Related papers: Asymptotic Analysis of Run-Length Encoding

Recently, in the ref. Physica A \bfm{296} 405 (2001), a new one parameter deformation for the exponential function $\exp_{_{\{{\scriptstyle \kappa}\}}}(x)= (\sqrt{1+\kappa^2x^2}+\kappa x)^{1/\kappa}; \exp_{_{\{{\scriptstyle 0}\}}}(x)=\exp…

We study an asymptotic behavior of the probabilities of first-order properties of random graph G(N,p) in the article. We conider p such that lnp=-alnN, a>0. We find values of parameter a from (1-exp(ln2(1-k)),1) such that the random graph…

Text compression schemes and compact data structures usually combine sophisticated probability models with basic coding methods whose average codeword length closely match the entropy of known distributions. In the frequent case where basic…

Optimal prefix codes are studied for pairs of independent, integer-valued symbols emitted by a source with a geometric probability distribution of parameter $q$, $0{<}q{<}1$. By encoding pairs of symbols, it is possible to reduce the…

We consider the problem of constructing prefix-free codes in which a designated symbol, a space, can only appear at the end of codewords. We provide a linear-time algorithm to construct almost-optimal codes with this property, meaning that…

In this work, we construct energy-efficient variable-to-fixed length (V2F), fixed-to-variable length (F2V), and variable-to-variable length (V2V) prefix-free codes, which are optimal (or near-optimal) in the sense that no (or few) other…

We propose a new, efficient non-deterministic decoding algorithm for square-free Goppa codes over $\F_p$ for any prime $p$. If the code in question has degree $t$ and the average distance to the closest codeword is at least $(4/p)t + 1$,…

Denote by $p(k)$ the limit, as $n \rightarrow \infty$, of the probability that a random permutation on a set of size $n$ has an invariant set of size $k$. We give an asymptotic formula for $p(k)$, showing that it is asymptotically…

The Pitman sampling formula has been intensively studied as a distribution of random partitions. One of the objects of interest is the length $K (= K_{n,\theta,\alpha})$ of a random partition that follows the Pitman sampling formula, where…

For the discrete memoryless sources with a countably infinite alphabet, we prove that for any positive integer $k$, there exists a corresponding probability interval such that if the largest symbol probability $p_{1}$ falls in this…

We study the general fragmentation process starting from one element of size unity (E=1). At each elementary step, each existing element of size $E$ can be fragmented into $k\,(\ge 2)$ elements with probability $p_k$. From the continuous…

We characterise the behavior of the maximum Diaconis--Ylvisaker prior penalized likelihood estimator in high-dimensional logistic regression, where the number of covariates is a fraction $\kappa \in (0,1)$ of the number of observations $n$,…

We describe an algorithm computing an optimal prefix free code for $n$ unsorted positive weights in time within $O(n(1+\lg \alpha))\subseteq O(n\lg n)$, where the alternation $\alpha\in[1..n-1]$ measures the amount of sorting required by…

This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's analysis are presented, yielding several asymptotic and non-asymptotic bounds on…

We prove several asymptotic results for partial and false theta functions arising from Jacobi forms, as the modular variable $\tau$ tends to $0$ along the imaginary axis, and the elliptic variable $z$ is unrestricted in the complex plane.…

Let $ \{\varphi_i(z;\alpha)\}_{i=0}^\infty $, corresponding to $ \alpha\in(-1,1) $, be orthonormal Geronimus polynomials. We study asymptotic behavior of the expected number of real zeros, say $ \mathbb E_n(\alpha) $, of random polynomials…

We design and analyze an algorithm for first-order stochastic optimization of a large class of functions on $\mathbb{R}^d$. In particular, we consider the \emph{variationally coherent} functions which can be convex or non-convex. The…

We investigate the behavior of the periods and border lengths of random words over a fixed alphabet. We show that the asymptotic probability that a random word has a given maximal border length $k$ is a constant, depending only on $k$ and…

The damped and parametrically driven nonlinear Dirac equation with arbitrary nonlinearity parameter $\kappa$ is analyzed, when the external force is periodic in space and given by $f(x) =r\cos(K x)$, both numerically and in a variational…

We present a novel bit-parallel representation, based on the run-length encoding, of the nondeterministic KMP and suffix automata for a string $P$ with at least two distinct symbols. Our method is targeted to the case of long strings over…