The science of complexity aims to answer the question of what rules nature chooses when
assembling the basic constituents of matter and energy into structures and dynamical …

We analyze the occurrence frequencies of over 15 million words recorded in millions of
books published during the past two centuries in seven different languages. For all …

We propose a stochastic model for the number of different words in a given database which
incorporates the dependence on the database size and historical changes. The main feature …

Mathematical Linguistics introduces the mathematical foundations of linguistics to computer
scientists, engineers, and mathematicians interested in natural language processing. The …

Background Zipf's law and Heaps' law are observed in disparate complex systems. Of
particular interests, these two laws often appear together. Many theoretical models and …

In this note we will consider the following problem: how many coupons we have to purchase
(on average) to complete a collection. This problem, which takes everybody back to his …

Circular convolution and random permutation have each been proposed as neurally
plausible binding operators capable of encoding sequential information in semantic …

The dependence on text length of the statistical properties of word occurrences has long
been considered a severe limitation on the usefulness of quantitative linguistics. We …

In this paper, we combine statistical analysis of written texts and simple stochastic models to
explain the appearance of scaling laws in the statistics of word frequencies. The average …

In this paper we present statistical analysis of English texts from Wikipedia. We try to address
the issue of language complexity empirically by comparing the simple English Wikipedia …