Related papers: Existence Proofs of Some EXIT Like Functions
In graph theory, the Szemer\'edi regularity lemma gives a decomposition of the indicator function for any graph $G$ into a structured component, a uniform part, and a small error. This result, in conjunction with a counting lemma that…
Generalized product codes (GPCs) are extensions of product codes (PCs) where code symbols are protected by two component codes but not necessarily arranged in a rectangular array. We consider a deterministic construction of GPCs (as opposed…
We present a systematic study of the steep decay emission from gamma-ray bursts (GRBs) observed by the Swift X-Ray Telescope (XRT). In contrast to the analysis described in recent literature, we produce composite Burst Alert Telescope (BAT)…
Let $E_1$ and $E_2$ be $\overline{\mathbb{Q}}$-nonisogenous, semistable elliptic curves over $\mathbb{Q}$, having respective conductors $N_{E_1}$ and $N_{E_2}$ and both without complex multiplication. For each prime $p$, denote by…
This is the second in a series of articles devoted to showing that a typical covering map of large degree to a fixed, regular graph has its new adjacency eigenvalues within the bound conjectured by Alon for random regular graphs. The first…
Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…
The Bethe approximation is a successful method for approximating partition functions of probabilistic models associated with a graph. Recently, Chertkov and Chernyak derived an interesting formula called Loop Series Expansion, which is an…
We introduce EXOFIT, a Bayesian tool for estimating orbital parameters of extrasolar planets from radial velocity measurements. EXOFIT can search for either one or two planets at present. EXOFIT employs Markov Chain Monte Carlo method…
Arakelov-Green functions defined on metrized graphs have important role in relating arithmetical problems on algebraic curves into graph theoretical problems. In this paper, we clarify the combinatorial interpretation of certain…
Consider non-intersecting Brownian motions on the real line, starting from the origin at t=0, with a number of particles forced to reach p distinct target points at time t=1. This work shows that the transition probability, that is the…
Static binary lifting is essential in binary rewriting frameworks. Existing tools overlook the impact of External Function Completion (EXFC) in static binary lifting. EXFC recovers the prototypes of External Functions (EXFs, functions…
We develop a categorical index calculus for elliptic symbol families. The categorified index problems we consider are a secondary version of the traditional problem of expressing the index class in K-theory in terms of…
The objective of this paper is to establish a general asymptotic representation (\textit{GAR}) for a wide range of statistics, employing two fundamental processes: the functional empirical process (\textit{fep}) and the residual functional…
We introduce the notion of orbit equivalence of directed graphs, following Matsumoto's notion of continuous orbit equivalence for topological Markov shifts. We show that two graphs in which every cycle has an exit are orbit equivalent if…
The Asymmetric Simple Exclusion Process is one of the most extensively studied models in non-equilibrium statistical mechanics. The macroscopic particle current produced in its steady state is directly related to the breaking of detailed…
In this paper, we first introduce the extended binary representation of non-binary codes, which corresponds to a covering graph of the bipartite graph associated with the non-binary code. Then we show that non-binary codewords correspond to…
In this note, we want to provide a comparison among the efficiency of different approaches for the verification of K-step and infinite-step opacity based on three different graphs: the Extended Basis Reachability Graph (EBRG), the Basis…
We continue the investigation of the spectral theory and exponential asymptotics of Markov processes, following Kontoyiannis and Meyn (2003). We introduce a new family of nonlinear Lyapunov drift criteria, characterizing distinct subclasses…
We propose Scrambler, and e-graph-based MBA obfuscation tool using Equality Expansion to efficiently generate complex and diverse expressions with equivalence guaranteed by construction. Experiments show Scrambler improves existing tools in…
Generalized Zeckendorf decompositions are expansions of integers as sums of elements of solutions to recurrence relations. The simplest cases are base-$b$ expansions, and the standard Zeckendorf decomposition uses the Fibonacci sequence.…