All Inequalities for the Relative Entropy

The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party to a smaller number $m$ of parties is always less than or equal to the relative entropy of the two original n-party states. This is the monotonicity of relative entropy. Using techniques from convex geometry, we prove that monotonicity under restrictions is the only general inequality satisfied by relative entropies. In doing so we make a connection to secret sharing schemes with general access structures. A suprising outcome is that the structure of allowed relative entropy values of subsets of multiparty states is much simpler than the structure of allowed entropy values. And the structure of allowed relative entropy values (unlike that of entropies) is the same for classical probability distributions and quantum states.Comment: 15 pages, 3 embedded eps figure

The genetic architecture of the human cerebral cortex

INTRODUCTION The cerebral cortex underlies our complex cognitive capabilities. Variations in human cortical surface area and thickness are associated with neurological, psychological, and behavioral traits and can be measured in vivo by magnetic resonance imaging (MRI). Studies in model organisms have identified genes that influence cortical structure, but little is known about common genetic variants that affect human cortical structure. RATIONALE To identify genetic variants associated with human cortical structure at both global and regional levels, we conducted a genome-wide association meta-analysis of brain MRI data from 51,665 individuals across 60 cohorts. We analyzed the surface area and average thickness of the whole cortex and 34 cortical regions with known functional specializations. RESULTS We identified 306 nominally genome-wide significant loci (P < 5 × 10−8) associated with cortical structure in a discovery sample of 33,992 participants of European ancestry. Of the 299 loci for which replication data were available, 241 loci influencing surface area and 14 influencing thickness remained significant after replication, with 199 loci passing multiple testing correction (P < 8.3 × 10−10; 187 influencing surface area and 12 influencing thickness). Common genetic variants explained 34% (SE = 3%) of the variation in total surface area and 26% (SE = 2%) in average thickness; surface area and thickness showed a negative genetic correlation (rG = −0.32, SE = 0.05, P = 6.5 × 10−12), which suggests that genetic influences have opposing effects on surface area and thickness. Bioinformatic analyses showed that total surface area is influenced by genetic variants that alter gene regulatory activity in neural progenitor cells during fetal development. By contrast, average thickness is influenced by active regulatory elements in adult brain samples, which may reflect processes that occur after mid-fetal development, such as myelination, branching, or pruning. When considered together, these results support the radial unit hypothesis that different developmental mechanisms promote surface area expansion and increases in thickness. To identify specific genetic influences on individual cortical regions, we controlled for global measures (total surface area or average thickness) in the regional analyses. After multiple testing correction, we identified 175 loci that influence regional surface area and 10 that influence regional thickness. Loci that affect regional surface area cluster near genes involved in the Wnt signaling pathway, which is known to influence areal identity. We observed significant positive genetic correlations and evidence of bidirectional causation of total surface area with both general cognitive functioning and educational attainment. We found additional positive genetic correlations between total surface area and Parkinson’s disease but did not find evidence of causation. Negative genetic correlations were evident between total surface area and insomnia, attention deficit hyperactivity disorder, depressive symptoms, major depressive disorder, and neuroticism. CONCLUSION This large-scale collaborative work enhances our understanding of the genetic architecture of the human cerebral cortex and its regional patterning. The highly polygenic architecture of the cortex suggests that distinct genes are involved in the development of specific cortical areas. Moreover, we find evidence that brain structure is a key phenotype along the causal pathway that leads from genetic variation to differences in general cognitive function

KINETICS OF GLASS FORMATION AND DEVITRIFICATION BEHAVIOR

La formation du verre est considérée sous un aspect cinétique. La cinétique de nucléation, aussi bien homogène qu'hétérogène, ainsi que la croissance du cristal sont initialement suivies. Les informations obtenues dans ces domaines sont réunies avec des traitements de cristallisation pendant un refroidissement constant afin d'évaluer des vitesses critiques de refroidissement nécessaires à la formation de verres de différents matériaux. Les paramètres du matériau contribuant à la formation et au procédé de cristallisation à chaud du verre sont considérés. Le traitement cinétique est aussi utilisé pour décrire d'autres phénomènes comme les effets d'hétérogénéités de nucléation sur la formation du verre et l'utilisation d'expériences de DTA pour évaluer les barrières de la nucléation du cristal.The process of glass formation is viewed from a kinetic perspective. Initial attention is directed to the kinetics of nucleation, both homogeneous and heterogeneous, and of crystal growth. Information obtained in these areas is combined with treatments of crystallization during continuous cooling to evaluate the critical cooling rates required to form glasses of various materials. Consideration is given to the material parameters which are conducive to glass formation, and to the process of crystallization on reheating of glass. The kinetic treatment is also used to describe other phenomena such as the effects of nucleating heterogeneities on glass formation and the use of DTA experiments to evaluate the barriers to crystal nucleation

A Model of The Metal-Ferroelectric-Metal Capacitor

AbstractFerroelectric (FE) films, especially PZT films, have received increasing attention for microelectronic applications such as ferroelectric memory and high density DRAM. There has been significant progress in the preparation of high quality PZT films involving wet chemical and physical vapor deposition techniques. Metal-FE-metal structures, typified by Pt-PZT-Pt capacitors, are the basic building blocks for the ferroelectric devices. The leakage currents of the capacitors are known to be non-ohmic and exhibit an exponential dependence on applied voltage.The present paper presents a model based on totally depleted back-to-back Shottky barriers. Predictions based on the model can provide significant new understanding of the FE behavior of thin films. For example, the assumption of total depletion leads to the presence of a built-in field within the film which can explain the ubiquitously higher values of coercive field in FE films than found in bulk ceramics. It will be shown that the agreement between model predictions and actual device I-V characteristics of Pt-PZT-Pt capacitors is very close. Further, the model can also explain the observed hysteresis loop asymmetry and low dielectric constants of films of relaxor FE's, whose dielectric constants are much smaller than those of bulk materials.</jats:p