from two materials with zero photoelasticity can combine to make a composite that is strongly photoelastic. I will examine the role of the unexpected photoelastic contribution in a selection of composite geometries, describing the effect in closed-form.

Mathematical Biology Seminar

Speaker: Nouf Alghamdi (University of Liverpool)

13:00-14:00  Room: MATH-105

Abstract: Based on a set of data reported in (Libberton, Horsburgh and Brockhurst, 2015) we constructed a simple model for dynamics of interacting bacterial populations and this was reported earlier.  The used experimental data describe the evolution of interacting populations under different conditions which include mutual invasions of toxin and non-toxin producing population of S. epidermidis and susceptible populations of S. aureus with varied initial frequencies, and in mixed and structured environments. Our model is based on the logistic equations and by modifying this model to consider the adaption behaviour of the susceptible populations, we were able to reproduce some of the experimental observations in our simulations. However, after careful investigation of the data and our model, we concluded that further experimental data is needed. The results of these new experiments will be reported in this talk.

[1] Libberton, B., Horsburgh, M. and Brockhurst, M. (2015). The effects of spatial structure, frequency dependence and resistance evolution on the dynamics of toxin-mediated microbial invasions. Evolutionary Applications, 8(7), pp.738-750.

EPSRC Liverpool Centre for Mathematics in Healthcare (LCMH)

Speaker: Professor Ronald Lui, The Chinese University of Hong Kong

13:00-14:00 MATH-104

Abstract: Shape analysis is important in anthropology, bioarchaeology and forensic science for interpreting useful information from human remains. In particular, teeth are morphologically stable and hence well-suited for shape analysis. In this work, we propose a framework for tooth morphometry using quasi-conformal theory. Landmark-matching Teichmuller maps are used for establishing a 1-1 correspondence between tooth surfaces with prescribed anatomical landmarks. Then, a quasi-conformal statistical shape analysis model based on the Teichmu ̈ller mapping results is proposed for building a tooth classification scheme. We deploy our framework on a dataset of human premolars to analyse the tooth shape variation among genders and ancestries. Experimental results show that our method achieves much higher classification accuracy with respect to both gender and ancestry when compared to the existing methods. Furthermore, our model reveals the underlying tooth shape difference between different genders and ancestries in terms of the local geometric distortion and curvatures.

Mathematical Biology Seminar

Speaker: Mohit Dalwadi (University of Oxford)

13:00-14:00  Room: MATH-105

Abstract: One goal of synthetic biology is to manipulate the metabolic pathways of microorganisms to create 'cell factories' which produce, for example, environmentally friendly biofuels and cheaper medicines. In this talk, we show how mathematical modelling can be used to provide insight into several multiscale processes involved in this aspect of synthetic biology, and thus to expedite the exploration of experimental parameter space for faster technological growth.

In the first part of this talk, we investigate the feasibility of various metabolic pathways through an exploration of their reaction kinetics. As the experimental parameter space is fairly large, we exploit a small parameter to perform an asymptotic analysis. This maximizes our analytic progress, allowing us to determine how each system behaves as a function of its experimental parameters and the key reactions in each pathway.

In the second part of this talk, we show how the effective nutrient uptake over a colony of bacteria depends on the bacterial properties by systematically upscaling an appropriate reaction-diffusion system. We use asymptotic homogenization to obtain an effective equation which takes the bacterial information into account. This will show us when the intuitive volume and surface area scalings are each valid, as well as the correct form of the effective uptake when neither of these scalings is appropriate.

Speaker: Dr Stewart Haslinger (Imperial College, London)

15:00-16:00  Room: MATH-303

Abstract: Many industrial ultrasonic NDE inspections use shear waves to detect and characterise rough defects. Certain types of components require insonification by shear waves, which are also able to locate areas of concern with higher sensitivity than longitudinal waves. The roughness of a defect has a strong effect on the reflection of ultrasound, and every rough defect is unique, so modelling techniques must incorporate the element of randomness, rather than relying solely on the well-established methods for smooth and regular defects, such as Kirchhoff Approximation (KA) and Geometrical Theory of Diffraction (GTD).

A statistical approach is investigated, whereby rough surfaces are characterised by two parameters σ and λ_0, known as, respectively, the RMS height and correlation length. Recent progress has been made using Monte Carlo stochastic methods for KA theory, and a stationary phase approximation which produces formulae for the expected scattering for the case of longitudinal incidence.

Analysis and validations for shear wave incidence have often been neglected in the literature. This issue has now been addressed, showing that shear waves bring novel features, both in the modelling and the results for scattering by rough surfaces. Theoretical expected values have been validated using Monte Carlo FE simulations. Good agreement is obtained for a range of incident and scattered angles within the range of validity for KA, which is shown to be much more strict for shear, rather than longitudinal, waves. The importance of mode-converted surface waves is also discussed.

Acknowledgements: The talk is based on joint work with Michael J.S. Lowe₁, Fan Shi₁, Peter Huthwaite₁, Richard V. Craster₂

₁Department of Mechanical Engineering, Imperial College, London, SW7 2AZ, UK; ₂Department of Mathematics, Imperial College, London, SW7 2AZ, UK.

Mathematical Biology Seminar

Speaker: Chris Overton (University of Liverpool)

13:00-14:00  Room: MATH-105

Abstract: In finite structured populations the dynamics of the stochastic SIS model will always go to extinction. The dynamics prior to extinction can exhibit interesting behaviour, but in the long term the model will always yield the degenerate disease free state, which gives no insight into the impact the infection had on the population. Therefore, a common tool to understand the infection is by studying the quasi-stationary distribution (QSD), i.e. the steady state solution given that extinction has not been reached, which is information rich. The aim of this work is to develop efficient and accurate techniques to approximate the QSD for any population structure. We do this using moment closure, developing multiple computationally feasible methods that can facilitate the study of important statistics of the quasi-stationary distribution, such as the invasion probability.

Speaker: Dr Theodosios Papathanasiou (Brunel University)

15:00-16:00  Room: MATH-303

Abstract: Rhythmic hydroelastic oscillations of ice shelves are a key mechanism believed to affect several phenomena observed in Polar Regions. These phenomena include the disintegration of ice shelves due to water wave impact or the formation of localised distinctive atmospheric waves. The fundamental and lower hydroelastic modes of an ice-shelf/sub-ice-shelf cavity system can be studied by coupling shallow water theory and the dynamics of a slender, floating, cantilever beam. A simple Finite Element procedure is introduced for the solution of the resulting eigenvalue problem. The eigenvalues are correlated to the characteristic frequencies of a wave impact Reflection-Transmission problem. Such characteristic frequencies maximise specific norms of the ice-shelf response and are indicative of resonant behaviour. The proposed methodology is used to predict characteristic periods of the Ross and Larsen C ice shelves.

Mathematical Biology Seminar

Speaker: Marianne Scott (University of Liverpool)

13:00-14:00  Room: MATH-105

Abstract: With the advent of a host of new techniques to capture live 3 dimensional images of cells, there has been increased interest in in vitro models of cell motility. There is however a lack of mathematical tools to analyse the large amounts of tracking data coming from these experiments, especially when the data is 3 dimensional in nature. In this talk I will outline the framework we have developed to try and bridge the gap between the data and the testing of cell motility hypotheses. Simulating cell tracks using the Persistent Random Walk model, we first use in silico simulations and statistical measures to validate the framework. We then test the framework on experimental data from Glioblastoma cells and use this to parametrise the model before assessing the model’s suitability and the appropriateness of including extra terms in the model motivated by biological observations.

Mathematical Biology Seminar

Speaker: David Graham (University of Plymouth)

12:00-13:00  Room: MATH-117

Abstract: The virtual source method (VSM) has been developed to simulate water waves based upon the solution of Laplace’s equation for the velocity potential. The basis of the method is the use of specific Green’s functions for a rectangular ‘virtual domain’ which is an extension of the physical domain. The solution variables are frequency components of the velocity potential at the upper virtual boundary and these are found by specifying appropriate conditions on the physical boundaries (i.e. wavemaker, walls and wave surfaces). We have shown that the model successfully simulates both linear and nonlinear standing waves and simple sloshing problems and is more effective and efficient than simple boundary element methods for these problems. We have further developed the VSM to generate nonlinear progressive waves in a numerical wave tank. The eventual aim is extend the model to account for wave/structure interaction problems.

Mathematical Biology Seminar

Speaker: Andrew Dean (University of Liverpool)

13:00-14:00  Room: MATH-105

Abstract: We study one-dimensional travelling waves in a two-species bacterial ecosystem, in which a monoculture in one species is connected to a monoculture in the other via. While both species are competing for resources, we allow one to also produce a toxin which inhibits the growth of its susceptible competitor. When the bacteria are completely immotile, we can find an analytical stationary solution; if the toxin is strong enough, an inhibition zone forms separating the two monocultures, in which the susceptible species is completely suppressed. This solution is then used to inform our understanding of the dynamics of slowly moving travelling waves for small but non-vanishing bacterial diffusion. In particular, we show that the formation of an inhibition zone in this case corresponds to a decoupling of the competitive dynamics, allowing the toxin producer to invade its competitor without hindrance.

EPSRC Liverpool Centre for Mathematics in Healthcare Seminar

Speaker: Dr Yang Han (University of Manchester)

13:00-14:00  Room: MATH-211

Abstract: Construction of simultaneous confidence bands for a percentile line has been considered by several authors. However only conservative symmetric bands, which use critical constants over the whole covariate range (-∞,∞), are available in the literature. Our new methods allow the construction of exact symmetric bands for a percentile line over a finite interval of the covariate x. The exact symmetric bands can be substantially narrower than the corresponding conservative symmetric bands. Several exact symmetric confidence bands are compared under the average band-width criterion. Furthermore, new asymmetric confidence bands for a percentile line are proposed. They are uniformly (and can be very substantially) narrower than the corresponding exact symmetric bands. Therefore, asymmetric bands should always be used under the average band-width criterion. The propose methods are illustrated with a real example of a drug stability study.

Many modern medicines are targeted therapies, targeting specific pathways. A biomarker that is informative of how sick a patient in the targeted pathway is could be sufficiently predictive of the effect on the patients to allow such medicine to be personalized. Baseline HbA1c for diabetic patients is an example of such potential biomarkers. If a candidate biomarker is continuously valued, it is typically dichotomized to classify patients into target (marker-positive) and non-target (marker-negative) subgroups. The question, for each potential cut-point, is therefore whether the drug has sufficient efficacy in the overall population, or only in the marker-positive patients, or neither. This question can be fully answered by providing simultaneous confidence intervals on the effect of the drug on the marker-positive patients, on the marker-negative patients, and on their mixture. To confidently decide whether a continuously-valued biomarker is useful for targeting patients, such simultaneous confidence intervals need to be further adjusted for the multiplicity of searching through all possible cut-point values. This presentation gives, for continuously-valued outcome measures such as reduction in HbA1c for Type II Diabetes, a neat method providing exact (fully) multiplicity-adjusted simultaneously confidence intervals. An app is also available, which conveniently implements the method we propose.

Mathematical Biology Seminar

Speaker: Karan Pattni (University of Liverpool)

13:00-14:00  Room: MATH-105

Abstract: In this talk a framework that allows the modelling of structured populations with fixed and variable size is described. It is then shown that the fixation probability of a mutant in a resident population of fixed size is a special case of the fixation probability in a population with variable size. As an application of this modelling framework, the fixation probability as studied in the evolutionary graph theory framework is derived from a model with Lotka-Volterra type competitive interactions.

Mathematical Biology Seminar

Speaker: Dr Mirela Domijan (University of Liverpool)

13:00-14:00  Room: MATH-105

Abstract: I will give a short overview  on two recent pieces of work that I completed this year: (1) Hajdu et al. ELONGATED HYPOCOTYL 5 mediates blue light signalling to the Arabidopsis circadian clock, Plant Journal, 2018 and (2) Vimont et al. Hormonal balance finely tunes dormancy status in sweet cherry flower buds, BiorXiv:https://doi.org/10.1101/423871

Mathematical Biology Seminar

Speaker: Dr Joe Leedale (University of Liverpool)

13:00-14:00  Room: MATH-105

Abstract: New drugs are tested for toxic side effects in the laboratory using isolated cells. These toxicity tests traditionally involve cells cultured in a flat, 2D environment. However, emerging experiments where cells are cultured in 3D have been shown to more closely resemble the functionality of cells within the body. While the increasing usage of 3D experiments represent more realistic biology, the underlying physical processes of what happens to the drug in these environments is not fully understood. Our research shows how mathematical models can be used to simulate the activity and transport of drugs in 3D, informing experimentalists on how best to use these systems to test for toxicity.

A multiscale mathematical modelling framework to describe the temporal and spatial dynamics of drugs in multicellular environments will be presented. The model combines information relating to the diffusion, transport and metabolism of chemical species (drugs) in 3D environments. A simplified 3D microscale single-cell model was analysed to study different transport mechanisms by varying boundary conditions on the cell membrane. A more complex multicellular model has been developed to study the effects of cellular arrangement and density on the transport and penetration of drugs to simulate the problem for in vitro microtissue environments. Following the preliminary theoretical work, integration of experimental data is incorporated to develop realistic geometries and parameterise the model for a range of pharmacologically realistic scenarios.

Mathematical Biology Seminar

Speaker: Dr Panayiota Katsamba (University of Birmingham)

13:00-14:00  Room: MATH-105

Abstract: A prevalent morphology in the microscopic world of artificial microbots, bacteria and viruses is that of a helix. The intriguingly different physics at play at the small scale level make it necessary for bacteria to employ swimming strategies different from our everyday experience, such as the rotation of a helical filament. Bio-inspired microswimmers that mimic bacterial locomotion achieve propulsion at the microscale level using magnetically actuated, rotating helical filaments, and have promising applications in non-invasive medicine, for example drug delivery to tumours or microsurgery. The first part of my talk will address the control and adaptivity features in the application-driven design of biomedical microbots. In the second part of the talk I will turn to the sub-bacterial scale of bacteriophage viruses, ‘phages’ for short, that infect bacteria. Given the rise in antibiotics resistance, phages can offer valuable insight in our fight against pathogenic bacteria and phage therapy is a possible alternative to antibiotics. I will share our latest findings on a surprising infection strategy by which some phages manage to `ride' along the propulsive machinery of bacteria and infect them.

Speaker: Professor Sergey Foss (Heriot-Watt University)

14:00-15:00  Room: MATH-117

Abstract: Consider a countably infinite collection of coupled queues representing a large wireless network with a queue at each point of the d-dimensional integer grid. These queues have independent Poisson arrivals, but are coupled through their service rates which is the signal to interference ratio of wireless network theory. More precisely, the service discipline is translation invariant and of the processor sharing type, with the service rate in each queue slowed down, when the neighboring queues have a larger workload. The dynamics is infinite dimensional Markov, with each queue having a non compact state space. It is neither reversible nor asymptotically product form, as in the mean-field setting. Coupling and percolation techniques are first used to show that this dynamics has well defined trajectories. Coupling from the past techniques of the Loynes' type are then proposed to build its minimal stationary regime. This regime is the one obtained when starting from the all empty initial condition in the distant past. The rate conservation principle of Palm calculus is then used to identify the stability condition of this system, namely the condition on the interference sequence and arrival rates guaranteeing the finiteness of this minimal regime. Remarkably, the rate conservation principle also provides a closed form expression for its mean queue size. When the stability condition holds, this minimal solution is the unique stationary regime, provided it has finite second moments, and this is the case if the arrival rate is small enough. In addition, there exists a range of small initial conditions for which the dynamics is attracted to the minimal regime. Surprisingly however, there exists another range of larger though finite initial conditions for which the dynamics diverges, even though stability criterion holds.

Joint work with Abishek Ananthararam and Francois Baccelli

Speaker: Francisco Herrerias-Azcue (University of Manchester)

13:00-14:00  Room: MATH-105

Abstract: In evolutionary dynamics, the notion of a “well-mixed” population is usually associated with all-to-all interactions at all times. This assumption simplifies the mathematics of evolutionary processes, and makes analytical solutions possible. At the same time the term “well-mixed” suggests that this situation can be achieved by physically stirring the population. Using simulations of populations in chaotic flows, we show that in most cases this is not true: conventional well-mixed theories do not predict fixation probabilities correctly, regardless of how fast or thorough the stirring is. We propose a new analytical description in the fast-flow limit. This approach is valid for processes with global and local selection, and accurately predicts the suppression of selection as competition becomes more local. It provides a modelling tool for biological or social systems with individuals in motion.

Joint work with Vicente Pérez-Muñuzuri (University of Santiago de Compostela, Spain) and Tobias Galla (PhD supervisor, University of Manchester)

Speakers: Caterina La Porta and Stefano Zapperi (Center for Complexity & Biosystems, Università degli Studi di Milano, Italy)

13:00-14:00  Room: MATH-117

Abstract: In this talk, we review our recent work on the mechanical properties of cells combining experiments and mathematical models. In particular, we discuss the collective dynamics of cell sheets during wound healing and the relation with the jamming transition, the dynamics of cell formation in zebrafish primordial germ cells and the mechanics of cell division during development.

Speaker: Professor Graeme Milton (University of Utah, USA)

14:00-15:00  Room: MATH-G16

Abstract: Classic physics text-books teach that the sign of the Hall-coefficient tells one the sign of the charge carrier. However metamaterials of interlinked rings provide a counterexample. This has been shown theoretically, numerically, and experimentally. Additionally, metamaterials allow one to create Hall-effect materials where the electric field generated by the Hall voltage is parallel to the magnetic field - the so-called parallel Hall effect. Here we will review these results, and the more general question of how one can channel the current in the unit cell. We also provide some completely novel geometries that display reversal of the sign of the Hall-coefficient. One reroutes the contacts in the unit cell of periodicity. It achieves at a microscope what at a macroscale can be achieved by crossing the leads that pick up the Hall voltage. Another metamaterial displaying reversal of the sign of the Hall-coefficient reroutes the magnetic field at a microscopic scale through the use of constituents with high magnetic permeability. While these metamaterials operate at low frequency, their analysis opens the door to manipulating Faraday rotation, and the associated non-reciprocal effects that may lead to new optical devices. Our most recent paper can be found at arXiv:1806.04914 [cond-mat.mes-hall]. This is work by Christian Kern, Marc Briane, Muamer Kadic, Martin Wegener, and Graeme Milton.

Speaker: Dr Maciej Hermanowicz, GlaxoSmithKline

14:00-15:00  Room: SIRE Seminar Room

Abstract: Maciej will present a selection of the past and present challenges in computer vision and image analysis that GlaxoSmithKline Scientists encounter in their work to discover new medicines. The context of the project ranges from authomated high throughput fluorescent microscopy to analysis of CT scans.

Speaker: Etienne Farcot (University of Nottingham)

13:00-14:00  Room: MATH-117

Abstract: Since their discovery in the 1960's, gene regulatory networks and their dynamics have been modelled using a range of mathematical representations. For instance both discrete and continuous representations are used. In this talk, after a quick review of gene networks and their main mathematical models, I will present two theoretical results and an application.The first result, dating back to 2006, will show how discrete models can typically be expected to be strictly over-approximating the dynamics of their continuous counterparts, and for instance have a strictly larger topological entropy. The second result, obtained recently by Elisa Tonello, is a complete answer to the conjecture: does the existence of a cyclic attractor in Boolean models imply the existence of a local negative circuit in the regulatory graph? Finally, I will present a model, developed with Jean-Louis Dinh and Charlie Hodgman, of the transition from stem to floral identity in the model plant Arabidopsis thaliana.

Speaker: Bulat Rakhimberdiev (CheckMobile GmbH)

10:00-11:00  Room: Lecture Theatre D, Central Teaching Hub

Abstract: Retail chains and small retailers have limited access to algorithms that solve their more complex operational issues, because existing implementations are closed source and have a prohibitively high license cost. This opens room for academic work in this area to produce public-domain solutions to these problems. We look at the following business problems: forecasting consumer demand for a product; determining the optimal sales price for a product; finding an optimal loading plan for a fleet of trucks; finding the optimal plan to fulfill an order from multiple possible locations. In this talk we outline these problems to start a discussion on avenues of collaboration between academic science and smaller business – specifically, retail.

Speaker: Professor Zakaria Belhachmi (University of Haute Alsace, France)

15:00-16:00  Room: SIRE Seminar Room, Chadwick Building

Abstract: We consider a unified variational PDEs model to solve the optic flow problem for large displacements and varying illumination. In this problem, the energy functional is nonconvex and severely nonlinear, moreover phenomena like occlusions and brutal changes in the scene increase strongly the difficulties and constitute a great challenge for any mathematical model or numerical method. We present an approach which aims to solve such problem within a solid mathematical framework and with efficient effective algorithms. In particular, we resort to a combined space-time parallel programming strategy which gives raise to several iterative schemes and allows us to obtain a good balance between several objectives, e.g. sparsity of the optic flow, edge-preserving, as well as high accuracy and cost reduction. We present several numerical simulations to validate the different algorithms and to compare their performances.

Speaker: Professor Weihong Guo (Case Western Reserve University, USA)

14:00-15:00  Room: SIRE Seminar Room, Chadwick Building

Abstract: From pictures taken by smart phones to x-ray pictures doctors use for diagnosis, images become an important part of our life. High quality images of various dimensions are important for both visualization and analysis purpose. Image super resolution algorithms aim at enhancing resolution of images obtained from hard ware devices with limited resolution for better image quality. Different from most of the existing approaches that focus on discrete modeling and computing, we study how to recover the analog image, the underlying intensity function defined on a continuous domain, which provides more details in more flexible resolution. The idea is to find a “basis” that might be redundant to represent the underlying intensity function and use known information to find the coefficients of the basis. Various methods have been explored to account for modeling discrepancy. We will also present recent results on applying the idea to multispectral and hyperspectral imaging. Competitive numerical results have been obtained.

Speaker: Ozgur Akman (University of Exeter)

13:00-14:00  Room: MATH-103

Abstract: The gene networks that comprise the circadian clock modulate biological function across a range of scales, from gene expression to performance and adaptive behaviour. In recent years, computational models of these networks based on differential equations have become useful tools for quantifying the complex regulatory relationships underlying the clock’s oscillatory dynamics. However, optimising the large parameter sets characteristic of these models places intense demands on both computational and experimental resources, limiting the scope of this approach. In this talk, a complementary approach based on combining Boolean logic with evolutionary optimisation will be introduced that dramatically reduces the parametrisation and computational load, making the state and parameter spaces more tractable. Through the construction of Boolean models fitted to both synthetic and experimental time courses, it will be shown that logic models can reproduce the complex responses to environmental inputs generated by more detailed differential equation formulations. In particular, it will be demonstrated that logic models have sufficient predictive power to identify optimal regulatory structures from experimental data. This suggests that the capacity of logic models to provide a computationally efficient representation of system behaviour could facilitate the reverse-engineering of large-scale biochemical networks.

Speaker: Professor Albert Nikolaevich Shiryaev (Steklov Mathematical Institute)

15:00  Room-116, 126 Mount Pleasant

The talk will concentrate on the following:

1. Quickest detection problems (discrete and continuous time). Case of the expensive cost.
2. About general results of Optimal Stopping.
3. Financial statistics, stochastics and optimization (in optimal option).

Speaker: Maya Wardeh (University of Liverpool)

13:00  Room-MATH-103

Abstract: Emerging infectious diseases continue to pose major threats to humans, animals and plants. Recent years have seen significant outbreaks of several emerging diseases, ranging from the well-known (Ebola and Olive quick decline syndrome), to the previously little known (Zika), to the entirely novel (Schmallenberg). It is well established that the ability of a pathogen to infect multiple hosts, particularly hosts in different taxonomic orders or wildlife, is a risk factor for emergence in human and livestock pathogens. The main focus of my current work is to develop network models to investigate sharing, transmission and emergence of pathogens between host species, asking the following questions:

1. What are the characteristics of the networks that connect species via shared pathogens? How central are humans and their domesticated animals and crops in these networks and which other species are each of those communities most closely connected to?
2. What is the role of different pathogen transmission routes on the nature of these networks? Are the potential species-to-species transmission pathways different for direct, food-borne, water-borne and vector-borne pathogens?
3. What factors determine the host ranges of pathogens? Are host species more likely to become exposed to pathogens that infect a wide range of species? From species that are closer to them genetically? Or from those species with which they often interact?
4. What are we missing? Given the networks, transmission routes and host ranges, what is the risk associated with each pathogen emerging in new species? What are the pathogens that can be prioritised as more-likely to emerge in the future?

Speaker: Pavitra Kannan (Oxford University)

13:00  Room-MATH-103

Abstract: Prostate cancer is a heterogeneous, multi-clonal disease that is commonly treated with external beam radiotherapy. Local recurrence in prostate cancer remains a challenge in treatment. Theoretical studies have suggested that better tumour control can be achieved by accounting for biological heterogeneity in radiation treatment plans. We sought to provide biological evidence for this hypothesis by determining whether heterogeneous populations with different radiation sensitivities have altered growth and radiation response in prostate cancer. We found that radiation resistant cells enhance the survival and radiation resistance of sensitive cells in 3D but not in 2D. Mathematical modelling revealed that these phenotypic changes are consistent with competitive interactions between resistant and sensitive populations. The observed changes are mediated both by hypoxic microenvironment and by transferred factors between the cell populations, because we found that adaptation to hypoxia and transferred factors released in hypoxic conditions enhance survival of the sensitive populations. Our ongoing work investigates the biological mechanism of competition and whether accounting for cellular heterogeneity in treatment plans can lead to more accurate predictions of radiation response.

Speaker: Dr Stéphane Brûle (Menard & Institut Frenel)

11:00  Room-MATH-211

Speaker: Theo Kypraios (Nottingham University)

13:00  Room-MATH-103

Abstract: Healthcare-associated infections (HCAIs) remain a problem worldwide, and can cause severe illness and death. It is estimated that 5-10% of acute-care patients are affected by nosocomial infections in developed countries, with higher levels in developing countries.

Statistical modelling has played a significant role in increasing understanding of HCAI transmission dynamics. For instance, many studies have investigated the dynamics of MRSA transmission in hospitals, estimating transmission rates and the effectiveness of various infection control measures. However, uncertainty about the true routes of transmission remains and that is reflected on the uncertainty of parameters governing transmission.

Until recently, the collection of whole genome sequence (WGS) data for bacterial organisms has been prohibitively complex and expensive. However, technological advances and falling costs mean that DNA sequencing is becoming feasible on a larger scale.

In this talk we first describe how to construct statistical models which incorporate WGS data with regular HCAIs surveillance data (admission/discharge dates etc) to describe the pathogen's transmission dynamics in a hospital ward. Then, we show how one can fit such models to data within a Bayesian framework accounting for unobserved colonisation times and imperfect screening sensitivity using efficient Markov Chain Monte Carlo algorithms. Finally, we illustrate the proposed methodology using MRSA surveillance data collected from a hospital in North-East Thailand.

Speaker: Ross Kelly (Liverpool John Moores University)

13:00  Room-MATH-103

Abstract: Themodynamic-based in silico models provide a platform from which cellular bioenergetic function and toxicity may be investigated. Detailed biochemical thermodynamic models account for rapid equilibria of biochemical species and proton and metal ion buffering, allowing simulation of a dynamic pH time course. This facilitates a unique coupling opportunity with extracellular flux analysis (EFA), which is used to measure cellular bioenergetics and investigate bioenergetic compromise in vitro. This study explores how consolidation of drug physicochemical properties into a mathematical framework can be combined with thermodynamic-based in silicomodelling and in vitro EFA to explore bioenergetic function and toxicity.

Speaker: Dr. Jianhai Bao (Central South University, P.R. China and University of Swansea, U.K.)

16:00  Room-MATH-104

Abstract: The asymptotic log-Harnack inequality is established  for several different models of stochastic differential systems with infinite memory: non-degenerate SDEs, Neutral SDEs, semi-linear SPDEs, and stochastic Hamiltonian systems. As applications, the following properties are derived for the associated segment Markov semigroups: asymptotic heat kernel estimate; uniqueness of the invariant probability measure; asymptotic gradient estimate and hence,  asymptotically strong Feller property; and asymptotic irreducibility.

EPSRC Liverpool Centre for Mathematics in Healthcare (LCMH) Seminar

Speaker: Professor Joachim Weickert, Faculty of Mathematics and Computer Science, Saarland University, Germany

2-3PM Room-MATH-103

Abstract: The displacement field between subsequent frames in an image sequence is called optic flow. It describes the apparent motion in an image sequence and has much in common with other correspondence problems such as registration. Its applications range from video coding to robotics. In recent years, variational approaches have proven to be well-suited for computing dense optic flow fields with very high accuracy.

The goal of the talk is to survey work on variational optic flow computation that has been developed in our group within the last 15 years. Specific emphasis is put on aspects that have some relevance for image registration, such as ways to handle large displacements, the filling-in effect, design of sophisticated smoothness terms, and complementarity of data and smoothness terms. A number of experiments illustrate the performance of these concepts. Finally, an unconventional application to a non-biomedical registration problem is presented.

Biography: Professor Joachim Weickert is a professor of mathematics and computer science at Saarland University where he heads the Mathematical Image Analysis Group since 2001. He received a diploma and a Ph.D. degree in mathematics from the University of Kaiserslautern (1991, 1996), and a habilitation degree in computer science from the University of Mannheim (2001). He worked as research assistant at the University of Kaiserslautern, as post-doctoral researcher at the universities of Utrecht and Copenhagen, and as assistant professor at the University of Mannheim.

The scientific work of Joachim Weickert covers more than 300 refereed publications. They have led to over 22000 citations and an h-index of 68. Joachim Weickert is editor-in-chief of the Journal of Mathematical Imaging and Vision. He has been serving in the editorial boards of ten international journals and book series, and he has been reviewer for more than 70 journals and 20 funding organisations. He has given over 180 invited talks at conferences, workshops and other universities, and was area chair of seven ECCV, ICCV or CVPR conferences. Joachim Weickert has received 32 research, teaching and reviewing awards, including a Gottfried Wilhelm Leibniz Prize which belongs to the highest German research awards. In 2017 he has been awarded an ERC Advanced Grant. He is elected member of the Academia Europaea - The Academy of Europe.

Speaker: Professor Ross McPhedran (University of Sydney) 

2-3PM Room-427a

Abstract: A canonical problem in Physics is the scattering of electromagnetic waves by a dielectric sphere, first solved by Gustav Mie. Surprisingly, aspects of this problem are still under active investigation, for example, the so-called anapole resonances. These arise for spheres with  strong contrast in dielectric permittivities, and are characterised by zeros in the multipole scattering coefficients. Treatments in the literature of anapoles have relied on a combination of Mie multipoles and Cartesian coordinate based ‘toroidal’ currents. We show that in fact the toroidal currents are not necessary, but that the anapole resonances can be described accurately using a small number of complex Mie terms, within the context of a rational representation, combined with an explicit exponential term which imposes causality upon the solution.

Speaker: Professor Jingzhi Li (Southern University of Science and Technology, Shenzhen, China)

2-3PM Room-211

Abstract: In this talk, we present an intrinsic perspective in differential forms of shape derivatives of the solutions to PDEs, which is of immense significance in the field of PDE-constrained shape design, optimization and sensitivity analysis. We first depict two fundamental Hadamard structure theorems for shape derivatives of boundary and domain integrals by the exterior calculus of differential forms, whereby the Lie derivative plays a pivotal role in deriving the structure results. Higher order shape derivatives can be systematically derived in a recursive way. It is revealed that the symmetry of the shape Hessian of domain and boundary integrals depends only on the Lie bracket of the two velocity fields associated with the transformations. With resort to such an approach, one can express the abstract framework for variational formulations of concrete PDEs and incarnate the differential forms in terms of avatars like scalar functions and vector fields to derive explicit formulae by straightforward calculus for shape derivatives of solutions to certain PDE under concern. As a model problem, we illustrate the power of the theory by deriving the shape derivatives of solutions to acoustic and electromagnetic scattering problems.

Dr Jingzhi Li completed his PhD in Chinese University of Hong Kong in 2009. Then he took up a postdoc position in ETH, Switzerland between 2009-2011 before joining the Chinese Academy of Sciences for 1 year prior to SUSTech. He is currently an associate professor in SUSTech. His research expertise covers scientific computing, finite element methods, inverse problems in mathematical physics, shape optimization in differential forms and computational finance. He is well-known for his work on modeling and analysis of inverse problems.

Tuesday 18^th July 2017

Wednesday 19^th July 2017

Speaker: Daniele Avitabile (University of Nottingham)

4pm-5pm Room MATH-104 (TBC)

Abstract: I will discuss level-set based approaches to study the existence and bifurcation structure of spatio-temporal patterns in biological neural networks. Using this framework, which extends previous ideas in the analysis of neural field models, we study the first example of canards in an infinite-dimensional dynamical system, and perform a computational reduction of dimensionality in certain neural network models.

Phenomenological neural field models have been intensively studied in the past and are known to support a variety of coherent structures observed experimentally (localised bumps of activity, travelling fronts, travelling bumps, lurching waves, rotating waves). These models are typically written as integro-differential equations, where the integral term is a Hammerstein nonlinear operator, featuring a sigmoidal firing rate and a synaptic kernel. Successful strategies for the analysis of these models include special choices of the synaptic kernels (leading to equivalent PDE formulations) and interface methods.

The main message of the talk is that the latter can be used effectively to construct or compute coherent structures in multiple-scale, heterogeneous, and possibly stochastic systems.

I will initially consider a spatially-extended network with heterogeneous synaptic kernel. Interfacial methods allow for the explicit construction of a bifurcation equation for localised steady states, so that analytical, closed-form expressions for a classical "snakes and ladders” bifurcation scenario can be derived.

Speaker: Alexander Plakhov

3pm-4pm Room MATH-104 (TBC)

Abstract: A parallel bundle of light rays is transformed into another (and codirectional) parallel bundle by several reflections from curved mirrors. This transformation induces a diffeomorphism of two plane domains representing the cross sections of the original and the final bundles. The question is: which diffeomorphisms can be realized this way, and how many reflections are needed? We prove that (a) a gradient diffeomorphism can be realized by 2 reflections, (b) an orientation reversing diffeomorphism can be realized by 4 reflections, and (c) a general diffeomorphism can be realized by (at most) 6 reflections. This is a joint work with S. Tabachnikov (Penn State, USA) and D. Treschev (Academy of Science, Russia). There still are interesting open problems related to this problem. In particular, given a PDE of 2nd order in a plane domain, does there exist a solution whose gradient is a diffeomorphism of two plane domains. Another open question: is it true that each diffeomorphism of bounded domains on the plane is the composition of two gradient diffeomorphisms.

Speaker: Prof Alexander Zadorojniy (IBM Research, Haifa) 

2:00PM Room MATH-211

Abstract: The use of gesture and activity recognition using wearable sensors, such as accelerometers and gyroscopes in popular wrist bands or smart watches, has been gaining popularity in recent years. Applications include presentation with gestures, media player use, detection of gym exercises, and validation of correct movements in physiotherapy or nursing hygiene. In these problems, the state of the system is unobservable and needs to be estimated using available observations. Hidden Markov Models (HMM) and Decision Trees are the state-of-the-art methods for solving gesture and activity recognition problems, respectively. We demonstrate an application of an ensemble algorithm using both techniques to detect when a person is eating.

Partially Observable Markov Decision Process (POMDP) extends HMM with control. Consider a person running on a treadmill. Initially he needs to choose the type of exercise he wants to perform, such as a course with preprogrammed angle and speed change. However, his actual goal is to improve his fitness or lose weight. Doing this in a static way could be far from optimal for achieving the actual goal, and it may even lead to injuries. We are developing a solution in which the person sets his real goal and the treadmill will dynamically control and reconfigure itself to help the person to achieve this goal. The system ensures that the person accomplishes this in an optimal and safe fashion by analyzing data from wearable devices such as heart rate and galvanic skin response monitors, accelerometers, gyroscopes, etc. We are working on developing theory and algorithms to solve a wide range of practical problems, such as the one above.

Joint work with Sergey Zeltyn and Michael Masin.

Speaker: Mathieu Desroches (INRIA, France)

4:00PM Room MATH-106

Abstract: In this talk I will present recent work on multiple timescale dynamical systems displaying complex oscillations with both slow processes and bursts. After reviewing the essential definitions and results about canards in planar and three-dimensional systems, I will focus on two examples of canard-induced spike-adding phenomena in bursting systems. The first one corresponds to square-wave bursting with a slowly-varying input current. Starting from the Hindmarsh-Rose burster, I will explain how the number of spikes per burst can vary through sharp transitions referred to as spike-adding canard explosions, when the applied current I is considered as a bifurcation parameter. Considering a slow evolution for I induces in the resulting four-dimensional model a dynamic passage through the spike-adding regime, which is characterised by ‘Mixed-Mode Bursting Oscillations’ (MMBOs). MMBOs display sub-threshold oscillations, which appear in between the bursts of the original Hindmarsh-Rose model. These small-amplitude oscillations are controlled by so-called folded-node canards. I will give an example of experimental data for which this modelling framework seems relevant. The second example will allow me to revisit parabolic bursting, a type of bursting that also requires four state variables, two fast and two slow, from the viewpoint of canards. Focusing on two examples; a conductance-based model called the Plant model and a new polynomial caricature of it, I will show that the number of spikes per burst is as well controlled by canards, but this time through the presence of a so-called folded-saddle singularity.

Joint work with Tasso Kaper (Boston University, USA), Martin Krupa (University College Cork, Ireland) and Serafim Rodrigues (Ikerbasque & BCAM, Bilbao, Spain). 

Speaker: Dr. Aiko Kurushima (Sophia University, Japan)

3:00PM Room MATH-105

Speaker: Dr Olga Kubassova – CEO of Image Analysis Group

2:00PM Room MATH-211

Abstract: Imaging algorithms for quantitative analysis of MRI scans allow us to extract information from the images with a level of precision impossible for human eye. The number of imaging biomarkers allow recognition of quick changes (as these were captured by MRI) as early as a few days after the treatment. By comparison a human eye is less sensitive and can only recognize these a few weeks or months later.

In this talk, I shall discuss several key algorithms that underpin the software package, DYNAMIKA, which was originally created for use in clinical practice; but over the time, the software has migrated to the cloud allowing efficient management of all stakeholders in a trial. It has become not only a key product of Image Analysis (IA) Ltd but also a platform for various therapeutic areas and more innovative techniques have been integrated into the software, making it a platform integrated across imaging technologies, data management and compliance. DYNAMIKA for image analysis has been used by major pharmaceutical companies, biotech enterprises and clinicians to understand at the earliest possible time point if the patient has positive reaction to the treatment. Various auto-immune, cancerous and inflammatory conditions were analysed. Examples of selected applications are illustrated and some clinical and image challenges are also highlighted in this talk.

Speaker: Prof Isaac Sonin, University of North Carolina, Charlotte, USA

10:00AM Room MATH-211

Abstract: An important, though not well-known tool for the study of Markov chains (MCs) is the notion of a Censored (Embedded) MC. It is based on a simple and insightful idea of Kolmogorov and Doeblin: a MC observed only on a subset of its state space is again a MC with a reduced state space and a new transition matrix. The sequential application of this idea leads to an amazing variety of important algorithms in Probability Theory and its Applications. The brief list of such Applications and algorithms is as follows.

A. State Reduction approach to recursively calculate many important characteristic of MCs, e.g. GTH /S algorithm to calculate the limiting distribution of an ergodic MC.

B. The solution of the Optimal stopping of MCs. In deterministic terms this is equivalent to the solution of the Bellman equation v = max(g; c+Pv), where c(x) is a one step reward function, g(x) is a terminal reward function, v is the value function and P is an averaging operator.

C. An algorithm to calculate the well-known Gittins Index and so called Generalized Gittins Index. Their relationship with Katehakis-Veinot and Whittle indices. Evolution of random graphs and Gittins theorem in a general form.

D. There is a remarkable theorem in the theory of finite MCs – the MC Tree theorem (MCTT), initially discovered by G. Kirchhoff, which expresses the limiting distribution for an ergodic MC in terms of directed spanning trees and a transition matrix. This theorem serves as a bridge between MCs and Graph Theory. The applications of MCTT were limited by the fact that the number of trees directed to a point grows exponentially. In my paper (Adv. in Mathematics, 1999) it was noted and proved that there is a polynomial algorithm to calculate a crucial characteristic in this theorem. Recently in B. Benek Gursoy, S. Kirkland, O. Mason and S. Sergeev 2015, (The Markov Chain Tree Theorem in commutative semirings and the State Reduction Algorithm in commutative semi elds, Linear Algebra and its Applications), this algorithm and corresponding theorem were generalized to the case of so called idempotent (tropical) calculus.

E. One of the main approaches to studying Markov models with large and “very large” state spaces is based on the idea of selecting “clusters” – groups of states with many strong connections inside the cluster and weak connections between clusters. There is a more narrow model – called the “Islands” and “Ports” model, which allows us to obtain exact results in such a way that the main volume of calculations is performed in parallel.

In my talk I will briefly touch on a couple of other questions: Continue, Quit, Restart model and Insertion, a new operation for MCs; Some Remarks about Independence; Decomposition-Separation (DS) Theorem, describing the behaviour of a family of nonhomogeneous MCs de fined by the sequence of stochastic matrices (Pn) when there are no assumptions about this sequence; Tanks model of clearing in financial networks.

Speaker: Dr Annabelle Ballesta, Systems Biology Centre, University of Warwick

3:00PM Room MATH-103

Abstract: Anticancer chemotherapy personalisation needs to reliably account for the activation of molecular pathways triggered by drug administration in each individual patient. Indeed, underlying gene and protein intracellular networks ultimately drive treatment antitumor efficacy and side effects in cancer and healthy tissues respectively, and they highly depend on patient- and tumourspecific genetic mutations or epigenetic alterations. However, clinical molecular data is usually minimally available in individual patients so that physiologically-based models designed through multi-scale approaches integrating preclinical and clinical investigations appears as an adapted solution. The models are based on ordinary differential equations (ODEs), and represent the relevant intracellular protein networks together with the pharmacokinetics-pharmacodynamics (PK-PD) of drugs of interest in both the tumour and the healthy tissues for which chemotherapy is critically toxic. While PK quantifies the transport and metabolism of the drug and its metabolites that are driving exposure concentration over time, PD quantifies drug interactions with cellular targets and subsequent cytotoxicity. Basing mathematical models on physiology allows the use of in vitro studies to design wholebody preclinical rodent models, to be further scaled to patient population data. Partial re-calibration of the resulting human model for a given cancer patient according to individual biomarker recordings, genetic background and therapeutic history further allow for chemotherapy personalisation. The patient-specific models would then initiate a novel kind of clinical trial in which each individual patient would receive personalised drug combinations/scheduling computed via mathematical models informed with a continuous flow of multidimensional information obtained and tele-transmitted from patients. I will first present how this multi-scale approach is currently undertaken for designing clinically-relevant models of the PK-PD of temozolomide, the cornerstone of treatments against brain tumours, and how they can be used to personalize combination chemotherapies [1]. Next, I will discuss the promises of personalized cancer chronotherapeutics, that is administering anticancer drugs according to the patient’s biological rhythms over the 24h span. The project focuses on individualizing the circadian delivery of the anticancer drug irinotecan, one of the three drugs of the current gold standard protocols against digestive cancers [2-4].

References

1. Ballesta, A., et al., Multiscale design of cell-type-specific pharmacokinetic/pharmacodynamic models for personalized medicine: application to temozolomide in brain tumors. CPT Pharmacometrics Syst Pharmacol, 2014. 3: p. e112.

2. Dulong, S., et al., Identification of Circadian Determinants of Cancer Chronotherapy through In Vitro Chronopharmacology and Mathematical Modeling. Mol Cancer Ther, 2015.

3. Ballesta, A., et al., A systems biomedicine approach for chronotherapeutics optimization: focus on the anticancer drug irinotecan, in New Challenges for Cancer Systems Biomedicine. 2012, Springer.

4. Ballesta, A., et al., A combined experimental and mathematical approach for molecularbased optimization of irinotecan circadian delivery. PLoS Comput Biol, 2011. 7(9): p. e1002143.

Speaker: Professor David Rand (University of Warwick)

4:00PM Room MATH-104

Abstract: I will discuss a new mathematical approach to information and decisions in signalling systems and relate this to new experimental results about the NF-kappaB signalling system. NF-kappaB is an exemplar system that controls inflammation and in different contexts has varying effects on cell death and cell division. It is activated by various stress stimuli, including inflammatory cytokines such as TNFalpha and IL-1beta and is regarded as one of the most important stress response pathways in the mammalian cell. In a variety of conditions it displays oscillatory dynamics when stimulated, with the transcription factor entering the nucleus in a pulsatile fashion with a period of roughly 100 minutes. It is commonly claimed that it is information processing hub, taking in signals about the infection and stress status of the tissue environment and as a consequence of the oscillations, transmitting higher amounts of information to the hundreds of genes it controls. My aim is to develop a conceptual and mathematical framework to enable a rigorous quantifiable discussion of information in this context in order to follow Francis Crick's counsel that it is better in biology to follow the flow of information than those of matter or energy. In my approach the value of the information in the signalling system is defined by how well it can be used to make the "correct decisions" when those "decisions" are made by molecular networks. As part of this I will introduce a new mathematical approach for the analysis and simulation of large stochastic non-linear oscillating systems. This allows an analytic analysis of the stochastic relationship between input and response and shows that for tightly-coupled systems like those based on current models for signalling systems, clocks, and the cell cycle this relationship is highly constrained and non-generic.

Speaker: Professor Muamer Kadic (CNRS FEMTO-ST, University of Franche-Comté)

11:00AM Room 211

Abstract: Cloaking is surprisingly demanding in mechanics. Electromagnetic waves are usually transverse ; acoustic compression waves are longitudinal. In sharp contrast, both transverse and longitudinal polarizations are generally relevant in elastic solids. Here, we ask whether the direct-lattice-transformation design approach, which we have recently introduced for static mechanics, is also applicable to mechanical waves at finite frequencies. A major hurdle for answering this question numerically has been the absence of perfectly matched layers (PMLs) for microstructures in mechanics, whereas PMLs for effective media are standard in electromagnetism.

Speaker: Dr Paul J. Harris (University of Brighton)

2:00PM Room MATH-104

Abstract: In biological experiments small clusters of cells have been observed to move together and combine to form larger clusters of cells. These cells move by a process called chemotaxis where the cells detect a chemical signal and its gradient, and move in the direction in which the signal is increasing.

A number of mathematical models for simulating the motion of cells due to chemotaxis have been proposed, ranging from simple diffusion-reaction equations for finding the density of the cells to complete simulations of how the chemical receptors on the cell membrane react to the chemical signal and cause the cell membrane to move. This work presents a simple equations of motion model to describe how the cells move which is coupled to a diffusion equation solution of how the chemical signal spreads out from individual cells.

The talk will be illustrated with some typical examples.

Speaker: Professor Zhilin Li (North Carolina State University, USA)

4:00PM Room MATH-104

Abstract: Free boundary/moving interface problems are challenging both theoretically and numerically. In this general talk, I will introduce some application examples and corresponding differential equations models. The applications include Stefan problems of unstable crystal growth; drop spreading, and multi-phase flows. Then I will give a brief review of numerical methods for solving those challenging problems, particularly Cartesian grid method such as Peskin's Immersed Boundary (IB) method, the Immersed Interface Method (IIM), Augmented IIM, and Immersed finite element method (IFEM) developed by myself.

Another major component in solving free boundary/moving interface problems is how to evolve the interface. In our approach, both the front tracking and the level set methods are used. The level set method is simple and robust and can handle topological changes for any dimensions. I am going to discuss some issues about how to combine the level set method with IIM to achieve high order accuracy.

If time allows, I will introduce some recent work Stokes and Darcy and Navier-Stokes and Darcy coupling problems for fluid structure interactions between a fluid flow and a porous media.

Speaker: Professor Yuri Antipov (Louisiana State University, USA)

4:00PM Room MATH G16

Abstract: Wiener-Hopf factorization is the centerpiece of the solution technique for the Riemann-Hilbert problem of the theory of analytic functions and of many analytical methods applied in fracture mechanics. We will present factorization of piece-wise constant matrices with three points of discontinuity by means of hypergeometric functions and apply it to a problem on propagation of a semi-infinite crack with a friction zone ahead. Matrix factorization by a technique based on the theory of Riemann surfaces and hyperelliptic functions will be illustrated by a static problem on $n$ cracks induced by $n$ inclusions (a generalization of the classical Sherman-Muskhelishvili problem). Finally, we will discuss a numerical method of partial factorization and integral equations and show how it can be employed for the solution of the problem on propagation of a semi-infinite crack beneath the boundary of a half-plane.

Speaker: Dr Davit Harutyunyan (Ecole polytechnique Fédérale de Lausanne (EPFL), Switzerland)

4:00PM Room MATH-103

Abstract: In has been known that the rigidity of a shell (for instance under compression) is closely related to the optimal Korn's constant in the nonlinear first Korn's inequality (geometric rigidity estimate) for W^{1,2} fields under the appropriate Dirichlet type boundary conditions (arising from the nature of the compression). In their recent work Frisecke, James and Mueller (2002, 2006) derived a geometric rigidity estimate for plates, which gave rise to a derivation of a hierarchy of plate theories for different scaling regimes of the elastic energy depending on the thickness of the plate. FJM type theories have been derived by Gamma-convergence and rely on $L^p$ compactness arguments and of course the underlying nonlinear Korn's inequality. While the rigidity of plates has been understood almost completely, the rigidity, in particular the buckling of shells is much less well understood. This was due to the luck of rigidity estimates and $L^p$ compactness as understood by Grabovsky and Harutyunyan (2014) for cylindrical shells. In the case of shells, when there is enough rigidity, is has been understood that actually the linear first Korn's inequality can replace the nonlinear one, Frisecke, James Mueller (2002), Grabovsky, Truskinovsky (2007). The important mathematical question is: What makes the shells more rigid than plates and how can one compare the rigidity of two different shells? In this talk we give the answer to that question by classifying shells according to the Gaussian and principal curvatures. We derive sharp first Korn's inequalities for shells of zero, positive and negative Gaussian curvature. It turns out, that for zero Gaussian curvature (one principal curvature zero, the other one never zero) the amount of rigidity is h^{1.5}, for negative Gaussian curvature it is h^{4/3} and for positive Gaussian curvature it is h, i.e., the positive Gaussian curvature shell is the most rigid one. Here h is the shell thickness. All three exponents are completely new in ever appeared geometric rigidity estimates, however the exponents 4/3 and 1 appear in the engineering work of Tovstik and Smirnov (2000) in a different context. This is partially joint work with Yury Grabovsky (Temple University).

Speaker: Martin Benning (University of Cambridge)

3:00PM Room MATH-105

Abstract: In the first part of the talk, we present a spectral decomposition method that generalises popular multi-scale decomposition techniques such as Fourier- and wavelet-decomposition, and demonstrate the methods’ versatility by applying it to numerous applications such as (facial) image fusion, tone-mapping and artistic image manipulation. In the second part of the talk we analyse under which conditions the spectral decomposition can be proven to decompose a signal into objects of different scale. This involves establishing a theory of generalised Eigenfunctions, respectively singular vectors, that allows us to define a generalised notion of scale.

Speaker: Professor Chris Poulton (University of Technology, Sydney) 

4:00PM Room MATH-105

Abstract: The interaction between electromagnetic and elastodynamic vibrations has a long and distinguished history, dating from the work of Brillouin in the early 20th century. More recently researchers have begun to rediscover these interactions in the context of nanophotonics, in which light is trapped or guided within structures that possess features that are typically as large as the wavelength of light (and sound) in the material. These interactions can lead to several interesting and unusual effects, including"slow-light", by which the speed of light is reduced to a fraction of its value in vacuum. However at these small scales the mathematics of the different types of waves, and of the forces that cause them to interact, can become complicated, and modelling of the interlinked PDEs is a difficult task. In addition a number of different competing effects, arising from the electronic properties of the light-bearing medium, can have an outsized influence on the interaction. Here we discuss the journey towards a comprehensive and accurate mathematical description of light-sound interactions in nanophotonics, and review recent progress in using these models in on-chip optical waveguides for a range of novel applications.

Speaker: Dr Andrew Hoyle (University of Stirling)

4:00PM Room 211

Abstract: For too long have antibiotic dosage regimes against bacterial infections followed the traditional approach of a fixed quantity X for N days. With the rise of antibiotic resistance, the need to find better, more efficient strategies is essential. Here we combine mathematical modelling of an infection, with evolutionary algorithms from computational optimisation, to find optimal dosage regimes. These regimes improve the treatment success while also minimising total antibiotic usage.

Speaker: Professor Antonin Chambolle (Ecole Polytechnique, Paris)

3:00PM Room 514

Abstract: I will describe the mathematical analysis of a variational model for fracture growth (initially due to Francfort and Marigo) which is based on a non-interpenetrating variant of the (linearized elasticity) Mumford Shah functional.

Speaker: Prof. John Billingham (University of Nottingham)

2:00PM Room MATH-211

Abstract: In this talk I will describe three energy beam techniques (Abrasive Waterjet, Pulsed Laser Ablation and Focussed Ion Beam), that use very different physics to remove material from solid surfaces on the macro, micro and nano scales, respectively. After a brief discussion of some detailed physical modelling, I will describe how these three techniques can be unified into a single, simplified modelling framework that forms the basis of a practical method of designing beam paths to mill freeform surfaces.

Speaker: Professor Leonid Slepyan (Tel Aviv University)

11:00AM Room 105

Abstract: For steady-state and binary mechanical waves of an arbitrary form and nature, we present the following. Relations for the axial and angular momenta as they directly follow from the conservation laws. The mass and rotational inertia associated with the wave. The binary wave structure which possesses a self-equilibrated momentum, in particular, transverse-longitudinal wave formed upon excitation of flexural waves. Conditions under which longitudinal sinusoidal waves can carry momentum and the physical meaning of the so-called "wave momentum" are also discussed in the lecture.

Speaker: Professor Eugene Feinberg (Stony Brook University)

1:30PM Room MATH-103

Abstract: The talk describes the solutions to Kolmogorov's backward and forward equations for jump Markov processes. This study was motivated by applications to continuous-time Markov decision processes, and one of the applications will be discussed in the talk. The first attempt to solve Kolmogorov's equations for jump Markov processes was undertaken by William Feller in 1940.

Speaker: Dr Steven Webb (Liverpool John Moores University)

4:00PM Room MATH-211

Abstract: Current 2D in vitro test systems are poorly predictive of the toxicity of chemicals entering the systemic circulation. There is therefore an urgent need for models of systemic toxicity with improved predictivity across the pharmaceutical and chemical industry. We are currently developing a hollow fibre bioreactor (HFB) system for hepatotoxicity testing.

Previously HFBs have shown promise for use as bioartificial livers and their use in hepatotoxicity testing is a natural extension to this work. To assist with the development of the HFB, the design has been mathematically modelled to inform its operating set up, interpret data from HFB outputs and aid in optimizing design to mimic certain hepatic physiological conditions. Additionally, the mathematical model has been used to identify the key HFB and compound parameters that will affect xenobiotic clearance.

The analysis of this model has produced novel analytical results that allow the operating set up to be calculated and predictions of compound clearance generated efficiently and in a highly accessible form. The mathematical model predicts the inlet oxygen concentration and volumetric flow rate that gives a physiological oxygen gradient in the HFB to mimic a liver sinusoid. It has also been used to predict the concentration gradients and clearance of a test drug and paradigm hepatotoxin, paracetamol (APAP).

The effect of altering the HFB dimensions and fibre properties on paracetamol clearance under the condition of a physiological oxygen gradient is analysed. These theoretical predictions can be used to help design the most appropriate 3D in vitro experimental set up and data analysis to quantitatively compare the functionality of cell types that are cultured within the HFB to those in other systems.

Speaker: Bangti Jin from University College London (Centre for Medical Image Computing)

3:00PM Room 604

Abstract: Electrical impedance tomography is a noninvasive medial imaging modality. It aims at determining the electrical conductivity distribution from electrode voltages measured on the boundary. In this talk I will discuss some theoretical and computational issues on reconstruction by means of regularization techniques.

Speaker: Professor Vladyslav Danishevskyy (Keele University)

14:00 Room MATH-105

Abstract: The processes of wave propagation in non-linear elastic media with microstructure are studied. As an illustrative example, a 1D model of a layered composite material is considered. Geometrical nonlinearity is described by the Cauchy-Green strain tensor. For predicting physical non-linearity, the energy of deformation is expressed as a series expansion in powers of the strains (this is a so called Murnaghan elastic potential). The effective wave equation is derived by the higher-order asymptotic homogenization method. Analytical expressions for the effective moduli are presented. The balance between non-linearity and dispersion results in formation of stationary non-linear waves that are described explicitly in terms of elliptic functions. Propagation of non-stationary waves is simulated numerically by a pseudo-spectral procedure. The time integration is performed by the Runge-Kutta method; the approximation with respect to the spatial co-ordinate is provided by the Fourier series expansion. The convergence of the Fourier series is substantially improved and the Gibbs-Wibraham phenomenon is reduced with the help of Fourier-Padé approximants. A number of nonlinear phenomena are detected and their practical significance is discussed.

Speaker: David Richards (Exeter University)

3:00PM Room MATH-104

Abstract: Despite being of vital importance to the immune system, the mechanism by which cells engulf relatively large solid particles during phagocytosis is still poorly understood. I will discuss my recent work on the rate of engulfment during phagocytosis, which combines modelling with analysis of time-lapse images of neutrophil phagocytosis. This shows that engulfment is actually a two-stage process, with an initially slow diffusive stage followed by a much quicker, probably actively driven second stage. Interestingly, the model is related to the Stefan problem, which describes how the boundary between phases moves during a phase transition. I will then discuss the role of target shape and orientation during phagocytosis, and show how the modelling explains why non-spherical particles engulf quickest when presented to the cell tip-first. Finally, I will discuss possible future directions for both the modelling and time-lapse imaging.