Related papers: Growth fluctuation in preferential attachment dyna…
In this paper we consider the normalized lengths of the factors of some factorizations of random words. First, for the \emph{Lyndon factorization} of finite random words with $n$ independent letters drawn from a finite or infinite totally…
In his pioneering research, G. K. Zipf observed that more frequent words tend to have more meanings, and showed that the number of meanings of a word grows as the square root of its frequency. He derived this relationship from two…
We consider an opinion dynamics model where, during random pair interactions, each agent modifies her opinions about both agents of the random pair and also about some other agents, chosen randomly. Moreover, each agent belongs to a single…
Taylor's law describes the fluctuation characteristics underlying a system in which the variance of an event within a time span grows by a power law with respect to the mean. Although Taylor's law has been applied in many natural and social…
We introduce the notion of a Young generating function for a probability measure on integer partitions. We use this object to characterize probability distributions over integer partitions satisfying a law of large numbers and those that…
It was previously shown that the superdroplet algorithm for modeling the collision-coalescence process can faithfully represent mean droplet growth in turbulent clouds. But an open question is how accurately the superdroplet algorithm…
In large asexual populations, multiple beneficial mutations arise in the population, compete, interfere with each other, and accumulate on the same genome, before any of them fix. The resulting dynamics, although studied by many authors, is…
We consider the asymptotic behaviour of the fluctuation process for large stochastic systems of interacting particles driven by both idiosyncratic and common noise with an interaction kernel \(k \in L^2(\R^d) \cap L^\infty(\R^d)\). Our…
We study the fluctuation properties and return-time statistics on inhomogeneous scale-free networks using packets moving with two different dynamical rules; random diffusion and locally navigated diffusive motion with preferred edges.…
We present the first systematic investigation of Martin's Law - the empirical relationship between word frequency and polysemy - in text generated by neural language models during training. Using DBSCAN clustering of contextualized…
The main theme of this paper is the enumeration of the occurrence of a pattern in words and permutations. We mainly focus on asymptotic properties of the sequence $f_r^v(k,n),$ the number of $n$-array $k$-ary words that contain a given…
A selection problem that appears in the Lifshitz-Slyozov (LS) theory of Ostwald ripening is reexamined. The problem concerns selection of a self-similar distribution function (DF) of the minority domains with respect to their sizes from a…
It has been recently discovered that some random processes may satisfy limit theorems even though they exhibit intermittency, namely an unusual growth of moments. In this paper we provide a deeper understanding of these intricate limiting…
We consider the limiting behavior of fluctuations of small noise diffusions with multiple scales around their homogenized deterministic limit. We allow full dependence of the coefficients on the slow and fast motion. These processes arise…
We extract the individual names of persons mentioned in news reports from a Philippine-based daily in the English language from 2010-2012. Names are extracted using a learning algorithm that filters adjacent capitalized words and runs it…
The formation of sentences is a highly structured and history-dependent process. The probability of using a specific word in a sentence strongly depends on the 'history' of word-usage earlier in that sentence. We study a simple…
Systems that evolve towards a state from which they cannot depart are common in nature. But the fluctuation-dissipation theorem, a fundamental result in statistical mechanics, is mainly restricted to systems near-stationarity. In processes…
Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…
Children can use the statistical regularities of their environment to learn word meanings, a mechanism known as cross-situational learning. We take a computational approach to investigate how the information present during each observation…
The rate of occurrence of words is not uniform but varies from document to document. Despite this observation, parameters for conventional n-gram language models are usually derived using the assumption of a constant word rate. In this…