A poster session will be held during the workshop. If you want to participate, send an email to Giambattista Giacomin (giambattista.giacomin.AT.univ-paris-diderot.fr) with a tentative title.
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Luisa Andreis and Daniele Tovazzi (Università di Padova)
Coexistence of stable limit cycles in a generalized Curie-Weiss model with dissipation
See the abstract.
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Manon Baudel (University Orléans)
Spectral theory for random Poincaré maps
See the abstract.
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Daniela Bertacchi (Università Milano Bicocca) and Fabio Zucca (Politecnico di Milano)
The timing of life history events in the presence of soft disturbances
We study a model for the evolutionarily stable strategy (ESS) used by biological populations for choosing the time of life-history events, such as arrival from migration and breeding. In our model we account for both intra-species competition (early individuals have a competitive advantage) and a disturbance which strikes at a random time, killing a fraction $1-p$ of the population. Disturbances include spells of bad weather, such as freezing or heavily raining days. It has been shown by Iwasa and Levin 1995, that when $p=0$, then the ESS is a mixed strategy (individuals choose their arrival date in an interval of possible dates, according to a certain probability distribution). In this case, individuals wait for a certain time and afterwards they start arriving (or breeding) every day. We prove that if 0<p<1 the ESS is still a mixed choice of times, however with respect to the case of hard disturbance, a new phenomenon arises: if competition is sufficiently strong, the waiting time disappears and a fraction of the population arrives at the earliest day possible, while the rest will arrive throughout the whole period during which the disturbance may occur. We study the behaviour of the ESS and of the average fitness of the population, depending on the parameters involved. We also investigate how a population, which does not rapidly adapt, is affected by climate change. In particular, the changes which are in act can reduce the average fitness of population and endanger species which still follow the old strategy.
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Joe P. Chen (Colgate University)
Strong shape theorems in cellular automata models on fractal graphs
We consider four types of cellular automata models---internal diffusion-limited aggregation (IDLA), rotor-router aggregation, divisible sandpiles, and abelian sandpiles---on self-similar fractal graphs, the Sierpinski gasket (SG) being the prime example. Our motivation is to address the conjecture that the limit shapes in all four models coincide regardless of the state space (but this is far from proven).
It turns out that on SG, when launching particles from a fixed corner vertex, the cluster in each of the four models always fills balls (in the graph metric), albeit at (slightly) rates and exhibiting (much) different orders of fluctuations. We show precisely the growth rates and the orders of fluctuations; most of them are proved (as of this workshop) and some others are conjectures supported by strong numerical evidence. While the geometric structure of SG is somewhat special, we think that some of the proof techniques are flexible enough to work on other state spaces.
This presentation covers joint works with Wilfried Huss (TU Graz), Ecaterina Sava-Huss (TU Graz), Alexander Teplyaev (UConn), and Jonah Kudler-Flam (Colgate).
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Perla El Kettani (Univ. Paris Sud)
The stochastic mass conserved Allen-Cahn equation with nonlinear diffusion
See the abstract.
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Jannes Quer (ZIB, Berlin)
An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates
In this poster we propose an adaptive importance sampling scheme for dynamical quantities of high dimensional complex systems which are metastable. The main idea of this poster is to combine a method coming from Molecular Dynamics Simulation, Metadynamics, with a theorem from stochastic analysis, Girsanov’s theorem. The proposed algorithm has two advantages compared to a standard estimator of dynamic quantities: firstly, it is possible to produce estimators with a lower variance and, secondly, we can speed up the sampling. One of the main problems for building importance sampling schemes for metastable systems is to find the metastable region in order to manipulate the potential accordingly. Our method circumvents this problem by using an assimilated version of the Metadynamics algorithm and thus creates a non-equilibrium dynamics which is used to sample the equilibrium quantities. We will show first results with Alanin Dipetide.
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Jonas Ranft (IBENS, Institut de Biologie de l’ENS, Paris)
Lifetime of a structure evolving by cluster aggregation and particle loss; application to postsynaptic scaffold domains
The aggregation of proteins in the cell membrane plays an important role in the formation of mesoscopic biological structures such as E-cadherin clusters or postsynaptic scaffold domains in neurons. Recent works have addressed how diffusion-limited protein aggregation combined with protein turnover allows the generation of well-defined, tunable distributions of aggregate sizes. The out-of-equilibrium nature of the aggregation-removal process is reflected by the size fluctuations of the formed structures, which can grow by fusion with impinging protein aggregates or shrink due to stochastic particle loss. These fluctuations affect the stability of the formed structures, and one may ask what is the typical timescale during which they persist. Here, we calculate the characteristic lifetime of such structures formed by aggregation and removal, and discuss implications for the stability of inhibitory postsynaptic scaffold domains. Joint work with Vincent Hakim.
