On the critical point of the Random Walk Pinning Model in dimension d=3

We consider the Random Walk Pinning Model studied in [3,2]: this is a random walk X on Z^d, whose law is modified by the exponential of \beta times L_N(X,Y), the collision local time up to time N with the (quenched) trajectory Y of another d-dimensional random walk. If \beta exceeds a certain critical value \beta_c, the two walks stick together for typical Y realizations (localized phase). A natural question is whether the disorder is relevant or not, that is whether the quenched and annealed systems have the same critical behavior. Birkner and Sun proved that \beta_c coincides with the critical point of the annealed Random Walk Pinning Model if the space dimension is d=1 or d=2, and that it differs from it in dimension d\ge4 (for d\ge 5, the result was proven also in [2]). Here, we consider the open case of the marginal dimension d=3, and we prove non-coincidence of the critical points.Comment: 23 pages; v2: added reference [4], where a result similar to Th. 2.8 is proven independently for the continuous-time mode

A max-type recursive model: some properties and open questions

We consider a simple max-type recursive model which was introduced in the study of depinning transition in presence of strong disorder, by Derrida and Retaux. Our interest is focused on the critical regime, for which we study the extinction probability, the first moment and the moment generating function. Several stronger assertions are stated as conjectures.Comment: A version accepted to Charles Newman Festschrift (to appear by Springer

The effect of disorder on the free-energy for the Random Walk Pinning Model: smoothing of the phase transition and low temperature asymptotics

We consider the continuous time version of the Random Walk Pinning Model (RWPM), studied in [5,6,7]. Given a fixed realization of a random walk Y$ on Z^d with jump rate rho (that plays the role of the random medium), we modify the law of a random walk X on Z^d with jump rate 1 by reweighting the paths, giving an energy reward proportional to the intersection time L_t(X,Y)=\int_0^t \ind_{X_s=Y_s}\dd s: the weight of the path under the new measure is exp(beta L_t(X,Y)), beta in R. As beta increases, the system exhibits a delocalization/localization transition: there is a critical value beta_c, such that if beta>beta_c the two walks stick together for almost-all Y realizations. A natural question is that of disorder relevance, that is whether the quenched and annealed systems have the same behavior. In this paper we investigate how the disorder modifies the shape of the free energy curve: (1) We prove that, in dimension d larger or equal to three 3, the presence of disorder makes the phase transition at least of second order. This, in dimension larger or equal to 4, contrasts with the fact that the phase transition of the annealed system is of first order. (2) In any dimension, we prove that disorder modifies the low temperature asymptotic of the free energy.Comment: 18 page

The free energy in the Derrida--Retaux recursive model

We are interested in a simple max-type recursive model studied by Derrida and Retaux (2014) in the context of a physics problem, and find a wide range for the exponent in the free energy in the nearly supercritical regime

Frame Permutation Quantization

Frame permutation quantization (FPQ) is a new vector quantization technique using finite frames. In FPQ, a vector is encoded using a permutation source code to quantize its frame expansion. This means that the encoding is a partial ordering of the frame expansion coefficients. Compared to ordinary permutation source coding, FPQ produces a greater number of possible quantization rates and a higher maximum rate. Various representations for the partitions induced by FPQ are presented, and reconstruction algorithms based on linear programming, quadratic programming, and recursive orthogonal projection are derived. Implementations of the linear and quadratic programming algorithms for uniform and Gaussian sources show performance improvements over entropy-constrained scalar quantization for certain combinations of vector dimension and coding rate. Monte Carlo evaluation of the recursive algorithm shows that mean-squared error (MSE) decays as 1/M^4 for an M-element frame, which is consistent with previous results on optimal decay of MSE. Reconstruction using the canonical dual frame is also studied, and several results relate properties of the analysis frame to whether linear reconstruction techniques provide consistent reconstructions.Comment: 29 pages, 5 figures; detailed added to proof of Theorem 4.3 and a few minor correction

Membrane Permeability Threshold for Osmotic Power Plant Efficiency

In a context of ever-growing electricity consumption and need for less polluting sources of energy, salinity gradient power (SGP) based on osmosis is a promising technology. Salinity difference between two solutions separated by a semi-permeable membrane leads to the pressure increase. The aim of this study is to find the critical permeability threshold of a membrane for the dimensioning an osmotic power plant. Using Spiegler-Kedem equations, the various fluxes across the membrane have been calculated, and delivered power is explicitly derived in terms of system parameters. A necessary condition for economic viability is that its upper bound is larger than a critical threshold value below which osmotic power plant is not profitable. As it is directly proportional to membrane permeability, fixing the optimal membrane permeability value will in turn enable conceive more efficient membranes specifically made for osmotic energy production, as such membranes do not exist today

Altered distribution of mucosal NK cells during HIV infection.

The human gut mucosa is a major site of human immunodeficiency virus (HIV) infection and infection-associated pathogenesis. Increasing evidence shows that natural killer (NK) cells have an important role in control of HIV infection, but the mechanism(s) by which they mediate antiviral activity in the gut is unclear. Here, we show that two distinct subsets of NK cells exist in the gut, one localized to intraepithelial spaces (intraepithelial lymphocytes, IELs) and the other to the lamina propria (LP). The frequency of both subsets of NK cells was reduced in chronic infection, whereas IEL NK cells remained stable in spontaneous controllers with protective killer immunoglobulin-like receptor/human leukocyte antigen genotypes. Both IEL and LP NK cells were significantly expanded in immunological non-responsive patients, who incompletely recovered CD4+ T cells on highly active antiretroviral therapy (HAART). These data suggest that both IEL and LP NK cells may expand in the gut in an effort to compensate for compromised CD4+ T-cell recovery, but that only IEL NK cells may be involved in providing durable control of HIV in the gut

Modification of the Landau-Lifshitz Equation in the Presence of a Spin-Polarized Current in CMR and GMR Materials

We derive a continuum equation for the magnetization of a conducting ferromagnet in the presence of a spin-polarized current. Current effects enter in the form of a topological term in the Landau-Lifshitz equation . In the stationary situation the problem maps onto the motion of a classical charged particle in the field of a magnetic monopole. The spatial dependence of the magnetization is calculated for a one-dimensional geometry and suggestions for experimental observation are made. We also consider time-dependent solutions and predict a spin-wave instability for large currents.Comment: 4 two-column pages in RevTex, 3 ps-figure