The IRIS network of excellence: future directions in interactive storytelling

The IRIS Network of Excellence (NoE) started its work in January 2009. In this paper we highlight some new research directions developing within the network: one is revisiting narrative formalisation through the use of Linear Logic and the other is challenging the conventional framework of basing Interactive Storytelling on computer graphics to explore the content-based recombination of video sequences

Polymorphic evolution sequence and evolutionary branching

We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large and the mutation rate small. We prove that under a good combination of these two scales, the population process is approximated in the long time scale of mutations by a Markov pure jump process describing the successive trait equilibria of the population. This process, which generalizes the so-called trait substitution sequence, is called polymorphic evolution sequence. Then we introduce a scaling of the size of mutations and we study the polymorphic evolution sequence in the limit of small mutations. From this study in the neighborhood of evolutionary singularities, we obtain a full mathematical justification of a heuristic criterion for the phenomenon of evolutionary branching. To this end we finely analyze the asymptotic behavior of 3-dimensional competitive Lotka-Volterra systems

A simple mathematical model of gradual Darwinian evolution: Emergence of a Gaussian trait distribution in adaptation along a fitness gradient

We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.Comment: 21 pages, 2 figures, as accepted to J Math Biol 2013/03/1

The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields

We consider an "elastic" version of the statistical mechanical monomer-dimer problem on the n-dimensional integer lattice. Our setting includes the classical "rigid" formulation as a special case and extends it by allowing each dimer to consist of particles at arbitrarily distant sites of the lattice, with the energy of interaction between the particles in a dimer depending on their relative position. We reduce the free energy of the elastic dimer-monomer (EDM) system per lattice site in the thermodynamic limit to the moment Lyapunov exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value and covariance function are the Boltzmann factors associated with the monomer energy and dimer potential. In particular, the classical monomer-dimer problem becomes related to the MLE of a moving average GRF. We outline an approach to recursive computation of the partition function for "Manhattan" EDM systems where the dimer potential is a weighted l1-distance and the auxiliary GRF is a Markov random field of Pickard type which behaves in space like autoregressive processes do in time. For one-dimensional Manhattan EDM systems, we compute the MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a compact transfer operator on a Hilbert space which is related to the annihilation and creation operators of the quantum harmonic oscillator and also recast it as the eigenvalue problem for a pantograph functional-differential equation.Comment: 24 pages, 4 figures, submitted on 14 October 2011 to a special issue of DCDS-

3D Fluid Flow Estimation with Integrated Particle Reconstruction

The standard approach to densely reconstruct the motion in a volume of fluid is to inject high-contrast tracer particles and record their motion with multiple high-speed cameras. Almost all existing work processes the acquired multi-view video in two separate steps, utilizing either a pure Eulerian or pure Lagrangian approach. Eulerian methods perform a voxel-based reconstruction of particles per time step, followed by 3D motion estimation, with some form of dense matching between the precomputed voxel grids from different time steps. In this sequential procedure, the first step cannot use temporal consistency considerations to support the reconstruction, while the second step has no access to the original, high-resolution image data. Alternatively, Lagrangian methods reconstruct an explicit, sparse set of particles and track the individual particles over time. Physical constraints can only be incorporated in a post-processing step when interpolating the particle tracks to a dense motion field. We show, for the first time, how to jointly reconstruct both the individual tracer particles and a dense 3D fluid motion field from the image data, using an integrated energy minimization. Our hybrid Lagrangian/Eulerian model reconstructs individual particles, and at the same time recovers a dense 3D motion field in the entire domain. Making particles explicit greatly reduces the memory consumption and allows one to use the high-res input images for matching. Whereas the dense motion field makes it possible to include physical a-priori constraints and account for the incompressibility and viscosity of the fluid. The method exhibits greatly (~70%) improved results over our recently published baseline with two separate steps for 3D reconstruction and motion estimation. Our results with only two time steps are comparable to those of sota tracking-based methods that require much longer sequences.Comment: To appear in International Journal of Computer Vision (IJCV

The frequency-dependent Wright-Fisher model: diffusive and non-diffusive approximations

We study a class of processes that are akin to the Wright-Fisher model, with transition probabilities weighted in terms of the frequency-dependent fitness of the population types. By considering an approximate weak formulation of the discrete problem, we are able to derive a corresponding continuous weak formulation for the probability density. Therefore, we obtain a family of partial differential equations (PDE) for the evolution of the probability density, and which will be an approximation of the discrete process in the joint large population, small time-steps and weak selection limit. If the fitness functions are sufficiently regular, we can recast the weak formulation in a more standard formulation, without any boundary conditions, but supplemented by a number of conservation laws. The equations in this family can be purely diffusive, purely hyperbolic or of convection-diffusion type, with frequency dependent convection. The particular outcome will depend on the assumed scalings. The diffusive equations are of the degenerate type; using a duality approach, we also obtain a frequency dependent version of the Kimura equation without any further assumptions. We also show that the convective approximation is related to the replicator dynamics and provide some estimate of how accurate is the convective approximation, with respect to the convective-diffusion approximation. In particular, we show that the mode, but not the expected value, of the probability distribution is modelled by the replicator dynamics. Some numerical simulations that illustrate the results are also presented

Brainstem Respiratory Oscillators Develop Independently of Neuronal Migration Defects in the Wnt/PCP Mouse Mutant looptail

The proper development and maturation of neuronal circuits require precise migration of component neurons from their birthplace (germinal zone) to their final positions. Little is known about the effects of aberrant neuronal position on the functioning of organized neuronal groups, especially in mammals. Here, we investigated the formation and properties of brainstem respiratory neurons in looptail (Lp) mutant mice in which facial motor neurons closely apposed to some respiratory neurons fail to migrate due to loss of function of the Wnt/Planar Cell Polarity (PCP) protein Vangl2. Using calcium imaging and immunostaining on embryonic hindbrain preparations, we found that respiratory neurons constituting the embryonic parafacial oscillator (e-pF) settled at the ventral surface of the medulla in Vangl2Lp/+ and Vangl2Lp/Lp embryos despite the failure of tangential migration of its normally adjacent facial motor nucleus. Anatomically, the e-pF neurons were displaced medially in Lp/+ embryos and rostro-medially Lp/Lp embryos. Pharmacological treatments showed that the e-pF oscillator exhibited characteristic network properties in both Lp/+ and Lp/Lp embryos. Furthermore, using hindbrain slices, we found that the other respiratory oscillator, the preBötzinger complex, was also anatomically and functionally established in Lp mutants. Importantly, the displaced e-pF oscillator established functional connections with the preBötC oscillator in Lp/+ mutants. Our data highlight the robustness of the developmental processes that assemble the neuronal networks mediating an essential physiological function

Limited role of spatial selfstructuring in emergent trade-offs during pathogen evolution

Pathogen transmission and virulence are main evolutionary variables broadly assumed to be linked through trade-offs. In well-mixed populations, these trade-offs are often ascribed to physiological restrictions, while populations with spatial self-structuring might evolve emergent trade-offs. Here, we reexamine a spatially-explicit, SIR model of the latter kind proposed by Ballegooijen and Boerlijst with the aim of characterising the mechanisms causing the emergence of the trade-off and its structural robustness. Using invadability criteria, we establish the conditions under which an evolutionary feedback between transmission and virulence mediated by pattern formation can poise the system to a critical boundary separating a disordered state (without emergent trade-off) from a self-structured phase (where the trade-off emerges), and analytically calculate the functional shape of the boundary in a certain approximation. Beyond evolutionary parameters, the success of an invasion depends on the size and spatial structure of the invading and invaded populations. Spatial self-structuring is often destroyed when hosts are mobile, changing the evolutionary dynamics to those of a well-mixed population. In a metapopulation scenario, the systematic extinction of the pathogen in the disordered phase may counteract the disruptive effect of host mobility, favour pattern formation and therefore recover the emergent trade-off.This work has been supported by the Spanish Ministerio de Economía, Industria y Competitividad and FEDER funds of the EU through grants ViralESS (FIS2014-57686-P and FIS2017-84256-P). The internship of VB was financed by the Severo Ochoa Centers of Excellence Program (SEV-2013-0347)