Uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree

We consider models with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k\geq 1$. It is known that the "splitting Gibbs measures" of the model can be described by solutions of a nonlinear integral equation. For arbitrary $k\geq 2$ we find a sufficient condition under which the integral equation has unique solution, hence under the condition the corresponding model has unique splitting Gibbs measure.Comment: 13 page

MicroRNA Expression Is Down-Regulated and Reorganized in Prefrontal Cortex of Depressed Suicide Subjects

<div><h3>Background</h3><p>Recent studies suggest that alterations in expression of genes, including those which regulate neural and structural plasticity, may be crucial in the pathogenesis of depression. MicroRNAs (miRNAs) are newly discovered regulators of gene expression that have recently been implicated in a variety of human diseases, including neuropsychiatric diseases.</p> <h3>Methodology/Principal Findings</h3><p>The present study was undertaken to examine whether the miRNA network is altered in the brain of depressed suicide subjects. Expression of miRNAs was measured in prefrontal cortex (Brodmann Area 9) of antidepressant-free depressed suicide (n = 18) and well-matched non-psychiatric control subjects (n = 17) using multiplex RT-PCR plates. We found that overall miRNA expression was significantly and globally down-regulated in prefrontal cortex of depressed suicide subjects. Using individual tests of statistical significance, 21 miRNAs were significantly decreased at p = 0.05 or better. Many of the down-regulated miRNAs were encoded at nearby chromosomal loci, shared motifs within the 5′-seeds, and shared putative mRNA targets, several of which have been implicated in depression. In addition, a set of 29 miRNAs, whose expression was not pairwise correlated in the normal controls, showed a high degree of co-regulation across individuals in the depressed suicide group.</p> <h3>Conclusions/Significance</h3><p>The findings show widespread changes in miRNA expression that are likely to participate in pathogenesis of major depression and/or suicide. Further studies are needed to identify whether the miRNA changes lead to altered expression of prefrontal cortex mRNAs, either directly (by acting as miRNA targets) or indirectly (e.g., by affecting transcription factors).</p> </div