Optimal policies for Bayesian olfactory search in turbulent flows.

In many practical scenarios, a flying insect must search for the source of an emitted cue which is advected by the atmospheric wind. On the macroscopic scales of interest, turbulence tends to mix the cue into patches of relatively high concentration over a background of very low concentration, so that the insect will detect the cue only intermittently and cannot rely on chemotactic strategies which simply climb the concentration gradient. In this work we cast this search problem in the language of a partially observable Markov decision process and use the Perseus algorithm to compute strategies that are near-optimal with respect to the arrival time. We test the computed strategies on a large two-dimensional grid, present the resulting trajectories and arrival time statistics, and compare these to the corresponding results for several heuristic strategies, including (space-aware) infotaxis, Thompson sampling, and QMDP. We find that the near-optimal policy found by our implementation of Perseus outperforms all heuristics we test by several measures. We use the near-optimal policy to study how the search difficulty depends on the starting location. We also discuss the choice of initial belief and the robustness of the policies to changes in the environment. Finally, we present a detailed and pedagogical discussion about the implementation of the Perseus algorithm, including the benefits-and pitfalls-of employing a reward-shaping function.

Environmental training is beneficial to clinical symptoms and cortical presynaptic defects in mice suffering from experimental autoimmune encephalomyelitis.

The effect of "prophylactic" environmental stimulation on clinical symptoms and presynaptic defects in mice suffering from the experimental autoimmune encephalomyelitis (EAE) at the acute stage of disease (21 ±â€¯1 days post immunization, d.p.i.) was investigated. In EAE mice raised in an enriched environment (EE), the clinical score was reduced when compared to EAE mice raised in standard environment (SE).Concomitantly, gain of weight and increased spontaneous motor activity and curiosity were observed, suggesting increased well-being in mice. Impaired glutamate exocytosis and cyclic adenosine monophosphate (cAMP) production in cortical terminals of SE-EAE mice were evident at 21 ±â€¯1 d.p.i.. Differently, the 12 mM KCl-evoked glutamate exocytosis from cortical synaptosomes of EE-EAE mice was comparable to that observed in SE and EE-control mice, but significantly higher than that in SE-EAE mice. Similarly, the 12 mM KCl-evoked cAMP production in EE-EAE mice cortical synaptosomes recovered to the level observed in SE and EE-control mice. MUNC-18 and SNAP25 contents, but not Syntaxin-1a and Synaptotagmin 1 levels, were increased in cortical synaptosomes from EE-EAE mice when compared to SE-EAE mice. Circulating IL-1ß was increased in the spinal cord, but not in the cortex, of SE-EAE mice, and it did not recover in EE-EAE mice. Inflammatory infiltrates were reduced in the cortex but not in the spinal cord of EE-EAE mice. Demyelination was observed in the spinal cord; EE significantly diminished it. We conclude that "prophylactic" EE is beneficial to synaptic derangements and preserves glutamate transmission in the cortex of EAE mice. This article is part of the Special Issue entitled "Neurobiology of Environmental Enrichment".

Complete coverage of space favors modularity of the grid system in the brain.

Grid cells in the entorhinal cortex fire when animals that are exploring a certain region of space occupy the vertices of a triangular grid that spans the environment. Different neurons feature triangular grids that differ in their properties of periodicity, orientation, and ellipticity. Taken together, these grids allow the animal to maintain an internal, mental representation of physical space. Experiments show that grid cells are modular, i.e., there are groups of neurons which have grids with similar periodicity, orientation, and ellipticity. We use statistical physics methods to derive a relation between variability of the properties of the grids within a module and the range of space that can be covered completely (i.e., without gaps) by the grid system with high probability. Larger variability shrinks the range of representation, providing a functional rationale for the experimentally observed comodularity of grid cell periodicity, orientation, and ellipticity. We obtain a scaling relation between the number of neurons and the period of a module, given the variability and coverage range. Specifically, we predict how many more neurons are required at smaller grid scales than at larger ones.

Inference in particle tracking experiments by passing messages between images.

Methods to extract information from the tracking of mobile objects/particles have broad interest in biological and physical sciences. Techniques based on simple criteria of proximity in time-consecutive snapshots are useful to identify the trajectories of the particles. However, they become problematic as the motility and/or the density of the particles increases due to uncertainties on the trajectories that particles followed during the images' acquisition time. Here, we report an efficient method for learning parameters of the dynamics of the particles from their positions in time-consecutive images. Our algorithm belongs to the class of message-passing algorithms, known in computer science, information theory, and statistical physics as belief propagation (BP). The algorithm is distributed, thus allowing parallel implementation suitable for computations on multiple machines without significant intermachine overhead. We test our method on the model example of particle tracking in turbulent flows, which is particularly challenging due to the strong transport that those flows produce. Our numerical experiments show that the BP algorithm compares in quality with exact Markov Chain Monte Carlo algorithms, yet BP is far superior in speed. We also suggest and analyze a random distance model that provides theoretical justification for BP accuracy. Methods developed here systematically formulate the problem of particle tracking and provide fast and reliable tools for the model's extensive range of applications.

Repulsion and metabolic switches in the collective behavior of bacterial colonies.

Bacteria inoculated on surfaces create colonies that spread out, forming patterns shaped by their mutual interactions. Here, by a combination of experiments and modeling, we address two striking phenomena observed when colonies spread out circularly, without dendritic instabilities. First, the velocity of spreading is generically found to decrease as levels of nutrients initially deposited on the surface increase. We demonstrate that the slowdown is due to phenomena of differentiation, leading to the coexistence of bacteria in different states of motility and we model their dynamics. Second, colonies spreading out from different inocula on the same surface are observed to merge or repel (halting at a finite distance), depending on experimental conditions. We identify the parameters that determine the fate of merging versus repulsion, and predict the profile of arrest in the cases of repulsion.

Inferring maps of forces inside cell membrane microdomains.

Mapping of the forces on biomolecules in cell membranes has spurred the development of effective labels, e.g., organic fluorophores and nanoparticles, to track trajectories of single biomolecules. Standard methods use particular statistics, namely the mean square displacement, to analyze the underlying dynamics. Here, we introduce general inference methods to fully exploit information in the experimental trajectories, providing sharp estimates of the forces and the diffusion coefficients in membrane microdomains. Rapid and reliable convergence of the inference scheme is demonstrated on trajectories generated numerically. The method is then applied to infer forces and potentials acting on the receptor of the toxin labeled by lanthanide-ion nanoparticles. Our scheme is applicable to any labeled biomolecule and results show its general relevance for membrane compartmentation.

Intermittency in two-dimensional Ekman-Navier-Stokes turbulence.

We study the statistics of the vorticity field in two-dimensional Navier-Stokes turbulence with linear Ekman friction. We show that the small-scale vorticity fluctuations are intermittent, as conjectured by Bernard [Europhys. Lett. 50, 333 (2000)] and Nam et al. [Phys. Rev. Lett. 84, 5134 (2000)]. The small-scale statistics of vorticity fluctuations coincide with that of a passive scalar with finite lifetime transported by the velocity field itself.

Statistical conservation laws in turbulent transport.

We address the statistical theory of fields that are transported by a turbulent velocity field, both in forced and in unforced (decaying) experiments. With very few provisos on the transporting velocity field, correlation functions of the transported field in the forced case are dominated by statistically preserved structures. In decaying experiments we identify infinitely many statistical constants of the motion, which are obtained by projecting the decaying correlation functions on the statistically preserved functions. We exemplify these ideas and provide numerical evidence using a simple model of turbulent transport. This example is chosen for its lack of Lagrangian structure, to stress the generality of the ideas.

Universal decay of scalar turbulence.

The asymptotic decay of passive scalar fields is solved analytically for the Kraichnan model, where the velocity has a short correlation time. At long times, two universality classes are found, both characterized by a distribution of the scalar-generally non-Gaussian-with global self-similar evolution in time. Analogous behavior is found numerically with a more realistic flow resulting from an inverse energy cascade.

Statistical geometry in scalar turbulence.

A general link between geometry and intermittency in passive scalar turbulence is established. The anomalous part of the scalar correlation functions is shown to be dominated by special functions of particle configurations. Their major property is that those functions calculated along the particle trajectories remain statistically constant in time. Those conservation laws qualitatively imply the persistence of scalar particles in strongly clustered geometries.

Universality and saturation of intermittency in passive scalar turbulence

The statistical properties of a scalar field advected by the nonintermittent Navier-Stokes flow arising from a two-dimensional inverse energy cascade are investigated. The universality properties of the scalar field are probed by comparing the results obtained with two types of injection mechanisms. Scaling properties are shown to be universal, even though anisotropies injected at large scales persist down to the smallest scales and local isotropy is not fully restored. Scalar statistics is strongly intermittent and scaling exponents saturate to a constant for sufficiently high orders. This is observed also for the advection by a velocity field rapidly changing in time, pointing to the genericity of the phenomenon.

Inverse energy cascade in two-dimensional turbulence: deviations from gaussian behavior

High-resolution numerical simulations of stationary inverse energy cascade in two-dimensional turbulence are presented. Deviations from Gaussian behavior of velocity differences statistics are quantitatively investigated. The level of statistical convergence is pushed enough to permit reliable measurement of the asymmetries in the probability distribution functions of longitudinal increments and odd-order moments, which bring the signature of the inverse energy flux. No measurable intermittency corrections could be found in their scaling laws. The seventh order skewness increases by almost two orders of magnitude with respect to the third, thus becoming of order unity.