Abstract:
See research article: http://www.neuraldevelopment.com/content/6/1/3/abstract webciteUnderstanding how the brain becomes wired-up during development is essential not only to gain insight into its normal functioning, but also to progress in the comprehension of neurological and psychiatric disease. Indeed, there is increasing evidence that defects occurring during embryonic development lead to impaired functioning of the cerebral cortex, and that such defects may underlie the etiology of several human pathologies, including schizophrenia and autism spectrum disorders. Genetic studies in both humans and mice have enabled clinicians and neurobiologists to dissect molecular cascades that govern the formation of the cerebral cortex, in particular those directing the generation and migration of different populations of cortical neurons. However, similar large-scale unbiased studies have yet to be developed to study the formation of the major axonal tracts that wire the cerebral cortex.The dorsal thalamus is a sensory gateway of the brain that receives visual, somatosensory and auditory information. Thalamocortical axons convey this sensory information from the dorsal thalamus to the cerebral cortex and hence are essential to brain function. They follow a long and complex path to reach their final cortical targets, making successive changes in direction as they navigate from one intermediate target to another (Figure 1). Indeed, from embryonic day 13 (E13) in mice, dorsal thalamus axons extend ventrally, turn laterally close to the hypothalamus to cross the boundary between embryonic diencephalon and telencephalon, enter the ventral telencephalon, grow in the internal capsule, and fan out into smaller axonal bundles before crossing the cortico-striatal boundary at E15. The axons then turn dorsally into the intermediate zone of the cerebral cortex, where they interact with cells of the cortical subplate before extending collateral branches to reach their final target in lay

Abstract:
We study the propagation of electromagnetic waves in a chiral fluid, where the molecules are described by a simplified version of the Kuhn coupled oscillator model. The eigenmodes of Maxwell's equations are circularly polarized waves. The application of a static magnetic field further leads to a magnetochiral term in the index of refraction of the fluid, which is independent of the wave polarization. A similar result holds when absorption is taken into account. Interference experiments and photochemical reactions have recently demonstrated the existence of the magnetochiral term. The comparison with Faraday rotation in an achiral fluid emphasizes the different symmetry properties of the two effects.

Abstract:
Understanding the deflection of light by a massive deflector, as well as the associated gravitational lens phenomena, require the use of the theory of General Relativity. I consider here a classical approach, based on Newton's equation of motion for massive particles. These particles are emitted by a distant source and deflected by the gravitational field of a (opaque) star or of a (transparent) galaxy. The dependence of the deviation angle $D$ on the impact parameter $b$, and the geometry of the (source, deflector, earth) triplet, imply that different particle trajectories may reach an earth based observer. Since $D(b)$ does not depend on the mass of the particles, it is tempting to set the particles' velocity equal to the speed of light to get a (Newtonian) flavor of gravitational lenses phenomena. Orders of magnitude are obtained through a non technical approach and can be compared to the General Relativity results.

Abstract:
Different aspects of protein folding are illustrated by simplified polymer models. Stressing the diversity of side chains (residues) leads one to view folding as the freezing transition of an heteropolymer. Technically, the most common approach to diversity is randomness, which is usually implemented in two body interactions (charges, polar character,..). On the other hand, the (almost) universal character of the protein backbone suggests that folding may also be viewed as the crystallization transition of an homopolymeric chain, the main ingredients of which are the peptide bond and chirality (proline and glycine notwithstanding). The model of a chiral dipolar chain leads to a unified picture of secondary structures, and to a possible connection of protein structures with ferroelectric domain theory.

Abstract:
The corpus callosum (CC) is the main pathway responsible for interhemispheric communication. CC agenesis is associated with numerous human pathologies, suggesting that a range of developmental defects can result in abnormalities in this structure. Midline glial cells are known to play a role in CC development, but we here show that two transient populations of midline neurons also make major contributions to the formation of this commissure. We report that these two neuronal populations enter the CC midline prior to the arrival of callosal pioneer axons. Using a combination of mutant analysis and in vitro assays, we demonstrate that CC neurons are necessary for normal callosal axon navigation. They exert an attractive influence on callosal axons, in part via Semaphorin 3C and its receptor Neuropilin-1. By revealing a novel and essential role for these neuronal populations in the pathfinding of a major cerebral commissure, our study brings new perspectives to pathophysiological mechanisms altering CC formation.

Abstract:
We consider the non-equilibrium dynamics of disordered systems as defined by a master equation involving transition rates between configurations (detailed balance is not assumed). To compute the important dynamical time scales in finite-size systems without simulating the actual time evolution which can be extremely slow, we propose to focus on first-passage times that satisfy 'backward master equations'. Upon the iterative elimination of configurations, we obtain the exact renormalization rules that can be followed numerically. To test this approach, we study the statistics of some first-passage times for two disordered models : (i) for the random walk in a two-dimensional self-affine random potential of Hurst exponent $H$, we focus on the first exit time from a square of size $L \times L$ if one starts at the square center. (ii) for the dynamics of the ferromagnetic Sherrington-Kirkpatrick model of $N$ spins, we consider the first passage time $t_f$ to zero-magnetization when starting from a fully magnetized configuration. Besides the expected linear growth of the averaged barrier $\bar{\ln t_{f}} \sim N$, we find that the rescaled distribution of the barrier $(\ln t_{f})$ decays as $e^{- u^{\eta}}$ for large $u$ with a tail exponent of order $\eta \simeq 1.72$. This value can be simply interpreted in terms of rare events if the sample-to-sample fluctuation exponent for the barrier is $\psi_{width}=1/3$.

Abstract:
For Anderson localization models, there exists an exact real-space renormalization procedure at fixed energy which preserves the Green functions of the remaining sites [H. Aoki, J. Phys. C13, 3369 (1980)]. Using this procedure for the Anderson tight-binding model in dimensions $d=2,3$, we study numerically the statistical properties of the renormalized on-site energies $\epsilon$ and of the renormalized hoppings $V$ as a function of the linear size $L$. We find that the renormalized on-site energies $\epsilon$ remain finite in the localized phase in $d=2,3$ and at criticality ($d=3$), with a finite density at $\epsilon=0$ and a power-law decay $1/\epsilon^2$ at large $| \epsilon |$. For the renormalized hoppings in the localized phase, we find: ${\rm ln} V_L \simeq -\frac{L}{\xi_{loc}}+L^{\omega}u$, where $\xi_{loc}$ is the localization length and $u$ a random variable of order one. The exponent $\omega$ is the droplet exponent characterizing the strong disorder phase of the directed polymer in a random medium of dimension $1+(d-1)$, with $\omega(d=2)=1/3$ and $\omega(d=3) \simeq 0.24$. At criticality $(d=3)$, the statistics of renormalized hoppings $V$ is multifractal, in direct correspondence with the multifractality of individual eigenstates and of two-point transmissions. In particular, we measure $\rho_{typ}\simeq 1$ for the exponent governing the typical decay $\overline{{\rm ln} V_L} \simeq -\rho_{typ} {\rm ln}L$, in agreement with previous numerical measures of $\alpha_{typ} =d+\rho_{typ} \simeq 4$ for the singularity spectrum $f(\alpha)$ of individual eigenfunctions. We also present numerical results concerning critical surface properties.

Abstract:
A disorder-dependent Gaussian variational approach is applied to the problem of a $d$ dimensional polymer chain in a random medium (or potential). Two classes of variational solutions are obtained. For $d<2$, these two classes may be interpreted as domain and domain wall. The critical exponent $\nu$ describing the polymer width is $\nu={1\over (4-d)}$ (domain solution) or $\nu={3\over (d+4)}$ (domain wall solution). The domain wall solution is equivalent to the (full) replica symmetry breaking variational result. For $d>2$, we find $\nu={1\over 2}$. No evidence of a phase transition is found for $2< d< 4$: one of the variational solutions suggests that the polymer chain breaks into Imry-Ma segments, whose probability distribution is calculated. For $d>4$, the other variational solution undergoes a phase transition, which has some similarity with B. Derrida's random energy models.

Abstract:
We study a single self avoiding hydrophilic hydrophobic polymer chain, through Monte Carlo lattice simulations. The affinity of monomer $i$ for water is characterized by a (scalar) charge $\lambda_{i}$, and the monomer-water interaction is short-ranged. Assuming incompressibility yields an effective short ranged interaction between monomer pairs $(i,j)$, proportional to $(\lambda_i+\lambda_j)$. In this article, we take $\lambda_i=+1$ (resp. ($\lambda_i=- 1$)) for hydrophilic (resp. hydrophobic) monomers and consider a chain with (i) an equal number of hydro-philic and -phobic monomers (ii) a periodic distribution of the $\lambda_{i}$ along the chain, with periodicity $2p$. The simulations are done for various chain lengths $N$, in $d=2$ (square lattice) and $d=3$ (cubic lattice). There is a critical value $p_c(d,N)$ of the periodicity, which distinguishes between different low temperature structures. For $p >p_c$, the ground state corresponds to a macroscopic phase separation between a dense hydrophobic core and hydrophilic loops. For $p

Abstract:
We consider various random models (directed polymer, random ferromagnets, spin-glasses) in their disorder-dominated phases, where the free-energy cost $F(L)$ of an excitation of length $L$ presents fluctuations that grow as a power-law $\Delta F(L) \sim L^{\theta}$ with the 'droplet' exponent $\theta$. Within the droplet theory, the energy and entropy of such excitations present fluctuations that grow as $\Delta E(L) \sim \Delta S(L) \sim L^{d_s/2}$ where $d_s$ is the dimension of the surface of the excitation. These systems usually present a positive 'chaos' exponent $\zeta=d_s/2-\theta>0$, meaning that the free-energy fluctuation of order $L^{\theta}$ is a near-cancellation of much bigger energy and entropy fluctuations of order $L^{d_s/2}$. Within the standard droplet theory, the dynamics is characterized by a barrier exponent $\psi$ satisfying the bounds $\theta \leq \psi \leq d-1$. In this paper, we argue that a natural value for this barrier exponent is $\psi=d_s/2$ : (i) for the directed polymer where $d_s=1$, this corresponds to $\psi=1/2$ in all dimensions; (ii) for disordered ferromagnets where $d_s=d-1$, this corresponds to $\psi=(d-1)/2$; (iii) for spin-glasses where interfaces have a non-trivial dimension $d_s$ known numerically, our conjecture $\psi=d_s/2$ gives numerical predictions in $d=2$ and $d=3$. We compare these values with the available numerical results for each case, in particular with the measure $\psi \simeq 0.49$ of Kolton, Rosso, Giamarchi, Phys. Rev. Lett. 95, 180604 (2005) for the non-equilibrium dynamics of a directed elastic string.