Periinfarct rewiring supports recovery after primary motor cortex stroke.

After stroke restricted to the primary motor cortex (M1), it is uncertain whether network reorganization associated with recovery involves the periinfarct or more remote regions. We studied 16 patients with focal M1 stroke and hand paresis. Motor function and resting-state MRI functional connectivity (FC) were assessed at three time points: acute (<10 days), early subacute (3 weeks), and late subacute (3 months). FC correlates of recovery were investigated at three spatial scales, (i) ipsilesional non-infarcted M1, (ii) core motor network (M1, premotor cortex (PMC), supplementary motor area (SMA), and primary somatosensory cortex), and (iii) extended motor network including all regions structurally connected to the upper limb representation of M1. Hand dexterity was impaired only in the acute phase (P = 0.036). At a small spatial scale, clinical recovery was more frequently associated with connections involving ipsilesional non-infarcted M1 (Odds Ratio = 6.29; P = 0.036). At a larger scale, recovery correlated with increased FC strength in the core network compared to the extended motor network (rho = 0.71;P = 0.006). These results suggest that FC changes associated with motor improvement involve the perilesional M1 and do not extend beyond the core motor network. Core motor regions, and more specifically ipsilesional non-infarcted M1, could hence become primary targets for restorative therapies

Exactly Solvable Birth and Death Processes

Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable `matrix' quantum mechanics, which is recently proposed by Odake and the author. The ($q$-)Askey-scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of $q^x$ ($x$ being the population) corresponding to the $q$-Racah polynomial.Comment: LaTeX, amsmath, amssymb, 24 pages, no figure

Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model

We apply the nonlinear steepest descent method to a class of 3x3 Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix random model. The general case of two equilibrium measures supported on an arbitrary number of intervals is considered. In this case, we solve the Riemann-Hilbert problem for the outer parametrix in terms of sections of a spinorial line bundle on a three-sheeted Riemann surface of arbitrary genus and establish strong asymptotic results for the Cauchy biorthogonal polynomials.Comment: 31 pages, 12 figures. V2; typos corrected, added reference

Can education change the world? Education amplifies differences in liberalization values and innovation between developed and developing countries

The present study investigated the relationship between level of education and liberalization values in large, representative samples administered in 96 countries around the world (total N = 139,991). These countries show meaningful variation in terms of the Human Development Index (HDI), ranging from very poor, developing countries to prosperous, developed countries. We found evidence of cross-level interactions, consistently showing that individuals' level of education was associated with an increase in their liberalization values in higher HDI societies, whereas this relationship was curbed in lower HDI countries. This enhanced liberalization mindset of individuals in high HDI countries, in turn, was related to better scores on national indices of innovation. We conclude that this 'education amplification effect' widens the gap between lower and higher HDI countries in terms of liberalized mentality and economic growth potential. Policy implications for how low HDI countries can counter this gap are discussed

Critical behavior in Angelesco ensembles

We consider Angelesco ensembles with respect to two modified Jacobi weights on touching intervals [a,0] and [0,1], for a < 0. As a \to -1 the particles around 0 experience a phase transition. This transition is studied in a double scaling limit, where we let the number of particles of the ensemble tend to infinity while the parameter a tends to -1 at a rate of order n^{-1/2}. The correlation kernel converges, in this regime, to a new kind of universal kernel, the Angelesco kernel K^{Ang}. The result follows from the Deift/Zhou steepest descent analysis, applied to the Riemann-Hilbert problem for multiple orthogonal polynomials.Comment: 32 pages, 9 figure

Continuous variable private quantum channel

In this paper we introduce the concept of quantum private channel within the continuous variables framework (CVPQC) and investigate its properties. In terms of CVPQC we naturally define a "maximally" mixed state in phase space together with its explicit construction and show that for increasing number of encryption operations (which sets the length of a shared key between Alice and Bob) the encrypted state is arbitrarily close to the maximally mixed state in the sense of the Hilbert-Schmidt distance. We bring the exact solution for the distance dependence and give also a rough estimate of the necessary number of bits of the shared secret key (i.e. how much classical resources are needed for an approximate encryption of a generally unknown continuous-variable state). The definition of the CVPQC is analyzed from the Holevo bound point of view which determines an upper bound of information about an incoming state an eavesdropper is able to get from his optimal measurement.Comment: upper bound on information Eve can get was revised and substantially lowered (chapter IV), part of chapter III rewritten, several typos correcte