相关论文: Corrections of Zipf's and Heaps' Laws Derived from…

Fitts' law is a linear equation relating movement time to an index of movement difficulty. The recent finding that Fitts' law applies to voluntary movement of the vocal tract raises the question of whether the theory of speech production…

We report a method of estimating what percentage of people who cited a paper had actually read it. The method is based on a stochastic modeling of the citation process that explains empirical studies of misprint distributions in citations…

Words in natural language follow a Zipfian distribution whereby some words are frequent but most are rare. Learning representations for words in the "long tail" of this distribution requires enormous amounts of data. Representations of rare…

We introduce time variation in the flip-rates of the Voter Model. This type of generalisation is relevant to models of ageing in language change, allowing the representation of changes in speakers' learning rates over their lifetime and may…

We study the cost-minimization problem posed by Ferrer i Cancho and Sol\'e in their model of communication that aimed at explaining the origin of Zipf's law [PNAS 100, 788 (2003)]. Direct analysis shows that the minimum cost is $\min…

Analyzing and modeling the mobility process with tour behavior is fundamental to understanding a wide range of complex systems, including animal foraging, human mobility and freight transportation. However, despite their importance, the…

The uniform information density (UID) hypothesis proposes that speakers aim to distribute information evenly throughout a text, balancing production effort and listener comprehension difficulty. However, language typically does not maintain…

We observe the statistical properties of blogs that are expected to reflect social human interaction. Firstly, we introduce a basic normalization preprocess that enables us to evaluate the genuine word frequency in blogs that are…

We introduce a simple and generic model that reproduces Zipf's law. By regarding the time evolution of the model as a random walk in the logarithmic scale, we explain theoretically why this model reproduces Zipf's law. The explanation shows…

Background: Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings…

We show that statistical criticality, i.e. the occurrence of power law frequency distributions, arises in samples that are maximally informative about the underlying generating process. In order to reach this conclusion, we first identify…

This work lists and describes the main recent strategies for building fixed-length, dense and distributed representations for words, based on the distributional hypothesis. These representations are now commonly called word embeddings and,…

We consider the Hopfield model with $n$ neurons and an increasing number $p=p(n)$ of randomly chosen patterns and use Stein's method to obtain rates of convergence for the central limit theorem of overlap parameters, which holds for every…

We review recent progress in understanding the meaning of mutual information in natural language. Let us define words in a text as strings that occur sufficiently often. In a few previous papers, we have shown that a power-law distribution…

Goodwin's model is a cornerstone in the study of dynamical systems within macroeconomics, explaining the interaction between employment ratio and wage share in a closed economy. Analogous to predator-prey dynamics in mathematical economics,…

Recent works on word representations mostly rely on predictive models. Distributed word representations (aka word embeddings) are trained to optimally predict the contexts in which the corresponding words tend to appear. Such models have…

Most of various large-size complex systems in nature and society can be well described as complex networks (graphs) to better understand the evolutional mechanisms and dynamical functions behind themselves. Of some part follow scale-free…

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…

An expression is proposed for determining the error caused on entropy estimates by finite sample effects. This expression is based on the Ansatz that the ranked distribution of probabilities tends to follow an empirical Zipf law.

Biosemiosis is a process of choice-making between simultaneously alternative options. It is well-known that, when sufficiently young children encounter a new word, they tend to interpret it as pointing to a meaning that does not have a word…