Harms and benefits from social imitation

We study the role of imitation within a model of economics with adaptive agents. The basic ingredients are those of the Minority Game. We add the possibility of local information exchange and imitation of the neighbour's strategy. Imitators should pay a fee to the imitated. Connected groups are formed, which act as if they were single players. Coherent spatial areas of rich and poor agents result, leading to the decrease of local social tensions. Size and stability of these areas depends on the parameters of the model. Global performance measured by the attendance volatility is optimised at certain value of the imitation probability. The social tensions are suppressed for large imitation probability, but due to the price paid by the imitators the requirements of high global effectivity and low social tensions are in conflict, as well as the requirements of low global and low local wealth differences.Comment: 11 pages, elsart style, to appear in the proceedings of NATO ARW on Application of Physics in Economic Modelling, Prague, 8-10 February 200

Equivalence of replica and cavity methods for computing spectra of sparse random matrices

We show by direct calculation that the replica and cavity methods are exactly equivalent for the spectrum of Erdos-Renyi random graph. We introduce a variational formulation based on the cavity method and use it to find approximate solutions for the density of eigenvalues. We also use this variational method for calculating spectra of sparse covariance matrices

Influence of railway No. 024 on population and houses changes and regional development in Ústí nad Orlicí district in period 1869-2011

Práce se zabývá historickým vlivem železniční infrastruktury Orlickoústecka na regionální rozvoj ve sledované oblasti v období 1869-2011, se zvláštním ohledem na trať č. 024. Hlavním cílem práce je posoudit vliv trati č. 024 na sledované území v daném časovém horizontu a určit proměny jejího významu v procesu sídelního vývoje a regionálního rozvoje. Dílčím úkolem je pak charakterizovat obecný význam železnice na Orlickoústecku v jednotlivých časových úsecích. Úvodem jsou shrnuty obecné dopady železnice na územní rozvoj a z těchto dopadů vybrány efekty podstatné pro oblast Orlickoústecka. Dále je trať charakterizována z obecného hlediska pomocí historické a regionální literatury. Jsou nastíněny okolnosti vzniku trati č. 024, její možné varianty a současná podoba. V následujících kapitolách, které jsou rozčleněny na dvě části, se v té první práce věnuje dobovému kontextu Orlickoústecka pomocí historické a regionální literatury. Ve druhé části se nacházejí mapové výstupy, které prezentují indexy změn počtů obyvatel a domů v jednotlivých časových úsecích a jsou doplněny o komentář autora objasňující jednotlivé změny pozorovaných jevů. Závěrem jsou indexy změn za celé časové období znázorněny graficky s ohledem na populační velikost jednotlivých obcí a také na jejich horizontální geografickou polohou...This thesis deals with the historical influence of the railway infrastructure of Orlickoústecko on regional development in the monitored area in the period of 1869-2011, with special regard to the road No. 024. The main goal of this work is to assess the impact of line No. 024 on the monitored area in a given time horizon and to determine the changes of its importance in the process of settlement development and regional development. A partial task is to characterize the general significance of the railway in the Orlickoústecko region in the given time periods. The introduction summarizes the general impacts of the railway on territorial development and from these impacts the effects essential for the Orlickoústecko region are selected. Furthermore, the track is characterized from a general point of view using historical and regional literature. The circumstances of the origin of line No. 024 are outlined and its possible variants and current form are presented. In the following chapters, which are divided into two parts, the first one deals with the contemporary context of Orlickoústecko with the help of historical and regional literature. In the second part map outputs are included, which present indices of changes in the number of inhabitants and houses in individual time periods and are...Department of Social Geography and Regional Develop.Katedra sociální geografie a region. rozvojePřírodovědecká fakultaFaculty of Scienc

Loop expansion around the Bethe-Peierls approximation for lattice models

We develop an effective field theory for lattice models, in which the only non-vanishing diagrams exactly reproduce the topology of the lattice. The Bethe-Peierls approximation appears naturally as the saddle point approximation. The corrections to the saddle-point result can be obtained systematically. We calculate the lowest loop corrections for magnetisation and correlation function.Comment: 8 page

Kinetics of step bunching during growth: A minimal model

We study a minimal stochastic model of step bunching during growth on a one-dimensional vicinal surface. The formation of bunches is controlled by the preferential attachment of atoms to descending steps (inverse Ehrlich-Schwoebel effect) and the ratio $d$ of the attachment rate to the terrace diffusion coefficient. For generic parameters ($d > 0$) the model exhibits a very slow crossover to a nontrivial asymptotic coarsening exponent $\beta \simeq 0.38$. In the limit of infinitely fast terrace diffusion ($d=0$) linear coarsening ($\beta$ = 1) is observed instead. The different coarsening behaviors are related to the fact that bunches attain a finite speed in the limit of large size when $d=0$, whereas the speed vanishes with increasing size when $d > 0$. For $d=0$ an analytic description of the speed and profile of stationary bunches is developed.Comment: 8 pages, 10 figure

Extremal dynamics model on evolving networks

We investigate an extremal dynamics model of evolution with a variable number of units. Due to addition and removal of the units, the topology of the network evolves and the network splits into several clusters. The activity is mostly concentrated in the largest cluster. The time dependence of the number of units exhibits intermittent structure. The self-organized criticality is manifested by a power-law distribution of forward avalanches, but two regimes with distinct exponents tau = 1.98 +- 0.04 and tau^prime = 1.65 +- 0.05 are found. The distribution of extinction sizes obeys a power law with exponent 2.32 +- 0.05.Comment: 4 pages, 5 figure

Collective Behavior of Asperities in Dry Friction at Small Velocities

We investigate a simple model of dry friction based on extremal dynamics of asperities. At small velocities, correlations develop between the asperities, whose range becomes infinite in the limit of infinitely slow driving, where the system is self-organized critical. This collective phenomenon leads to effective aging of the asperities and results in velocity dependence of the friction force in the form $F\sim 1- \exp(-1/v)$.Comment: 7 pages, 8 figures, revtex, submitted to Phys. Rev.

Cracking Piles of Brittle Grains

A model which accounts for cracking avalanches in piles of grains subject to external load is introduced and numerically simulated. The stress is stochastically transferred from higher layers to lower ones. Cracked areas exhibit various morphologies, depending on the degree of randomness in the packing and on the ductility of the grains. The external force necessary to continue the cracking process is constant in wide range of values of the fraction of already cracked grains. If the grains are very brittle, the force fluctuations become periodic in early stages of cracking. Distribution of cracking avalanches obeys a power law with exponent $\tau = 2.4 \pm 0.1$.Comment: RevTeX, 6 pages, 7 postscript figures, submitted to Phys. Rev.