Explosive Percolation: Unusual Transitions of a Simple Model

In this paper we review the recent advances on explosive percolation, a very sharp phase transition first observed by Achlioptas et al. (Science, 2009). There a simple model was proposed, which changed slightly the classical percolation process so that the emergence of the spanning cluster is delayed. This slight modification turns out to have a great impact on the percolation phase transition. The resulting transition is so sharp that it was termed explosive, and it was at first considered to be discontinuous. This surprising fact stimulated considerable interest in "Achlioptas processes". Later work, however, showed that the transition is continuous (at least for Achlioptas processes on Erdos networks), but with very unusual finite size scaling. We present a review of the field, indicate open "problems" and propose directions for future research.Comment: 27 pages, 4 figures, Review pape

Evolution of Vocabulary on Scale-free and Random Networks

We examine the evolution of the vocabulary of a group of individuals (linguistic agents) on a scale-free network, using Monte Carlo simulations and assumptions from evolutionary game theory. It is known that when the agents are arranged in a two-dimensional lattice structure and interact by diffusion and encounter, then their final vocabulary size is the maximum possible. Knowing all available words is essential in order to increase the probability to ``survive'' by effective reproduction. On scale-free networks we find a different result. It is not necessary to learn the entire vocabulary available. Survival chances are increased by using the vocabulary of the ``hubs'' (nodes with high degree). The existence of the ``hubs'' in a scale-free network is the source of an additional important fitness generating mechanism.Comment: 10 pages, 3 Figures, accepted in Physica

Statistical Mechanical Approach to Human Language

We use the formulation of equilibrium statistical mechanics in order to study some important characteristics of language. Using a simple expression for the Hamiltonian of a language system, which is directly implied by the Zipf law, we are able to explain several characteristic features of human language that seem completely unrelated, such as the universality of the Zipf exponent, the vocabulary size of children, the reduced communication abilities of people suffering from schizophrenia, etc. While several explanations are necessarily only qualitative at this stage, we have, nevertheless, been able to derive a formula for the vocabulary size of children as a function of age, which agrees rather well with experimental data.Comment: 20 pages,4 figures, Accepted in Physica

“The value relevance of dividend announcement: An empirical study of the Greek Stock Market”

Purpose: Dividend policy and its impact on share pricing, has been an issue of great concern for the academic society. Over the years, many theories evolved in an effort to explain dividend policy impact on corporate value. A widely accepted approach is the signaling effect theory. The purpose of this paper is to assess the value relevance of dividend announcement. Design/methodology/approach: Our empirical work uses Greek stock market data. We adopt the event study methodology and incorporate in our research elements that differentiate Greek stock market from other developing markets. Findings: Our empirical results tend to support the theory. Decisions on dividend policy seem to affect corporate value. Investors perceive incremented dividend payments as an indication of positive future prospect and vice versa. Research limitations/implications: Different results between large and medium capitalization shares comprise an interesting element for future research

Language Time Series Analysis

We use the Detrended Fluctuation Analysis (DFA) and the Grassberger-Proccacia analysis (GP) methods in order to study language characteristics. Despite that we construct our signals using only word lengths or word frequencies, excluding in this way huge amount of information from language, the application of Grassberger- Proccacia (GP) analysis indicates that linguistic signals may be considered as the manifestation of a complex system of high dimensionality, different from random signals or systems of low dimensionality such as the earth climate. The DFA method is additionally able to distinguish a natural language signal from a computer code signal. This last result may be useful in the field of cryptography.Comment: 21 pages, 5 figures, accepted in Physica

A Random Matrix Approach to Language Acquisition

Since language is tied to cognition, we expect the linguistic structures to reflect patterns we encounter in nature and analyzed by physics. Within this realm we investigate the process of protolanguage acquisition, using analytical and tractable methods developed within physics. A protolanguage is a mapping between sounds and objects (or concepts) of the perceived world. This mapping is represented by a matrix and the linguistic interaction among individuals is described by a random matrix model. There are two essential parameters in our approach. The strength of the linguistic interaction $\beta$, which following Chomsky's tradition, we consider as a genetically determined ability, and the number $N$ of employed sounds (the lexicon size). Our model of linguistic interaction is analytically studied using methods of statistical physics and simulated by Monte Carlo techniques. The analysis reveals an intricate relationship between the innate propensity for language acquisition $\beta$ and the lexicon size $N$, $N \sim \exp(\beta)$. Thus a small increase of the genetically determined $\beta$ may lead to an incredible lexical explosion. Our approximate scheme offers an explanation for the biological affinity of different species and their simultaneous linguistic disparity.Comment: 16 pages, 4 figures. Submitted to JSTA