Stéphane Blanco

Modeling Collective Animal Behavior with a Cognitive Perspective: A Methodological Framework

The last decades have seen an increasing interest in modeling collective animal behavior. Some studies try to reproduce as accurately as possible the collective dynamics and patterns observed in several animal groups with biologically plausible, individual behavioral rules. The objective is then essentially to demonstrate that the observed collective features may be the result of self-organizing processes involving quite simple individual behaviors. Other studies concentrate on the objective of establishing or enriching links between collective behavior researches and cognitive or physiological ones, which then requires that each individual rule be carefully validated. Here we discuss the methodological consequences of this additional requirement. Using the example of corpse clustering in ants, we first illustrate that it may be impossible to discriminate among alternative individual rules by considering only observational data collected at the group level. Six individual behavioral models are described: They are clearly distinct in terms of individual behaviors, they all reproduce satisfactorily the collective dynamics and distribution patterns observed in experiments, and we show theoretically that it is strictly impossible to discriminate two of these models even in the limit of an infinite amount of data whatever the accuracy level. A set of methodological steps are then listed and discussed as practical ways to partially overcome this problem. They involve complementary experimental protocols specifically designed to address the behavioral rules successively, conserving group-level data for the overall model validation. In this context, we highlight the importance of maintaining a sharp distinction between model enunciation, with explicit references to validated biological concepts, and formal translation of these concepts in terms of quantitative state variables and fittable functional dependences. Illustrative examples are provided of the benefits expected during the often long and difficult process of refining a behavioral model, designing adapted experimental protocols and inversing model parameters.

How Do Ants Make Sense of Gravity? A Boltzmann Walker Analysis of Lasius niger Trajectories on Various Inclines

The goal of this study is to describe accurately how the directional information given by support inclinations affects the ant Lasius niger motion in terms of a behavioral decision. To this end, we have tracked the spontaneous motion of 345 ants walking on a 0.5×0.5 m plane canvas, which was tilted with 5 various inclinations by rad ( data points). At the population scale, support inclination favors dispersal along uphill and downhill directions. An ants decision making process is modeled using a version of the Boltzmann Walker model, which describes an ants random walk as a series of straight segments separated by reorientation events, and was extended to take directional influence into account. From the data segmented accordingly ( segments), this extension allows us to test separately how average speed, segments lengths and reorientation decisions are affected by support inclination and current walking direction of the ant. We found that support inclination had a major effect on average speed, which appeared approximately three times slower on the incline. However, we found no effect of the walking direction on speed. Contrastingly, we found that ants tend to walk longer in the same direction when they move uphill or downhill, and also that they preferentially adopt new uphill or downhill headings at turning points. We conclude that ants continuously adapt their decision making about where to go, and how long to persist in the same direction, depending on how they are aligned with the line of maximum declivity gradient. Hence, their behavioral decision process appears to combine klinokinesis with geomenotaxis. The extended Boltzmann Walker model parameterized by these effects gives a fair account of the directional dispersal of ants on inclines.

Feedback characteristics of nonlinear dynamical systems

We propose a method to extend the concept of feedback gain to nonlinear models. The method is designed to dynamically characterise a feedback mechanism along the system natural trajectory. The numerical efficiency of the method is proved using the Lorenz (1963) classical model. Finally, a simple climate model of water vapour feedback shows how nonlinearity impacts feedback intensity along the seasonal cycle.

Radiative, conductive and convective heat-transfers in a single Monte Carlo algorithm

It was recently shown that null-collision algorithms could lead to grid-free radiative- transfer Monte Carlo algorithms that immediately benefit of computer-graphics tools for an efficient handling of complex geometries [1, 2]. We here explore the idea of extending the approach to heat transfer problems combining radiation, conduction and convection. This is possible as soon as the model can be given the form of a second-kind Fredholm equation. In the following pages, we show that this is quite straightforward at the stationnary limit in the linear case. The oral presentation will provide corresponding simulation examples. Perspectives will then be drawn concerning the extension to non-stationnary cases and non-linear coupling.

Coordination of construction behavior in the termite Procornitermes araujoi : structure is a stronger stimulus than volatile marking

We studied the behavioral coordination mechanisms underlying morphogenesis in shelter construction by the termite Procornitermes araujoi. We detected positive feedback in both digging and pellet deposition behavior. The literature suggests two stimuli for these positive feedbacks: the emerging structure itself or volatile chemical marking added to the construction material. The experiments showed that the most important stimulus is the change in structure, but indirect evidence suggests that there is also some chemical marking involved. Beyond shedding light on the behavioral mechanisms of termite shelter construction, these results also stress the necessity of direct experimental approaches in order to identify and properly weight different coordination mechanisms underlying morphogenesis in biological systems.

Kinetic Approach for Solid Inertial Particle Deposition in Turbulent Near-Wall Region Flow Lattice Boltzmann Based Numerical Resolution

The purpose of the paper is the deposition on the wall of inertial solid particles suspended in turbulent flow. The modeling of such a system is based on a statistical description using a Probability Density Function. In the PDF transport equation, an original model proposed Aguinaga et al. (2009) is used to close the term representing the fluid-particle interactions. The resulting kinetic equation may be difficult to solve especially in the case of the particle response time is smaller than the integral time scale of the turbulence. In the present paper, the Lattice Boltzmann Method is used in order to overcome such numerical problems. The accuracy of the method and its ability to solve the two-phase kinetic equation is analyzed in the simple case of inertial particles in homogeneous isotropic turbulence for which Lagrangian random walk simulation results are available. The results from LBM are in accordance with the random walk simulations.© 2011 ASME

APPLICATIONS OF SENSITIVITY ESTIMATIONS BY MONTE CARLO METHODS

Parametric sensitivity estimations have been recently discussed in the frame of radiative transfer along two methodological lines. On the one hand, differential approaches have been studied by Spurr et al.[1] leading to a linearized discrete ordinate radiative transfer model. On the other hand, de Lataillade et al.[2] have observed that in most cases the Monte Carlo method can be easily extended to provide statistical estimates of sensitivities to all types of physical parameters (such as temperatures, surfaces emissivities, absorption and scattering coefficients, phase function parameters, etc). In particular, it was shown that adding a sensitivity computation procedure to an existing Monte Carlo code was simple to implement and required very limited additional computational costs. The aim of this paper is first to recall the principle of such Monte Carlo sensitivity computations and to illustrate the corresponding application potential via practical examples in three distinct research contexts. In a second part, the question is then raised of estimating geometric sensitivities (sensitivities to parameters defining the geometry, such as surface positions, obstacle sizes, etc) with similar procedures. Simple examples are presented in which a geometric sensitivity problem can be turned into a standard parametric sensitivity problem, allowing then to make use of todays existing techniques.

Mathematical modeling supports fate restriction in neurogenic progenitors of the embryonic ventral spinal cord

In the developing neural tube in chicken and mammals, neural stem cells proliferate and differentiate according to a stereotyped spatio-temporal pattern. Several actors have been identified in the control of this process, from tissue-scale morphogens patterning (Shh, BMP) to intrinsic determinants in neural progenitor cells. In a previous study (Bonnet et al. eLife 7, 2018), we have shown that the CDC25B phosphatase promotes the transition from proliferation to differentiation in a cell-cycle independent fashion. In this study, we set up a mathematical model linking progenitor modes of division to the dynamics of progenitors and differentiated populations. Here, we build on this previous model to propose a complete dynamical picture of this process. We start from the standard model in which progenitors are homogeneous and can perform any type of divisions (proliferative division yielding two progenitors, asymmetric neurogenic divisions yielding one progenitor and one neuron, and terminal symmetric divisions yielding two neurons). We constraint this model using published data about mode of divisions and population dynamics of progenitors/neurons at different developmental stages (Saade et al. Cell Reports 4, 2013), and check the effect of CDC25B gain of function in this context. Next, we explore the scenarios in which progenitors population is actually split into two different pools, one of which composed of cells that have lost the capacity to perform proliferative divisions (fate restriction). We show that one such scenario appears relevant and calls for further identification of the alternative role of CDC25B in such a fate restriction.

Addressing nonlinearities in Monte Carlo

Monte Carlo is famous for accepting model extensions and model refinements up to infinite dimension. However, this powerful incremental design is based on a premise which has severely limited its application so far: a state-variable can only be recursively defined as a function of underlying state-variables if this function is linear. Here we show that this premise can be alleviated by projecting nonlinearities onto a polynomial basis and increasing the configuration space dimension. Considering phytoplankton growth in light-limited environments, radiative transfer in planetary atmospheres, electromagnetic scattering by particles, and concentrated solar power plant production, we prove the real-world usability of this advance in four test cases which were previously regarded as impracticable using Monte Carlo approaches. We also illustrate an outstanding feature of our method when applied to acute problems with interacting particles: handling rare events is now straightforward. Overall, our extension preserves the features that made the method popular: addressing nonlinearities does not compromise on model refinement or system complexity, and convergence rates remain independent of dimension.

Diffusion approximation and short-path statistics at low to intermediate Knudsen numbers

In the field of first-return statistics in bounded domains, short paths may be defined as those paths for which the diffusion approximation is inappropriate. However, general integral constraints have been identified that make it possible to address such short-path statistics indirectly by application of the diffusion approximation to long paths in a simple associated first-passage problem. This approach is exact in the zero Knudsen limit (Blanco S. and Fournier R., Phys. Rev. Lett., 97 (2006) 230604). Its generalization to the low to intermediate Knudsen range is addressed here theoretically and the corresponding predictions are compared to both one-dimension analytical solutions and three-dimension numerical experiments. Direct quantitative relations to the solution of the Schwarzschild-Milne problem are identified.