A Stochastic Method for Solving Time-Fractional Differential Equations

We present a stochastic method for efficiently computing the solution of time-fractional partial differential equations (fPDEs) that model anomalous diffusion problems of the subdiffusive type. After discretizing the fPDE in space, the ensuing system of fractional linear equations is solved resorting to a Monte Carlo evaluation of the corresponding Mittag-Leffler matrix function. This is accomplished through the approximation of the expected value of a suitable multiplicative functional of a stochastic process, which consists of a Markov chain whose sojourn times in every state are Mittag-Leffler distributed. The resulting algorithm is able to calculate the solution at conveniently chosen points in the domain with high efficiency. In addition, we present how to generalize this algorithm in order to compute the complete solution. For several large-scale numerical problems, our method showed remarkable performance in both shared-memory and distributed-memory systems, achieving nearly perfect scalability up to 16,384 CPU cores.Comment: Submitted to the Journal of Computational Physic

A Fast Monte Carlo algorithm for evaluating matrix functions with application in complex networks

We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function. This contrasts with the "classical" Monte Carlo method which only works with one entry at a time, resulting in a significant better convergence rate than the "classical" approach. To assess the applicability of our method, we compute the subgraph centrality and total communicability of several large networks. In all benchmarks analyzed so far, the performance of our method was significantly superior to the competition, being able to scale up to 64 CPU cores with a remarkable efficiency.Comment: Submitted to the Journal of Scientific Computin

MICROSCOPE mission: first results of a space test of the equivalence principle

According to the weak equivalence principle, all bodies should fall at the same rate in a gravitational field. The MICROSCOPE satellite, launched in April 2016, aims to test its validity at the 10−15 precision level, by measuring the force required to maintain two test masses (of titanium and platinum alloys) exactly in the same orbit. A nonvanishing result would correspond to a violation of the equivalence principle, or to the discovery of a new long-range force. Analysis of the first data gives δ(Ti,Pt)=[−1±9(stat)±9(syst)]×10−15 (1σ statistical uncertainty) for the titanium-platinum Eötvös parameter characterizing the relative difference in their free-fall accelerations

Lymphotoxin signaling is initiated by the viral polymerase in HCV-linked tumorigenesis

Exposure to hepatitis C virus (HCV) typically results in chronic infection that leads to progressive liver disease ranging from mild inflammation to severe fibrosis and cirrhosis as well as primary liver cancer. HCV triggers innate immune signaling within the infected hepatocyte, a first step in mounting of the adaptive response against HCV infection. Persistent inflammation is strongly associated with liver tumorigenesis. The goal of our work was to investigate the initiation of the inflammatory processes triggered by HCV viral proteins in their host cell and their possible link with HCV-related liver cancer. We report a dramatic upregulation of the lymphotoxin signaling pathway and more specifically of lymphotoxin-beta in tumors of the FL-N/35 HCV-transgenic mice. Lymphotoxin expression is accompanied by activation of NF-kappaB, neosynthesis of chemokines and intra-tumoral recruitment of mononuclear cells. Spectacularly, IKKbeta inactivation in FL-N/35 mice drastically reduces tumor incidence. Activation of lymphotoxin-beta pathway can be reproduced in several cellular models, including the full length replicon and HCV-infected primary human hepatocytes. We have identified NS5B, the HCV RNA dependent RNA polymerase, as the viral protein responsible for this phenotype and shown that pharmacological inhibition of its activity alleviates activation of the pro-inflammatory pathway. These results open new perspectives in understanding the inflammatory mechanisms linked to HCV infection and tumorigenesis