ICMS

Kinetic and Mean-field models in the Socio-Economic Sciences

Jul 27, 2009 - Jul 31, 2009

e-Science Centre, 15 South College Street, Edinburgh

Organisers

Name	Institution
Burger, Martin	Westfälische Wilhelms-Universität Münster
Carrillo, José A	ICREA & Universitat Autònoma de Barcelona
Di Francesco, Marco	University of L'Aquila
Markowich, Peter	University of Cambridge

 

Mean-field and kinetic equations in socio-economic applications are approaches of strongly increasing importance and high potential for future quantitative research. These techniques relate well to the nowadays wide-spread agent-based models, several approaches have been developed to coarse-grain the agent-based description. The coarse-graining itself is already a mathematically challenging topic, which requires modern and partly still to be developed techniques, and there are further open and challenging questions to be answered for the resulting mean-field and kinetic equations (structure of solutions, analysis of model properties, numerical solution, asymptotic limits, optimal control / design, …). This workshop will be mostly focused in particular on the following recently developed topics:

• Models for opinion formation: Microscopic models of both social and political phenomena describing collective behaviours and self-organization in a society framed within the methodologies of statistical mechanics. Description of opinion formation by mean-field PDEs of diffusive type. Models derived by coarse-graining microscopic interaction models based on Brownian agents.
• Models for human crowds: Microscopic models for local and nonlocal interaction, panic models, pedestrian flow in presence of a target.
• Models using conservation laws, saturated diffusion, eikonal-type coupling.
• Models for financial markets: Differential games, models with transition rates, Brownian agents, models with heterogeneity of agents (traders) and their interaction in the modelling, coarse-grained to mean-field or kinetic PDEs (or systems thereof). Implications of heterogeneous agents on asset pricing and optimal portfolio management.
• Models for wealth distribution analysis: Pareto type models, kinetic models of an open market economy. Boltzmann-type and Fokker-Planck type models.

 

Arrangements

Venue
The workshop will be held at 15 South College Street, Edinburgh. 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. Follow this link for a map showing the location of 15 South College Street, or this map may also prove useful.

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.

Travel
Information about travel to the UK and Edinburgh is available here.

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.

Accommodation
ICMS will arrange accommodation for participants who require it. Participants are also free to make their own arrangements. A list of Edinburgh accommodation of various sorts and prices can be found on the Accommodation Page on the ICMS web site. Section 4 is particularly relevant. July is busy in Edinburgh and early booking is recommended.

Meals and Refreshments
Buffet lunches will be provided on Monday 27 July and Friday 31 July only. For the remainder of the days, participants are free to go out for lunch and explore the many cafes, restaurants, sandwich shops and bars in the surrounding area. On arrival we will provide you with a ‘welcome’ pack which will contain information about eating places nearby.

Morning and afternoon refreshments will be provided throughout the workshop.

There will be an informal wine reception at 14 India Street, on Monday 27 July as well as an informal supper at Nargile on Tuesday 28 July.

The workshop dinner will take place at Blonde on the evening of Wednesday 29 July.

Computer access
At Registration you will be issued with a password for the wireless network at 15 South College Street. If you wish to use a computer while in 15 South College Street please ask a member of the ICMS staff.

Registration
Registration will take place on Monday 27 July in the Chapterhouse on the ground floor of 15 South College Street.

Financial Arrangements
Unless otherwise specified in your invitation letter, the workshop grant will cover the cost of your bed and breakfast accommodation, tea/coffee throughout the workshop, lunch on Monday and Friday only, the wine reception, the informal supper on Tuesday and the Workshop Dinner on Wednesday evening.

If we have agreed to pay some of your travel costs, you will be informed by email. Reimbursement will take place after the workshop and will involve payment directly into your bank account. At Registration you will be given an expenses claim form and this should be submitted to ICMS, with original receipts. It would be helpful if you could bring your bank details to the workshop. In addition to the bank account number, participants from the USA and Canada will require their bank’s routing number, those from the UK will be asked for the bank sort code, and those from Europe and the rest of the world, their IBAN and SWIFT/BIC code. We cannot reimburse any item without a signed claim form and original receipts.

Programme

Provisional programme - subject to change

Monday 27 July 2009

08.30 - 09.30	Registration Ground Floor, 15 South College Street
09.30 - 10.15	Dirk Helbing (ETH Zurich) A kinetic approach to Game Theory: from opinions to norms
10.15 - 11.00	Michel Rascle (University of Nice) pdf Nonlinear waves and oscillations in mathematical models of traffic flow
11.00-11.25	Coffee break
11.25 - 11.50	Olivier Guéant (Université Paris-Dauphine) A reference case for mean field games
11.50 - 12.15	Maria Pia Gualdani (The University Of Texas at Austin) Global existence of a free boundary problem with non-standard sources
12.15 - 12.40	Jan Pietschmann (University of Cambridge) pdf On a parabolic free boundary problem modeling price formation
12.40 - 14.45	Buffet lunch, Chapterhouse, Ground Floor, 15 South College Street
14.45 - 15.30	Eli Ben Naim (Los Alamos National Laboratory) pdf Bifurcations and patterns in opinion dynamics
15.30-15.55	Richard Tsai (The University Of Texas at Austin) Efficient solutions for a class of inverse source problems in domains with obstacles
15.55 - 17.00	Coffee break and discussion
18.00 - 19.30	Wine Reception, 14 India Street, Edinburgh

Tuesday 28 July 2009

09.15 - 10.00	Andrea Bertozzi (University of California, Los Angeles) Mathematical modelling of crime
10.00 - 10.45	Bikas Chakrabahrti (Saha Institute of Nuclear Physics) pdf Kinetic models for markets and their microeconomic foundations
10.45 - 11.15	Coffee break
11.15 - 11.40	Jian Guo Liu (Duke University) A simple proof of Cucker-Smale flocking dynamics and the mean field limit
11.40 - 12.05	Daniel Matthes (Vienna University of Technology) Distribution of wealth in market economies - a kinetic approach
12.05 - 12.30	Martin Short (University of California, Los Angeles) Modelling the formation and dynamics of crime hotspots
12.30 - 14.45	Lunch
14.45 - 15.30	Barbara Niethammer (University of Oxford) Dynamics and self-similarity in min-driven clustering
15.30-15.55	Maria Rita D'Orsogna (CSUN) Patterns, stability and collapse for interacting agents
15.55 - 16.10	Coffee break
16.10 - 16.35	José Cañizo (Universitat Autònoma de Barcelona) pdf Well-posedness in a space of measures of kinetic models for collective motion
16.35 - 17.00	Jesus Rosado (Universitat Autònoma de Barcelona) A refined result of flocking for the Cucker-Smale model
18.30	15 South College Street closes
19.00	Informal meal at Nargile, Hanover Street, Edinburgh

Wednesday 29 July 2009

09.15 - 10.00	Giuseppe Toscani (University of Pavia) A kinetic approach to the formation of wealth distribution curves
10.00 - 10.45	Lorenzo Pareschi (University of Ferrara) Kinetic modelling of financial markets
10.45 - 11.15	Coffee break
11.15 - 11.40	Stephane Cordier (Université d'Orleans) pdf Mesoscopic modelling of financial markets
11.40 - 12.05	Bertram Düring (Vienna University of Technology) pdf Kinetic modelling of opinion leadership
12.05 - 12.30	Francesco Salvarani (Universita' degli Studi di Pavia) A kinetic approach to the study of opinion formation
12.30 - 14.45	Lunch
14.45 - 15.30	Michael Grinfeld (University of Strathclyde) pdf Locating the threshold in Bak-Sneppen type models
15.30-15.55	Corrado Lattanzio (Università degli Studi dell'Aquila) pdf Flocking and synchronization of particle models
15.55 - 17.00	Coffee break and discussion
18.30	15 South College Street closes
19.00	Workshop Dinner, Blonde, Edinburgh

Thursday 30 July 2009

09.15- 10.00	Ansgar Jeungel (Vienna University of Technology) pdf Cross-diffusion models in biology
10.00 - 10.45	Charlotte Hemelrijk (University of Groningen) Simple local interactions explain complex aerial displays of thousands of starlings
10.45 - 11.15	Coffee break
11.15 - 11.40	Klemens Fellner (Université d'Orleans) pdf On non-local interaction equations
11.40 - 12.05	Bärbel Schlake (University of Munster) pdf Nonlinear cross diffusion models for crowds
12.05 - 12.30	Adrien Blanchet (Université de Toulouse) Regular and singular points in the parabolic obstacle problem and application to American options
12.30 - 14.00	Buffet lunch, Chapterhouse, Ground Floor, 15 South College Street
14.00 - 17.30	Knowledge Transfer networking event
14.00 - 14.55	David Simmons (Benfield Group) Modelling with Limited Loss Data in the Reinsurance Industry
14.55 - 15.50	Darren Unwin (Heriot-Watt University) Using game theory to engage stakeholders and develop catchment flood risk management plans
15.50 - 16.30	Coffee and discussions

Friday 31 July 2009

9.00 - 9.45	Ingenuin Gasser (University of Hamburg) pdf On a Model for a Solar Updraft Tower
09.45 - 10.15	Mariko Arisawa (University of Cambridge) Stochastic volatility model with jumps - viscosity solution’s approach
10.15 - 10.40	Marie Therese Wolfram (University of Cambridge) Ion channels and beyond
10.40 - 11.15	Coffee break
11.15 - 11.40	Alethea Barbaro (University of California, Los Angeles) pdf Fish migration, interacting particles, and scaling laws
11.40 - 12.05	Massimo Fornasier (RICAM) pdf Kinetic models for flocking
12.05 - 12.20	Peter Markowich (University of Cambridge) tba
12.20	Close of workshop. 15 South College Street will close at 13.30.

Presentations:

Presentation Details
Arisawa, Mariko
Stochastic volatility model with jumps - viscosity solution’s approach
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We are interested in the stochastic volatility model in the option pricing, with the jump-diffusion and the pure jump underlying processes. These processes are ergodic, and have the mean-reverting property. To compare with the constant volatility case (classical B-S model), an asymptotic analysis with respect to the rate of mean-reversion was proposed by Fouque, Papanicolau and Sircar, for the diffusion-based stochastic volatility model. We present a homogenization technique for the integro-differential equation with L´evy operators, infinitesmal generator of the jump processes, to study the asymptotic analysis for the present case, the volatility model with jumps.
Barbaro, Alethea
Fish migration, interacting particles, and scaling laws
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We present a model for fish migration which uses a discrete interacting particle model coupled to environmental data. We show that this model is able to reproduce and predict migration routes for the Icelandic capelin. We also derive and discuss the scaling which one needs to consider when working with such a model.
Ben Naim, Eli
Bifurcations and patterns in opinion dynamics
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A widely-used opinion dynamics model, the compromise process, will be introduced and analysed using pattern formation and scaling methods. Overall, the phenomenology associated with this simple stochastic process is surprisingly realistic. In the compromise process, two agents may interact and reach consensus, and additionally, individual agents may spontaneously change their opinions by a random, diffusive process. There are three distinct scenarios. For strong diffusion, the distribution of opinions is uniform and no political organizations (parties) are formed. For weak diffusion, parties do form and furthermore, the political landscape continually evolves as small parties merge into larger ones. Without diffusion, a pattern develops: parties have the same size and they possess equal niches.
Bertozzi, Andrea
Mathematical modelling of crime
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I will give a talk about recent work at UCLA on modelling of crime, including pattern formation (hot spots), statistical density estimation from data, and social networks.
Blanchet, Adrien
Regular and singular points in the parabolic obstacle problem and application to American options
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To follow
Cañizo, José Alfredo
Well-posedness in a space of measures of kinetic models for collective motion
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There has been a recent interest in models for the complex behaviour of large groups of animals, such as flocks of birds, swarms, or schools of fish. Kinetic equations, which involve the time evolution of the distribution function of individuals depending on their position and velocity, are tentative models for these phenomena, and raise many interesting mathematical questions. In this work, we give a well-posedness theory for kinetic PDE models for the collective behaviour of a group of individuals that interact through a pair potential and/or try to adapt their velocity to the average velocity of their neighbours, possibly including also self-propulsion effects. The aim is to give a solid mathematical basis for the study of these models and the range of phenomena they display.
Chakrabarti, Bikas
Kinetic models for markets and their microeconomic foundations
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Increasingly, a huge amount of statistics have been gathered which clearly indicates that income and wealth distributions in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas in equilibrium, deviating both in the low income and more significantly for the high income ranges. Application of kinetic exchange models have already provided illuminating ideas and understanding, complementing the observations. We have also develop recently a framework based on microeconomic theory from which such ideal gas like market models can be addressed. Intend to discuss that as well.
Cordier, Stephane
Mesoscopic modelling of financial markets
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In this talk, we present a mesoscopic description of the behaviour of a simple financial market where the agents can create their own portfolio between two investment alternatives: a stock and a bond. The model is derived starting from the Levy-Levy-Solomon microscopic model using the methods of kinetic theory and consists of a linear Boltzmann equation for the wealth distribution of the agents coupled with an equation for the price of the stock. From this model, under a suitable scaling, we derive a Fokker-Planck equation and show that the equation admits a self-similar lognormal behaviour. Numerical examples will be shown.
D'Orsogna, Maria Rita
Patterns, stability and collapse for interacting agents
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Interacting agents such as members of a biological community, or as a team of man-made robots, often assemble into self-organized, coherent, leader-free structures. In this talk we study the properties of a collection of swarming agents, relating individual characteristics to collective behaviours. In particular, we investigate a non-linear system of self-propelled discrete individuals that interact via pairwise attractive and repulsive potentials. We are able to predict distinct aggregation morphologies, such as flocks, vortices and double mills. By utilizing statistical mechanics tools, we can also relate the interaction potential to the collapsing or dispersing behaviour of aggregates as the number of constituents increases. We also discuss passage to the continuum and derive both the hydrodynamic equations and the related kinetic description starting from the initial discrete system.
Düring, Bertram
Kinetic modelling of opinion leadership
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We propose a kinetic model for opinion formation in the presence of strong opinion leaders. Our approach is based on an opinion formation model introduced in Toscani (2006) and borrows ideas from the kinetic theory of mixtures of rarefied gases. Starting from microscopic interactions among individuals, we arrive at a macroscopic description of the opinion formation process which is characterized by a system of Fokker-Planck type equations. We discuss the steady states of this system and present numerical results.
Fellner, Klemens
On non-local interaction equations
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We study non-local evolution equations for a density of individuals, which interact through a given symmetric potential. In particular, we are interested in interaction potentials, which behave locally repulsive, but confining on large scales. We present results on the structure and stability of steady states, which may or may not be probability measures depending on the regularity of the repulsion.
Fornasier, Massimo
Kinetic models for flocking
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In this talk we introduce and analyse a continuous version of the flocking model of Cucker and Smale, which describes the state of a population of birds. Within the same idea that a bird adjusts its velocity towards the average of neighbours' velocities, we construct a spatially dependent Boltzmann-type equation which describes the behaviour of the flock in terms of a density f =f(x,v,t). The large-time behaviour of f is subsequently studied by means of mass transportation techniques. A continuous analogue of the theorems of Cucker and Smale which ensures convergence to a "compact flock" is shown to hold for the solution. Several modifications are also presented as well as numerical examples. (The results presented in this talk are a joint work with José Carrillo, Jesus Rosado, and Giuseppe Toscani)
Gasser, Ingenuin
On a model for a solar updraft tower
Grinfeld, Michael
Locating the threshold in Bak-Sneppen type models
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In this talk I will describe the main features of the classical Bak-Sneppen model of evolution and its simpler asymmetric version. I will show a construction that makes it possible to bring methods of denumerable Markov chains to bear on this problem. In particular, I will show how to derive non-trivial lower bounds for the threshold very easily, and I will give a plausibility argument why the value of the threshold in such modes is rational. (Joint work with P Knight, Strathclyde)
Gualdani, Maria Pia
Global existence of a free boundary problem with non-standard sources
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We consider a nonlinear free boundary problem, proposed by J M Lasry and P L Lions in 2006 in the framework of mean field games. The model describes the evolution of a scalar price which is realized as a free boundary of a diffusion equation with evolving sources. The talk focuses on global existence, uniqueness and regularity of solutions. The proof uses tools from non-interacting stochastic particle systems and multiscale analysis. Joint work with L Chayes, M d M Gonzalez and I Kim.
Guéant, Olivier
A reference case for mean field games
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The paper aims at presenting the Lasry-Lions' theory of mean field games in an archetypal example. This example deals with population distribution in space or in more complex spaces. The mean field games PDEs happen to have explicit solutions. Two notions of stability are introduced. Eductive stability is shown to be a powerful tool to solve forward/backward systems of PDEs. Numerical recipes may be given. (Paper in JMPA - Journal de Mathématiques Pures et Appliquées)
Helbing, Dirk
A kinetic approach to Game Theory: from opinions to norms
Hemelrijk, Charlotte
Simple local interactions explain complex aerial displays of thousands of starlings
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Aerial displays of starlings (Sturnus vulgaris) at their communal roosts are complex: they consist of multiple flocks of thousands of individuals which are continually changing shape and density, while splitting and merging. To understand these complex displays both empirical data and models are needed. Whereas detailed empirical data were recently collected of flocks of thousands of starlings, there are as yet no models that generate these complex patterns. Numerous computer models in biology, however, suggest that patterns of single groups of moving animals may emerge by self-organisation from movement and local coordination (through attraction, alignment and avoidance of collision). In this talk we show that, to generate in a model most of the empirical patterns measured in real starlings, we have to extend the usual rules of local coordination with a few specifics of starling behaviour, namely 1) their aerial locomotion, 2) a low and constant number of interaction-partners and 3) preferential movement above a ‘roosting area’. Our model provides new hypotheses about the mechanisms underlying these displays and of swarming patterns in biological systems in general.
Juengel, Ansgar
Cross-diffusion models in biology
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In the seventies, Shigesada et al. proposed a generalization of the Lotka-Volterra differential equations to model spatial segregation of interacting population species. Segregation comes from the cross-diffusion terms present in the evolution equations. Since the diffusion matrix is generally neither symmetric nor positive definite, an existence theory is far from being trivial. In this talk, we present global existence results for the population model obtained in collaboration with Li Chen. The main ideas of the analysis are "symmetrising" variable transformations and the use of entropy techniques. Related cross-diffusion systems arising in chemotaxis and tumour growth modelling are also mentioned.
Lattanzio, Corrado
Flocking and synchronization of particle models
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We present a multi-dimensional flocking model rigorously derived from a vector oscillatory chain model, and study the connection between the Cucker-Smale flocking model and the Kuramoto synchronization model appearing in the statistical mechanics of nonlinear oscillators. We provide an alternative direct approach for frequency synchronization to the Kuramoto model as an application of flocking estimate for the Cucker-Smale model. (Joint work with Seung-Yeal Ha, Seoul National University, Bruno Rubino, University of L'Aquila, and Marshall Slemrod, University of Wisconsin-Madison)
Liu, Jian Guo
A simple proof of Cucker-Smale flocking dynamics and the mean field limit
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Flocking, a universal phenomenon, has found applications in many areas ranging from animal herding to swarming of insects, to opinion formation, cultural dissemination or crowd behaviour. Flocking refers to autonomous agents reaching a consensus by self-propelling and limited environmental information. Felipe Cucker and Steve Smale postulated a model for flocking of birds and showed convergence to consensus (the same velocity) exponentially. In this talk, I will show a simple proof of the flocking behavior for the Cucker-Smale system based on a construction of Lyapunov function. A simple phase plane analysis provides a unified condition on the initial states in which the convergence to consensus will occur. For large agent systems and their mean field limit, we give a uniform bound on the velocity field. This enable us to show the stability of measure valued solutions in bounded Lipschitz distance, hence the convergence of large agent systems to the unique measure valued solution of a Vlasov type equation (mean field limit). We also gave a convergence analysis and error estimate for the particle method (PIC) of the underlined Vlasov type equation. (Joint work with S Ha)
Matthes, Daniel
Distribution of wealth in market economies - a kinetic approach
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Kinetic equations model the redistribution of energy and momentum in an ensemble of particles due to binary collisions. The Boltzmann equation, where the collisions are taken literally, i.e., particles interact according to the laws of classical mechanics, provides one possible interpretation. Recently, various alternative interpretations have become popular. In this talk, we are concerned with the econophysics approach, where particles are thought of as interacting agents in a closed economy, the particle energy is identified with an agent's wealth, and the binary "collisions" are trades, in which wealth is exchanged according to certain laws, which obviously differ from those of classical mechanics. In particular, some randomness is involved, which corresponds to gains or losses due to risky investments. I intend to provide an overview on the recently obtained analytical results: existence and uniqueness of transient and stationary solutions, the creation of Pareto tails and the phenomenon of wealth condensation, the regularity of solutions and their equilibration behaviour. (Joint work with Giuseppe Toscani, University of Pavia, Italy and Bertram Duering, Vienna University of Technology, Austria)
Niethammer, Barbara
Dynamics and self-similarity in min-driven clustering
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We study a mean-field model for a clustering process that may be described informally as follows. At each step a random integer k is chosen with probability p_k, and the smallest cluster merges with k randomly chosen clusters. We prove that the model determines a continuous dynamical system on the space of probability measures and we establish necessary and sufficient conditions for approach to self-similar form.
Pareschi, Lorenzo
Kinetic modelling of financial markets
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In this talk we introduce a kinetic description of a financial market composed of interacting agents.
Pietschmann, Jan F
On a parabolic free boundary problem modelling price formation
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We discuss existence and uniqueness of solutions for a one dimensional parabolic evolution equation with a free boundary. This problem was introduced by J-M Lasry and P-L Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in.time-extension of the local solution which is intimately connected to the regularity of the free boundary. We also present numerical result.
Rascle, Michel
Nonlinear waves and oscillations in mathematical models of traffic flow
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I will talk about traffic flow modelling, which is a (nice) canonical toy problem, simple enough (in particular, it is obviously 1D), yet rich enough to be fun ... I will first describe a few discrete models 'Follow the Leader', which in most of the cases contain two parts: a "convective" part, which involves the difference of velocities with the previous car, and a relaxation part, e.g. Bando's model, which adapts (more slowly) the speed to the local traffic density. I will then discuss the corresponding macroscopic versions, and recent works to try to combine the corresponding macroscopic versions of these two parts, and in particular how much instability should be included in the relaxation part to describe oscillations (stop and go waves) experimentally observed in real traffic, without producing crazy things, like negative velocities or crashes, thanks to the hyperbolic part. In particular, I will explain the relations between variants of the well known "Intelligent Driver Model" of Helbing-Treiber and the class of (second order) mathematical models introduced several years ago by Aw and myself.
Rosado, Jesus
A refined result of flocking for the Cucker-Smale model
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I will present and analyse the asymptotic behaviour of solutions of the continuous kinetic version of flocking by Cucker and Smale, which describes the collective behaviour of an ensemble of organisms, animals or devices. This kinetic version introduced by Ha and Tadmor is obtained from a particle model. The large-time behaviour of the distribution in phase space is subsequently studied by means of particle approximations and a stability property in distances between measures. A continuous analogue of the theorems of Cucker and Smale will be shown to hold for the solutions on the kinetic model. More precisely, the solutions concentrate exponentially fast their velocity to their mean while in space they will converge towards a translational flocking solution. (The presentation is based on a work in collaboration with J A Carrillo, M Fornasier, and G Toscani)
Salvarani, Francesco
A kinetic approach to the study of opinion formation
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In this talk we show a strategy, based on the methods of nonequilibrium statistical mechanics, in order to derive a model describing some mechanisms of opinion formation. After proving the main mathematical properties of the model, we provide some numerical results.
Schlake, Bärbel
Nonlinear cross diffusion models for crowds
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Subject of this talk is the mathematical modelling of diffusing particles with size exclusion. Motion can be described in terms of stochastic and partial differential equations. Treatment of finite size of the particles is of utmost importance for many applications such as human crowds, swarming, chemotaxis and ion channels. We introduce an effective model for crowded particles based on stochastic approaches and derive a system of nonlinear cross diffusion equations. We investigate the transient problem, which is a gradient flow with doubly degenerate diffusivity for an appropriate entropy functional. Equilibria can be characterised as entropy-minima and are linear stable. We highlight some non-standard structure of these equations and discuss some issues related to their analysis.
Short, Martin
Modelling the formation and dynamics of crime hotspots
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Using the known criminological phenomena of repeat and near-repeat victimization, we develop an agent-based model of residential burglary. Simulations of this model produce crime hotspots, as seen in the real world. We then derive a hydrodynamic limit of this model, arriving at a coupled set of partial differential equations that generically resemble those of a reaction-diffusion system. Analysis of these equations indicates that hotspot formation may be due to a linear instability of the model. Furthermore, examining the possible bifurcations of this system reveals the presence of hysteresis, which may have a strong influence on the effectiveness of hotspot policing.
Simmons, David
Modelling with limited loss data in the Reinsurance Industry
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A common problem for the reinsurance industry is a lack of homogeneous data to use. We are often looking at catastrophic events, by definition rare. Traditional actuarial loss data based methods cannot apply. Increasingly catastrophe models have been built and used, but (as per an earlier seminar) these models are to an extent black boxes and almost certainly underestimate the uncertainty within their damage estimates. So the problem: we have more than one model and limited loss data. How can we use the data and models we have (with credibility estimates) to arrive at our best guess OEP or AEP curve across all probability ranges?
Toscani, Giuseppe
A kinetic approach to the formation of wealth distribution curves
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Kinetic market models have been proposed recently to account for the redistribution of wealth in simple market economies. These models allow to develop a qualitative theory, which is based on methods borrowed from the kinetic theory of rarefied gases. The aim of this lecture is to present a unifying approach to the study of the evolution of wealth in the large-time regime.
Tsai, Richard
Efficient solutions for a class of inverse source problems in domains with obstacles
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We consider a class of inverse source problems in the context of robotic applications. Contamination is spreading in a complex domain by either Poisson or the heat equation with a few but unknown number of point sources. Measurements are taken depending on the robot's location. We shall present our algorithms for efficiently solving the inverse source problems assuming the presence of noise, and for determining where measurements should be taken so that the point sources can be identified with just a few measurements.
Unwin, Darren
Using Game Theory to engage stakeholders and develop catchment flood risk management plans
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The presentation will report on the initial phases of the research undertaken at Heriot-Watt University which forms a key part of the transnational Interreg IVB project, Strategic Alliance for Integrated Water Management Actions (SAWA). The research presented focuses onapplying Game Theory techniques to analyse and inform the selection processes used when deploying adaptive flood risk management measures. In addition to considering competing flood risk management measures, the approach adopted looks to capture data (numerical and descriptive) relating to the nature of the measure (type and dimension) and stakeholder benefits (economic and intangible). Specifically, the research will attempt to define how benefits can be evaluated, and how these benefits will be used to highlight the 'choices' made by different stakeholders involved in producing and implementing Catchment Flood Risk Management Plans. The methodologies presented show a significant desire of the project members to move beyond the 'traditional' approaches of cataloguing a series of numeric case study data-sets or managing simple/relational databases. To focus much more on capturing qualitative and quantitative data related to "strategies and experiences", and produce an output which has an impact outside SAWA.
Wolfram, Marie Therese

Participants

Name	Institution
Arisawa, Mariko	University of Cambridge
Barbaro, Alethea	University of California, Los Angeles
Ben Naim, Eli	Los Alamos National Laboratory
Bertozzi, Andrea	University of California Los Angeles
Blanchet, Adrien	Université de Toulouse
Burger, Martin	Westfälische Wilhelms-Universität Münster
Cañizo, José Alfredo	Universitat Autònoma de Barcelona
Carrillo, José A	ICREA & Universitat Autònoma de Barcelona
Chakrabarti, Bikas	Saha Institute of Nuclear Physics
Cordier, Stephane	Université d'Orleans
D'Orsogna, Maria Rita	CSUN
Di Francesco, Marco	University of L'Aquila
Düring, Bertram	Vienna University of Technology
Fellner, Klemens	University of Cambridge
Fornasier, Massimo	RICAM
Franek, Marzena	University of Munster
Gasser, Ingenuin	University of Hamburg
Grinfeld, Michael	University of Strathclyde
Gualdani, Maria Pia	University Of Texas at Austin
Guéant, Olivier	Université Paris-Dauphine
Helbing, Dirk	ETH Zurich
Hemelrijk, Charlotte	University of Groningen
Juengel, Ansgar	Vienna University of Technology
Lattanzio, Corrado	Università degli Studi dell'Aquila
Liu, Jian Guo	Duke University
Maldarella, Dario	University of Ferrara
Markowich, Peter	University of Cambridge
Matthes, Daniel	Vienna University of Technology
Maurizi, Amelio	University of L'Aquila
Niethammer, Barbara	University of Bonn
Pareschi, Lorenzo	University of Ferrara
Pietschmann, Jan F	University of Cambridge
Rascle, Michel	University of Nice
Rosado, Jesus	Universitat Autònoma de Barcelona
Salvarani, Francesco	Università degli Studi di Pavia
Schlake, Bärbel	University of Munster
Short, Martin	University of California, Los Angeles
Simmons, David	Benfield Group
Toscani, Giuseppe	University of Pavia
Tsai, Richard	The University of Texas at Austin
Unwin, Darren	Heriot-Watt University
Wolfram, Marie Therese	University of Cambridge