Whisker's Directional Selectivity: Orientation Columns in the Barrel Field?

Using voltage-sensitive dye optical imaging methods, we visualized neural activity in the rat barrel cortex in response to the deflection of a single whisker in different directions. Obtained data indicates that fast movements of single whiskers in varying directions correlate with different patterns of activation in the somatosensory cortex. A functional map was created based on the voltage-sensitive dye optical signal. This supports prior research that vibrissae deflections cause responses in different cortical neurons within the barrel field according to the direction of the deflection. By analogy with the orientation columns in the visual cortex, directionally-biased single whisker responses to different directions of deflection could be a possible mechanism for the directional selectivity of this important sensory response

Entropy: The Markov Ordering Approach

The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a monotonic transformation which makes the functional additive with respect to the joining of independent systems and (ii) existence of a monotonic transformation which makes the functional additive with respect to the partitioning of the space of states. All Lyapunov functionals for Markov chains which have properties (i) and (ii) are derived. We describe the most general ordering of the distribution space, with respect to which all continuous-time Markov processes are monotonic (the {\em Markov order}). The solution differs significantly from the ordering given by the inequality of entropy growth. For inference, this approach results in a convex compact set of conditionally "most random" distributions.Comment: 50 pages, 4 figures, Postprint version. More detailed discussion of the various entropy additivity properties and separation of variables for independent subsystems in MaxEnt problem is added in Section 4.2. Bibliography is extende

Comment on "Periodic Phase Synchronization in Coupled Chaotic Oscillators"

2 pages.-- PACS numbers: 05.45.Xt, 05.45.Pq.-- Final full-text version of the paper available at: http://dx.doi.org/10.1103/PhysRevE.73.038201.Kye et al. [Phys. Rev. E 68, 025201(R) (2003)] have recently claimed that, before the onset of Chaotic Phase Synchronization in coupled phase coherent oscillators, there exists a temporally coherent state called Periodic Phase Synchronization (PPS). Here we give evidence that some of their numerical calculations are flawed, while we provide theoretical arguments that indicate that PPS is not to be expected generically in this type of systems.This work was supported by MEC (Spain) and FEDER under Grant Nos. BFM2001-0341-C02-02, FIS2004-00953 (CONOCE2), and FIS2004-05073-C04-03.http://dx.doi.org/10.1103/PhysRevE.73.03820

Local Equivalence of Reversible and General Markov Kinetics

We consider continuous--time Markov kinetics with a finite number of states and a given positive equilibrium distribution P*. For an arbitrary probability distribution $P$ we study the possible right hand sides, dP/dt, of the Kolmogorov (master) equations. We describe the cone of possible values of the velocity, dP/dt, as a function of P and P*. We prove that, surprisingly, these cones coincide for the class of all Markov processes with equilibrium P* and for the reversible Markov processes with detailed balance at this equilibrium. Therefore, for an arbitrary probability distribution $P$ and a general system there exists a system with detailed balance and the same equilibrium that has the same velocity dP/dt at point P. The set of Lyapunov functions for the reversible Markov processes coincides with the set of Lyapunov functions for general Markov kinetics. The results are extended to nonlinear systems with the generalized mass action law.Comment: Significantly extended version, 21 page

Polariton effect in distributed feedback microcavities

The excitonic and photonic states in distributed feedback (DFB) microcavities may strongly couple to form DFB cavity polaritons, provided that excitonic oscillator strength is large enough. In this paper we theoretically analyse the optical properties of DFB microcavities related to polariton effect. A numerical method based on scattering matrix formalism has been developed to solve the Maxwell's equations for layered system with periodical patterning of layers. To incorporate polaritonic effect in our model we included the exciton poles in dielectric susceptibility of one of the patterned layers. Using this method we reproduce the characteristic features, demonstrated in recent experiments [Fujita et al.: Phys. Rev. B 57 (1998) 12428], such as anticrossing behavior of transmission dips in vicinity of the excitonic resonance and strong polarization dependence of their position and depth. ©2001 The Physical Society of Japa