Thermodynamic properties of extremely diluted symmetric Q-Ising neural networks

Using the replica-symmetric mean-field theory approach the thermodynamic and retrieval properties of extremely diluted {\it symmetric} $Q$-Ising neural networks are studied. In particular, capacity-gain parameter and capacity-temperature phase diagrams are derived for $Q=3, 4$ and $Q=\infty$. The zero-temperature results are compared with those obtained from a study of the dynamics of the model. Furthermore, the de Almeida-Thouless line is determined. Where appropriate, the difference with other $Q$-Ising architectures is outlined.Comment: 16 pages Latex including 6 eps-figures. Corrections, also in most of the figures have been mad

Even-visiting random walks: exact and asymptotic results in one dimension

We reconsider the problem of even-visiting random walks in one dimension. This problem is mapped onto a non-Hermitian Anderson model with binary disorder. We develop very efficient numerical tools to enumerate and characterize even-visiting walks. The number of closed walks is obtained as an exact integer up to 1828 steps, i.e., some $10^{535}$ walks. On the analytical side, the concepts and techniques of one-dimensional disordered systems allow to obtain explicit asymptotic estimates for the number of closed walks of $4k$ steps up to an absolute prefactor of order unity, which is determined numerically. All the cumulants of the maximum height reached by such walks are shown to grow as $k^{1/3}$, with exactly known prefactors. These results illustrate the tight relationship between even-visiting walks, trapping models, and the Lifshitz tails of disordered electron or phonon spectra.Comment: 24 pages, 4 figures. To appear in J. Phys.

Finite time and asymptotic behaviour of the maximal excursion of a random walk

We evaluate the limit distribution of the maximal excursion of a random walk in any dimension for homogeneous environments and for self-similar supports under the assumption of spherical symmetry. This distribution is obtained in closed form and is an approximation of the exact distribution comparable to that obtained by real space renormalization methods. Then we focus on the early time behaviour of this quantity. The instantaneous diffusion exponent $\nu_n$ exhibits a systematic overshooting of the long time exponent. Exact results are obtained in one dimension up to third order in $n^{-1/2}$. In two dimensions, on a regular lattice and on the Sierpi\'nski gasket we find numerically that the analytic scaling $\nu_n \simeq \nu+A n^{-\nu}$ holds.Comment: 9 pages, 4 figures, accepted J. Phys.

Estrogen regulation of TRPM8 expression in breast cancer cells

<p>Abstract</p> <p>Background</p> <p>The calcium-permeable cation channel TRPM8 (melastatin-related transient receptor potential member 8) is over-expressed in several cancers. The present study aimed at investigating the expression, function and potential regulation of TRPM8 channels by ER alpha (estrogen receptor alpha) in breast cancer.</p> <p>Methods</p> <p>RT-PCR, Western blot, immuno-histochemical, and siRNA techniques were used to investigate TRPM8 expression, its regulation by estrogen receptors, and its expression in breast tissue. To investigate the channel activity in MCF-7 cells, we used the whole cell patch clamp and the calcium imaging techniques.</p> <p>Results</p> <p>TRPM8 channels are expressed at both mRNA and protein levels in the breast cancer cell line MCF-7. Bath application of the potent TRPM8 agonist Icilin (20 μM) induced a strong outwardly rectifying current at depolarizing potentials, which is associated with an elevation of cytosolic calcium concentration, consistent with established TRPM8 channel properties. RT-PCR experiments revealed a decrease in TRPM8 mRNA expression following steroid deprivation for 48 and 72 hours. In steroid deprived medium, addition of 17-beta-estradiol (E₂, 10 nM) increased both TRPM8 mRNA expression and the number of cells which respond to Icilin, but failed to affect the Ca²⁺entry amplitude. Moreover, silencing ERα mRNA expression with small interfering RNA reduced the expression of TRPM8. Immuno-histochemical examination of the expression of TRPM8 channels in human breast tissues revealed an over-expression of TRPM8 in breast adenocarcinomas, which is correlated with estrogen receptor positive (ER⁺) status of the tumours.</p> <p>Conclusion</p> <p>Taken together, these results show that TRPM8 channels are expressed and functional in breast cancer and that their expression is regulated by ER alpha.</p

An Update on the Multifaceted Roles of STAT3 in the Heart

Signal transducer and activator of transcription 3 (STAT3) is a signaling molecule and transcription factor that plays important protective roles in the heart. The protection mediated by STAT3 is attributed to its genomic actions as a transcription factor and other non-genomic roles targeting mitochondrial function and autophagy. As a transcription factor, STAT3 upregulates genes that are anti-oxidative, anti-apoptotic, and pro-angiogenic, but suppresses anti-inflammatory and anti-fibrotic genes. Its suppressive effects on gene expression are achieved through competing with other transcription factors or cofactors. STAT3 is also linked to the modification of mRNA expression profiles in cardiac cells by inhibiting or inducing miRNA. In addition to these genomic roles, STAT3 is suggested to function protectively in mitochondria, where it regulates ROS production, in part by regulating the activities of the electron transport chain complexes, although our recent evidence calls this role into question. Nonetheless, STAT3 is a key player known to be activated in the cardioprotective ischemic conditioning protocols. Through these varied roles, STAT3 participates in various mechanisms that contribute to cardioprotection against different heart pathologies, including myocardial infarction, hypertrophy, diabetic cardiomyopathy, and peripartum cardiomyopathy. Understanding how STAT3 is involved in the protective mechanisms against these different cardiac pathologies could lead to novel therapeutic strategies to treat them