optimal network configuration for maximal coherence resonance in excitable systems we analyze the coherence resonance phenomenon in an ensemble of noise driven excitable neurons giving special attention to the role of the interaction topology the neural architecture is modeled using a spatially embedded network in which we can tune the network organization between scale free like with dominating long range connections and a network with mostly adjacent neurons connected we found that besides an optimal noise intensity also an optimal network configuration exists at which the largest average coherence of noise induced spikes is achieved furthermore we show that long as well as short range interactions between neurons should exist in order to achieve the optimal response of the neuronal network

rigorous proof of the boltzmann gibbs distribution of money on connected graphs models in econophysics i e the emerging field of statistical physics that applies the main concepts of traditional physics to economics typically consist of large systems of economic agents who are characterized by the amount of money they have in the simplest model at each time step one agent gives one dollar to another agent with both agents being chosen independently and uniformly at random from the system numerical simulations of this model suggest that at least when the number of agents and the average amount of money per agent are large the distribution of money converges to an exponential distribution reminiscent of the boltzmann gibbs distribution of energy in physics the main objective of this paper is to give a rigorous proof of this result and show that the convergence to the exponential distribution holds more generally when the economic agents are located on the vertices of a connected graph and interact locally with their neighbors rather than globally with all the other agents we also study a closely related model where at each time step agents buy with a probability proportional to the amount of money they have and prove that in this case the limiting distribution of money is poissonian

a theoretical and numerical finite element analysis of spatial rod systems abstract in this paper a general finite element fe formulation has been developed for spatial rods within the present model the beams spatially curved and pretwisted rods with either constant and or varying cross section on distributed elastic or point supports can be analyzed conveniently first the equilibrium equations the kinematical relations and the constitutive relations are established for a rod element having 6 degrees of freedom at each end then the kinematical relations are solved for linear curvature change to yield the rigid body and the deformation modes these deformation modes are then used to find the basis functions for the development of the fe method the element stiffness matrix is developed to include the general features of spatial rods based on this approach a general computer program isar has been developed to verify the formulations and the computer program several numerical examples are worked out the examples include a haunched continuous beam a pretwisted rod a semicircular fixed ended ring and a circular beam on an elastic foundation prismatic and curved elements with constant and linear curvature change are tested and compared with the existing results it is shown that the theoretical computational methodology developed herein is quite accurate by using elements with linear curvature change the accuracy of the results would enhance and the solution would converge to the exact solutions in most cases

scaling in income inequalities and its dynamical origin abstract we provide an analytically treatable model that describes in a unified manner income distribution for all income categories the approach is based on a master equation with growth and reset terms the model assumptions on the growth and reset rates are tested on an exhaustive database with incomes on individual level spanning a nine year period in the cluj county romania in agreement with our theoretical predictions we find that income distributions computed for several years collapse on a master curve when a properly normalised income is considered the beta prime distribution is appropriate to fit the collapsed data and it is shown that distributions derived for other countries are following similar trends with different fit parameters the non universal feature of the fit parameters suggests that for a more realistic modelling the model parameters have to be linked with specific socio economic regulations

scale free property of local world networks and their community structures abstract the scale free property and community structures of complex networks formed by local events have been studied theoretically numerically and empirically we showed analytically and numerically that the degree distribution function p k of the local world evolving network exhibits a crossover from an exponential to power law form by increasing the local world size m for m much larger than the crossover local world size m co the distribution function p k has a power law form for any degree k 1 below m co however p k obeys a power law for 1 k k co and decays exponentially for k k co the crossover size m co and the crossover degree k co have been also elucidated in addition we constructed the drug prescription network dpn as a real local world network in which the local world subsets are definitely specified to reveal how the local world nature affects properties of real world networks we found that the community structure of the dpn strongly correlates with the local worlds

an algebraic slice in the coadjoint space of the borel and the coxeter element abstract let g be a complex simple lie algebra and b a borel subalgebra the algebra y of polynomial semi invariants on the dual b of b is a polynomial algebra on rank g generators grothendieck and dieudonne 1965 1967 16 the analogy with the semisimple case suggests there exists an algebraic slice to coadjoint action that is an affine translate y v of a vector subspace of b such that the restriction map induces an isomorphism of y onto the algebra r y v of regular functions on y v this holds in type a and even extends to all biparabolic subalgebras joseph 2007 20 but the construction fails in general even with respect to the borel moreover already in type c 2 no algebraic slice exists very surprisingly the exception of type c 2 is itself an exception indeed an algebraic slice for the coadjoint action of the borel subalgebra is constructed for all simple lie algebras except those of types b 2 m c n and f 4 outside type a the slice obtained meets an open dense subset of regular orbits even though the special point y of the slice is not itself regular this explains the failure of our previous construction

a variational analysis of small finite deformations of pretwisted elastic beams abstract the principle of minimum potential energy in conjunction with a suitably assumed strain energy density and in conjunction with suitably assumed expressions for strain and displacement components is used to derive a system of non linear ordinary differential equations for the problem of stretching shearing bending twisting and warping of pre twisted originally straight beams two problems which are considered in some detail concern the combined finite stretching and twisting of beams with doubly symmetric cross section and the influence of pretwist on shear and twist center locations

quantum generalized harish chandra isomorphisms abstract we give a different proof of generalized harish chandra isomorphisms proven by khoroshkin nazarov and vinberg 9 and joseph 6 7 as well as of their analogues in the quantum case

compatibility as underlying mechanism behind the evolution of networks abstract in this work we propose a dynamic network model based on an evolutive rule called compatibility the presence of common topological properties observed in two real complex networks are well reproduced by the proposed model these results suggest that the compatibility between nodes is sufficient to generate the complexity observed in real systems even considering that the new added nodes do not have the ability to know global information of the system

a fully nonlinear theory of curved and twisted composite rotor blades accounting for warpings and three dimensional stress effects abstract a new approach is used to develop a geometrically exact nonlinear beam model for naturally curved and twisted solid composite rotor blades undergoing large vibrations in three dimensional space a combination of the new concepts of local displacements and local engineering stresses and strains a new interpretation and manipulation of the virtual local rotations an exact coordinate transformation and the extended hamilton principle is used to derive six fully nonlinear equations of motion describing one extension two bending one torsion and two shearing vibrations of composite beams the formulation is based on an energy approach but the derivation is fully correlated with the newtonian approach and provides a straightforward explanation of all nonlinear structural terms without using complex tensor operations or asymptotic expansions the theory accounts for in plane and out of plane warpings due to bending extensional shearing and torsional loadings elastic couplings among warpings and three dimensional stress effects by using the results of a two dimensional static sectional finite element analysis also the theory fully accounts for extensionality initial curvatures and geometric nonlinearities the equations display linear elastic couplings due to structural anisotropy and initial curvatures and nonlinear geometric couplings the theory contains most of the existing beam theories as special cases and the final equations of motion are put in compact matrix form

wealth condensation in a barabasi albert network abstract we study the flow of money among agents in a barabasi albert ba scale free network where each network node represents an agent and money exchange interactions are established through links the system allows money trade between two agents at a time betting a fraction f of the poorer s agent wealth we also allow for the bet to be biased giving the poorer agent a winning probability p in the no network case there is a phase transition involving a relationship between p and f in the networked case we also found a condensation interface however this is not a complete condensation due to the presence of clusters in the network and its topology as can be expected the winner is always a well connected agent but we also found that the mean wealth decreases with the agents connectivity

wealth dynamics on complex networks abstract we study a model of wealth dynamics physica a 282 2000 536 which mimics transactions among economic agents the outcomes of the model are shown to depend strongly on the topological properties of the underlying transaction network the extreme cases of a fully connected and a fully disconnected network yield power law and log normal forms of the wealth distribution respectively we perform numerical simulations in order to test the model on more complex network topologies we show that the mixed form of most empirical distributions displaying a non smooth transition from a log normal to a power law form can be traced back to a heterogeneous topology with varying link density which on the other hand is a recently observed property of real networks

organization of growing random networks the organizational development of growing random networks is investigated these growing networks are built by adding nodes successively and linking each to an earlier node of degree k with an attachment probability a k when a k grows more slowly than linearly with k the number of nodes with k links n k t decays faster than a power law in k while for a k growing faster than linearly in k a single node emerges which connects to nearly all other nodes when a k is asymptotically linear n k t ensuremath sim mathrm tk ensuremath ensuremath nu with ensuremath nu dependent on details of the attachment probability but in the range 2l ensuremath nu l ensuremath infty the combined age and degree distribution of nodes shows that old nodes typically have a large degree there is also a significant correlation in the degrees of neighboring nodes so that nodes of similar degree are more likely to be connected the size distributions of the in and out components of the network with respect to a given node namely its descendants and ancestors are also determined the in component exhibits a robust s ensuremath 2 power law tail where s is the component size the out component has a typical size of order mathrm ln t and it provides basic insights into the genealogy of the network

large scale topological and dynamical properties of the internet we study the large scale topological and dynamical properties of real internet maps at the autonomous system level collected in a 3 yr time interval we find that the connectivity structure of the internet presents statistical distributions settled in a well defined stationary state the large scale properties are characterized by a scale free topology consistent with previous observations correlation functions and clustering coefficients exhibit a remarkable structure due to the underlying hierarchical organization of the internet the study of the internet time evolution shows a growth dynamics with aging features typical of recently proposed growing network models we compare the properties of growing network models with the present real internet data analysis

a generalized harish chandra isomorphism abstract for any complex reductive lie algebra g and any locally finite g module v we extend to the tensor product u g v the harish chandra description of g invariants in the universal enveloping algebra u g

social aggregation as a cooperative game abstract a new approach for the description of phenomena of social aggregation is suggested on the basis of psychological concepts as for instance social norms and cultural coordinates we deduce a general mechanism for social aggregation in which different clusters of individuals can merge according to cooperation among the agents in their turn the agents can cooperate or defect according to the clusters distribution inside the system the fitness of an individual increases with the size of its cluster but decreases with the work the individual had to do in order to join it in order to test the reliability of such a new approach we introduce a couple of simple toy models with the features illustrated above we see from this preliminary study how cooperation is the most convenient strategy only in the presence of very large clusters while on the other hand it is not necessary to have one hundred percent of cooperators for reaching a totally ordered configuration with only one megacluster filling the whole system

random networks with tunable degree distribution and clustering we present an algorithm for generating random networks with arbitrary degree distribution and clustering frequency of triadic closure we use this algorithm to generate networks with exponential power law and poisson degree distributions with variable levels of clustering such networks may be used as models of social networks and as a testable null hypothesis about network structure finally we explore the effects of clustering on the point of the phase transition where a giant component forms in a random network and on the size of the giant component some analysis of these effects is presented

interacting individuals leading to zipf s law institut de physique th eorique universit e de fribourg ch 1700 february 1 2008 we present a general approach to explain the zipf s law of city distribution if the simplestinteraction pairwise is assumed individuals tend to form cities in agreement with the well knownstatisticspacs numbers 89 50 r 05 20 y 05 40 j

scale free networks from varying vertex intrinsic fitness a new mechanism leading to scale free networks is proposed in this letter it is shown that in many cases of interest the connectivity power law behavior is neither related to dynamical properties nor to preferential attachment assigning a quenched fitness value x i to every vertex and drawing links among vertices with a probability depending on the fitnesses of the two involved sites gives rise to what we call a good get richer mechanism in which sites with larger fitness are more likely to become hubs i e to be highly connected

non linear theory for elastic spatial rods abstract starting with a three dimensional non linear formulation of elasticity and employing the variational procedure together with a suitable and proper strain and displacement field general forms of kinematical relations equilibrium equations and a set of one dimensional constitutive equations have been derived for spatial rods undergoing small finite deformations these equations can be employed to study different types of spatial rod elements for different geometries loading and cross sectional shapes the formulations take account of the influence of the loading behavior either conservative or non conservative loading the corresponding equations for the classical rod theory are extracted from the derived general non linear equations

structure and evolution of the world trade network the world trade web wtw the network defined by the international import export trade relationships has been recently shown to display some important topological properties which are tightly related to the gross domestic product of world countries while our previous analysis focused on the static undirected version of the wtw here we address its full evolving directed description this is accomplished by exploiting the peculiar reciprocity structure of the wtw to recover the directed nature of international trade channels and by studying the temporal dependence of the parameters describing the wtw topology

degree and wealth distribution in a network induced by wealth abstract a network induced by wealth is a social network model in which wealth induces individuals to participate as nodes and every node in the network produces and accumulates wealth utilizing its links more specifically at every time step a new node is added to the network and a link is created between one of the existing nodes and the new node innate wealth producing ability is randomly assigned to every new node and the node to be connected to the new node is chosen randomly with odds proportional to the accumulated wealth of each existing node analyzing this network using the mean value and continuous flow approaches we derive a relation between the conditional expectations of the degree and the accumulated wealth of each node from this relation we show that the degree distribution of the network induced by wealth is scale free we also show that the wealth distribution has a power law tail and satisfies the 80 20 rule we also show that over the whole range the cumulative wealth distribution exhibits the same topological characteristics as the wealth distributions of several networks based on the bouchaud mezard model even though the mechanism for producing wealth is quite different in our model further we show that the cumulative wealth distribution for the poor and middle class seems likely to follow by a log normal distribution while for the richest the cumulative wealth distribution has a power law behavior

what big data tells sampling the social network by communication channels big data has become the primary source of understanding the structure and dynamics of the society at large scale the network of social interactions can be considered as a multiplex where each layer corresponds to one communication channel and the aggregate of all of them constitutes the entire social network however usually one has information only about one of the channels or even a part of it which should be considered as a subset or sample of the whole here we introduce a model based on a natural bilateral communication channel selection mechanism which for one channel leads to consistent changes in the network properties for example while it is expected that the degree distribution of the whole social network has a maximum at a value larger than one we get a monotonically decreasing distribution as observed in empirical studies of single channel data we also find that assortativity may occur or get strengthened due to the sampling method we analyze the far reaching consequences of our findings

a family network model for wealth distribution in societies a model based on first degree family relations network is used to describe the wealth distribution in societies the network structure is not a priori introduced in the model it is generated in parallel with the wealth values through simple and realistic dynamical rules the model has two main parameters governing the wealth exchange in the network choosing their values realistically leads to wealth distributions in good agreement with measured data the cumulative wealth distribution function has an exponential behavior in the low and medium wealth limit and shows the pareto like power law tail for the upper 5 of the society the obtained pareto indexes are in good agreement with the measured ones the generated family networks also converge to a statistically stable topology with a simple poissonian degree distribution on this family network many interesting correlations are studied and the main factors leading to wealth diversification and the formation of the pareto law are identified

wealth condensation in a simple model of economy abstract we introduce a simple model of economy where the time evolution is described by an equation capturing both exchange between individuals and random speculative trading in such a way that the fundamental symmetry of the economy under an arbitrary change of monetary units is insured we investigate a mean field limit of this equation and show that the distribution of wealth is of the pareto power law type the pareto behaviour of the tails of this distribution appears to be robust for finite range models as shown using both a mapping to the random directed polymer problem as well as numerical simulations in this context a phase transition between an economy dominated by a few individuals and a situation where the wealth is more evenly spread out is found an interesting outcome is that the distribution of wealth tends to be very broadly distributed when exchanges are limited either in amplitude or topologically favouring exchanges and less surprisingly increasing taxes seems to be an efficient way to reduce inequalities

multifractal network generator we introduce a new approach to constructing networks with realistic features our method in spite of its conceptual simplicity it has only two parameters is capable of generating a wide variety of network types with prescribed statistical properties e g with degree or clustering coefficient distributions of various very different forms in turn these graphs can be used to test hypotheses or as models of actual data the method is based on a mapping between suitably chosen singular measures defined on the unit square and sparse infinite networks such a mapping has the great potential of allowing for graph theoretical results for a variety of network topologies the main idea of our approach is to go to the infinite limit of the singular measure and the size of the corresponding graph simultaneously a very unique feature of this construction is that with the increasing system size the generated graphs become topologically more structured we present analytic expressions derived from the parameters of the to be iterated initial generating measure for such major characteristics of graphs as their degree clustering coefficient and assortativity coefficient distributions the optimal parameters of the generating measure are determined from a simple simulated annealing process thus the present work provides a tool for researchers from a variety of fields such as biology computer science biology or complex systems enabling them to create a versatile model of their network data