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Christian Schulze

Publications and source records attributed to Christian Schulze.

34 records · Page 2Linked to original sources
arXiv2006

Modelling linguistic taxonomic dynamics

This paper presents the results of the application of a bit-string model of languages (Schulze and Stauffer 2005) to problems of taxonomic patterns. The questions addressed include the following: (1) Which parameters are minimally ne eded for the development of a taxonomic dynamics leading to the type of distribution of language family sizes currently attested (as measured in the i number of languages per family), which appears to be a power-law? (2) How may such a model be coupled with one of the dynamics of speaker populations leading to the type of language size seen today, which appears to follow a log-normal distribution?

physics.soc-ph↗
arXiv2006

Computer simulation of language competition by physicists

Computer simulation of languages is an old subject, but since the paper of Abrams and Strogatz (2003) several physics groups independently took up this field. We shortly review their work and bring more details on our own simulations.

physics.soc-ph↗
arXiv2005

Simulation of language competition by physicists

Following Abrams and Strogatz 2003 and Patriarca and Leppanen 2004, five other physics groups independently started to simulate the competition of languages, as opposed to the evolution of a human language out of ape sounds, or the learning of a language by a child. This talk concentrates on the models of Christian Schulze et al and of Viviane de Oliveira et al which allow the simulation of a large number of languages, similar to today's 8,000 human languages. The first model deals with a continuous process of random mutations of a language, transfer from and to other languages, and flight away from languages spoken by only a few people. The second model combines these flight and mutation aspects, ignores transfer and describes the colonization of a large geographical region by people starting at one lattice point. The size of a language is defined by the number of people speaking it. The first model gives a realistic log-normal shape for the histogram of language sizes but the numbers are bad. For the second model our Monte Carlo simulations give sizes up to thousand million, but not the nearly log-normal shape. A meeting is planned for mid-September 2006 in Poland.

physics.soc-ph↗
arXiv2005

Microscopic and Macroscopic Simulation of Competition between Languages

The similarity of the evolution of human languages (or alphabets, bird songs, >...) to biological evolution of species is utilized to study with up to $10^9$ people the rise and fall of languages either by macroscopic differential equations similar to biological Lotka-Volterra equation, or by microscopic Monte Carlo simulations of bit-strings incorporating the birth, maturity, and death of every individual. For our bit-string model, depending on parameters either one language comprises the majority of speakers (dominance), or the population splits into many languages having in order of magnitude the same number of speakers (fragmentation); in the latter case the size distribution is log-normal, with upward deviations for small sizes, just as in reality for human languages. On a lattice two different dominating languages can coexist in neighbouring regions, without being favoured or disfavoured by different status. We deal with modifications and competition for existing languages, not with the evolution or learning of one language.

physics.soc-ph↗
arXiv2005

Sociophysics Simulations I: Language Competition

Using a bit-string model similar to biological simulations, the competition between different languages is simulated both without and with spatial structure. We compare our agent-based work with differential equations and the competing bit-string model of Kosmidis et al.

physics.soc-ph↗
arXiv2004

Monte Carlo simulation of the rise and the fall of languages

Similar to biological evolution and speciation we define a language through a string of 8 or 16 bits. The parent gives its language to its children, apart from a random mutation from zero to one or from one to zero; initially all bits are zero. The Verhulst deaths are taken as proportional to the total number of people, while in addition languages spoken by many people are preferred over small languages. For a fixed population size, a sharp phase transition is observed: For low mutation rates, one language contains nearly all people; for high mutation rates, no language dominates and the size distribution of languages is roughly log-normal as for present human languages. A simple scaling law is valid.

cond-mat.dis-nn↗
arXiv2004

Phase diagram in Bonabeau social hierarchy model with individually different abilities

The 1995 model of Bonabeau et al is generalized by giving each individual a different ability to win or lose a fight. We also introduce different groups such that the losers of fights between different groups are eliminated. The overall phase diagram for the first-order transition between egalitarian and hierarchical societies does not change much by these generalizations.

cond-mat.dis-nn↗
arXiv2004

Sznajd opinion dynamics with global and local neighbourhood

In this modification of the Sznajd consensus model on the square lattice, two people of arbitrary distance who agree in their opinions convince their nearest neighbours of this opinion. Similarly to the mean field theory of Slanina and Lavicka, the times needed to reach consensus are distributed exponentially and are quite small. The width of the phase transition vanishes reciprocally to the linear lattice dimension. Advertising has effects independent of the system size. For more than two opinions, three opinions reach a consensus in roughly half of the samples, and four only rarely and only for small lattices.

cond-mat.stat-mech↗
arXiv2003

Advertising, consensus, and ageing in multilayer Sznajd model

In the Sznajd consensus model on the square lattice, two people who agree in their opinions convince their neighbours of this opinion. We generalize it to many layers representing many age levels, and check if still a consensus among all layers is possible. Advertising sometimes but not always produces a consensus on the advertised opinion.

cond-mat.stat-mech↗
arXiv2002

Long-range interactions in Sznajd consensus model

The traditional Sznajd model, as well as its Ochrombel simplification, for opinion spreading are modified to have a convincing strength proportional to a negative power of the spatial distance. We find the usual phase transition in the full Sznajd model, but not in the Ochrombel simplification. We also mix the two rules, which favours a phase transition.

cond-mat.stat-mech↗
arXiv2002

Advertising effects in Sznajd marketing model

The traditional Sznajd model, as well as its Ochrombel simplification for opinion spreading, are applied to marketing with the help of advertising. The larger the lattice is the smaller is the amount of advertising needed to convince the whole market

cond-mat.stat-mech↗
arXiv2002

Market simulation with hierarchical information flux

We assume the market price to diffuse in a hierarchical comb of barriers, the heights of which represent the importance of new information entering the market. We find fat tails with the desired exponent for the price change distribution, and effective multifractality for intermediate times.

cond-mat.stat-mech↗
arXiv2002

Sornette-Ide model for markets: Trader expectations as imaginary part

A nonlinear differential equation of Sornette-Ide type with noise, for a complex variable, yields endogenous crashes, preceded by roughly log-periodic oscillations in the real part, and a strong increase in the imaginary part. The latter is interpreted as the trader expectation.

cond-mat.stat-mech↗
arXiv2001

The domino effect for markets

A generalization of the Cont-Bouchaud market model to three markets agrees with the correlations netween New York, Tokyo, and Frankfurt observed by Vandewalle et al.

cond-mat.stat-mech↗
arXiv1997

Lattice Electrons on a Cylinder Surface in the Presence of Rational Magnetic Flux and Disorder

We consider a disordered two-dimensional system of independent lattice electrons in a perpendicular magnetic field with rigid confinement in one direction and generalized periodic boundary conditions (GPBC) in the other direction. The objects investigated numerically are the orbits in the plane spanned by the energy eigenvalues and the corresponding center of mass coordinate in the confined direction, parameterized by the phase characterizing the GPBC. The Kubo Hall conductivity is expressed in terms of the winding numbers of these orbits. For vanishing disorder the spectrum of the system consists of Harper bands with energy levels corresponding to the edge states within the band gaps. Disorder leads to broadening of the bands. For sufficiently large systems localized states occur in the band tails. We find that within the mobility gaps of bulk states the Diophantine equation determines the value of the Hall conductivity as known for systems with torus geometry (PBCs in both directions). Within the spectral bands of extended states the Hall conductivity fluctuates strongly. For sufficiently large systems the generic behavior of localization-delocalization transitions characteristic for the quantum Hall effect are recovered.

cond-mat.mes-hall↗