Related papers: Chaos at Fifty
Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively…
In 1967, Frederick Lord posed a conundrum that has confused scientists for over half a century. Subsequently named Lord's 'paradox', the puzzle centres on the observation that two different approaches to estimating the effect of an exposure…
Special relativity was discovered at the eve of the century, but finds its roots in the 19th century efforts to understand the optics and electromagnetism of moving bodies. These roots are reviewed in Parts 1 and 2, the latter being…
Exponentiation makes the difference between the bit-size of this line and the number (<< 2^{300}) of particles in the known Universe. The expulsion of exponential time algorithms from Computer Theory in the 60's broke its umbilical cord…
Recently, a new concept, primitive chaos, was proposed, as a concept closely related to the fundamental problems of physics itself such as determinism, causality, free will, predictability, and irreversibility [J. Phys. Soc. Jpn. {\bf 79},…
In this work, a variant of the birth and death chain with constant intensities, originally introduced by Bruno de Finetti way back in 1957, is revisited. This fact is also underlined by the choice of the title, which is clearly a literal…
In 1975 James Pickands III showed that the excesses over a high threshold are approximatly Generalized Pareto distributed. Since then, a variety of estimators for the parameters of this cdf have been studied, but always assuming the…
This article provides a self-contained comprehensive review of the phenomenon of synchronization in dynamical systems, with a particular focus on chaotic systems in both continuous-time and discrete-time contexts. Synchronization, initially…
This anniversary paper is an occasion to recall some of the events that shaped institutional econophysics. But in these thoughts about the evolution of econophysics in the last 15 years we also express some concerns. Our main worry concerns…
Since their appearance in the 1950s, computational models capable of performing probabilistic choices have received wide attention and are nowadays pervasive in almost every areas of computer science. Their development was also inextricably…
Information is everywhere in nature which is very uncertain and unpredictable. But information, in itself, is a very ambiguous term. In this cursory write-up, we attempt to understand the formal meaning of information by quantifying…
This paper, which is dedicated to Alan Turing on the 50th anniversary of his death, gives an overview and discusses the philosophical implications of incompleteness, uncomputability and randomness.
The Talbot effect, also referred to as self-imaging or lensless imaging, was originally discovered in the 1830's by Henry Fox Talbot. Over the years, various investigators have found different aspects of this phenomenon, and a theory of the…
In 1957, Lindley published "A statistical paradox" in Biometrika, revealing a fundamental conflict between frequentist and Bayesian inference as sample size approaches infinity. We present a new paradox of a different kind: a conflict…
In the year 1876 the mathematician Charles Dodgson, who wrote fiction under the now more famous name of Lewis Carroll, devised a beautiful voting system that has long fascinated political scientists. However, determining the winner of a…
Percolation models describe the inside of a porous material. The theory emerged timidly in the middle of the twentieth century before becoming one of the major objects of interest in probability and mathematical physics. The golden age of…
In 1908, Minkowski put forward the idea that invariance under what we call today the Lorentz group, $GL(1,3, {\bf R})$, would be more meaningful in a four-dimensional space-time continuum. This suggestion implies that space and time are…
In his monumental discoveries, the driving force for Einstein was, I believe, consistency of concept and principle rather than conflict with experiment. In this spirit, I would like to look at the journey from the classical to the…
This is the introductory paper to the special issue of Topology and Its Applications entirely dedicated to the theory of continuous selections of multivalued mappings. Since the pioneering work of Ernest Michael from 1956 can rightfully be…
Deterministic chaos, and even maximum computational complexity, have been discovered within Newtonian dynamics. Economists assume that prices and price changes can also obey abstract mathematical laws of motion. Sociologists and other…