Related papers: Historical Dynamics of Lexical System as Random Wa…

Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the…

We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The transition…

The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…

We study an unbiased, discrete time random walk on the nonnegative integers, with the origin absorbing. The process has a history-dependent step length: the walker takes steps of length v while in a region which has been visited before, and…

Phylogenetic trees can be reconstructed from the matrix which contains the distances between all pairs of languages in a family. Recently, we proposed a new method which uses normalized Levenshtein distances among words with same meaning…

Hierarchies are the hidden backbones of complex systems and their analysis allows for a deeper understanding of their structure and how they evolve. We consider languages also to be complex adaptive systems with several intricate networks…

We consider random walks in dynamic random environments and propose a criterion which, if satisfied, allows to decompose the random walk trajectory into i.i.d. increments, and ultimately to prove limit theorems. The criterion involves the…

Based on the Aristotelian concept of potentiality vs. actuality allowing for the study of energy and dynamics in language, we propose a field approach to lexical analysis. Falling back on the distributional hypothesis to statistically model…

The syntactic structure of a sentence can be represented as a graph, where vertices are words and edges indicate syntactic dependencies between them. In this setting, the distance between two linked words is defined as the difference…

Many seemingly disparate Markov chains are unified when viewed as random walks on the set of chambers of a hyperplane arrangement. These include the Tsetlin library of theoretical computer science and various shuffling schemes. If only…

A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…

We consider the problem of stochastic flow of multiple particles traveling on a closed loop, with a constraint that particles move without passing. We use a Markov chain description that reduces the problem to a generalized random walk on a…

Languages evolve over time in a process in which reproduction, mutation and extinction are all possible, similar to what happens to living organisms. Using this similarity it is possible, in principle, to build family trees which show the…

The senses of words evolve. The sense of the same word may change from today to tomorrow, and multiple senses of the same word may be the result of the evolution of each other, that is, they may be parents and children. If we view Juba as…

Statistical models of word-sense disambiguation are often based on a small number of contextual features or on a model that is assumed to characterize the interactions among a set of features. Model selection is presented as an alternative…

The definition of period in finite-state Markov chains can be extended to regular languages by considering the transitions of DFAs accepting them. For example, the language $(\Sigma\Sigma)^*$ has period two because the length of a recursion…

We propose a new computational approach for tracking and detecting statistically significant linguistic shifts in the meaning and usage of words. Such linguistic shifts are especially prevalent on the Internet, where the rapid exchange of…

The functional approach to compositional distributional semantics considers transitive verbs to be linear maps that transform the distributional vectors representing nouns into a vector representing a sentence. We conduct an initial…

Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…

Previous models for learning the semantic vectors of items and their groups, such as words, sentences, nodes, and graphs, using distributed representation have been based on the assumption that the basic sense of an item corresponds to one…