Non-fixation for Biased Activated Random Walks

We prove that the model of Activated Random Walks on Z^d with biased jump distribution does not fixate for any positive density, if the sleep rate is small enough, as well as for any finite sleep rate, if the density is close enough to 1. The proof uses a new criterion for non-fixation. We provide a pathwise construction of the process, of independent interest, used in the proof of this non-fixation criterion

Enabling Disaster Resilient 4G Mobile Communication Networks

The 4G Long Term Evolution (LTE) is the cellular technology expected to outperform the previous generations and to some extent revolutionize the experience of the users by taking advantage of the most advanced radio access techniques (i.e. OFDMA, SC-FDMA, MIMO). However, the strong dependencies between user equipments (UEs), base stations (eNBs) and the Evolved Packet Core (EPC) limit the flexibility, manageability and resiliency in such networks. In case the communication links between UEs-eNB or eNB-EPC are disrupted, UEs are in fact unable to communicate. In this article, we reshape the 4G mobile network to move towards more virtual and distributed architectures for improving disaster resilience, drastically reducing the dependency between UEs, eNBs and EPC. The contribution of this work is twofold. We firstly present the Flexible Management Entity (FME), a distributed entity which leverages on virtualized EPC functionalities in 4G cellular systems. Second, we introduce a simple and novel device-todevice (D2D) communication scheme allowing the UEs in physical proximity to communicate directly without resorting to the coordination with an eNB.Comment: Submitted to IEEE Communications Magazin

B_K from quenched QCD with exact chiral symmetry

We present a calculation of the standard model \Delta S=2 matrix element relevant to indirect CP violation in K->\pi\pi decays which uses Neuberger's chiral formulation of lattice fermions. The computation is performed in the quenched approximation on a 16^3x32 lattice that has a lattice spacing a\sim 0.1 fm. The resulting bare matrix element is renormalized non-perturbatively. Our main result is B_K^{RGI}=0.87(8)^{+2+14}_{-1-14}, where the first error is statistical, the second is systematic and the third is an estimate of the uncertainty associated with the quenched approximation and with the fact that our kaons are composed of degenerate s and d quarks with masses \sim m_s/2.Comment: 5 pages (revtex4), 2 figure

Forwarding Tables Verification through Representative Header Sets

Forwarding table verification consists in checking the distributed data-structure resulting from the forwarding tables of a network. A classical concern is the detection of loops. We study this problem in the context of software-defined networking (SDN) where forwarding rules can be arbitrary bitmasks (generalizing prefix matching) and where tables are updated by a centralized controller. Basic verification problems such as loop detection are NP-hard and most previous work solves them with heuristics or SAT solvers. We follow a different approach based on computing a representation of the header classes, i.e. the sets of headers that match the same rules. This representation consists in a collection of representative header sets, at least one for each class, and can be computed centrally in time which is polynomial in the number of classes. Classical verification tasks can then be trivially solved by checking each representative header set. In general, the number of header classes can increase exponentially with header length, but it remains polynomial in the number of rules in the practical case where rules are constituted with predefined fields where exact, prefix matching or range matching is applied in each field (e.g., IP/MAC addresses, TCP/UDP ports). We propose general techniques that work in polynomial time as long as the number of classes of headers is polynomial and that do not make specific assumptions about the structure of the sets associated to rules. The efficiency of our method rely on the fact that the data-structure representing rules allows efficient computation of intersection, cardinal and inclusion. Finally, we propose an algorithm to maintain such representation in presence of updates (i.e., rule insert/update/removal). We also provide a local distributed algorithm for checking the absence of black-holes and a proof labeling scheme for locally checking the absence of loops

The method of polarized traces for the 2D Helmholtz equation

We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media, with online parallel complexity that scales optimally as O(NL), where N is the number of volume unknowns, and L is the number of processors, as long as L grows at most like a small fractional power of N. The solver decomposes the domain into layers, and uses transmission conditions in boundary integral form to explicitly define "polarized traces", i.e., up- and down-going waves sampled at interfaces. Local direct solvers are used in each layer to precompute traces of local Green's functions in an embarrassingly parallel way (the offline part), and incomplete Green's formulas are used to propagate interface data in a sweeping fashion, as a preconditioner inside a GMRES loop (the online part). Adaptive low-rank partitioning of the integral kernels is used to speed up their application to interface data. The method uses second-order finite differences. The complexity scalings are empirical but motivated by an analysis of ranks of off-diagonal blocks of oscillatory integrals. They continue to hold in the context of standard geophysical community models such as BP and Marmousi 2, where convergence occurs in 5 to 10 GMRES iterations. While the parallelism in this paper stems from decomposing the domain, we do not explore the alternative of parallelizing the systems solves with distributed linear algebra routines. Keywords: Domain decomposition; Helmholtz equation; Integral equations; High-frequency; Fast methodsUnited States. Air Force Office of Scientific Research (Grant FA9550-15-1-0078)United States. Office of Naval Research (Grant N00014-13-1-0403)National Science Foundation (U.S.) (Grant DMS-1255203

A short note on the nested-sweep polarized traces method for the 2D Helmholtz equation

We present a variant of the solver in Zepeda-Núñez and Demanet (2014), for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media. By changing the domain decomposition from a layered to a grid-like partition, this variant yields improved asymptotic online and offline runtimes and a lower memory footprint. The solver has online parallel complexity that scales sublinearly as θ(N/P), where N is the number of volume unknowns, and P is the number of processors, provided that P = θ(N[superscript 1/5]). The variant in Zepeda-Núñez and Demanet (2014) only afforded P = θ(N[superscript 1/5]). Algorithmic scalability is a prime requirement for wave simulation in regimes of interest for geophysical imaging. Keywords: frequency-domain, finite difference, modeling, wave equation, numericalNational Science Foundation (U.S.)United States. Office of Naval ResearchUnited States. Air Force. Office of Scientific Researc

Greedy clearing of persistent Poissonian dust

Given a Poisson point process on R, assign either one or two marks to each point of this process, independently of the others. We study the motion of a particle that jumps deterministically from its current location to the nearest point of the Poisson point process which still contains at least one mark, and removes one mark per each visit. A point of the Poisson point process which is left with no marks is removed from the system. We prove that the presence of any positive density of double marks leads to the eventual removal of every Poissonian point.Fil: Trivellato Rolla, Leonardo. Conselho Nacional de Desenvolvimiento Cientf y Tec. Associacao Instituto Nacional de Matemática Pura E Aplicada; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaFil: Sidoravicius, V.. Conselho Nacional de Desenvolvimiento Cientf y Tec. Associacao Instituto Nacional de Matemática Pura E Aplicada; BrasilFil: Tournier, Laurent. Universite de Paris 13-Nord; Franci