International Journal of Modern Physics C

Old and recent theoretical works by Andrzej Pȩkalski (APE) are recalled as possible sources of interest for describing network formation and clustering in complex (scientific) communities, through self-organization and percolation processes. Emphasis is placed on APE self-citation network over four decades. The method is that used for detecting scientists' field mobility by focusing on author's self-citation, co-authorships and article topics networks as in Refs. 1 and 2. It is shown that APE's self-citation patterns reveal important information on APE interest for research topics over time as well as APE engagement on different scientific topics and in different networks of collaboration. Its interesting complexity results from "degrees of freedom" and external fields leading to so called internal shock resistance. It is found that APE network of scientific interests belongs to independent clusters and occurs through rare or drastic events as in irreversible "preferential attachment processes", similar to those found in usual mechanics and thermodynamics phase transitions.

The Schelling model of 1971 is a complicated version of a square-lattice Ising model at zero temperature, to explain urban segregation, based on the neighbor preferences of the residents, without external reasons. Various versions between Ising and Schelling models give about the same results. Inhomogeneous "temperatures" T do not change the results much, while a feedback between segregation and T leads to a self-organization of an average T.

A two-temperature Ising-Schelling model is introduced and studied for describing human segregation. The self-organized Ising model with Glauber kinetics simulated by Müller et al. exhibits a phase transition between segregated and mixed phases mimicking the change of tolerance (local temperature) of individuals. The effect of external noise is considered here as a second temperature added to the decision of individuals who consider a change of accommodation. A numerical evidence is presented for a discontinuous phase transition of the magnetization.

We examine an evolutionary naming-game model where communicating agents are equipped with an evolutionary selected learning ability. Such a coupling of biological and linguistic ingredients results in an abrupt transition: upon a small change of a model control parameter a poorly communicating group of linguistically unskilled agents transforms into almost perfectly communicating group with large learning abilities. When learning ability is kept fixed, the transition appears to be continuous. Genetic imprinting of the learning abilities proceeds via Baldwin effect: initially unskilled communicating agents learn a language and that creates a niche in which there is an evolutionary pressure for the increase of learning ability. Our model suggests that when linguistic (or cultural) processes became intensive enough, a transition took place where both linguistic performance and biological endowment of our species experienced an abrupt change that perhaps triggered the rapid expansion of human civilization.

We review a series of models of sociophysics introduced by Galam and Galam et al. in the last 25 years. The models are divided into five different classes, which deal respectively with democratic voting in bottom-up hierarchical systems, decision making, fragmentation versus coalitions, terrorism and opinion dynamics. For each class the connexion to the original physical model and techniques are outlined underlining both the similarities and the differences. Emphasis is put on the numerous novel and counterintuitive results obtained with respect to the associated social and political framework. Using these models several major real political events were successfully predicted including the victory of the French extreme right party in the 2000 first round of French presidential elections, the voting at fifty–fifty in several democratic countries (Germany, Italy, Mexico), and the victory of the "no" to the 2005 French referendum on the European constitution. The perspectives and the challenges to make sociophysics a predictive solid field of science are discussed.

Our publication focuses on two different but related topics in politics: in the first part of this publication, we investigate the influence of election results in the elections for the parliaments of the German states and for the German Diet (federal parliament) on the member numbers of the largest parties in the various states. In the second part of this publication, we consider the correlations between opinion polls and election results and focus on the question whether real election results can be predicted by opinion polls.

We analyzed the rising and relaxation of the cusp-like local peaks superposed with oscillations which were well defined by the Warsaw Stock Exchange index WIG in a daily time horizon. We found that the falling paths of all index peaks were described by a generalized exponential function or the Mittag-Leffler (ML) one superposed with various types of oscillations. However, the rising paths (except the first one of WIG which rises exponentially and the most important last one which rises again according to the ML function) can be better described by bullish anti-bubbles or inverted bubbles.^2–4 The ML function superposed with oscillations is a solution of the nonhomogeneous fractional relaxation equation which defines here our Fractional Market Model (FMM) of index dynamics which can be also called the Rheological Model of Market. This solution is a generalized analog of an exactly solvable fractional version of the Standard or Zener Solid Model of viscoelastic materials commonly used in modern rheology.⁵ For example, we found that the falling paths of the index can be considered to be a system in the intermediate state lying between two complex ones, defined by short and long-time limits of the Mittag-Leffler function; these limits are given by the Kohlrausch-Williams-Watts (KWW) law for the initial times, and the power-law or the Nutting law for asymptotic time. Some rising paths (i.e., the bullish anti-bubbles) are a kind of log-periodic oscillations of the market in the bullish state initiated by a crash. The peaks of the index can be viewed as precritical or precrash ones since:

(i) the financial market changes its state too early from the bullish to bearish one before it reaches a scaling region (defined by the diverging power-law of return per unit time), and

(ii) they are affected by a finite size effect.

These features could be a reminiscence of a significant risk aversion of the investors and their finite number, respectively. However, this means that the scaling region (where the relaxations of indexes are described by the KWW law or stretched exponential decay) was not observed. Hence, neither was the power-law of the instantaneous returns per unit time observed. Nevertheless, criticality or crash is in a natural way contained in our FMM and we found its "finger print".

The time evolution of Earth with her cities, languages and countries is considered in terms of the multiplicative noise¹ and the fragmentation processes, where the related families, size distributions, lifetimes, bilinguals, etc. are studied. Earlier we treated the cities and the languages differently (and as connected; languages split since cities split, etc.). Hence, two distributions are obtained in the same computation at the same time. The same approach is followed here and Pareto–Zipf law for the distribution of the cities, log-normal for the languages, decreasing exponential for the city families (countries) in the rank order over population, and power law -2 for the language families over the number of languages in rank order are obtained theoretically in this combination for the first time (up to our knowledge) in the literature; all of which are in good agreement with the present empirical data.

We study the train aggregation behavior in a railway subsystem using the Markov approach. This approach is different from the queue theory, which is a main method to design some railway subsystems in the literature. With some simple assumptions, we solve the corresponding master equation describing the train aggregation behavior. Using the least square trigonometric approximation, we construct a continuous rate function for a real example, and show the evolution of the size of train cluster with time. Also the variance and relative error of the train aggregation are calculated.

This paper considers an agent-based labor market simulation to examine the influence of skills on wages and unemployment rates. Therefore less and highly skilled workers as well as less and highly productive vacancies are implemented. The skill distribution is exogenous whereas the distribution of the less and highly productive vacancies is endogenous. The different opportunities of the skill groups on the labor market are established by skill requirements. This means that a highly productive vacancy can only be filled by a highly skilled unemployed. Different skill distributions, which can also be interpreted as skill-biased technological change, are simulated by incrementing the skill level of highly skilled persons exogenously. This simulation also provides a microeconomic foundation of the matching function often used in theoretical approaches.

We have investigated the liquid state of atomic clusters interacting through a classical pair-wise Lennard–Jones 6–12 potential, using constant energy molecular dynamics simulations. For larger clusters (N ≳ 500–600 atoms) desorption events are frequent and a cluster in the liquid state eventually always converts to a solid state. To study the cluster as it cools, one must isolate the central cluster from the desorbed atoms. In this paper, we investigate using the atomic potential energy as a very simple criterion for removing desorbed atoms from the simulation, and examine the spatial profile of atomic potential energy in various size liquid and solid clusters.

A very common problem in science is the numerical diagonalization of symmetric or hermitian 3 × 3 matrices. Since standard "black box" packages may be too inefficient if the number of matrices is large, we study several alternatives. We consider optimized implementations of the Jacobi, QL, and Cuppen algorithms and compare them with an alytical method relying on Cardano's formula for the eigenvalues and on vector cross products for the eigenvectors. Jacobi is the most accurate, but also the slowest method, while QL and Cuppen are good general purpose algorithms. The analytical algorithm outperforms the others by more than a factor of 2, but becomes inaccurate or may even fail completely if the matrix entries differ greatly in magnitude. This can mostly be circumvented by using a hybrid method, which falls back to QL if conditions are such that the analytical calculation might become too inaccurate. For all algorithms, we give an overview of the underlying mathematical ideas, and present detailed benchmark results. C and Fortran implementations of our code are available for download from .