The spectrum of the random environment and localization of noise

We consider random walk on a mildly random environment on finite transitive d- regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An interesting phenomenon occurs at d = 2: as the limit graph changes from a regular tree to the integers, the noise becomes localized.Comment: 18 pages, 1 figur

First Passage Properties of the Erdos-Renyi Random Graph

We study the mean time for a random walk to traverse between two arbitrary sites of the Erdos-Renyi random graph. We develop an effective medium approximation that predicts that the mean first-passage time between pairs of nodes, as well as all moments of this first-passage time, are insensitive to the fraction p of occupied links. This prediction qualitatively agrees with numerical simulations away from the percolation threshold. Near the percolation threshold, the statistically meaningful quantity is the mean transit rate, namely, the inverse of the first-passage time. This rate varies non-monotonically with p near the percolation transition. Much of this behavior can be understood by simple heuristic arguments.Comment: 10 pages, 9 figures, 2-column revtex4 forma

Amenability of groups and GG-sets

This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals of the text are (1) to be as self-contained as possible, so as to serve as a good introduction for newcomers to the field; (2) to stress the use of combinatorial tools, in collaboration with functional analysis, probability etc., with discrete groups in focus; (3) to consider from the beginning the more general notion of amenable actions; (4) to describe recent classes of examples, and in particular groups acting on Cantor sets and topological full groups

Self-avoiding walks and connective constants

The connective constant $\mu(G)$ of a quasi-transitive graph $G$ is the asymptotic growth rate of the number of self-avoiding walks (SAWs) on $G$ from a given starting vertex. We survey several aspects of the relationship between the connective constant and the underlying graph $G$. $\bullet$ We present upper and lower bounds for $\mu$ in terms of the vertex-degree and girth of a transitive graph. $\bullet$ We discuss the question of whether $\mu\ge\phi$ for transitive cubic graphs (where $\phi$ denotes the golden mean), and we introduce the Fisher transformation for SAWs (that is, the replacement of vertices by triangles). $\bullet$ We present strict inequalities for the connective constants $\mu(G)$ of transitive graphs $G$, as $G$ varies. $\bullet$ As a consequence of the last, the connective constant of a Cayley graph of a finitely generated group decreases strictly when a new relator is added, and increases strictly when a non-trivial group element is declared to be a further generator. $\bullet$ We describe so-called graph height functions within an account of "bridges" for quasi-transitive graphs, and indicate that the bridge constant equals the connective constant when the graph has a unimodular graph height function. $\bullet$ A partial answer is given to the question of the locality of connective constants, based around the existence of unimodular graph height functions. $\bullet$ Examples are presented of Cayley graphs of finitely presented groups that possess graph height functions (that are, in addition, harmonic and unimodular), and that do not. $\bullet$ The review closes with a brief account of the "speed" of SAW.Comment: Accepted version. arXiv admin note: substantial text overlap with arXiv:1304.721

Small doubling in groups

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos Centenary conferenc

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

Combined loss of the BH3-only proteins Bim and Bmf restores B-cell development and function in TACI-Ig transgenic mice.

Terminal differentiation of B cells depends on two interconnected survival pathways, elicited by the B-cell receptor (BCR) and the BAFF receptor (BAFF-R), respectively. Loss of either signaling pathway arrests B-cell development. Although BCR-dependent survival depends mainly on the activation of the v-AKT murine thymoma viral oncogene homolog 1 (AKT)/PI3-kinase network, BAFF/BAFF-R-mediated survival engages non-canonical NF-κB signaling as well as MAPK/extracellular-signal regulated kinase and AKT/PI3-kinase modules to allow proper B-cell development. Plasma cell survival, however, is independent of BAFF-R and regulated by APRIL that signals NF-κB activation via alternative receptors, that is, transmembrane activator and CAML interactor (TACI) or B-cell maturation (BCMA). All these complex signaling events are believed to secure survival by increased expression of anti-apoptotic B-cell lymphoma 2 (Bcl2) family proteins in developing and mature B cells. Curiously, how lack of BAFF- or APRIL-mediated signaling triggers B-cell apoptosis remains largely unexplored. Here, we show that two pro-apoptotic members of the 'Bcl2 homology domain 3-only' subgroup of the Bcl2 family, Bcl2 interacting mediator of cell death (Bim) and Bcl2 modifying factor (Bmf), mediate apoptosis in the context of TACI-Ig overexpression that effectively neutralizes BAFF as well as APRIL. Surprisingly, although Bcl2 overexpression triggers B-cell hyperplasia exceeding the one observed in Bim(-/-)Bmf(-/-) mice, Bcl2 transgenic B cells remain susceptible to the effects of TACI-Ig expression in vivo, leading to ameliorated pathology in Vav-Bcl2 transgenic mice. Together, our findings shed new light on the molecular machinery restricting B-cell survival during development, normal homeostasis and under pathological conditions. Our data further suggest that Bcl2 antagonists might improve the potency of BAFF/APRIL-depletion strategies in B-cell-driven pathologies

Senescence rewires microenvironment sensing to facilitate anti-tumor immunity

Cellular senescence involves a stable cell cycle arrest coupled to a secretory program that, in some instances, stimulates the immune clearance of senescent cells. Using an immune competent liver cancer model in which senescence triggers CD8 T cell-mediated tumor rejection, we show that senescence also remodels the cell surface proteome to alter how tumor cells sense environmental factors, as exemplified by Type II interferon (IFN-y). Compared to proliferating cells, senescent cells upregulate the IFN-y receptor, become hypersensitized to microenvironmental IFN-y, and more robustly induce the antigen presenting machinery--effects also recapitulated in human tumor cells undergoing therapy-induced senescence. Disruption of IFN-y sensing in senescent cells blunts their immune-mediated clearance without disabling the senescence state or its characteristic secretory program. Our results demonstrate that senescent cells have an enhanced ability to both send and receive environmental signals, and imply that each process is required for their effective immune surveillance