Related papers: Typical Sequences for Polish Alphabets
In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) v D,…
Prokhorov's Theorem in probability theory states that a family $\Gamma$ of probability measures on a Polish space is tight if and only if every sequence in $\Gamma$ has a weakly convergent subsequence. Due to the highly non-constructive…
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.…
In extracting predictions from theories that describe a multiverse, we face the difficulty that we must assess probability distributions over possible observations, prescribed not just by an underlying theory, but by a theory together with…
We adjust the notion of typicality originated with Russell, which was introduced and studied in a previous paper for general first-order structures, to make it expressible in the language of set theory. The adopted definition of the class…
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations…
Examples are constructed of sparse subsequences of the integers for which the associated maximal averages operator is of weak type (1,1). A consequence, by transference, is that an almost everywhere L^1 -- type ergodic theorem holds for…
The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. This problem is very important in applications but there is no systematic study of it. We present here a new technique, which…
Our goal in this article is to review the known properties of the mysterious Kolakoski sequence and at the same time look at generalizations of it over arbitrary two letter alphabets. Our primary focus will here be the case where one of the…
In this work, we study the problems of counting and sampling Mazurkiewicz traces that a regular language touches. Fix an alphabet $\Sigma$ and an independence relation $\mathbb{I} \subseteq \Sigma \times \Sigma$. The input consists of a…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…
The perturbation theory based on typicality introduced in Ref. [1] and further refined in Refs. [2, 3] provides a powerful tool since it is intended to be applicable to a wide range of scenarios while relying only on a few parameters. Even…
A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a…
A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…
In a language corpus, the probability that a word occurs $n$ times is often proportional to $1/n^2$. Assigning rank, $s$, to words according to their abundance, $\log s$ vs $\log n$ typically has a slope of minus one. That simple Zipf's law…
An occurrence of a classical pattern p in a permutation \pi is a subsequence of \pi whose letters are in the same relative order (of size) as those in p. In an occurrence of a generalized pattern, some letters of that subsequence may be…
Natural languages are described in this paper in terms of networks of synonyms: a word is identified with a node, and synonyms are connected by undirected links. Our statistical analysis of the network of synonyms in Polish language showed…
Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with…
Extracting predictions from cosmological theories that describe a multiverse, for what we are likely to observe in our domain, is crucial to establishing the validity of these theories. One way to extract such predictions is from…