There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

This book concerns the use of concepts from statistical physics in the description of financial systems. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully developed turbulent fluids. These concepts are then applied to financial time series. The authors also present a stochastic model that displays several of the statistical properties observed in empirical data. Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling permit an understanding of the global behaviour of economic systems without first having to work out a detailed microscopic description of the system. Physicists will find the application of statistical physics concepts to economic systems interesting. Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.

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Introduction to Econophysics: Correlations and Complexity in Finance

The synchronization of chaotic systems

The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.

"relative State" Formulation of Quantum Mechanics

The evolution of languages closely resembles the evolution of haploid organisms. This similarity has been recently exploited \cite{GA,GJ} to construct language trees. The key point is the definition of a distance among all pairs of languages which is the analogous of a genetic distance. Many methods have been proposed to define these distances, one of this, used by glottochronology, compute distance from the percentage of shared ``cognates''. Cognates are words inferred to have a common historical origin, and subjective judgment plays a relevant role in the identification process. Here we push closer the analogy with evolutionary biology and we introduce a genetic distance among language pairs by considering a renormalized Levenshtein distance among words with same meaning and averaging on all the words contained in a Swadesh list \cite{Sw}. The subjectivity of process is consistently reduced and the reproducibility is highly facilitated. We test our method against the Indo-European group considering fifty different languages and the two hundred words of the Swadesh list for any of them. We find out a tree which closely resembles the one published in \cite{GA} with some significant differences.

Indo-European languages tree by Levenshtein distance

The evolution of languages closely resembles the evolution of haploid organisms. This similarity has been recently exploited (Gray R. D. and Atkinson Q. D., Nature, 426 (2003) 435; Gray R. D. and Jordan F. M., Nature, 405 (2000) 1052) to construct language trees. The key point is the definition of a distance among all pairs of languages which is the analogous of a genetic distance. Many methods have been proposed to define these distances; one of these, used by glottochronology, computes the distance from the percentage of shared "cognates". Cognates are words inferred to have a common historical origin, and subjective judgment plays a relevant role in the identification process. Here we push closer the analogy with evolutionary biology and we introduce a genetic distance among language pairs by considering a renormalized Levenshtein distance among words with same meaning and averaging on all words contained in a Swadesh list (Swadesh M., Proc. Am. Philos. Soc., 96 (1952) 452). The subjectivity of process is consistently reduced and the reproducibility is highly facilitated. We test our method against the Indo-European group considering fifty different languages and the two hundred words of the Swadesh list for any of them. We find out a tree which closely resembles the one published in Gray and Atkinson (2003), with some significant differences.

https://iopscience.iop.org/article/10.1209/0295-5075/81/68005/pdf

Multiscale behaviour of volatility autocorrelations in a financial market

We perform a scaling analysis on NYSE daily returns. We show that volatility correlations are power-laws on a time range from one day to one year and, more important, that they exhibit a multiscale behaviour.

The idea of measuring distance between languages seems to have its roots in the work of the French explorer Dumont D’Urville (1832) [13] . He collected comparative word lists for various languages during his voyages aboard the Astrolabe from 1826 to 1829 and, in his work concerning the geographical division of the Pacific, he proposed a method for measuring the degree of relation among languages. The method used by modern glottochronology, developed by Morris Swadesh in the 1950s, measures distances from the percentage of shared cognates, which are words with a common historical origin. Recently, we proposed a new automated method which uses the normalized Levenshtein distances among words with the same meaning and averages on the words contained in a list. Recently another group of scholars, Bakker et al. (2009) [8] and Holman et al. (2008)  [9] , proposed a refined version of our definition including a second normalization. In this paper we compare the information content of our definition with the refined version in order to decide which of the two can be applied with greater success to resolve relationships among languages.

Maurizio Serva

Papers

Indo-European languages tree by Levenshtein distance

Indo-European languages tree by Levenshtein distance

Multiscale behaviour of volatility autocorrelations in a financial market

Multiscale behaviour of volatility autocorrelations in a financial market

Measures of lexical distance between languages