ICMS

PDEs in kinetic theories: kinetic description of biological models

Nov 08, 2010 - Nov 12, 2010

15 South College Street, Edinburgh EH8 9AA

Organisers

Name	Institution
Bournaveas, Nikolaos	University of Edinburgh
Carrillo, José A	ICREA & Universitat Autònoma de Barcelona
Jin, Shi	University of Wisconsin
Markowich, Peter	University of Cambridge
Tadmor, Eitan	University of Maryland

 

This workshop is a satellite event of the semester on Kinetic PDEs at the Isaac Newton Institute.

This event is co-sponsored by KAUST.

Kinetic equations occur naturally in the modelling of the collective motion of large individual particle ensembles such as molecules in rarefied gases, beads in granular materials, charged particles in semiconductors and plasmas, dust in the atmosphere, cells in biology, or the behaviour of individuals in economical trading. They include several classical equations of mathematical physics: the Boltzmann equation of rarified gas dynamics, the fermionic and bosonic Boltzmann equations and the relativistic Vlasov-Maxwell system of particle physics, the quantistic Wigner-Poisson system, to name just a few.

The workshop will bring together leading researchers to review the recent developments in research on mathematical modelling, analysis, numerical schemes and simulation of kinetic models in Biology.

Arrangements

Participation
Participation in this workshop is by invitation only.  If you have a enquiry about participation please email Audrey Brown who will contact the Organisers on your behalf.

Venue
The venue for this INI satellite workshop will be ICMS, 15 South College Street, Edinburgh, EH8 9AA, (see this link and the 'Travel' section below for directions).  All lectures will be held in the Newhaven Lecture Theatre. To view this room and a list of the visual equipment available click here. In addition, two blackboards have recently been installed and a PC outputting to a high definition projector and audio system.

Wireless Access
The workshop venue, 15 South College Street, has wireless access throughout. On arrival at Registration you will be given instructions and a code for accessing the wireless network.  For those without laptops, there will also be a couple of computers available for you to check your emails.

UK Visas
If you are travelling from overseas you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and if so how to apply for one.

Travel
Information about international travel to the UK and Edinburgh is available here.   You may also find this map and this link useful for the workshop.  The map shows the workshop venue and other city centre landmarks. 

A taxi directly from the airport will cost approximately 15.00 - 20.00 GBP to the city centre for a one-way journey. There is also a bus service from the airport to the city centre.

Within the city, Lothian buses charge £1.20 for a single, £3.00 for a day ticket. Please note that the exact fare is required and no change is given.

If travelling by train, please note that Edinburgh has two railway stations - Waverley Railway Station being the main station and closest to the workshop venue at 15 South College Street. If you alight at Edinburgh Waverley, the workshop venue is an easy 10 minute walk over North and South Bridge map. The second railway station is called Haymarket and is at the West End of the city centre.

Travel Insurance
Please note that it is your responsibility to have adequate travel insurance to cover medical and other emergencies that may occur on your trip.

Accommodation
ICMS has arranged en-suite rooms in accommodation nearby for those who requested this. Accommodation is typically no more than 5-10 minutes walk from the workshop venue.

North British Differential Equations Seminar (NBDES)
On Tuesday 9 November the workshop will combine briefly with NBDES for a talk by Eitan Tadmor (University of Maryland) entitled “Linear PDEs in critical regularity spaces: hierarchical construction of their nonlinear solutions”.  There will be a brief pause in the workshop Programme between 14.50 and 15.00 to allow the NBDES visitors to be seated in the lecture theatre for the start of the talk at 15.00. 

Catering
Refreshments will be provided during the coffee breaks for the duration of the event.  A light lunch will be provided on Tuesday 9 November only.  On all other days participants are free to explore the many cafés, sandwich shops and restaurants nearby.  On Wednesday 10 November there will be a workshop dinner at the Magnum Restaurant, 1 Albany Street, Edinburgh, EH1 3PY.   All participants are welcome to attend free of charge.   

Financial Matters
For all 'invited participants' the workshop funding will cover the cost of bed and breakfast accommodation and refreshments during the coffee breaks for the duration of the workshop, lunch on Tuesday only, and a workshop dinner at the Magnum Restaurant on Wednesday evening.  

If it has been agreed that the INI will reimburse some of your travel costs, this will have been advised in your 'final information' email.  An INI expenses claim form will be issued at Registration and should be returned directly to the INI.  

 

Programme

Monday 8 November 2010

09.00 - 09.30	Registration and coffee
09.30 - 10.20	Pierre Degond (Université de Toulouse & CNRS) Modelling self-organization in complex systems  pdf of presentation
10.20 - 11.10	Mohammed Lemou (IRMAR, CNRS & Univestité Rennes 1) Non linear stability of gravitational systems
11.10 - 11.40	Coffee/tea in Chapterhouse (ground floor)
11.40 - 12.30	Raffaele Esposito (Università dell'Aquila) Stability and instability of equilibria in a Vlasov-Boltzman binary mixture undergoing a phase transition pdf of presentation
12.30 - 14.00	Lunch break
14.00 - 14.50	Rosanna Marra (Università di Roma Tor Vergata) Hydrodynamic limits for the Boltzmann equation in some slightly compressible cases
14.50 - 15.40	Sebastien Motsch (University of Maryland) Mathematical modelling of animal displacements: from microscopic to macroscopic description
15.40 - 16.10	Coffee/tea in Chapterhouse, (ground floor)
16.10 - 17.00	José Alfredo Cañizo (Universitat Autònoma de Barcelona) Estimates and exponential convergence to equilibrium for the growth-fragmentation equation  pdf of presentation

Tuesday 9 November 2010

09.30 - 10.20	José A Carrillo (Universitat Autònoma de Barcelona) Kinetic models for swarming: mean-field limit and qualitative properties pdf of presentation
10.20 - 11.10	Benoit Perthame (Université Pierre et Marie Curie) Kinetic models of chemotaxis and traveling bands   Kinetic models for swarming: mean-field limit and qualitative properties pdf of presentation
11.10 - 11.40	Coffee/tea in Chapterhouse (ground floor)
11.40 - 12.30	Timothy Pedley (University of Cambridge) Collective behaviour of swimming micro-organisms
12.30 - 14.00	Lunch provided in the Chapterhouse (ground floor)
14.00 - 14.50	Massimo Fornasier (RICAM)   Particle systems and kinetic equations modelling interacting agents in high-dimension
14.50 - 15.00	Short pause in Programme to allow NBDES guests to be seated.
15.00 - 15.50	North British Differential Equations Seminar (NBDES) Eitan Tadmor (University of Maryland) Linear PDEs in critical regularity spaces: hierarchical construction of their nonlinear solutions    pdf of abstract
15.50 - 16.20	Coffee/tea in Chapterhouse, (ground floor)
16.20 - 17.10	Jorge Zubelli (Instituto Nacional de Matemática Pura e Aplicada) Structured population models: direct and inverse problems  pdf of presentation

 

Wednesday 10 November 2010

09.30 - 10.20	Adrien Blanchet (Université de Toulouse) Asymptotics for the critical mass Keller-Segel model   pdf of presentation
10.20 - 11.10	Zhongyi Huang (Tsinghua University) Bloch decomposition based method for waves in periodic media pdf of presentation
11.10 - 11.40	Coffee/tea in Chapterhouse (ground floor)
11.40 - 12.30	Klemens Fellner (University of Cambridge) Aggregation-pattern in non-local evolution equation pdf of presentation
12.30 - 14.00	Lunch break
14.00 - 14.50	Piotr Gwiazda (University of Warsaw) Split-up algorithm in the metric space for the equations of structured population dynamics
14.50 - 15.40	Clement Mouhot (University of Cambridge) A new quantitative method for the mean-field limit
15.40 - 16.10	Coffee/tea in Chapterhouse, (ground floor)
16.10 - 17.00	Francesco Salvarani (Università degli Studi di Pavia) Modelling gas flows in the lower pulmonary airways pdf of presentation
19.00	Workshop dinner at Magnum Restaurant, 1 Albany Street (dress informal)

 

Thursday 11 November 2010

09.30 - 10.20	Thierry Paul (CNRS & CMLS, École Polytechnique) Semiclassical methods with rough potentials
10.20 - 11.10	Laurent Desvillettes (École Normale Supérieure de Cachan) Infinite-dimensional reaction-diffusion equations, modelling and analysis pdf of presentation
11.10 - 11.40	Coffee/tea in Chapterhouse (ground floor)
11.40 - 12.30	Alexander Lorz (University of Cambridge) Dirac concentration in a multidimensional nonlocal parabolic equation
12.30 - 14.00	Lunch break
14.00 - 14.50	Athanasios Tzavaras (University of Crete) Kinetic models for dilute suspensions of rigid rods  pdf of presentation
14.50 - 15.40	Clemens Heitzinger (University of Cambridge) Homogenization and related topics for transport in nano-structures  pdf of presentation
15.40 - 16.10	Coffee/tea in Chapterhouse (ground floor)
16.10 - 17.00	Armando Majorana (Università degli Studi di Catania) A deterministic numerical model for the nonlinear Boltzmann equation pdf of presentation

 

Friday 12 November 2010

09.30 - 10.20	Pierre-Emmanuel Jabin (University of Nice) Dynamics of toxic algae in the mediterranean pdf of presentation
10.20 - 11.10	Kevin Painter (Heriot-Watt University) Amoeboid and mesenchymal migration of cells in the extracellular matrix
11.10 - 11.40	Coffee/tea in Chapterhouse (ground floor)
11.40 - 12.30	Anne Nouri (CMI, Université de Provence) Well-posedness of a diffusive gyrokinetic model
12.30	Close of workshop

 

Presentations:

Presentation Details
Blanchet, Adrien
Asymptotics for the critical mass Keller-Segel model
View Abstract Hide Abstract
We investigate the long time behaviour of the critical mass Patlak-Keller-Segel equation. This equation has a one parameter family of steady-state solutions $rhohls$, $lambda>0$, with thick tails whose second moment is not bounded. We show that these steady state solutions are stable, and find basins of attraction for them using an entropy functional coming from the critical fast diffusion equation in $R^2$. We construct solutions of Patlak-Keller-Segel equation satisfying an entropy-entropy dissipation inequality. While the entropy dissipation is strictly positive, it turns out to be a difference of two terms, neither of which need to be small when the dissipation is small. We introduce a strategy of {em controlled concentration} to deal with this issue, and then use the regularity obtained from the entropy-entropy dissipation inequality to prove the existence of basins of attraction for each stationary state composed by certain initial data converging towards $rhohls$. In the present paper, we do not provide any estimate of the rate of convergence, but we discuss how this would result from a stability result for a certain sharp Gagliardo-Nirenberg-Sobolev inequality.
Cañizo, José Alfredo
Estimates and exponential convergence to equilibrium for the growth-fragmentation equation
View Abstract Hide Abstract
We consider a model for cellular or polymer growth, a linear equation for the size distribution of the population. The entropy method may be applied to this model, and we show that once we obtain precise estimates on both the solution and the conserved quantity, one can prove through an entropy-entropy dissipation inequality that relaxation to equilibrium is exponentially fast for a wide range of fragmentation coefficients.
Carrillo, José A
Kinetic models for swarming: mean-field limit and qualitative properties
View Abstract Hide Abstract
I will discuss the mean-field limit for a general kinetic model of swarming including attraction, repulsion and reorientation effects with and without noise. Some qualitative properties of the solution will be discussed in particular instances such as the Cucker-Smale model.
Degond, Pierre
Modelling self-organization in complex systems
View Abstract Hide Abstract
Complex systems are systems of mutually interacting agents which exhibit large scale coordinated structures. This self-organization capability emerges spontaneously as a product of the interaction rules between the agents and is only possible through the build-up of statistical correlations. We will provide a certain number of examples where this feature may - or may not - be detrimental to the validity of kinetic and fluid models. We will also discuss how these self-organization capabilities can be encoded into macroscopic models.
Desvillettes, Laurent
Infinite-dimensional reaction-diffusion equations, modelling and analysis
View Abstract Hide Abstract
We present a few examples of population dynamics models leading to a class of equations having features belonging to both kinetic equations and reaction-diffusion equations: we call those equations "infinite-dimensional reaction-diffusion". We also present some of the mathematical properties of those equations.
Esposito, Raffaele
Stability and instability of equilibria in a Vlasov-Boltzman binary mixture undergoing a phase transition
View Abstract Hide Abstract
I present a two-fluids kinetic model, with repulsive interaction between different species, described by a couple of Vlasov-Boltzmann equations, which exhibits a segregation phase transitions below a critical temperature. I give an overview of some recent stability and instability results on the real line for this and related model and discuss the extension to a large finite interval.
Fellner, Klemens
Aggregation-pattern in non-local evolution equation
View Abstract Hide Abstract
We study non-local evolution equations for a density of individuals, which interact through a given symmetric potential. Such models appear in many applications such as swarming and flocking, opinion formation, inelastic materials, .... In particular, we are interested in interaction potentials, which behave locally repulsive, but aggregating over large scales. A particular example for such potentials was recently given in models of the alignment of the directions of filaments in the cytoskeleton.
Fornasier, Massimo
Particle systems and kinetic equations modelling interacting agents in high-dimension
View Abstract Hide Abstract
Particle systems and kinetic equations classically model problems from physics, where the states are defined in terms of space, velocity, and time parameters. When such models are addressed to more complex interacting agents, such as the collective action of animals, cells, human individuals, then 3+3+1 parameters might not be sufficient to describe the single individual. For instance, we may think of the financial market as a situation where every player is characterized by the portfolio of investments, with a possible large number of choices/parameters, and the behavior depends on the interaction with the other players. Unfortunately presently we do not dispose of accurate and efficient numerical techniques to approximate solutions of these systems because of the "curse of dimensionality" for which standard approximations depend exponentially on the dimension. For specific systems for which the interaction between the agents depend on the mutual distance, for instance by means of suitable functions of the adjacency matrix, we show that we can utilize Johnson-Lindenstrauss embeddings to simulate high-dimensional particle systems by random projections to lower dimension. We also show how this technique can be extended to describe solutions of kinetic equations in high dimension.
Gwiazda, Piotr
Split-up algorithm in the metric space for the equations of structured population dynamics
View Abstract Hide Abstract
As the example of the structured population equations we mean the equation of so-called age-structured model (transport equation in a half space with non-local boundary conditions) or size structured model (transport equation with an integral term in space on the right hand side), see for more details B. Perthame "Transport equations in mathematical biology" 2007. From the biological reason there is a need for using initial data in the space of Radon measures. Using the Lipschitz-bounded distance (flat metric) we prove Lipschitz dependence of the solutions to linear and nonlinear system w.r.t. initial data and coefficients of equations. Significant simplifications of the calculations is done by using the split-up algorithm, dealing separately with a semigroup of transport and a semigroup of an integral kernel operator. The talk is based on the joint research with Jose Carillo, Rinaldo Colombo, Anna Marciniak-Czochra and Agnieszka Ulikowska.
Heitzinger, Clemens
Homogenization and related topics for transport in nano-structures
View Abstract Hide Abstract
We present results for the mathematical modelling of nanotechnological field-effect sensors. First, we show how a homogenization problem for the electrostatics in these structures can be solved to find an effective equation with two jump conditions. Based on this homogenized equation, an existence and uniqueness (around equilibrium) result and estimates for the solution of a 3d self-consistent charge-transport model are given. This model has been implemented as a parallelized 3d simulator that can simulate realistic structures. In order to investigate noise in nanostructures, we present a homogenization result for a stochastic elliptic PDE that yields an effective equation for the (co-)variance and a scaling law. Finally, we present the derivation of a transport equation for 3d structures that are confined in one or two dimensions from the Boltzmann transport equation. Examples for these structures are nanowires, ion channels, etc. In the case of confinement in two directions (which corresponds to tubes) we find a diffusive transport equation. A crucial feature of this equation is that we can give explicit expressions for the transport coefficients as functions of the parabolic confinement potential. Computationally, this means that we have reduced the six-dimensional problem to a 2d diffusion-type equation. Entropy estimates are also given. Numerical simulation results are presented for all the models as well, as are comparisons to experimental data (field-effect biosensors, ion channels) where available.
Huang, Zhongyi
Bloch decomposition based method for waves in periodic media
View Abstract Hide Abstract
In this talk, we introduce the Bloch decomposition based time splitting spectral method to conduct numerical simulations of the (non)linear dispersive wave equations in periodic media. In particular we discuss three-dimensional simulations for Bose-Einstein condensates in the superfluid regime with different potentials.
Jabin, Pierre-Emmanuel
Dynamics of toxic algae in the Mediterranean
View Abstract Hide Abstract
We present a first modelling approach for the populations of Ostreopsis ovata in the Mediterranean sea. Those are unicellular microalgae that are developing during the summer months and present significant health and economic problems because of their toxicity. Their behaviour is quite complex (a dispersed phase in the sea, reproduction phase on a biological film at the bottom), making the modelling delicate.
Lemou, Mohammed
Non linear stability of gravitational systems
View Abstract Hide Abstract
The gravitational Vlasov Poisson system a canonical model in astrophysics to describe the dynamics of galactic clusters. A well known conjecture is the stability of all spherical steady state models which are non-increasing functions of their microscopic total energy. This conjecture was proved at the linear level by several authors in the continuation of the breakthrough work by Antonov in 1961. In a previous work, we derived the stability of anisotropic models under spherically symmetric perturbations using fundamental monotonicity properties of the Hamiltonian under suitable generalized symmetric rearrangements first observed in the physics literature. In this work, we show how this approach combined with a new generalized Antonov-Poincaré type inequality implies the orbital stability of spherical models under general perturbations. Some extensions of this approach to other systems will also be discussed.
Lorz, Alexander
Dirac concentration in a multidimensional nonlocal parabolic equation
View Abstract Hide Abstract
Nonlocal Lotka-Volterra models have the property that solutions concentrate as Dirac masses in the limit of small diffusion. Is it possible to describe the dynamics of the concentration points and of the mass of the Dirac? We will explain how this relates to the so-called 'constrained Hamilton-Jacobi equation' and how numerical simulations can exhibit unexpected dynamics well explained by this equation. Our motivation comes from 'populational adaptive evolution' a branch of mathematical ecology which models the darwinian evolution. (Joint work with S. Mirrahimi and B. Perthame, both at LJLL, Paris VI)
Majorana, Armando
A deterministic numerical model for the nonlinear Boltzmann equation
View Abstract Hide Abstract
We propose a new deterministic numerical scheme, based on the discontinuous Galerkin method, for solving the Boltzamnn equation for rarefied gases. The new scheme guarantees the conservation of the mass, momentum and energy. We avoid any stochastic procedures in the treatment of the collision operator of the Boltzmamn equation.
Marra, Rosanna
Hydrodynamic limits for the Boltzmann equation in some slightly compressible cases
View Abstract Hide Abstract
We consider various hydrodynamic diffusive limits for the Boltzmann equation which brings to limiting equations showing slightly compressible effects. One example is the so called ghost effect. One of the main tools is a new spectral inequality for a perturbation of the linearized Boltzmann operator.
Motsch, Sebastien
Mathematical modelling of animal displacements: from microscopic to macroscopic description
View Abstract Hide Abstract
The modelling of animal displacements can occur at two different scales. Some models describe the trajectories of each individual (“microscopic” scale), other models describe the dynamics of the all group using “macroscopic” quantities (density, flux...). The kinetic theory enables to link the two approaches, it allows to move from one description to the other. As a first example, we study a new model for fish displacement based on experimental data called "Persistent Turning Walker" model (PTW). The originality of the PTW model relies in the use of the curvature to describe the displacement of the fish. We prove that the PTW model becomes a diffusion equation at a macroscopic scale. Then we study the so-called Vicsek model. In this model, each individual tends to align his velocity with his neighbors. In this dynamics, the total momentum is not preserved which makes the derivation of a macroscopic model more tricky. We manage to overcome this issue using a new notion of generalized collisional invariant. We obtain at large scales a new type of hyperbolic system. But due to its non-classical form, the numerical simulations of the macroscopic model are very challenging.
Mouhot, Clement
A new quantitative method for the mean-field limit
View Abstract Hide Abstract
We present a recent work with Stephane Mischler about a new method for estimating in a quantitative way the propagation of chaos for many-particle Markov processes. It is based a consistency-stability viewpoints in an abstract functional framework. Main outcome is a proof of uniform in time chaos propagation for Kac's model of Boltzmann collision process for hard spheres.
Nouri, Anne
Well-posedness of a diffusive gyrokinetic model
View Abstract Hide Abstract
This is a joint work with Maxime Hauray, LATP, Aix-Marseille University. We study a finite Larmor radius model used to describe the ions distribution function in the core of a tokamak plasma, that consists in a gyro-kinetic transport equation coupled with an electro-neutrality equation. Since the last equation does not provide enough regularity on the electric potential, we introduce a simple linear collision operator adapted to the finite Larmor radius approximation. We next study the two-dimensional dynamics in the direction perpendicular to the magnetic field. Thanks to the smoothing effects of the collision and the gyro-average operators, we prove the global existence of solutions, as well as short time uniqueness and stability.
Painter, Kevin
Amoeboid and mesenchymal migration of cells in the extracellular matrix
View Abstract Hide Abstract
The extracellular matrix (ECM) is a highly organised structure with the capacity to direct cell migration through their tendency to follow matrix fibres, a process known as contact guidance. In this talk I will describe a number of transport models that describe different forms of cell migration within the ECM. Through direct numerical simulation, we will explore how a combination of contact guidance and remodelling of the ECM by cells can organise migrating cell populations into distinctive spatial arrangements. These results will be discussed in the context of a simple model for tumour invasion, where it is shown that the interactions between invading cells and the ECM structure surrounding the tumour can have a profound impact on the pattern and rate of cell infiltration.
Paul, Thierry
Semiclassical methods with rough potentials
View Abstract Hide Abstract
We will present some new results concerning semiclassical methods for linear and non-linear partial differential equations with rough potentials. We will consider, mostly in the formalism of the Wigner function, results in weak and strong topologies.
Pedley, Timothy
Collective behaviour of swimming micro-organisms
View Abstract Hide Abstract
Suspensions of swimming micro-organisms exhibit a rich variety of collective behaviour, such as the bioconvection patterns seen for suspensions of upswimming cells that are denser than their surroundings, or the time-varying coherent structures seen in dense suspensions of swimming bacteria. Here we investigate the fluid dynamic mechanisms underlying these patterns, by means of (1) a continuum model for dilute suspensions, (2) hydrodynamic interactions between pairs of model micro-organisms, and (3) simulations and models for non-dilute suspensions. The talk will conclude with recent observations of ‘dancing’ algae.
Perthame, Benoit
Kinetic models of chemotaxis and travelling bands
View Abstract Hide Abstract
Kinetic models of chemotaxis have been used since the 80s, based on experimental observation or the run and tumble movement of bacteria. They are useful to include informations at the individual levels into macroscopic models as the famous Keller-Segel system. We will explain how some microscopic behaviour of E. coli give diffusion limits that sustain robust travelling bands.
Salvarani, Francesco
Modelling gas flows in the lower pulmonary airways
View Abstract Hide Abstract
We consider the problem of modelling the air flow in the lower respiratory airways (generations 15 to 23). Here, the gas behaviour is mainly diffusive, since the global velocity of the air is almost zero. The air being a multicomponent gaseous mixture, the correct setting for modelling the phenomenon, at a macroscopic level, is given by the Maxwell-Stefan diffusion equations: indeed, as we will show in the first part of the talk, the Maxwell-Stefan equations are the natural hydrodynamical limit of the Boltzmann equation for a mixture of gases. In the second part of the talk, after focusing on the main differences of the Maxwell-Stefan model with the Fickian diffusion, we study the equations governing a three-component gas mixture (like the air). We provide a qualitative and quantitative mathematical analysis of the model. We finally show some numerical simulations, pointing out the uphill diffusion phenomenon.
Tadmor, Eitan
Linear PDEs in critical regularity spaces: hierarchical construction of their nonlinear solutions
View Abstract Hide Abstract
Download the pdf file of this abstract
Tzavaras, Athanasios
Kinetic models for dilute suspensions of rigid rods
View Abstract Hide Abstract
I will present some results on modelling, and mathematical analysis for the Doi model for dilute suspensions of rigid rods. For the problem of sedimenting rods under the influence of gravity we discuss (i) the instability of the quiescent flow and (ii) the derivation of the collective response in the diffusive regime described by the Keller-Segel model.
Zubelli, Jorge
Structured population models: direct and inverse problems
View Abstract Hide Abstract
Structured population models in biology lead to integro-differential equations that describe the evolution in time of the population density taking into account a given feature such as the age, the size, or the volume. These models possess interesting analytic properties and have been used extensively in a number of areas. After giving an introduction to this subject, we will discuss the inverse problem. In this part, we consider a size-structured model for cell division and address the question of determining the division (birth) rate from the measured stable size distribution of the population. We formulate such question as an inverse problem for an integro-differential equation posed on the half line. We develop firstly a regular dependency theory for the solution in terms of the coefficients and, secondly, a regularization technique for tackling this inverse problem which takes into account the specific nature of the equation. Our results rely also on generalized relative entropy estimates and related Poincare inequalities. This second part is joint work with Benoit Perthame (UPMC, Paris) and Marie Doumic (ENS and INRIA, Paris). Finally, if time allows, we will discuss novel applications to stem cell modelling. In this part we study different mathematical aspects of a continuous model of stem cell developments. This is joint work with Anna Marciniak (Heidelberg), Benoit Perthame (UPMC, Paris), and Marie Doumic (INRIA, Paris).

Participants

Name	Institution
Blanchet, Adrien	Université de Toulouse
Bournaveas, Nikolaos	University of Edinburgh
Cañizo, José Alfredo	Universitat Autònoma de Barcelona
Carrillo, José A	ICREA & Universitat Autònoma de Barcelona
Chiarcos, Olga	Springer-Verlag GmbH
Crouseilles, Nicolas	INRIA
Degond, Pierre	Université de Toulouse & CNRS
Desvillettes, Laurent	École Normale Supérieure de Cachan
Dong, Xuanchun	National University of Singapore
Esposito, Raffaele	Università dell'Aquila
Fedotov, Sergei	University of Manchester
Fellner, Klemens	University of Cambridge
Fornasier, Massimo	RICAM
Gwiazda, Piotr	University of Warsaw
Heitzinger, Clemens	University of Cambridge
Hua, Jiale	Institut de Mathématiques de Toulouse
Huang, Zhongyi	Tsinghua University
Jabin, Pierre-Emmanuel	University of Nice
Lemou, Mohammed	IRMAR, CNRS & Univestité Rennes 1
Leroy-Lerêtre, Mathieu	Université de Toulouse & CNRS
Lorz, Alexander	University of Cambridge
Majorana, Armando	Università degli Studi di Catania
Markowich, Peter	University of Cambridge
Marra, Rosanna	Universita' di Roma Tor Vergata
Martin, Stephan	Technische Universität Kaiserslautern
Motsch, Sebastien	University of Maryland (CSCAMM)
Mouhot, Clement	University of Cambridge
Nouri, Anne	CMI, Université de Provence
Painter, Kevin	Heriot-Watt University
Paul, Thierry	École Polytechnique
Pedley, Timothy	University of Cambridge
Perthame, Benoit	Université Pierre et Marie Curie
Salvarani, Francesco	Università degli Studi di Pavia
Tadmor, Eitan	University of Maryland
Tzavaras, Athanasios	University of Crete
Vecil, Francesco	Universitat de Valencia
Watson, Stephen	University of Glasgow
Yang, Xiongfeng	Shanghai Jiao Tong University
Zubelli, Jorge	Instituto Nacional de Matemática Pura e Aplicada