response to worrying trends in econophysics this article is a response to the recent worrying trends in econophysics critique written by four respected theoretical economists 1 two of the four have written books and papers that provide very useful critical analyses of the shortcomings of the standard textbook economic model neo classical economic theory 2 3 and have even endorsed my book 4 largely their new paper reflects criticism that i have long made 4 5 6 7 and that our group as a whole has more recently made 8 but i differ with the authors on some of their criticism and partly with their proposed remedy

the attractor basin portrait of a cellular automaton local space time structures such as domains and the intervening dislocations dominate a wide class of cellular automaton ca behavior for such spatially extended dynamics regular domains vicinities and attractors are introduced as organizing principles to identify the discretized analogs of attractors basins and separatrices structures used in classifying dissipative continuous state dynamical systems we describe the attractor basin portrait of nonlinear elementary ca rule 18 whose global dynamics is largely determined by a single regular attracting domain the latter s basin is analyzed in terms of subbasin and portal structures associated with particle annihilation the conclusion is that the computational complexity of such ca is more apparent than real transducer machines are constructed that automatically identify domain and dislocation structures in space time count the number of dislocations in a spatial pattern and implement an isomorphism between rule 18 and rule 90 we use a transducer to trace dislocation trajectories and confirm that in rule 18 isolated dislocation trajectories as well as a dislocation gas agree extremely well with the classical model of annihilating diffusive particles the ca efficiently transforms randomness of an initial pattern ensemble into a random walk of dislocations in space time

random growth urban model with geographical fitness abstract this paper formulates a random growth urban model with a notion of geographical fitness using techniques of complex network theory we study our system as a type of preferential attachment model with fitness and we analyze its macro behavior to clarify the properties of the city size distributions it predicts first restricting the geographical fitness to take positive values and using a continuum approach we show that the city size distributions predicted by our model asymptotically approach pareto distributions with coefficients greater than unity then allowing the geographical fitness to take negative values we perform local coefficient analysis to show that the predicted city size distributions can deviate from pareto distributions as is often observed in actual city size distributions as a result the model we propose can generate a generic class of city size distributions including but not limited to pareto distributions for applications to city population projections our simple model requires randomness only when new cities are created not during their subsequent growth this property leads to smooth trajectories of city population growth in contrast to other models using gibrat s law in addition a discrete form of our dynamical equations can be used to estimate past city populations based on present day data this fact allows quantitative assessment of the performance of our model further study is needed to determine appropriate formulas for the geographical fitness

growth model for fractal scale free networks generated by a random walk abstract the diversity of networked systems with fractal structures suggests that knowing the underlying mechanism that generates the fractality is necessary for building a model of the development of complex networks in the present paper we propose a growth model of a network generated by a random walk and show that the evolving graph forms a fractal structure with various properties including the scale free property if the graph which provides a space where a random walk occurs by itself is formed by the random walk the proposed model is regulated by two parameters p v and p e which define the probability of either a roundabout path via a new vertex or a shortcut being formed by the random walk respectively the power law exponent describing the vertex degree distribution is determined by the ratio p e p v and is related to an internal factor f i via the relation 1 f i 1 where f i is a parameter that describes the local structure generated by the random walk a sufficiently small p v provides the small world property to the model network the small world property is usually considered to be incompatible with the fractal scaling property open m c l c d c where open m c is the average number of vertices which can be reached from a randomly chosen vertex in at most l c steps however we demonstrate that fractality can be reconciled with the small world property by introducing a size dependent fractal cluster dimension d c

role of initial conditions in the classification of the rule space of cellular automata dynamics in the qualitative classification of cellular automata ca rules by wolfram rev mod phys 55 601 1983 there exists a class of ca rules called class 4 which exhibit complex pattern formation and long lived dynamical activity long transients these properties of class 4 ca s has led to the conjecture that class 4 rules are universal turing machines i e they are bases for computational universality we describe the embedding of a small universal turing machine due to minski computation finite and infinite machines prentice hall englewood cliffs nj 1967 into a cellular automaton rule table this produces a collection of k 18 r 1 cellular automata all of which are computationally universal however we observe that these rules are distributed among the various wolfram classes more precisely we show that the identification of the wolfram class depends crucially on the set of initial conditions used to simulate the given ca this work among others indicates that a description of complex systems and information dynamics may need a new framework for nonequilibrium statistical mechanics

identifying and ranking influential spreaders in complex networks with consideration of spreading probability abstract identifying the influential spreaders in complex network has great theoretical and practical significance in order to evaluate the spreading ability of the nodes some centrality measures are usually computed which include degree centrality dc betweenness centrality bc closeness centrality cc k shell centrality ks and local centrality lc however we observe that the performance of different centrality measures may change when these measures are used in a real network with different spreading probabilities specifically dc performs well for small spreading probabilities and lc is more suitable for larger ones to alleviate the sensitivity of these centrality measures to the spreading probability we modify lc and then integrate it with dc by considering the spreading probability we call the proposed measure hybrid degree centrality hc hc can take the advantages of dc or lc depending on the given spreading probability we use sir model to evaluate the performance of hc in both real networks and artificial networks experimental results show that hc performs robustly under different spreading probabilities compared with these known centrality measures such as dc lc bc cc and ks hc can evaluate the spreading ability of the nodes more accurately on most range of spreading probabilities furthermore we show that our method can better distinguish the spreading ability of nodes

where do we stand on econophysics abstract this issue contains papers selected from the contributions presented at the 5th international conference on applications of physics in financial analysis apfa5 held in torino from june 29th to july 1st 2006 http www polito it apfa5 the issue collects recent applications of models and methods of statistical physics to economic problems this interdisciplinary field of research known as econophysics has seen intensive growth over the last decade the challenge for econophysicists will be to go beyond the traditional views of economics and physics unifying the separate lines of development followed by the two disciplines over great part of the 20th century the conventional view serves to protect us from the painful job of thinking john kenneth galbraith 1908 2006

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

topological properties of integer networks abstract inspired by pythagoras s belief that numbers represent the reality we study the topological properties of networks of composite numbers in which the vertices represent the numbers and two vertices are connected if and only if there exists a divisibility relation between them the network has a fairly large clustering coefficient c 0 34 which is insensitive to the size of the network the average distance between two nodes is shown to have an upper bound that is independent of the size of the network in contrast to the behavior in small world and ultra small world networks the out degree distribution is shown to follow a power law behavior of the form k 2 in addition these networks possess hierarchical structure as c k k 1 in accord with the observations of many real life networks

fractional calculus and continuous time finance in this paper we present a rather general phenomenological theory of tick by tick dynamics in financial markets many well known aspects such as the levy scaling form follow as particular cases of the theory the theory fully takes into account the non markovian and non local character of financial time series predictions on the long time behaviour of the waiting time probability density are presented finally a general scaling form is given based on the solution of the fractional diffusion equation

accuracy analysis of measurements on a stable power law distributed series of events we investigate how finite measurement time limits the accuracy with which the parameters of a stably distributed random series of events can be determined the model process is generated by timing the emigration of individuals from a population that is subject to deaths and a particular choice of multiple immigration events this leads to a scale free discrete random process where customary measures such as mean value and variance do not exist however converting the number of events occurring in fixed time intervals to a 1 bit clipped process allows the construction of well behaved statistics that still retain vestiges of the original power law and fluctuation properties these statistics include the clipped mean and correlation function from measurements of which both the power law index of the distribution of events and the time constant of its fluctuations can be deduced we report here a theoretical analysis of the accuracy of measurements of the mean of the clipped process this indicates that for a fixed experiment time the error on measurements of the sample mean is minimized by an optimum choice of the number of samples it is shown furthermore that this choice is sensitive to the power law index and that the approach to poisson statistics is dominated by rare events or outliers our results are supported by numerical simulation

weighted self similar networks under preferential attachment abstract we introduce an abstract evolutionary formalism that generates weighted networks whose growth under stochastic preferential attachment triggers unrestricted weight rearrangements in existing links the class of resulting algorithms for different parameter values includes the barabasi albert and barrat barthelemy vespignani models as special cases we solve the recursions that describe the average growth to derive exact solutions for the expected degree and strength distribution the individual strength and weight development and the joint distribution of neighboring degrees we find that the network exhibits a particular form of self similarity namely every sufficiently interconnected node has on average the same constitution of small degree neighbors as any other node of large degree finally we suggest potential applications in several fields of interest

local world evolving networks with tunable clustering abstract we propose an extended local world evolving network model including a triad formation tf step in the process of network evolution random fluctuation in the number of new edges is involved we derive analytical expressions for degree distribution clustering coefficient and average path length our model can unify the generic properties of real life networks scale free degree distribution high clustering and small inter node separation moreover in our model the clustering coefficient is tunable simply by changing the expected number of tf steps after a single local preferential attachment step

finding the shortest paths by node combination by repeatedly combining the source node s nearest neighbor we propose a node combination nc method to implement the dijkstra s algorithm the nc algorithm finds the shortest paths with three simple iterative steps find the nearest neighbor of the source node combine that node with the source node and modify the weights on edges that connect to the nearest neighbor the nc algorithm is more comprehensible and convenient for programming as there is no need to maintain a set with the nodes distances experimental evaluations on various networks reveal that the nc algorithm is as efficient as dijkstra s algorithm as the whole process of the nc algorithm can be implemented with vectors we also show how to find the shortest paths on a weight matrix

a new class of automata networks a new class of automata networks is defined their evolution rules are determined by a probability measure p on the set of all integers z and an indicator function ia on the interval 0 1 it is shown that any cellular automaton rule can be represented by a nonunique rule formulated in terms of a pair p ia this new class of automata networks contains discrete systems which are not cellular automata for a given p a metric can be defined on the space of all rules which induces a metric on the space of all cellular automata rules

pinning synchronization of delayed complex dynamical networks with nonlinear coupling abstract in this paper we find that complex networks with the watts strogatz or scale free ba random topological architecture can be synchronized more easily by pin controlling fewer nodes than regular systems theoretical analysis is included by means of lyapunov functions and linear matrix inequalities lmi to make all nodes reach complete synchronization numerical examples are also provided to illustrate the importance of our theoretical analysis which implies that there exists a gap between the theoretical prediction and numerical results about the minimum number of pinning controlled nodes

flexible construction of hierarchical scale free networks with general exponent extensive studies have been done to understand the principles behind architectures of real networks recently evidence for hierarchical organization in many real networks has also been reported here we present a hierarchical model that reproduces the main experimental properties observed in real networks scale free of degree distribution p k frequency of the nodes that are connected to k other nodes decays as a power law p k ensuremath sim k ensuremath ensuremath gamma and power law scaling of the clustering coefficient c k ensuremath sim k ensuremath 1 the major points of our model can be summarized as follows a the model generates networks with scale free distribution for the degree of nodes with general exponent ensuremath gamma g2 and arbitrarily close to any specified value being able to reproduce most of the observed hierarchical scale free topologies in contrast previous models cannot obtain values of ensuremath gamma g2 58 b our model has structural flexibility because i it can incorporate various types of basic building blocks e g triangles tetrahedrons and in general fully connected clusters of n nodes and ii it allows a large variety of configurations i e the model can use more than n ensuremath 1 copies of basic blocks of n nodes the structural features of our proposed model might lead to a better understanding of architectures of biological and nonbiological networks

dynamics of directed graphs the world wide web we introduce and simulate a growth model of the world wide web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real web to update outgoing links re directing them towards constantly changing selected nodes emergent statistical correlation between the distributions of outgoing and incoming links is a key feature of the dynamics of the web the growth phase is characterized by temporal fractal structures which are manifested in the hierarchical organization of links we obtain quantitative agreement with the recent empirical data in the real web for the distributions of in and out links and for the size of the connected component in a fully grown network of n nodes we study the structure of connected clusters of nodes that are accessible along outgoing links from a randomly selected node the distributions of size and depth of the connected clusters with a giant component exhibit supercritical behavior by decreasing the control parameter average fraction of updated and added links per time step towards c n 10 the web can resume a critical structure with no giant component in it we find a different universality class when the updates of links are not allowed i e for 0 corresponding to the network of science citations

automata network sir models for the spread of infectious diseases in populations of moving individuals automata network sir models for the spread of infectious diseases are studied the local rule consists of two subrules the first one applied sequentially describes the motion of the individuals the second is synchronous and models infection and removal or recovery the spatial correlations created by the application of the second subrule are partially destroyed according to the degree of mixing of the population which follows from the application of the first subrule one and two population models are considered in the second case individuals belonging to one population may be infected only by individuals belonging to the other population as is the case for example for the heterosexual propagation of a venereal disease it is shown that the occurrence of the epidemic in one population may be triggered by the occurrence of the epidemic in the other population the emphasis is on the influence of the degree of mixing of the individuals which follows from their diffusive motion in particular the asymptotic behaviours for very small and very large mixing are determined when the degree of mixing tends to infinity the correlations are completely destroyed and the time evolution of the epidemic is then correctly predicted by the mean field approximation

the simes method for multiple hypothesis testing with positively dependent test statistics abstract the simes method for testing intersection of more than two hypotheses is known to control the probability of type i error only when the underlying test statistics are independent although this method is more powerful than the classical bonferroni method it is not known whether it is conservative when the test statistics are dependent this article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple hypothesis testing situations the simes method indeed controls the probability of type i error this extends some results established very recently in the special case of two hypotheses

phase transition in the rich get richer mechanism due to finite size effects the rich get richer mechanism agents increase their wealth randomly at a rate proportional to their holdings is often invoked to explain the pareto power law distribution observed in many physical situations such as the degree distribution of growing scale free nets we use two different analytical approaches as well as numerical simulations to study the case where the number of agents is fixed and finite but large and the rich get richer mechanism is invoked a fraction r of the time the remainder of the time wealth is disbursed by a homogeneous process at short times we recover the pareto law observed for an unbounded number of agents in later times the moving distribution can be scaled to reveal a phase transition with a gaussian asymptotic form for and a pareto like tail on the positive side and a novel stretched exponential decay on the negative side for

maximal planar networks with large clustering coefficient and power law degree distribution in this article we propose a simple rule that generates scale free networks with very large clustering coefficient and very small average distance these networks are called random apollonian networks rans as they can be considered as a variation of apollonian networks we obtain the analytic results of power law exponent ensuremath gamma 3 and clustering coefficient c frac 46 3 ensuremath 36 phantom rule 0 2em 0ex mathrm ln phantom rule 0 2em 0ex frac 3 2 ensuremath approx 0 74 which agree with the simulation results very well we prove that the increasing tendency of average distance of rans is a little slower than the logarithm of the number of nodes in rans since most real life networks are both scale free and small world networks rans may perform well in mimicking the reality the rans possess hierarchical structure as c k ensuremath sim k ensuremath 1 that are in accord with the observations of many real life networks in addition we prove that rans are maximal planar networks which are of particular practicability for layout of printed circuits and so on the percolation and epidemic spreading process are also studied and the comparisons between rans and barab asi albert ba as well as newman watts nw networks are shown we find that when the network order n the total number of nodes is relatively small as n ensuremath sim 10 4 the performance of rans under intentional attack is not sensitive to n while that of ba networks is much affected by n and the diseases spread slower in rans than ba networks in the early stage of the suseptible infected process indicating that the large clustering coefficient may slow the spreading velocity especially in the outbreaks

helical minimal immersions of compact riemannian manifolds into a unit sphere an isometric immersion of a riemannian manifold m into a riemannian manifold m is called helical if the image of each geodesic has constant curvatures which are independent of the choice of the particular geodesic suppose m is a compact riemannian manifold which admits a minimal helical immersion of order 4 into the unit sphere if the weinstein integer of m equals that of one of the projective spaces then m is isometric to that projective space with its canonical metric 0 introduction in 2 besse constructed a minimal immersion with a nice property of a strongly harmonic manifold into a sphere this nice property is that the images of geodesics of the strongly harmonic manifold are of constant curvatures as curves in the sphere and the curvatures and the osculating orders are independent of geodesics immersions with such a property are said to be helical cf 8 sakamoto 8 studied a helical immersion of a riemannian manifold m into a unit sphere the result is that if m is compact then it is a blaschke manifold and moreover if the helical immersion is minimal then m is a globally harmonic manifold it is well known that if a globally harmonic manifold is compact and simply connected then it is a strongly harmonic manifold michel s theorem cf 2 thus we can declare that the theory of helical minimal immersions of compact simply connected riemannian manifolds into a unit sphere is a submanifold version of strongly harmonic manifold theory let f m s 1 be a helical immersion of a compact riemannian manifold m into a unit sphere s 1 since m is a blaschke manifold all geodesics of m are simply closed and of the same length furthermore if we denote the cut locus of x e m by cut x then the unit tangent vectors at x of geodesics emanating from x and entering to y e cut x compose a great sphere in the unit tangent sphere at x the dimension of the great sphere is independent of x and it is equal to 0 1 3 7 or n 1 n dim m which is the index of the first conjugate point y of x cf 2 proposition 5 39 and theorem 7 23 geodesics are also helical in the euclidean received by the editors march 15 1984 and in revised form june 20 1984 1980 mathematics subject classification primary 53c40 secondary 53c42

uniform synchronous criticality of diversely random complex networks abstract we investigate collective synchronous behaviors in random complex networks of limit cycle oscillators with the non identical asymmetric coupling scheme and find a uniform coupling criticality of collective synchronization which is independent of complexity of network topologies numerical simulations on categories of random complex networks have verified this conclusion

time cumulative scale free networks without both growth and preferential attachment abstract a model of nongrowing networks with time cumulative scale free sf property based on the apply reply process is proposed in this paper this model is not only without growth but also without a direct expression of preferential attachment the network structure is evolved by the change of nodes active probability which is mathematically equivalent to a special diffusion process this model only allows zero or one edge connecting on a node at any moment and the power law degree distributions can be exhibited from the statistic of the network after a long time accumulation our results imply that both growth and direct preferential attachments are not necessary in the generation of the sf property

a theory of fluctuations in stock prices abstract the distribution of price returns is studied for a class of market models with markovian dynamics the models have a non constant diffusion coefficient that depends on the value of the return an analytical expression for the distribution of returns is obtained and shown to match the results of computer simulations for two simple cases those two cases are shown to have exponential and fat tailed power law decaying distributions respectively

constant isotropic submanifolds with 4 planar geodesics let f be an isometric immersion of a riemannian manifold m into m we prove that if f is constant isotropic 4 planar geodesic and m is a euclidean sphere then m is isometric to one of compact symmetric spaces of rank equal to one and f is congruent to a direct sum of standard minimal immersions we also determine constant isotropic 4 planar geodesic totally real immersions into a complex projective space of constant holomorphic sectional curvature 0 introduction in 15 o neill studied isotropic immersions and showed that if the difference between the sectional curvatures of the submanifold and the ambient manifold is constant for any plane section tangent to the submanifold then the codimension must be high compared with the dimension of the submanifold unless the immersion is totally geodesic or umbilical the class of constant isotropic immersions for instance into a sphere seems to be too large to classify them for example the composition of two isotropic immersions is also isotropic and for two given isotropic immersions f1 and f2 into sp 1 and sq 1 respectively their direct sum tcosaf1 sinaf2 into sp q l 1 is also isotropic for any 0 furthermore it is well known that there are many constant isotropic immersions in equivariant isometric immersions of homogeneous spaces an isometric immersion f m m is said to be 4 planar geodesic if for each geodesic r of m the curve f oty is locally contained in a 4 dimensional totally geodesic submanifold of m the class of 4 planar geodesic immersions into a sphere is also large at least an isometric immersion of a surface into a 4dimensional riemannian manifold is always 4 planar geodesic in this paper we try to classify immersions in the intersection of these classes in particular we are able to classify constant isotropic 4 planar geodesic resp and totally real immersions of connected complete riemannian manifolds into a unit sphere resp complex projective space of constant holomorphic sectional curvature 4 in 1 we give basic equations used later and some definitions in 2 we prove that if f is a constant isotropic 4 planar geodesic resp and totally real immersion into a real space form resp cpq c then f is a helical immersion of order 4 here we recall that an isometric immersion f m m is called a helical immersion received by the editors april 3 1987 1980 mathematics subject classification 1985 revision primary 53c40

projective cluster synchronization in drive response dynamical networks abstract in this paper we study the projective cluster synchronization in a drive response dynamical network with 1 n coupled partially linear chaotic systems because the scaling factors characterizing the dynamics of projective synchronization remain unpredictable pinning control ideas are adopted to direct the different scaling factors onto the desired values it is also shown that the projection cluster synchronization can be realized by controlling only one node in each cluster numerical simulations on the chaotic lorenz system are illustrated to verify the theoretical results

discrete and integral hydrodynamic models of percolation networks abstract the hydrodynamic description of percolation is used to introduce permeability network models via discretization and leads to the study of random walks on lattices by decimation transformations decimation is exact in one dimension and provides the basis for understanding an approximate renormalization that has been reported for two and three dimensional lattices we discuss the question of existence of a block permeability picture by analysing the question whether decimation renormalization can be used to obtain a hierarchy of coarse grained descriptions of an arbitrary permeability distribution we show that both the block permeability and multiplicative multifractal pictures are valid in one dimension but that the method of proof breaks down in higher dimensions we conclude that there is presently no justification for assuming a multifractal permeability distribution or even a hierarchy of nonmultifractal block permeabilities for two and three dimensional permeability networks the difference between real rocks and reservoirs and artificial ones is emphasized to construct an artificial reservoir that agrees with observed nonuniversal scaling percolation models with variable topology are introduced based upon the integrated form of hydrodynamics the models considered are multifractal whenever the distribution of capillary tube exponents is binomial in connection with this modelling we argue that constraints derived from the experimental study of small rock samples can be used to test whether a given distribution of permeability applies to an entire geological layer within a reservoir finally the method of symbolic dynamics is adapted to the generation of pseudorandom permeability distributions on lattices

effect of node deleting on network structure abstract the ever increasing knowledge of the structure of various real world networks has uncovered their complex multi mechanism governed evolution processes therefore a better understanding of the structure and evolution of these networked complex systems requires us to describe such processes in a more detailed and realistic manner in this paper we introduce a new type of network growth rule which comprises addition and deletion of nodes and propose an evolving network model to investigate the effect of node deleting on network structure it is found that with the introduction of node deleting network structure is significantly transformed in particular degree distribution of the network undergoes a transition from scale free to exponential forms as the intensity of node deleting increases at the same time nontrivial disassortative degree correlation develops spontaneously as a natural result of network evolution in the model we also demonstrate that node deleting introduced in the model does not destroy the connectedness of a growing network so long as the increasing rate of edges is not excessively small in addition it is found that node deleting will weaken but not eliminate the small world effect of a growing network and generally it will decrease the clustering coefficient in a network

nonlinear barabasi albert network abstract in recent years there has been considerable interest in the structure and dynamics of complex networks one of the most studied networks is the linear barabasi albert model here we investigate the nonlinear barabasi albert growing network in this model a new node connects to a vertex of degree k with a probability proportional to k real each vertex adds m new edges to the network we derive an analytic expression for the degree distribution p k which is valid for all values of m and 1 in the limit the network is homogeneous if 1 there is a gel phase with m super connected nodes it is proposed a formula for the clustering coefficient which is in good agreement with numerical simulations the assortativity coefficient r is determined and it is shown that the nonlinear barabasi albert network is assortative disassortative if 1 and no assortative only when 1 in the limit the assortativity coefficient can be exactly calculated we find r 7 13 when m 2 finally the minimum average shortest path length l min is numerically evaluated increasing the network size l min diverges for 1 and it is equal to 1 when 1

a probabilistic automata network epidemic model with births and deaths exhibiting cyclic behaviour a probabilistic automata network model for the spread of an infectious disease in a population of moving individuals is studied the local rule consists of two subrules the first one applied synchronously models infection birth and death processes it is a probabilistic cellular automaton rule the second applied sequentially describes the motion of the individuals the model contains six parameters the probabilities p for a susceptible to become infected by contact with an infective the respective birth rates bs and bi of the susceptibles from either a susceptible or an infective parent the respective death rates ds and di of susceptibles and infectives and a parameter m characterizing the motion of the individuals the model has three fixed points the first is trivial it describes a stationary state with no living individuals the second corresponds to a disease free state with no infectives the third and last one characterizes an endemic state with non zero densities of susceptibles and infectives moreover the model may exhibit oscillatory behaviour of the susceptible and infective densities as functions of time through a hopf type bifurcation the influence of the different parameters on the stability of all these states is studied with a particular emphasis on the influence of motion which has been found to be a stabilizing factor of the cyclic behaviour

oscillatory epidemic prevalence in growing scale free networks we study the persistent epidemic prevalence with oscillatory behavior and the extinction of computer viruses via e mails on a contact relational network growing with new users for which scale free structure is estimated from real data typical oscillatory phenomenon is simulated in a stochastic model for the execution and detection of viruses the conditions of extinction by random and targeted immunizations for hubs are derived through bifurcation analysis for simpler deterministic models by using a mean field approximation without the connectivity correlations we can qualitatively understand the mechanisms of the spread in linearly growing scale free networks

how much information is needed to be the majority during the binary state opinion formation abstract in this paper we try to propose a toy model which follows the majority rule with the fermi function to uncover the role of the heterogeneous interaction between individuals in opinion formation in order to do this we define the impact factor i f i says individual i as the exponential function of its connectivity k i with the tunable parameter also shows the public information that can be collected by individuals in the system we realize our model in scale free networks with mean connectivity k we find that much more public information 2 and less public information 1 cannot let either of the two opinions be the majority during the opinion formation furthermore 1 is a constant and equal to 0 76 0 04 and 2 decreases as a power law function of the mean connectivity k of the network our work can provide some perspectives and tools to understand the diversity of opinion in social networks

nonintegrability chaos and complexity abstract two dimensional driven dissipative flows are generally integrable via a conservation law that is singular at equilibria nonintegrable dynamical systems are confined to n 3 dimensions even driven dissipative deterministic dynamical systems that are critical chaotic or complex have n 1 local time independent conservation laws that can be used to simplify the geometric picture of the flow over as many consecutive time intervals as one likes those conservation laws generally have either branch cuts phase singularities or both the consequence of the existence of singular conservation laws for experimental data analysis and also for the search for scale invariant critical states via uncontrolled approximations in deterministic dynamical systems is discussed finally the expectation of ubiquity of scaling laws and universality classes in dynamics is contrasted with the possibility that the most interesting dynamics in nature may be nonscaling nonuniversal and to some degree computationally complex

diversity of graphs with highly variable connectivity a popular approach for describing the structure of many complex networks focuses on graph theoretic properties that characterize their large scale connectivity while it is generally recognized that such descriptions based on aggregate statistics do not uniquely characterize a particular graph and also that many such statistical features are interdependent the relationship between competing descriptions is not entirely understood this paper lends perspective on this problem by showing how the degree sequence and other constraints e g connectedness no self loops or parallel edges on a particular graph play a primary role in dictating many features including its correlation structure building on recent work we show how a simple structural metric characterizes key differences between graphs having the same degree sequence more broadly we show how the often implicit choice of a background set against which to measure graph features has serious implications for the interpretation and comparability of graph theoretic descriptions

epidemic dynamics behavior in some bus transport networks abstract we abstract bus transport networks btns to complex networks using the space p approach first we select three actual btns in three major cities in china namely beijing shanghai and hangzhou using the sis model we simulate and study the epidemic spreading in the three btns we obtain the density of infected vertices varying with time and the stationary density of infected vertices varying with infection rate second we simulate and study the epidemic spreading in a recently introduced btn evolution model the network properties of which correspond well with those of actual btns third we use mean field theory to analyze the epidemic dynamics behavior of the btn evolution model and obtain the theoretical epidemic threshold of this model the theoretical value agrees well with the simulation results based on the work in this paper we provide the following possible forecasts for epidemic dynamics in actual btns an actual btn should have a finite positive epidemic threshold if the effective infection rate is above this threshold the epidemic spread in the network and the density of infected vertices finally stabilizes in a balanced state below this threshold the number of infected vertices decays exponentially fast and the epidemic cannot spread on a large scale

gradient mechanism in a communication network we study the efficiency of the gradient mechanism of message transfer in a two dimensional communication network of regular nodes and randomly distributed hubs each hub on the network is assigned some randomly chosen capacity and hubs with lower capacities are connected to the hubs with maximum capacity the average travel times of single messages traveling on the lattice decrease rapidly as the number of hubs increase the functional dependence of the average travel times on the hub density shows q exponential behavior with a power law tail we also study the relaxation behavior of the network when a large number of messages are created simultaneously at random locations and travel on the network toward their designated destinations for this situation in the absence of the gradient mechanism the network can show congestion effects due to the formation of transport traps we show that if hubs of high betweenness centrality are connected by the gradient mechanism efficient decongestion can be achieved the gradient mechanism is less prone to the formation of traps than other decongestion schemes we also study the spatial configurations of transport traps and propose minimal strategies for their elimination

equilibrium distributions in entropy driven balanced processes abstract for entropy driven balanced processes we obtain final states with poisson bernoulli negative binomial and polya distributions we apply this both for complex networks and particle production for random networks we follow the evolution of the degree distribution p n in a system where a node can activate k fixed connections from k possible partnerships among all nodes the total number of connections n is also fixed for particle physics problems p n is the probability of having n particles or other quanta distributed among k states phase space cells while altogether a fixed number of n particles reside on k states

a step up multiple test procedure abstract we consider the problem of simultaneously testing k 2 hypotheses on parameters 1 k in a typical application the s may be a set of contrasts for instance a set of orthogonal contrasts among population means or a set of differences between k treatment means and a standard treatment mean it is assumed that least squares estimators 1 k are available that are jointly normally distributed with a common variance known up to a scalar namely the error variance 2 and a common known correlation an independent 2 distributed unbiased estimator of 2 is also assumed to be available we propose a step up multiple test procedure for this problem which tests the t statistics for the k hypotheses in order starting with the least significant one and continues as long as an acceptance occurs by contrast the step down approach which is usually used starts with the most significant and continues as long as a rejection occurs critical constants required by this step up procedure to co

structure of n clique networks embedded in a complex network we propose the n clique network as a powerful tool for understanding global structures of combined highly interconnected subgraphs and provide theoretical predictions for statistical properties of the n clique networks embedded in a complex network using the degree distribution and the clustering spectrum furthermore using our theoretical predictions we find that the statistical properties are invariant between 3 clique networks and original networks for several observable real world networks with the scale free connectivity and the hierarchical modularity the result implies that structural properties are identical between the 3 clique networks and the original networks

critical behaviour of a probabilistic automata network sis model for the spread of an infectious disease in a population of moving individuals a probabilistic automata network sis susceptible infective susceptible model for the spread of an infectious disease in a population of moving individuals is studied the local rule consists of two subrules the first one applied synchronously models infection and recovery it is a probabilistic cellular automaton rule the second applied sequentially describes the motion of the individuals the model contains three parameters the probabilities pi to get infected and pr to recover and the average number of tentative moves per individual m depending upon the values of these parameters in the infinite time limit the system is either in the disease free state or in the endemic state it goes from one state to the other through a transcritical bifurcation similar to a second order phase transition characterized by a non negative order parameter whose role is played in this model by the stationary density of infected individuals the pi pr phase diagram and the critical behaviour of the stationary density of infectives in the neighbourhood of the phase transition are studied as a function of m according to whether the individuals perform short or long range moves it is found that the parameters characterizing the transition have a qualitatively different behaviour as m varies when m is very large the correlations created by the application of the subrule modelling infection and recovery are destroyed and as expected the behaviour of the system is then correctly predicted by a mean field type approximation which assumes a homogeneous mixing of the individuals when m is not large this assumption is no longer correct

markov processes hurst exponents and nonlinear diffusion equations with application to finance abstract we show by explicit closed form calculations that a hurst exponent h 1 2 does not necessarily imply long time correlations like those found in fractional brownian motion fbm we construct a large set of scaling solutions of fokker planck partial differential equations pdes where h 1 2 thus markov processes which by construction have no long time correlations can have h 1 2 if a markov process scales with hurst exponent h 1 2 then it simply means that the process has nonstationary increments for the scaling solutions we show how to reduce the calculation of the probability density to a single integration once the diffusion coefficient d x t is specified as an example we generate a class of student t like densities from the class of quadratic diffusion coefficients notably the tsallis density is one member of that large class the tsallis density is usually thought to result from a nonlinear diffusion equation but instead we explicitly show that it follows from a markov process generated by a linear fokker planck equation and therefore from a corresponding langevin equation having a tsallis density with h 1 2 therefore does not imply dynamics with correlated signals e g like those of fbm a short review of the requirements for fbm is given for clarity and we explain why the usual simple argument that h 1 2 implies correlations fails for markov processes with scaling solutions finally we discuss the question of scaling of the full green function g x t x t of the fokker planck pdes

random boolean network model exhibiting deterministic chaos this paper considers a simple boolean network with n nodes each node s state at time t being determined by a certain number of parent nodes which may vary from one node to another this is an extension of a model studied by andrecut and ali int j mod phys b 15 17 2001 who consider the same number of parents for all nodes we make use of the same boolean rule as andrecut and ali provide a generalization of the formula for the probability of finding a node in state 1 at a time t and use simulation methods to generate consecutive states of the network for both the real system and the model the results match well we study the dynamics of the model through sensitivity of the orbits to initial values bifurcation diagrams and fixed point analysis we show that the route to chaos is due to a cascade of period doubling bifurcations which turn into reversed period halving bifurcations for certain combinations of parameter values

making dynamic modeling effective in economics abstract mathematics has been extremely effective in physics but not in economics beyond finance to establish economics as science we should follow the galilean method and try to deduce mathematical models of markets from empirical data as has been done for financial markets financial markets are nonstationary this means that value is subjective nonstationarity also means that the form of the noise in a market cannot be postulated a priori but must be deduced from the empirical data i discuss the essence of complexity in a market as unexpected events and end with a biologically motivated speculation about market growth

synchronization diversity and topology of networks of integrate and fire oscillators we study synchronization dynamics of a population of pulse coupled oscillators in particular we focus our attention on the interplay between topological disorder and synchronization features of networks first we analyze synchronization time t in random networks and find a scaling law which relates t to network connectivity then we compare synchronization time for several other topological configurations characterized by a different degree of randomness the analysis shows that regular lattices perform better than a disordered network this fact can be understood by considering the variability in the number of links between two adjacent neighbors this phenomenon is equivalent to having a nonrandom topology with a distribution of interactions and it can be removed by an adequate local normalization of the couplings

boolean game on scale free networks abstract inspired by the local minority game we propose a network boolean game and investigate its dynamical properties on scale free networks the system can self organize to a stable state with better performance than the random choice game although only the local information is available to each agent by introducing the heterogeneity of local interactions we find that the system will achieve the best performance when each agent s interaction frequency is linearly correlated with its information capacity generally the agents with more information gain more than those with less information while in the optimal case each agent almost has the same average profit in addition we investigate the role of irrational factor and find an interesting symmetrical behavior

improving holm s procedure using pairwise dependencies summary seneta chen 2005 tightened the familywise error rate control of holm s procedure by sharpening its critical values using pairwise dependencies of the p values in this paper we further sharpen these critical values in the case where the distribution functions of the pairwise maxima of null p values are convex a property shown to hold in some applications of holm s procedure the newer critical values are uniformly larger providing tighter familywise error rate control than the approach of seneta chen 2005 significantly so under high pairwise positive dependencies the critical values can be further improved under exchangeable null p values control of the familywise error rate the probability of falsely rejecting at least one true null hypothesis is commonly undertaken when testing multiple hypotheses among procedures for controlling this error rate that of holm 1979 is one of the most popular seneta chen 2005 attempted to improve upon holm s procedure in situations where pairwise dependencies among the p values can be quantified they applied an inequality of kounias 1968 to obtain an upper bound for the distribution function of the minimum of a set of null p values which is tighter than that provided by bonferroni s inequality while modifying holm s critical values the modification tightens the familywise error rate control of holm s procedure and can be more powerful than the original step up procedure of hochberg 1988 as seneta chen 2005 showed for some multiple testing problems associated with normally distributed test statistics with known correlations we propose two improved versions of holm s step down procedure for p values such that the pairwise maxima of the null p values have known convex distribution functions the different versions depend on whether the null p values are exchangeable and each provides uniformly larger critical values than the method of seneta chen 2005 the convexity of p values is shown for some commonly used multivariate distributions numerical and simulation studies reveal that each of our proposed procedures is a better choice than the method of seneta chen 2005 especially for small scale multiple testing with high pairwise dependencies among the test statistics

scaling behaviors in differently developed markets scaling properties of four di erent stock market indices are studied in terms of a generalized hurst exponent approach we nd that the deviations from pure brownian motion behavior are associated with the degrees of development of the markets and we observe strong di erentiations in the scaling properties of markets at di erent development stage c

growing networks with mixed attachment mechanisms networks grow and evolve when new nodes and links are added in there are two methods to add the links uniform attachment and preferential attachment we take account of the addition of links with mixed attachment between uniform attachment and preferential attachment in proportion by using numerical simulations and analysis based on a continuum theory we obtain that the degree distribution p k has an extended power law form p k k k0 when the number of edges k of a node is much larger than a certain value k0 the degree distribution reduces to the power law form p k k and when k is much smaller than k0 the degree distribution degenerates into the exponential form it has been found that degree distribution possesses this extended power law form for many real networks such as the movie actor network the citation network of scientific papers and diverse protein interaction networks

lobby index in networks abstract we propose a new node centrality measure in networks the lobby index which is inspired by hirsch s h index it is shown that in scale free networks with exponent the distribution of the l index has power tail with exponent 1 properties of the l index and extensions are discussed

weighted scale free networks with stochastic weight assignments we propose a model of weighted scale free networks incorporating a stochastic scheme for weight assignments to the links taking into account both the popularity and fitness of a node as the network grows the weights of links are driven either by the connectivity with probability p or by the fitness with probability 1 ensuremath p numerical results show that the total weight exhibits a power law distribution with an exponent ensuremath sigma that depends on the probability p the exponent ensuremath sigma decreases continuously as p increases for p 0 the scaling behavior is the same as that of the connectivity distribution an analytical expression for the total weight is derived so as to explain the features observed in the numerical results numerical results are also presented for a generalized model with a fitness dependent link formation mechanism

cluster growth in two growing network models we analyse a simple model for growing tree networks and find that although it never percolates there is an anomalously large cluster at finite size we study the growth of both the maximal cluster and the cluster containing the original vertex and find that they obey power laws this property is also observed through simulations in a nonlinear model with loops and a true percolating phase

cellular automata with network incubation in information technology diffusion abstract innovation diffusion of network goods determines direct network externalities that depress sales for long periods and delay full benefits we model this effect through a multiplicative dynamic market potential driven by a latent individual threshold embedded in a special cellular automata representation the corresponding mean field approximation of its aggregate version is a riccati equation with a closed form solution this allows the detection of a change point time separating an incubation period from a subsequent take off due to a collective threshold critical mass weighted nonlinear least squares are the main inferential methodology an application is analysed with reference to usa fax machine diffusion

stochastic resonance in coupled threshold elements on a barabasi albert network abstract stochastic resonance is investigated in a system of threshold elements located at nodes and coupled along edges of a barabasi albert network driven by a common subthreshold periodic signal and independent noises array enhanced stochastic resonance is observed i e increase of the spectral power amplification evaluated from the mean output of the network due to proper coupling this enhancement occurs though the response of individual threshold elements to the periodic signal is very diverse due to a power law distribution of their connectivity numerical results are qualitatively explained using simple linear response theory in the mean field approximation

a statistical test of walrasian equilibrium by means of complex networks theory we represent an exchange economy in terms of statistical ensembles for complex networks by introducing the concept of market configuration this is defined as a sequence of nonnegative discrete random variables w ij describing the flow of a given commodity from agent i to agent j this sequence can be arranged in a nonnegative matrix w which we can regard as the representation of a weighted and directed network or digraph g our main result consists in showing that general equilibrium theory imposes highly restrictive conditions upon market configurations which are in most cases not fulfilled by real markets an explicit example with reference to the e mid interbank credit market is provided

fractional calculus and continuous time finance ii the waiting time distribution we complement the theory of tick by tick dynamics of financial markets based on a continuous time random walk ctrw model recently proposed by scalas et al 4 and we point out its consistency with the behaviour observed in the waiting time distribution for bund future prices traded at liffe london

social network growth with assortative mixing networks representing social systems display specific features that put them apart from biological and technological ones in particular the number of links attached to a node is positively correlated to that of its nearest neighbours we develop a model that reproduces this feature starting from microscopical mechanisms of growth the statistical properties arising from the simulations are in good agreement with those of the real world social networks of scientists co authoring papers in condensed matter physics moreover the model highlights the determinant role of correlations in shaping the network s topology

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved