Microscopic model for the logarithmic size effect on the Curie point in Barab\'asi-Albert networks

We found that numbers of fully connected clusters in Barab\'asi-Albert (BA) networks follow the exponential distribution with the characteristic exponent $\kappa=2/m$. The critical temperature for the Ising model on the BA network is determined by the critical temperature of the largest fully connected cluster within the network. The result explains the logarithmic dependence of the critical temperature on the size of the network $N$.Comment: 5 pages, 2 figure

Networks of companies and branches in Poland

In this study we consider relations between companies in Poland taking into account common branches they belong to. It is clear that companies belonging to the same branch compete for similar customers, so the market induces correlations between them. On the other hand two branches can be related by companies acting in both of them. To remove weak, accidental links we shall use a concept of threshold filtering for weighted networks where a link weight corresponds to a number of existing connections (common companies or branches) between a pair of nodes.Comment: 13 pages, 10 figures and 4 table

Majority-vote on undirected Barabasi-Albert networks

On Barabasi-Albert networks with z neighbours selected by each added site, the Ising model was seen to show a spontaneous magnetisation. This spontaneous magnetisation was found below a critical temperature which increases logarithmically with system size. On these networks the majority-vote model with noise is now studied through Monte Carlo simulations. However, in this model, the order-disorder phase transition of the order parameter is well defined in this system and this wasn't found to increase logarithmically with system size. We calculate the value of the critical noise parameter q_c for several values of connectivity $z$ of the undirected Barabasi-Albert network. The critical exponentes beta/nu, gamma/nu and 1/nu were calculated for several values of z.Comment: 15 pages with numerous figure

Simulation of majority rule disturbed by power-law noise on directed and undirected Barabasi-Albert networks

On directed and undirected Barabasi-Albert networks the Ising model with spin S=1/2 in the presence of a kind of noise is now studied through Monte Carlo simulations. The noise spectrum P(n) follows a power law, where P(n) is the probability of flipping randomly select n spins at each time step. The noise spectrum P(n) is introduced to mimic the self-organized criticality as a model influence of a complex environment. In this model, different from the square lattice, the order-disorder phase transition of the order parameter is not observed. For directed Barabasi-Albert networks the magnetisation tends to zero exponentially and for undirected Barabasi-Albert networks, it remains constant.Comment: 6 pages including many figures, for Int. J. Mod. Phys.

Self-organized criticality in a model of collective bank bankruptcies

The question we address here is of whether phenomena of collective bankruptcies are related to self-organized criticality. In order to answer it we propose a simple model of banking networks based on the random directed percolation. We study effects of one bank failure on the nucleation of contagion phase in a financial market. We recognize the power law distribution of contagion sizes in 3d- and 4d-networks as an indicator of SOC behavior. The SOC dynamics was not detected in 2d-lattices. The difference between 2d- and 3d- or 4d-systems is explained due to the percolation theory.Comment: For Int. J. Mod. Phys. C 13, No. 3, six pages including four figure

Ising model spin S=1 on directed Barabasi-Albert networks

On directed Barabasi-Albert networks with two and seven neighbours selected by each added site, the Ising model with spin S=1/2 was seen not to show a spontaneous magnetisation. Instead, the decay time for flipping of the magnetisation followed an Arrhenius law for Metropolis and Glauber algorithms, but for Wolff cluster flipping the magnetisation decayed exponentially with time. On these networks the Ising model spin S=1 is now studied through Monte Carlo simulations. However, in this model, the order-disorder phase transition is well defined in this system. We have obtained a first-order phase transition for values of connectivity m=2 and m=7 of the directed Barabasi-Albert network.Comment: 8 pages for Int. J. Mod. Phys. C; e-mail: [email protected]

Ising model simulation in directed lattices and networks

On directed lattices, with half as many neighbours as in the usual undirected lattices, the Ising model does not seem to show a spontaneous magnetisation, at least for lower dimensions. Instead, the decay time for flipping of the magnetisation follows an Arrhenius law on the square and simple cubic lattice. On directed Barabasi-Albert networks with two and seven neighbours selected by each added site, Metropolis and Glauber algorithms give similar results, while for Wolff cluster flipping the magnetisation decays exponentially with time.Comment: Expanded to 8 pages: additional author, additional result

Voter model on Sierpinski fractals

We investigate the ordering of voter model on fractal lattices: Sierpinski Carpets and Sierpinski Gasket. We obtain a power law ordering, similar to the behavior of one-dimensional system, regardless of fractal ramification.Comment: 7 pages, 5 EPS figures, 1 table, uses elsart.cl

A simple model of bank bankruptcies

Interbank deposits (loans and credits) are quite common in banking system all over the world. Such interbank co-operation is profitable for banks but it can also lead to collective financial failures. In this paper we introduce a new model of directed percolation as a simple representation for contagion process and mass bankruptcies in banking systems. Directed connections that are randomly distributed between junctions of bank lattice simulate flows of money in our model. Critical values of a mean density of interbank connections as well as static and dynamic scaling laws for the statistic of avalange bankruptcies are found. Results of computer simulations for the universal profile of bankruptcies spreading are in a qualitative agreement with the third wave of bank suspensions during The Great Depression in the USA.Comment: 8 pages, 6 Encapsulated Postscript figures, to be published in Physica A (2001

Names on the internet: towards electronic socio-onom@stics

The Internet represents an abundant source material for linguistic research, which continues to pose new challenges and opportunities on how language is used by its speakers. Its personal naming system, for example, has remained largely unexplored. Of the many facets of names on the Internet awaiting closer scrutiny, the phenomenon of usernames is perhaps the most fundamental. This thesis investigates the role they play in online life, the most suitable methods to approach them, and how they compare with the names used offline and where their place is in onomastics in general. With people’s names inevitably connected with one or another aspect of identity, this work focuses on the relationship between usernames and online identities. The data has been gathered from a forum on the Russian-speaking sector of the Internet (RuNet) and comprises all registered usernames (676 at the time of collection) as well as an extensive and methodically selected sample of users’ conversations. As a general analytical framework, it utilises Garfinkel’s (1967) ethnomethodology, which conceptualises identity as a result of the ongoing interaction that people negotiate and achieve in everyday life rather than a set of inherent inner qualities. More specifically, the following methodological tools devised by Sacks (e.g. 1995, 1984a, 1984b) have been used to perform the analysis: Membership Categorisation Analysis (MCA) to categorise the usernames of the forum participants, and Conversation Analysis (CA), to observe how usernames contribute to the construction of individual identities. Finally, the concept of Stance, as presented by Du Bois (2007), has been used as a lens to identify relevant evidence in the conversation samples. The analysis has demonstrated the need for a systematic categorisation of usernames. The way in which they associate sets of attributes, facilitates the allocation of named entities as members of certain categories of persons. Both linguistic and typographic elements of usernames contribute to how they are perceived and what impression they create. It is also argued that usernames have an important role to play in the active and ongoing construction of individual identities. The study concludes that CMC participants operate their usernames as meaningful linguistic devices to construct and co-construct each other’s identities. CA and MCD are confirmed to be relevant methods to analyse onomastic data. This study has generated a reliable body of evidence for the assertion that usernames are far from meaningless, and demonstrates, moreover, how their meanings are established. In so doing, it constitutes an important contribution to onomastic theory with the potential to shed new light on personal naming in general