Forthcoming events in this series


Thu, 16 Jun 2022

12:00 - 13:00
L2

Repulsive Geometry

Keenan Crane
(Carnegie Mellon Univeristy, School of Computer Science)
Further Information

 

Keenan Crane is the Michael B. Donohue Associate Professor in the School of Computer Science at Carnegie Mellon University, and a member of the Center for Nonlinear Analysis in the Department of Mathematical Sciences.  He is a Packard Fellow and recipient of the NSF CAREER Award, was a Google PhD Fellow in the Department of Computing and Mathematical Sciences at Caltech, and was an NSF Mathematical Postdoctoral Research Fellow at Columbia University.  His work applies insights from differential geometry and computer science to develop fundamental algorithms for working with real-world geometric data.  This work has been used in production at Fortune 500 companies, and featured in venues such as Communications of the ACM and Notices of the AMS, as well as in the popular press through outlets such as WIRED, Popular Mechanics, National Public Radio, and Scientific American.

Abstract

Numerous applications in geometric, visual, and scientific computing rely on the ability to nicely distribute points in space according to a repulsive potential.  In contrast, there has been relatively little work on equidistribution of higher-dimensional geometry like curves and surfaces—which in many contexts must not pass through themselves or each other.  This talk explores methods for optimization of curve and surface geometry while avoiding (self-)collision. The starting point is the tangent-point energy of Buck & Orloff, which penalizes pairs of points that are close in space but distant with respect to geodesic distance. We develop a discretization of this energy, and introduce a novel preconditioning scheme based on a fractional Sobolev inner product.  We further accelerate this scheme via hierarchical approximation, and describe how to incorporate into a constrained optimization framework. Finally, we explore how this machinery can be applied to problems in mathematical visualization, geometric modeling, and geometry processing.

 

 

Thu, 09 Jun 2022

12:00 - 13:00
L1

The ever-growing blob of fluid

Graham.Benham@maths.ox.ac.uk
(Mathematical Institute)
Abstract

Consider the injection of a fluid onto an impermeable surface for an infinite length of time... Does the injected fluid reach a finite height, or does it keep on growing forever? The classical theory of gravity currents suggests that the height remains finite, causing the radius to grow outwards like the square root of time. When the fluid resides within a porous medium, the same is thought to be true. However, recently I used some small scale experiments and numerical simulations, spanning 12 orders of magnitude in dimensionless time, to demonstrate that the height actually grows very slowly, at a rate ~t^(1/7)*(log(t))^(1/2). This strange behaviour can be explained by analysing the flow in a narrow "inner region" close to the source, in which there are significant vertical velocities and non-hydrostatic pressures. Analytical scalings are derived which match closely with both numerics and experiments, suggesting that the blob of fluid is in fact ever-growing, and therefore becomes unbounded with time.

Thu, 02 Jun 2022

12:00 - 13:00
L1

Hybrid modeling for the stochastic simulation of spatial and non-spatial multi-scale chemical kinetics

Konstantinos Zygalakis
(School of Mathematical Sciences University of Edinburgh)
Abstract

It is well known that stochasticity can play a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be adequately modeled by Markov processes and, for such systems, methods such as Gillespie’s algorithm are typically employed. While such schemes are easy to implement and are exact, the computational cost of simulating such systems can become prohibitive as the frequency of the reaction events increases. This has motivated numerous coarse-grained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation for systems where all reactants are present in large concentrations, the approximation breaks down when the fast chemical species exist in small concentrations, giving rise to significant errors in the simulation. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as computing observables of cell cycle models. In this talk, we present a hybrid scheme for simulating well-mixed stochastic kinetics, using Gillespie–type dynamics to simulate the network in regions of low reactant concentration, and chemical Langevin dynamics when the concentrations of all species are large. These two regimes are coupled via an intermediate region in which a “blended” jump-diffusion model is introduced. Examples of gene regulatory networks involving reactions occurring at multiple scales, as well as a cell-cycle model are simulated, using the exact and hybrid scheme, and compared, both in terms of weak error, as well as computational cost. If there is time, we will also discuss the extension of these methods for simulating spatial reaction kinetics models, blending together partial differential equation with compartment based approaches, as well as compartment based approaches with individual particle models.

This is joint work with Andrew Duncan (Imperial), Radek Erban (Oxford), Kit Yates (Bath), Adam George (Bath), Cameron Smith (Bath), Armand Jordana (New York )

Thu, 19 May 2022

12:00 - 13:00
L1

Hydrodynamics of swimming bacteria: reorientation during tumbles and viscoelastic lift

Masha Dvoriashyna
(Univeristy of Cambridge)
Abstract

Bacteria represent the major component of the world’s biomass. A number of these bacteria are motile and swim with the use of flagellar filaments, which are slender helical appendages attached to a cell body by a flexible hook. Low Reynolds number hydrodynamics is the key for flagella to generate propulsion at a microscale [1]. In this talk I will discuss two projects related to swimming of a model bacterium Escherichia coli (E. coli).

E. coli has many flagellar filaments that are wrapped in a bundle and rotate in a counterclockwise fashion (if viewed from behind the cell) during the so-called ‘runs’, wherein the cell moves steadily forward. In between runs, the cell undergoes quick ‘tumble’ events, during which at least one flagellum reverses its rotation direction and separates from the bundle, resulting in erratic motion in place. Alternating between runs and tumbles allows cells to sample space by stochastically changing their propulsion direction after each tumble. In the first part of the talk, I will discuss how cells reorient during tumble and the mechanical forces at play and show the predominant role of hydrodynamics in setting the reorientation angle [2].

In the second part, I will talk about hydrodynamics of bacteria near walls in visco-elastic fluids. Flagellar motility next to surfaces in such fluids is crucial for bacterial transport and biofilm formation. In Newtonian fluids, bacteria are known to accumulate near walls where they swim in circles [3,4], while experimental results from our collaborators at the Wu Lab (Chinese University of Hong Kong) show that in polymeric liquids this accumulation is significantly reduced. We use a combination of analytical and numerical models to propose that this reduction is due to a viscoelastic lift directed away from the plane wall induced by flagellar rotation. This viscoelastic lift force weakens hydrodynamic interaction between flagellated swimmers and nearby surfaces, which results in a decrease in surface accumulation for the cells. 

References

[1] Lauga, Eric. "Bacterial hydrodynamics." Annual Review of Fluid Mechanics 48 (2016): 105-130.

[2] Dvoriashyna, Mariia, and Eric Lauga. "Hydrodynamics and direction change of tumbling bacteria." Plos one 16.7 (2021): e0254551.

[3] Berke, Allison P., et al. "Hydrodynamic attraction of swimming microorganisms by surfaces." Physical Review Letters 101.3 (2008): 038102.

[4] Lauga, Eric, et al. "Swimming in circles: motion of bacteria near solid boundaries." Biophysical journal 90.2 (2006): 400-412.

 

Thu, 12 May 2022

12:00 - 13:00
L1

Averaged interface conditions: evaporation fronts in porous media (Ellen Luckins) & Macroscopic Transport in Heterogeneous Porous Materials (Lucy Auton)

Lucy Auton & Ellen Luckins
(Mathematical Institute, University of Oxford)
Abstract

Macroscopic Transport in Heterogeneous Porous Materials

Lucy Auton

Solute transport in porous materials is a key physical process in a wide variety of situations, including contaminant transport, filtration, lithium-ion batteries, hydrogeological systems, biofilms, bones and soils. Despite the prevalence of solute transport in porous materials, the effect of microstructure on flow and transport remains poorly understood and improving our understanding of this remains a major challenge.  In this presentation, I consider a two-dimensional microstructure comprising an array of obstacles of smooth but arbitrary shape, the size and spacing of which can vary along the length of the porous medium, allowing for anisotropy.  I use a nontrivial extension to classical homogenisation theory via the method of multiple scales to rigorously upscale the novel problem involving cells of varying area. This results in simple effective continuum equations for macroscale flow and transport where the effect of the microscale geometry on the macroscopic transport and removal is encoded within these simple macroscale equations via effective parameters such as an effective local anisotropic diffusivity and an effective local adsorption rate.  For a simple example geometry I exploit the two degrees of microstructural freedom in this problem, obstacle size and obstacle spacing, to investigate scenarios of uniform porosity but heterogenous microstructure, noting the impact this heterogeneity has on filter efficiency. 

This model constitutes the development of the core framework required to consider other crucial problems such as solute transport within soft porous materials for which there does not currently exist a simple macroscale model where the effective diffusivity and removal depend on the microstructure. Further, via this methodology I will  derive a  bespoke model for fluoride and arsenic removal filters. With this model I will be able to optimise the design of fluoride-removal filters which are being deployed across rural India. The design optimisation will both increase filter lifespan and reduce filter cost, enabling more people to access safe drinking water

 

Averaged interface conditions: evaporation fronts in porous media

Ellen Luckins

Homogenisation methods are powerful tools for deriving effective PDE models for processes incorporating multiple length-scales. For physical systems in which interface processes are crucial to the overall system, we might ask how the microstructure impacts the effective interface conditions, in addition to the PDEs in the bulk. In this talk we derive an effective model for the motion of an evaporation front through porous media, combining homogenisation and boundary layer analysis to derive averaged interface conditions at the evaporation front. Our analysis results in a new effective parameter in the boundary conditions, which encodes how the shape and speed of the porescale evaporating interfaces impact the overall drying process.

Thu, 05 May 2022

12:00 - 13:00
L1

When machine learning deciphers the 'language' of atmospheric air masses

Davide Faranda
(Université Paris Saclay)
Abstract

Latent Dirichlet Allocation (LDA) is capable of analyzing thousands of documents in a short time and highlighting important elements, recurrences and anomalies. It is generally used in linguistics to study natural language: its word analysis reveals the theme(s) of a document, each theme being identified by a specific vocabulary or, more precisely, by a particular statistical distribution of word frequency.
In the climatologists' use of LDA, the document is a daily weather map and the word is a pixel of the map. The theme with its corpus of words can become a cyclone or an anticyclone and, more generally, a 'pattern'  that the scientists term motif. Artificial intelligence – a sort of incredibly fast robot meteorologist – looks for correlations both between different places on the same map, and between successive maps over time. In a sense, it 'notices' that a particular location is often correlated with another location, recurrently throughout the database, and this set of correlated locations constitutes a specific pattern.
The algorithm performs statistical analyses at two distinct levels: at the word or pixel level of the map, LDA defines a motif, by assigning a certain weight to each pixel, and thus defines the shape and position of the motif;  LDA breaks down a daily weather map into all these motifs, each of which is assigned a certain weight.
In concrete terms, the basic data are the daily weather maps between 1948 and nowadays over the North Atlantic basin and Europe. LDA identifies a dozen or so spatially defined motifs, many of which are familiar meteorological patterns such as the Azores High, the Genoa Low or even the Scandinavian Blocking. A small combination of those motifs can then be used to describe all the maps. These motifs and the statistical analyses associated with them allow researchers to study weather phenomena such as extreme events, as well as longer-term climate trends, and possibly to understand their mechanisms in order to better predict them in the future.

The preprint of the study is available as:
 Lucas Fery, Berengere Dubrulle, Berengere Podvin, Flavio Pons, Davide Faranda. Learning a weather dictionary of atmospheric patterns using Latent Dirichlet Allocation. 2021. ⟨hal-03258523⟩ https://hal-enpc.archives-ouvertes.fr/X-DEP-MECA/hal-03258523v1
 

Thu, 28 Apr 2022

12:00 - 13:00
L1

Modeling and Design Optimization for Pleated Membrane Filters

Yixuan Sun & Zhaohe Dai
(Mathematical Institute (University of Oxford))
Abstract

Statics and dynamics of droplets on lubricated surfaces

Zhaohe Dai

The abstract is "Slippery liquid infused porous surfaces are formed by coating surface with a thin layer of oil lubricant. This thin layer prevents other droplets from reaching the solid surface and allows such deposited droplets to move with ultra-low friction, leading to a range of applications. In this talk, we will discuss the static and dynamic behaviour of droplets placed on lubricated surfaces. We will show that the layer thickness and the size of the substrate are key parameters in determining the final equilibrium. However, the evolution towards the equilibrium is extremely slow (on the order of days for typical experimental parameter values). As a result, we suggest that most previous experiments with oil films lubricating smooth substrates are likely to have been in an evolving, albeit slowly evolving, transient state.

 

Modeling and Design Optimization for Pleated Membrane Filters

Yixuan Sun

Membrane filtration is widely used in many applications, ranging from industrial processes to everyday living activities. With growing interest from both industrial and academic sectors in understanding the various types of filtration processes in use, and in improving filter performance, the past few decades have seen significant research activity in this area. Experimental studies can be very valuable, but are expensive and time-consuming, therefore theoretical studies offer potential as a cost-effective and predictive way to improve on current filter designs. In this work, mathematical models, derived from first principles and simplified using asymptotic analysis, are proposed for pleated membrane filters, where the macroscale flow problem of Darcy flow through a pleated porous medium is coupled to the microscale fouling problem of particle transport and deposition within individual pores of the membrane. Asymptotically-simplified models are used to describe and evaluate the membrane performance numerically and filter design optimization problems are formulated and solved for industrially-relevant scenarios. This study demonstrates the potential of such modeling to guide industrial membrane filter design for a range of applications involving purification and separation.

Thu, 10 Mar 2022

12:00 - 13:00
L1

Topological classification and synthesis of neuron morphologies

Kathryn Hess
(École Polytechnique Fédérale de Lausanne (EPFL))
Abstract

Motivated by the desire to automate classification of neuron morphologies, we designed a topological signature, the Topological Morphology Descriptor (TMD),  that assigns a so-called “barcode" to any geometric tree (i.e, any finite binary tree embedded in R^3). We showed that the TMD effectively determines  reliable clusterings of random and neuronal trees. Moreover, using the TMD we performed an objective, stable classification of pyramidal cells in the rat neocortex, based only on the shape of their dendrites.

We have also reverse-engineered the TMD, in order to digitally synthesize dendrites, to compensate for the relatively small number of available biological reconstructions. The algorithm we developed, called Topological Neuron Synthesis (TNS), stochastically generates a geometric tree from a barcode, in a biologically grounded manner. The synthesized neurons are statistically indistinguishable from real neurons of the same type, in terms of morpho-electrical properties and  connectivity. We synthesized networks of structurally altered neurons, revealing principles linking branching properties to the structure of large-scale networks.  We have also successfully applied these classification and synthesis techniques to microglia and astrocytes, two other types of cells that populate the brain.

In this talk I will provide an overview of the TMD and the TNS and then describe the results of our theoretical and computational analysis of their behavior and properties.

This talk is based on work in collaborations led by Lida Kanari at the Blue Brain Project.

 

Thu, 24 Feb 2022

12:00 - 13:00
L1

Axi-symmetric necking versus Treloar-Kearsley instability in a hyperelastic sheet under equibiaxial stretching

Yibin Fu
(Keele University))
Abstract

This is a preparatory study for our ultimate goal of understanding the various instabilities associated with an electrodes-coated dielectric membrane that is subject to mechanical stretching and electric loading. Leaving out electric loading for the moment, we consider bifurcations from the homogeneous solution of a circular or square hyperelastic sheet that is subjected to equibiaxial stretching under either force- or displacement-controlled edge conditions. We derive the condition for axisymmetric necking and show, for the class of strain-energy functions considered, that the critical stretch for necking is greater than the critical stretch for the Treloar-Kearsley (TK) instability and less than the critical stretch for the limiting-point instability. Abaqus simulations are conducted to verify the bifurcation conditions and the expectation that the TK instability should occur first under force control, but when the edge displacement is controlled the TK instability is suppressed, and it is the necking instability that will be observed. It is also demonstrated that axisymmetric necking follows a growth/propagation process typical of all such localization problems.

Thu, 17 Feb 2022

12:00 - 13:00
L1

Connectivity and percolation are two well studied phenomena in random graphs.

Omer Bobrowski
(Technion – Israel Institute of Technology)
Further Information

Omer Bobrowski, an electrical engineer and mathematician, is an Associate Professor in the Viterbi Faculty of Electrical and Computer Engineering at the Technion -

Abstract

Connectivity and percolation are two well studied phenomena in random graphs. 

In this talk we will discuss higher-dimensional analogues of connectivity and percolation that occur in random simplicial complexes.

Simplicial complexes are a natural generalization of graphs that consist of vertices, edges, triangles, tetrahedra, and higher dimensional simplexes.

We will mainly focus on random geometric complexes. These complexes are generated by taking the vertices to be a random point process, and adding simplexes according to their geometric configuration.

Our generalized notions of connectivity and percolation use the language of homology - an algebraic-topological structure representing cycles of different dimensions.

In this talk we will discuss recent results analyzing phase transitions related to these topological phenomena. 

Thu, 10 Feb 2022

12:00 - 13:00
L1

Extracting Autism's Biomarkers in Placenta Using Multiscale Methods

Karamatou A. Yacoubou Djima
(University of Amherst)
Abstract

The placenta is the essential organ of maternal-fetal interactions, where nutrient, oxygen, and waste exchange occur. In recent studies, differences in the morphology of the placental chorionic surface vascular network (PCSVN) have been associated with developmental disorders such as autism. This suggests that the PCSVN could potentially serve as a biomarker for the early diagnosis and treatment of autism. Studying PCSVN features in large cohorts requires a reliable and automated mechanism to extract the vascular networks. In this talk, we present a method for PCSVN extraction. Our algorithm builds upon a directional multiscale mathematical framework based on a combination of shearlets and Laplacian eigenmaps and can isolate vessels with high success in high-contrast images such as those produced in CT scans. 

Thu, 03 Feb 2022

12:00 - 13:00
L1

The role of mechanics in solid tumor growth

Davide Ambrosi
(Politecnico di Torino)
Further Information

I am an applied mathematician interested in revisiting the classical mathematical methods of continuum mechanics to investigate new emerging problems in biology.

Abstract

The experimental evidence of the existence of a feedback between growth and stress in tumors poses challenging questions. First, the rheological properties (the constitutive equations) of aggregates of malignant cells are to identified. Secondly, the feedback law (the "growth law") that relates stress and mitotic and apoptotic rate should be understood. We address these questions on the basis of a theoretical analysis of in vitro experiments that involve the growth of tumor spheroids. We show that solid tumors exhibit several mechanical features of a poroelastic material, where the cellular component behaves like an elastic solid. When the solid component of the spheroid is loaded at the boundary, the cellular aggregate grows up to an asymptotic volume that depends on the exerted compression.
Residual stress shows up when solid tumors are radially cut, highlighting a peculiar tensional pattern.
The features of the mechanobiological system can be explained in terms of a feedback of mechanics on the cell proliferation rate as modulated by the availability of nutrient, that is radially damped by the balance between diffusion and consumption. The volumetric growth profiles and the pattern of residual stress can be theoretically reproduced assuming a dependence of the target stress on the concentration of nutrient which is specific of the malignant tissue.

Thu, 27 Jan 2022

12:00 - 13:00
L1

OCIAM TBC

Luca Tubiana
(University of Trento)
Further Information

Luca Tubiana is Assistant Professor of applied Physics at Università di Trento.

Thu, 20 Jan 2022

12:00 - 13:00
L1

Symmetrically Colored Gaussian Graphical Models with Toric Vanishing Ideals (Jane Coons)

Gillian Grindstaff & Jane Coons
(University of Oxford)
Further Information

Jane Coons is a Supernumerary Teaching Fellow in Mathematics at St John's College. She is a member of OCIAM, and Algebraic Systems Biology research groups. Her research interests are in algebra, geometry and combinatorics, and their applications to statistics and biology.

 

Giliian Grindstaff is a post-doc working in the area of geometric and topological data analysis at the MI.

Abstract

Symmetrically Colored Gaussian Graphical Models with Toric Vanishing Ideals

Jane Coons

Gaussian graphical models are multivariate Gaussian statistical models in which a graph encodes conditional independence relations among the random variables. Adding colors to this graph allows us to describe situations where some entries in the concentration matrices in the model are assumed to be equal. In this talk, we focus on RCOP models, in which this coloring is obtained from the orbits of a subgroup of the automorphism group of the underlying graph. We show that when the underlying block graph is a one-clique-sum of complete graphs, the Zariski closure of the set of concentration matrices of an RCOP model on this graph is a toric variety. We also give a Markov basis for the vanishing ideal of this variety in these cases.

 

Topological persistence for multi-scale terrain profiling and feature detection in drylands hydrology

Gillian Grindstaff

With the growing availability of remote sensing products and computational resources, an increasing amount of landscape data is available, and with it, increasing demand for automated feature detection and useful morphological summaries. Topological data analysis, and in particular, persistent homology, has been applied successfully to detect landslides and characterize soil pores, but its application to hydrology is currently still limited. We demonstrate how persistent homology of a real-valued function on a two-dimensional domain can be used to summarize critical points and shape in a landscape simultaneously across all scales, and how that data can be used to automatically detect features of hydrological interest, such as: experimental conditions in a rainfall simulator, boundary conditions of landscape evolution models, and earthen berms and stock ponds, placed historically to alter natural runoff patterns in the American southwest.

Thu, 02 Dec 2021

12:00 - 13:00
L3

Mechanical instabilities in slender structures

Davide Riccobelli
(Polytechnic University of Milan)
Further Information

Davide Riccobelli is a researcher in Mathematical Physics at the MOX Laboratory, Dipartimento di Matematica
Politecnico di Milano. His research interests are in the field of Solid Mechanics. He is interested in the mathematical and physical modelling of biological tissues and soft active materials. You can read his work here.

Abstract

 In this talk, we show some recent results related to the study of mechanical instabilities in slender structures. First, we propose a model of metamaterial sheets inspired by the pellicle of Euglenids, unicellular organisms capable of swimming due to their ability of changing their shape. These structures are composed of interlocking elastic rods which can freely slide along their edges. We characterize the kinematics and the mechanics of these structures using the special Cosserat theory of rods and by assuming axisymmetric deformations of the tubular assembly. We also characterize the mechanics of a single elastic beam constrained to smoothly slide along a rigid support, where the distance between the rod midline and the constraint is fixed and finite. In the presence of a straight support, the rod can deform into shapes exhibiting helices and perversions, namely transition zones connecting together two helices with opposite chirality.

Finally, we develop a mathematical model of damaged axons based on the theory of continuum mechanics and nonlinear elasticity. In several pathological conditions, such as coronavirus infections, multiple sclerosis, Alzheimer's and Parkinson's diseases, the physiological shape of axons is altered and a periodic sequence of bulges appears. The axon is described as a cylinder composed of an inner passive part, called axoplasm, and an outer active cortex, composed mainly of F-actin and able to contract thanks to myosin-II motors. Through a linear stability analysis, we show that, as the shear modulus of the axoplasm diminishes due to the disruption of the cytoskeleton, the active contraction of the cortex makes the cylindrical configuration unstable to axisymmetric perturbations, leading to a beading pattern.

Thu, 25 Nov 2021

12:00 - 13:00
L3

Comparison of mathematical models by representation as simplicial complexes

Sean Vittadello
(University of Melbourne)
Further Information

Sean Vittadello joined the Theoretical Systems Biology Group at The University of Melbourne as a Postdoctoral Research Fellow in April 2020. His research interests are broadly in the study of biological systems with mathematics, using both analytical and algebraic techniques.

Abstract

The complexity of biological systems necessitates that we develop mathematical models to further our understanding of these systems. Mathematical models of these systems are generally based on heterogeneous sets of experimental data, resulting in a seemingly heterogeneous collection of models that ostensibly represent the same system. To understand the system, and to reveal underlying design principles, we therefore need to understand how the different models are related to each other with a view to obtaining a unified mathematical description. This goal is complicated by the number of distinct mathematical formalisms that may be employed to represent the same system, making direct comparison of the models very difficult. In this talk I will discuss two general methodologies, namely comparison by distance and comparison by equivalence, that allow us to compare model structures in a systematic way by representing models as labelled simplicial complexes. The distance can be obtained either directly from the simplicial complexes, or from the persistence intervals obtained by employing persistent homology with a flat filtration. Model equivalence is used to determine the conceptual similarity of models and can be automated by using group actions on the simplicial complexes. We apply our methodology for model comparison to demonstrate a particular equivalence between a positional-information model and a Turing-pattern model from developmental biology, which constitutes a novel observation for two classes of models that were previously regarded as unrelated. We also discuss an alternative framework for model comparison by representing models as groups, which allows for the application of group-theoretic techniques within our model comparison methodology.

Thu, 18 Nov 2021

12:00 - 13:00
L3

IAM Seminar (TBC)

Hélène de Maleprade
(Sorbonne Jean Le Rond d’Alembert Lab)
Further Information

Hélène de Maleprade is maîtresse de conférence (assistant professor) at Sorbonne Université, in the Institut Jean Le Rond ∂'Alembert, in Paris. Her research focus is now on the swimming of micro-organisms in complex environments inspired by pollution, using soft matter.

You can read her work here.

Abstract

Microscopic green algae show great diversity in structural complexity, and successfully evolved efficient swimming strategies at low Reynolds numbers. Gonium is one of the simplest multicellular algae, with only 16 cells arranged in a flat plate. If the swimming of unicellular organisms, like Chlamydomonas, is nowadays widely studied, it is less clear how a colony made of independent Chlamydomonas-like cells performs coordinated motion. This simple algae is therefore a key organism to model the evolution from single-celled to multicellular locomotion.

In the absence of central communication, how can each cell adapt its individual photoresponse to efficiently reorient the whole algae? How crucial is the distinctive Gonium squared structure?

In this talk, I will present experiments investigating the shape and the phototactic swimming of Gonium, using trajectory tracking and micro-pipette techniques. I will explain our model linking the individual flagella response to the colony trajectory. This eventually emphasises the importance of biological noise for efficient swimming.

Fri, 12 Nov 2021

15:00 - 16:00
Virtual

Stable ranks for data analysis

Professor Martina Scolamiero
(KTH Royal Institute of Technology)
Abstract

Hierarchical stabilisation, allows us to define topological invariants for data starting from metrics to compare persistence modules. In this talk I will highlight the variety of metrics that can be constructed in an axiomatic way, via so called Noise Systems. The focus will then be on one invariant obtained through hierarchical stabilisation, the Stable Rank, which the TDA group at KTH has been studying in the last years. In particular I will address the problem of using this invariant on noisy and heterogeneous data. Lastly, I will illustrate the use of stable ranks on real data within a project on microglia morphology description, in collaboration with S. Siegert’s group, K. Hess and L. Kanari. 

Thu, 11 Nov 2021

12:00 - 13:00
L3

(Timms) Simplified battery models via homogenisation

Travis Thompson & Robert Timms
(University of Oxford)
Further Information

Travis Thompson and Robert Timms are both OCIAM members. Travis is a post-doc working with Professor Alain Goriely in the Mathematics & Mechanics of Brain Trauma group. Robert Timms is a post-doc whose research focuses on the Mathematical Modelling of Batteries.

Abstract

 Mathematics for the mind: network dynamical systems for neurodegenerative disease pathology

Travis Thompson

Can mathematics understand neurodegenerative diseases?  The modern medical perspective on neurological diseases has evolved, slowly, since the 20th century but recent breakthroughs in medical imaging have quickly transformed medicine into a quantitative science.  Today, mathematical modeling and scientific computing allow us to go farther than observation alone.  With the help of  computing, experimental and data-informed mathematical models are leading to new clinical insights into how neurodegenerative diseases, such as Alzheimer's disease, may develop in the human brain.  In this talk, I will overview my work in the construction, analysis and solution of data and clinically-driven mathematical models related to AD pathology.  We will see that mathematical modeling and scientific computing are indeed indispensible for cultivating a data-informed understanding of the brain, AD and for developing potential treatments.

 

___________________________________________________________________________________________________

Simplified battery models via homogenisation  

Robert Timms

Lithium-ion batteries (LIBs) are one of the most popular forms of energy storage for many modern devices, with applications ranging from portable electronics to electric vehicles. Improving both the performance and lifetime of LIBs by design changes that increase capacity, reduce losses and delay degradation effects is a key engineering challenge. Mathematical modelling is an invaluable tool for tackling this challenge: accurate and efficient models play a key role in the design, management, and safe operation of batteries. Models of batteries span many length scales, ranging from atomistic models that may be used to predict the rate of diffusion of lithium within the active material particles that make up the electrodes, right through to models that describe the behaviour of the thousands of cells that make up a battery pack in an electric vehicle. Homogenisation can be used to “bridge the gap” between these disparate length scales, and allows us to develop computationally efficient models suitable for optimising cell design.

Thu, 04 Nov 2021

12:00 - 13:00
L3

Active Matter and Transport in Living Cells

Mike Shelley
(Courant Institute of Mathematical Sciences)
Further Information
Mike Shelley is Lilian and George Lyttle Professor of Applied Mathematics & Professor of Mathematics, Neural Science, and Mechanical Engineering, and Co-Director of the Applied Mathematics Laboratory. He is also Director of the Center for Computational Biology, and Group Leader of Biophysical ModelingThe Flatiron Institute, Simons Foundation
Abstract

The organized movement of intracellular material is part of the functioning of cells and the development of organisms. These flows can arise from the action of molecular machines on the flexible, and often transitory, scaffoldings of the cell. Understanding phenomena in this realm has necessitated the development of new simulation tools, and of new coarse-grained mathematical models to analyze and simulate. In that context, I'll discuss how a symmetry-breaking "swirling" instability of a motor-laden cytoskeleton may be an important part of the development of an oocyte, modeling active material in the spindle, and what models of active, immersed polymers tell us about chromatin dynamics in the nucleus.

Thu, 28 Oct 2021

12:00 - 13:00
L3

Active Matter and Transport in Living Cells

Camille Duprat
(LadHyX Ecole Polytechnique)
Further Information

Camille is mostly interested in problems involving the coupling of capillary-driven and low Reynolds number flows and elastic structures, especially from an experimental point of view.

Publications can be found here

Abstract

The organized movement of intracellular material is part of the functioning of cells and the development of organisms. These flows can arise from the action of molecular machines on the flexible, and often transitory, scaffoldings of the cell. Understanding phenomena in this realm has necessitated the development of new simulation tools, and of new coarse-grained mathematical models to analyze and simulate. In that context, I'll discuss how a symmetry-breaking "swirling" instability of a motor-laden cytoskeleton may be an important part of the development of an oocyte, modeling active material in the spindle, and what models of active, immersed polymers tell us about chromatin dynamics in the nucleus.

Thu, 21 Oct 2021

12:00 - 13:00
L3

Knotting in proteins and other open curves

Eric Rawdon
(University of St. Thomas)
Further Information

Eric Rawdon is a Professor in Mathematics & Data Analytics at the University of St. Thomas, Minnesota.

Research interests

Physical knot theory

Publications

Please see google scholar

Abstract

Some proteins (in their folded form) are classified as being knotted.

The function of the knotting is mysterious since knotting seemingly

would make the folding process unnecessarily complicated.  To

function, proteins need to fold quickly and reproducibly, and

misfolding can have catastrophic results.  For example, Mad Cow

disease and the human analog, Creutzfeldt-Jakob disease, come from

misfolded proteins.

 

Traditionally, knotting is only defined for closed curves, where the

topology is trapped in the loop.  However, proteins have free ends, as

well as most of the objects that humans consider as being knotted

(like shoelaces and strings of lights).  Defining knotting in open

curves is tricky and ambiguous.  We consider some definitions of

knotting in open curves and see how one of these definitions is used

to characterize the knotting in proteins.

Thu, 14 Oct 2021

12:00 - 13:00
L5

Dynamics Problems Discovered Off The Beaten Research Path

Oliver O'Reilly
((UC Berkeley))
Further Information

Oliver M. O’Reilly is a professor in the Department of Mechanical Engineering and Interim Vice Provost for Undergraduate Education at the University of California at Berkeley. 

Research interests:

Dynamics, Vibrations, Continuum Mechanics

Key publications:

To view a list of Professor O’Reilly’s publications, please visit the Dynamics Lab website.

Abstract

In this talk, I will discuss a wide range of mechanical systems,
including Hoberman’s sphere, Euler’s disk, a sliding cylinder, the
Dynabee, BB-8, and Littlewood’s hoop, and the research they inspired.
Studies of the dynamics of the cylinder ultimately led to a startup
company while studying Euler’s disk led to sponsored research with a
well-known motorcycle company.


This talk is primarily based on research performed with a number of
former students over the past three decades. including Prithvi Akella,
Antonio Bronars, Christopher Daily-Diamond, Evan Hemingway, Theresa
Honein, Patrick Kessler, Nathaniel Goldberg, Christine Gregg, Alyssa
Novelia, and Peter Varadi over the past three decades.

Thu, 17 Jun 2021

13:00 - 14:00
Virtual

Modulation of synchronization in neural networks by a slowly varying ionic current

Sue Ann Campbell
(University of Waterloo)
Further Information

Synchronized activity of neurons is important for many aspects of brain function. Synchronization is affected by both network-level parameters, such as connectivity between neurons, and neuron-level parameters, such as firing rate. Many of these parameters are not static but may vary slowly in time. In this talk we focus on neuron-level parameters. Our work centres on the neurotransmitter acetylcholine, which has been shown to modulate the firing properties of several types of neurons through its affect on potassium currents such as the muscarine-sensitive M-current.  In the brain, levels of acetylcholine change with activity.  For example, acetylcholine is higher during waking and REM sleep and lower during slow wave sleep. We will show how the M-current affects the bifurcation structure of a generic conductance-based neural model and how this determines synchronization properties of the model.  We then use phase-model analysis to study the effect of a slowly varying M-current on synchronization.  This is joint work with Victoria Booth, Xueying Wang and Isam Al-Darbasah.

Abstract

Synchronized activity of neurons is important for many aspects of brain function. Synchronization is affected by both network-level parameters, such as connectivity between neurons, and neuron-level parameters, such as firing rate. Many of these parameters are not static but may vary slowly in time. In this talk we focus on neuron-level parameters. Our work centres on the neurotransmitter acetylcholine, which has been shown to modulate the firing properties of several types of neurons through its affect on potassium currents such as the muscarine-sensitive M-current.  In the brain, levels of acetylcholine change with activity.  For example, acetylcholine is higher during waking and REM sleep and lower during slow wave sleep. We will show how the M-current affects the bifurcation structure of a generic conductance-based neural model and how this determines synchronization properties of the model.  We then use phase-model analysis to study the effect of a slowly varying M-current on synchronization.  This is joint work with Victoria Booth, Xueying Wang and Isam Al-Darbasah