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

Differential role of TRP channels in prostate cancer

Abstract A major clinical problem with PC (prostate cancer) is the cell's ability to survive and proliferate upon androgen withdrawal. Indeed, deregulated cell differentiation and proliferation, together with the suppression of apoptosis, provides the condition for abnormal tissue growth. Here, we examine the differential role of TRP (transient receptor potential) channels in the control of Ca 2+ homoeostasis and growth of PC cells

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.

Order statistics for d-dimensional diffusion processes

We present results for the ordered sequence of first passage times of arrival of N random walkers at a boundary in Euclidean spaces of d dimensions

Nonuniversal Critical Spreading in Two Dimensions

Continuous phase transitions are studied in a two dimensional nonequilibrium model with an infinite number of absorbing configurations. Spreading from a localized source is characterized by nonuniversal critical exponents, which vary continuously with the density phi in the surrounding region. The exponent delta changes by more than an order of magnitude, and eta changes sign. The location of the critical point also depends on phi, which has important implications for scaling. As expected on the basis of universality, the static critical behavior belongs to the directed percolation class.Comment: 21 pages, REVTeX, figures available upon reques

Series expansions of the percolation probability for directed square and honeycomb lattices

We have derived long series expansions of the percolation probability for site and bond percolation on directed square and honeycomb lattices. For the square bond problem we have extended the series from 41 terms to 54, for the square site problem from 16 terms to 37, and for the honeycomb bond problem from 13 terms to 36. Analysis of the series clearly shows that the critical exponent $\beta$ is the same for all the problems confirming expectations of universality. For the critical probability and exponent we find in the square bond case, $q_c = 0.3552994\pm 0.0000010$, $\beta = 0.27643\pm 0.00010$, in the square site case $q_c = 0.294515 \pm 0.000005$, $\beta = 0.2763 \pm 0.0003$, and in the honeycomb bond case $q_c = 0.177143 \pm 0.000002$, $\beta = 0.2763 \pm 0.0002$. In addition we have obtained accurate estimates for the critical amplitudes. In all cases we find that the leading correction to scaling term is analytic, i.e., the confluent exponent $\Delta = 1$.Comment: LaTex with epsf, 26 pages, 2 figures and 2 tables in Postscript format included (uufiled). LaTeX version of tables also included for the benefit of those without access to PS printers (note that the tables should be printed in landscape mode). Accepted by 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