Particle filtering in high-dimensional chaotic systems

We present an efficient particle filtering algorithm for multiscale systems, that is adapted for simple atmospheric dynamics models which are inherently chaotic. Particle filters represent the posterior conditional distribution of the state variables by a collection of particles, which evolves and adapts recursively as new information becomes available. The difference between the estimated state and the true state of the system constitutes the error in specifying or forecasting the state, which is amplified in chaotic systems that have a number of positive Lyapunov exponents. The purpose of the present paper is to show that the homogenization method developed in Imkeller et al. (2011), which is applicable to high dimensional multi-scale filtering problems, along with important sampling and control methods can be used as a basic and flexible tool for the construction of the proposal density inherent in particle filtering. Finally, we apply the general homogenized particle filtering algorithm developed here to the Lorenz'96 atmospheric model that mimics mid-latitude atmospheric dynamics with microscopic convective processes.Comment: 28 pages, 12 figure

Encoding Two-Dimensional Range Top-k Queries

We consider various encodings that support range top-k queries on a two-dimensional array containing elements from a total order. For an m x n array, we first propose an almost optimal encoding for answering one-sided top-k queries, whose query range is restricted to [1 ... m][1 .. a], for 1 <= a <= n. Next, we propose an encoding for the general top-k queries that takes m^2 * lg(binom((k+1)n)(n)) + m * lg(m) + o(n) bits. This generalizes the one-dimensional top-k encoding of Gawrychowski and Nicholson [ICALP, 2015]. Finally, for a 2 x n array, we obtain a 2 lg(binom(3n)(n)) + 3n + o(n)-bit encoding for answering top-2 queries

Reactivation of hepatitis B after liver transplantation: Current knowledge, molecular mechanisms and implications in management

Chronic hepatitis B (CHB) is a major global health problem affecting an estimated 350 million people with more than 786000 individuals dying annually due to complications, such as cirrhosis, liver failure and hepatocellular carcinoma (HCC). Liver transplantation (LT) is considered gold standard for treatment of hepatitis B virus (HBV)-related liver failure and HCC. However, post-transplant viral reactivation can be detrimental to allograft function, leading to poor survival. Prophylaxis with high-dose hepatitis B immunoglobulin (HBIG) and anti-viral drugs have achieved remarkable progress in LT by suppressing viral replication and improving long-term survival. The combination of lamivudine (LAM) plus HBIG has been for many years the most widely used. However, life-long HBIG use is both cumbersome and costly, whereas long-term use of LAM results in resistant virus. Recently, in an effort to develop HBIG-free protocols, high potency nucleos(t)ide analogues, such as Entecavir or Tenofovir, have been tried either as monotherapy or in combination with low-dose HBIG with excellent results. Current focus is on novel antiviral targets, especially for covalently closed circular DNA (cccDNA), in an effort to eradicate HBV infection instead of viral suppression. However, there are several other molecular mechanisms through which HBV may reactivate and need equal attention. The purpose of this review is to address post-LT HBV reactivation, its risk factors, underlying molecular mechanisms, and recent advancements and future of anti-viral therapy