stochastic and mixed flower graphs stochasticity is introduced to a well studied class of recursively grown graphs u v flower nets which have power law degree distributions as well as small world properties when u 1 the stochastic variant interpolates between different deterministic flower graphs thus adding flexibility to the model the random multiplicative growth process involved however leads to a spread ensemble of networks with finite variance for the number of links nodes and loops nevertheless the degree exponent and loopiness exponent attain unique values in the thermodynamic limit of infinitely large graphs we also study a class of mixed flower networks closely related to the stochastic flowers but which are grown recursively in a deterministic way the deterministic growth of mixed flower nets eliminates ensemble spreads and their recursive growth allows for exact analysis of their uniquely defined mixed properties

general framework for dynamic substructuring history review and classification of techniques four decades after the development of the first dynamic substructuring techniques there is a necessity to classify the different methods in a general framework that outlines the relations between them in this paper a certain vision on substructuring methods is proposed by recalling important historical milestones that allow us to understand substructuring as a domain decomposition concept thereafter based on the dual and primal assembly of substructures a general framework for the classification of the methods is presented this framework allows us to indicate how the various classes of methods proposed along the years can be derived from a clear mathematical description of substructured problems current bottlenecks in experimental dynamic substructuring as well as solutions found in literature will also be briefly discussed

spectra and eigenvectors of scale free networks we study the spectra and eigenvectors of the adjacency matrices of scale free networks when bidirectional interaction is allowed so that the adjacency matrix is real and symmetric the spectral density shows an exponential decay around the center followed by power law long tails at both spectrum edges the largest eigenvalue ensuremath lambda 1 depends on system size n as ensuremath lambda 1 ensuremath sim n 1 4 for large n and the corresponding eigenfunction is strongly localized at the hub the vertex with largest degree the component of the normalized eigenfunction at the hub is of order unity we also find that the mass gap scales as n ensuremath 0 68

random walks on graphs ideas techniques and results random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology in recent years relevant mathematical results have been obtained in this field and new ideas have been introduced which can be fruitfully extended to different areas and disciplines here we aim at giving a brief but comprehensive perspective of these progresses with a particular emphasis on physical aspects

generalized reflected bsdes driven by a levy process and an obstacle problem for pdies with a nonlinear neumann boundary condition in this paper we derive the existence and uniqueness of the solution for a class of generalized reflected backward stochastic differential equations grbsdes in short driven by a levy process which involve the integral with respect to a continuous process by means of the snell envelope the penalization method and the fixed point theorem in addition we obtain the comparison theorem for the solutions of the grbsdes as an application we give a probabilistic formula for the viscosity solution of an obstacle problem for a class of partial differential integral equations pdies in short with a nonlinear neumann boundary condition

stability analysis for neutral stochastic delay systems with markovian switching abstract this paper considers the exponential stability in p th p 1 moment and the almost sure exponential stability for neutral stochastic delay systems with markovian switching by using the generalized integral inequality and the nonnegative local martingale convergence theorem the lyapunov stability results on the exponential stability in p th p 1 moment and the almost sure exponential stability for such systems are given when the time varying delay is a bounded measurable function and the coefficients in the monotonicity condition are time varying the derived results are illustrated by two examples

reflected solutions of backward sde s and related obstacle problems for pde s we study reflected solutions of one dimensional backward stochastic differential equations the reflection keeps the solution above a given stochastic process we prove uniqueness and existence both by a fixed point argument and by approximation via penalization we show that when the coefficient has a special form then the solution of our problem is the value function of a mixed optimal stopping optimal stochastic control problem we finally show that when put in a markovian framework the solution of our reflected bsde provides a probabilistic formula for the unique viscosity solution of an obstacle problem for a parabolic partial differential equation

mapping between hopping on hierarchical structures and diffusion on a family of fractals the authors present a simple analytical approach to studying diffusion on hierarchical and fractal structures they show that hopping on one dimensional hierarchical structures can be mapped onto diffusion on a family of loopless fractals

epidemics and percolation in small world networks we study some simple models of disease transmission on small world networks in which either the probability of infection by a disease or the probability of its transmission is varied or both the resulting models display epidemic behavior when the infection or transmission probability rises above the threshold for site or bond percolation on the network and we give exact solutions for the position of this threshold in a variety of cases we confirm our analytic results by numerical simulation

importance of small degree nodes in assortative networks with degree weight correlations it has been known that assortative network structure plays an important role in spreading dynamics for unweighted networks yet its influence on weighted networks is not clear in particular when weight is strongly correlated with the degrees of the nodes as we empirically observed in twitter here we use the self consistent probability method and revised nonperturbative heterogenous mean field theory method to investigate this influence on both susceptible infective recovered sir and susceptible infective susceptible sis spreading dynamics both our simulation and theoretical results show that while the critical threshold is not significantly influenced by the assortativity the prevalence in the supercritical regime shows a crossover under different degree weight correlations in particular unlike the case of random mixing networks in assortative networks the negative degree weight correlation leads to higher prevalence in their spreading beyond the critical transmissivity than that of the positively correlated in addition the previously observed inhibition effect on spreading velocity by assortative structure is not apparent in negatively degree weight correlated networks while it is enhanced for that of the positively correlated detailed investigation into the degree distribution of the infected nodes reveals that small degree nodes play essential roles in the supercritical phase of both sir and sis spreadings our results have direct implications in understanding viral information spreading over online social networks and epidemic spreading over contact networks

solutions of neutral delay differential equations using a generalized lambert w function abstract the lambert w function is defined by w a e w a a 0 one of the many applications of the lambert w function is in solving delay differential equations ddes in 2003 asl and ulsoy provided a solution of some ddes in terms of the lambert w functions asl et al 2003 1 however the solutions are limited to differential equations with delay in the state variable scott et al 2006 2 introduced a generalized lambert function which was further studied by mez and baricz 2017 3 in our work we show that this generalization of the lambert w function provides an analytical solution to neutral delay differential equations nddes nddes are ddes with time delay not only in the state variables but also in the derivative terms this analytical solution is advantageous such that it is similar to the general solutions of linear odes also one can identify how the parameters affect the solution of the equation since our proposed solution is written in terms of these parameters we then propose a new numerical method to solve linear nddes using the generalized lambert w function we test our method to examples with known solutions we also provide a real world application by solving an ndde model of the population growth of an e coli culture using our proposed approach

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

topological properties of percolation clusters percolation properties including the total cluster mass s the shell mass b and the linear geometrical size r are studied as a function of the topological chemical distance parameter l all critical exponents are shown to be related to an apparently new exponent nu defined by r approximately lv critical exponents are calculated exactly for percolation clusters on the cayley tree a model for 6d percolation for which s approximately l2 b approximately l and r2 approximately l for diffusion on such clusters one finds that l3 approximately t numerical estimates of the exponents are obtained for other dimensions a conjecture which relates nu to beta and nu is discussed

tracking oscillations in the presence of delay induced essential instability hybrid testing which couples physical experiments and computer simulations bidirectionally and in real time is a promising experimental technique in engineering one fundamental problem of this technique are delays in the coupling between simulation and experiment we discuss this issue for a simple prototype hybrid system a pendulum that is vertically excited by coupling it to a simulated linear mass spring damper system under realistic conditions a small delay in the coupling can give rise to an essential instability the linearisation has infinitely many unstable eigenvalues for arbitrarily small delay this type of instability is impossible to compensate for with any of the standard compensation techniques we introduce an approach based on feedback control and newton iterations that is able to overcome this instability the basic idea behind our approach consists of two parts first we change the bidirectional coupling between experiment and computer simulation to a unidirectional coupling and stabilise the experiment with a feedback loop second we place the modified hybrid system into a newton iteration scheme if the iteration converges then the hybrid experiment behaves just as the original emulated system within the experimental accuracy we demonstrate by using a computer simulation for the experimental part that our approach is able to overcome the essential instability in combination with path following methods it allows us to track oscillations and their bifurcations systematically

on semi linear degenerate backward stochastic partial differential equations in this paper we study a class of one dimensional degenerate semilinear backward stochastic partial differential equations bspdes for short of parabolic type by establishing some new a priori estimates for both linear and semilinear bspdes we show that the regularity and uniform boundedness of the adapted solution to the semilinear bspde can be determined by those of the coefficients a special feature that one usually does not expect from a stochastic differential equation the proof follows the idea of the so called bootstrap method which enables us to analyze each of the derivatives of the solution under consideration some related results including some comparison theorems of the adapted solutions for semilinear bspdes as well as a nonlinear stochastic feynman kac formula are also given

search in power law networks many communication and social networks have power law link distributions containing a few nodes that have a very high degree and many with low degree the high connectivity nodes play the important role of hubs in communication and networking a fact that can be exploited when designing efficient search algorithms we introduce a number of local search strategies that utilize high degree nodes in power law graphs and that have costs scaling sublinearly with the size of the graph we also demonstrate the utility of these strategies on the gnutella peer to peer network

assortativity and act degree distribution of some collaboration networks empirical investigation results on weighted and un weighted assortativity act degree distribution degree distribution and node strength distribution of nine real world collaboration networks have been presented the investigations propose that act degree distribution degree distribution and node strength distribution usually show so called shifted power law spl function forms which can continuously vary from an ideal power law to an ideal exponential decay two parameters a and z can be used for description of the distribution functions another conclusion is that assortativity coefficient and the parameter a or z is monotonously dependent on each other by the collaboration network evolution model introduced in a reference p zhang et al physica a 360 2006 599 we analytically derived the spl distributions which typically appeared in general situations where nodes are selected partially randomly with a probability p and partially by linear preferential principle with the probability 1 p the analytic discussion gives an explicit expression on the relationship between the random selection proportion p and the parameters a and z the numerical simulation results by the model show a monotonic dependence of assortativity on the random selection proportion p the empirically obtained assortativity versus a or z curve for the four collaboration networks with small maximal act size t max shows a good agreement with the model prediction according to the curves one can qualitatively judge the random selection proportion of the real world network in its evolution process r 2007 elsevier b v all rights reserved

reaction spreading on graphs we study reaction diffusion processes on graphs through an extension of the standard reaction diffusion equation starting from first principles we focus on reaction spreading i e on the time evolution of the reaction product m t at variance with pure diffusive processes characterized by the spectral dimension d s the important quantity for reaction spreading is found to be the connectivity dimension d l numerical data in agreement with analytical estimates based on the features of n independent random walkers on the graph show that m t t d l in the case of erdos renyi random graphs the reaction product is characterized by an exponential growth m t e t with proportional to ln k where k is the average degree of the graph

estimates of the bistable region in metal cutting the classical model of regenerative vibration is investigated with new kinds of nonlinear cutting force characteristics the standard nonlinear characteristics are subjected to a critical review from the nonlinear dynamics viewpoint based on the experimental results available in the literature the proposed nonlinear model includes finite derivatives at zero chip thickness and has an essential inflexion point in the case of the one degreeof freedom model of orthogonal cutting the existence of unstable self excited vibrations is proven along the stability limits which is strongly related to the force characteristic at its inflexion point an analytical estimate is given for a certain area below the stability limit where stable stationary cutting and a chaotic attractor coexist it is shown how this domain of bistability depends on the theoretical chip thickness the comparison of these results with the experimental observations and also with the subcritical hopf bifurcation results obtained for standard nonlinear cutting force characteristics provides relevant information on the nature of the cutting force nonlinearity

resilience to damage of graphs with degree correlations the existence or nonexistence of a percolation threshold on power law correlated graphs is a fundamental question for which a general criterion is lacking in this work we investigate the problems of site and bond percolation on graphs with degree correlations and their connection with spreading phenomena we obtain some general expressions that allow the computation of the transition thresholds or their bounds using these results we study the effects of assortative and disassortative correlations on the resilience to damage of networks

attack vulnerability of complex networks we study the response of complex networks subject to attacks on vertices and edges several existing complex network models as well as real world networks of scientific collaborations and internet traffic are numerically investigated and the network performance is quantitatively measured by the average inverse geodesic length and the size of the largest connected subgraph for each case of attacks on vertices and edges four different attacking strategies are used removals by the descending order of the degree and the betweenness centrality calculated for either the initial network or the current network during the removal procedure it is found that the removals by the recalculated degrees and betweenness centralities are often more harmful than the attack strategies based on the initial network suggesting that the network structure changes as important vertices or edges are removed furthermore the correlation between the betweenness centrality and the degree in complex networks is studied

on topological properties of the octahedral koch network abstract in this article we propose an octahedral koch network exhibiting abundant new properties compared to the triangular koch network analytical expressions for the degree distribution clustering coefficient and average path length are presented the scale free feature and small world property of the octahedral koch network are obtained via numerical analysis furthermore we show that the octahedral koch network is assortative finally we show that the projection of the octahedral koch network on the plane is the nearest neighbor coupled koch network and the critical exponents of degree distribution in the octahedral koch network is greater than three

stochastic pdies and backward doubly stochastic differential equations driven by levy processes in this paper a new class of backward doubly stochastic differential equations driven by teugels martingales associated with a levy process satisfying some moment condition and an independent brownian motion is investigated we obtain the existence and uniqueness of solutions to these equations a probabilistic interpretation for solutions to a class of stochastic partial differential integral equations is given

random line graphs and a linear law for assortativity for a fixed number n of nodes the number of links l in the line graph h n l can only appear in consecutive intervals called a band of l we prove that some consecutive integers can never represent the number of links l in h n l and they are called a bandgap of l we give the exact expressions of bands and bandgaps of l we propose a model which can randomly generate simple graphs which are line graphs of other simple graphs the essence of our model is to merge step by step a pair of nodes in cliques which we use to construct line graphs obeying necessary rules to ensure that the resulting graphs are line graphs two nodes to be merged are randomly chosen at each step if the cliques are all of the same size the assortativity of the line graphs in each step are close to 0 and the assortativity of the corresponding root graphs increases linearly from 1 to 0 with the steps of the nodal merging process if we dope the constructing elements of the line graphs the cliques of the same size with a relatively smaller number of cliques of different size the characteristics of the assortativity of the line graphs is completely altered we also generate line graphs with the cliques whose sizes follow a binomial distribution the corresponding root graphs with binomial degree distributions zero assortativity and semicircle eigenvalue distributions are equivalent to erd s renyi random graphs

hamiltonian mean field model effect of network structure on synchronization dynamics the hamiltonian mean field model of coupled inertial hamiltonian rotors is a prototype for conservative dynamics in systems with long range interactions we consider the case where the interactions between the rotors are governed by a network described by a weighted adjacency matrix by studying the linear stability of the incoherent state we find that the transition to synchrony begins when the coupling constant k is inversely proportional to the largest eigenvalue of the adjacency matrix we derive a closed system of equations for a set of local order parameters to study the effect of network heterogeneity on the synchronization of the rotors when k is just beyond the transition to synchronization we find that the degree of synchronization is highly dependent on the network s heterogeneity but that for large k the degree of synchronization is robust to changes in the degree distribution our results are illustrated with numerical simulations on erd os renyi networks and networks with power law degree distributions

an empirical study of an agglomeration network recently researchers have reported many models mimicking real network evolution growth among which some are based on network aggregation growth however until now relatively few experiments have been reported accordingly in this paper photomicrographs of real materials the agglomeration in the filtrate of slurry formed by a gap nanoparticle conglomerate dispersed in water are analyzed within the framework of complex network theory by data mapping from photomicrographs we generate undirected networks and as a definition of degree we adopt the number of pixel s nearest neighbors while adjacent pixels define a connection or an edge we study the topological structure of these networks including degree distribution clustering coefficient and average path length in addition we discuss the self similarity and synchronizability of the networks we find that the synchronizability of high concentration agglomeration is better than that of low concentration agglomeration we also find that agglomeration networks possess good self similar features

spectra of real world graphs beyond the semicircle law results on the spectra of adjacency matrices corresponding to models of real world graphs we find that when the number of links grows as the number of nodes the spectral density of uncorrelated random matrices does not converge to the semicircle law furthermore the spectra of real world graphs have specific features depending on the details of the corresponding models in particular scale free graphs develop a trianglelike spectral density with a power law tail while small world graphs have a complex spectral density consisting of several sharp peaks these and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks

numerical aspects of a real time sub structuring technique in structural dynamics a time domain coupling technique involving combined computational and experimental modelling for vibration analysis of structures built up of linear non linear substructures is developed the study permits in principle one or more of the substructures to be modelled experimentally with measurements being made only on the interfacial degrees of freedom the numerical and experimental substructures are allowed to communicate in real time within the present framework the proposed strategy involves a two stage scheme the first is iterative in nature and is implemented at the initial stages of the solution in a non real time format the second is non iterative employs an extrapolation scheme and proceeds in real time issues on time delays during communications between different substructures are discussed an explicit integration procedure is shown to lead to solutions with high accuracy while retaining path sensitivity to initial conditions the stability of the integration scheme is also discussed and a method for numerically dissipating the temporal growth of high frequency errors is presented for systems with non linear substructures the integration procedure is based on a multi step transversal linearization method and to account for time delays we employ a multi step extrapolation scheme based on the reproducing kernel particle method numerical illustrations on a few low dimensional vibrating structures are presented and these examples are fashioned after problems of seismic qualification testing of engineering structures using real time substructure testing techniques

on solutions to backward stochastic partial differential equations for levy processes in this paper we prove the existence and uniqueness of the solution for a class of backward stochastic partial differential equations bspdes for short driven by the teugels martingales associated with a levy process satisfying some moment conditions and by an independent brownian motion an example is given to illustrate the theory

the mathematics of infectious diseases many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases threshold theorems involving the basic reproduction number r 0 the contact number sigma and the replacement number r are reviewed for the classic sir epidemic and endemic models similar results with new expressions for r 0 are obtained for mseir and seir endemic models with either continuous age or age groups values of r 0 and sigma are estimated for various diseases including measles in niger and pertussis in the united states previous models with age structure heterogeneity and spatial structure are surveyed

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

necessary conditions for optimal control of stochastic systems with random jumps a maximum principle is proved for optimal controls of stochastic systems with random jumps the control is allowed to enter into both diffusion and jump terms the form of the maximum principle turns out to be quite different from the one corresponding to the pure diffusion system the word pure here means the absence of the jump term in calculating the first order coefficient for the cost variation only a property for lebesgue integrals of scalar valued functions in the real number space cal r is used this shows that there is no essential difference between deterministic and stochastic systems as far as the derivation of maximum principles is concerned

inducing self organized criticality in a network toy model by neighborhood assortativity complex networks are a recent type of framework used to study complex systems with many interacting elements such as self organized criticality soc the network nodes tendency to link to other nodes of similar type is characterized by assortative mixing real networks exhibit assortative mixing by vertex degree however typical random network models such as the erd s renyi or the barabasi albert model show no assortative arrangements in this paper we introduce the notion of neighborhood assortativity as the tendency of a node to belong to a community its neighborhood showing an average property similar to its own imposing neighborhood assortative mixing by degree in a network toy model soc dynamics can be found these dynamics are driven only by the network topology the long range correlations resulting from criticality have been characterized by means of fluctuation analysis and show an anticorrelation in the node s activity the model contains only one parameter and its statistics plots for different values of the parameter can be collapsed into a single curve the simplicity of the model allows us to perform numerical simulations and also to study analytically the statistics for a specific value of the parameter making use of the markov chains

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

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

organization of networks with tagged nodes and biased links a priori distinct communities the case of intelligent design proponents and darwinian evolution defenders previously at grapes supratecs universit e de li ege b5a sart tilman b 4000 li ege eurolandabstractamong topics of opinion formation it is of interest to observe the characteristics ofnetworks with a priori distinct communities as an illustration we report on thecitation network s unfolded in the recent decades through web available works be longing to selected members of the neocreationist and intelligent design proponents idp and the darwinian evolution defenders ded communities an adjacencymatrix of tagged nodes is rst constructed it is not symmetric a generalizationof considerations pertaining to the case of networks with biased links directed orundirected is thus presented the main characteristic coe cients describing the structure of such partially di rected networks with tagged nodes are outlined the structural features are dis cussed searching for statistical aspects equivalence or not of subnetworks throughthe degree distributions each network assortativity the global and local cluster ing coe cients and the average overlap indices the various closed and open tri angles made from nodes moreover distinguishing the community are especiallylisted to calculate the clustering characteristics the distribution of elements inthe rectangular submatrices are specially examined since they represent inter community connexions the emphasis being on distinguishing the number of ver tices belonging to a given community using such informations one can distinguishbetween opinion leaders followers and main rivals and briey interpret their rela tionships through psychological like conditions intrinsic to behavior rules in eithercommunity considerations on other controversy cases with similar social constraintsare outlined as well as suggestions on further more general work deduced fromour observations on such networks preprint submitted to elsevier 30 april 2010

volatility behavior of visibility graph emd financial time series from ising interacting system abstract a financial market dynamics model is developed and investigated by stochastic ising system where the ising model is the most popular ferromagnetic model in statistical physics systems applying two graph based analysis and multiscale entropy method we investigate and compare the statistical volatility behavior of return time series and the corresponding imf series derived from the empirical mode decomposition emd method and the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model further we find that the degree distribution of visibility graph for the simulation series has the power law tails and the assortative network exhibits the mixing pattern property all these features are in agreement with the real market data the research confirms that the financial model established by the ising system is reasonable

backward stochastic differential equations with reflection and dynkin games we establish existence and uniqueness results for adapted solutions of backward stochastic differential equations bsde s with two reflecting barriers generalizing the work of el karoui kapoudjian pardoux peng and quenez existence is proved first by solving a related pair of coupled optimal stopping problems and then under different conditions via a penalization method it is also shown that the solution coincides with the value of a certain dynkin game a stochastic game of optimal stopping moreover the connection with the backward sde enables us to provide a pathwise deterministic approach to the game

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

description of diffusive and propagative behavior on fractals the known properties of diffusion on fractals are reviewed in order to give a general outlook of these dynamic processes after that we propose a description developed in the context of the intrinsic metric of fractals which leads us to a differential equation able to describe diffusion in real fractals in the asymptotic regime we show that our approach has a stronger physical justification than previous works on this field the most important result we present is the introduction of a dependence on time and space for the conductivity in fractals which is deduced by scaling arguments and supported by computer simulations finally the diffusion equation is used to introduce the possibility of reaction diffusion processes on fractals and analyze their properties specifically an analytic expression for the speed of the corresponding travelling fronts which can be of great interest for application purposes is derived

modelling real time dynamic substructuring using partial delay differential equations real time dynamic substructuring is a new component testing method for simulating the dynamics of complex engineering systems the physical component is tested within a computer generated virtual environment using real time control techniques delays in communication which occur between the component and the virtual environment can potentially destabilize the simulation in this paper the mechanism for this instability is examined using a beam oscillator system as a case study we will show how the stability and the amplitude response of the system change with the time delay numerical simulations of the reduced system as well as a full delayed beam equation are performed a series of experimental tests is carried out on a beam oscillator system comparison of the theoretical numerical and experimental results is presented and these agree remarkably well

computational complexity arising from degree correlations in networks we apply a bethe peierls approach to statistical mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices using the nondeterministic polynomial time hard optimization problem of finding minimal vertex covers on these graphs we show that such correlations may lead to a qualitatively different solution structure as compared to uncorrelated networks this results in a higher complexity of the network in a computational sense simple heuristic algorithms fail to find a minimal vertex cover in the highly correlated case whereas uncorrelated networks seem to be simple from the point of view of combinatorial optimization

perception of similarity a model for social network dynamics some properties of social networks e g the mixing patterns and the community structure appear deeply influenced by the individual perception of people in this work we map behaviors by considering similarity and popularity of people also assuming that each person has his her proper perception and interpretation of similarity although investigated in different ways depending on the specific scientific framework from a computational perspective similarity is typically calculated as a distance measure in accordance with this view to represent social network dynamics we developed an agent based model on top of a hyperbolic space on which individual distance measures are calculated simulations performed in accordance with the proposed model generate small world networks that exhibit a community structure we deem this model to be valuable for analyzing the relevant properties of real social networks

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

front propagation in reactive systems with anomalous diffusion abstract we study front propagation of reactive fields in systems whose diffusive behavior is anomalous both superdiffusive and subdiffusive the features of the front propagation depend not only on the scaling exponent x t 2 t 2 but also on the detailed shape of the probability distribution of the diffusive process from the analysis of different systems we have three possible behavior of front propagation the usual fisher kolmogorov like scenario i e the field has a spatial exponential tail moving with constant speed v f and thickness the field has a spatial exponential tail but v f and change in time as a power law and finally the field has a spatial power law tail and v f increases exponentially in time a linear analysis of the front tail is in quantitative agreement with the numerical simulations it is remarkable the fact that anomalous diffusion is neither necessary nor sufficient condition for the linear front propagation moreover if the probability distribution of the transport process follows the scaling relation given by the flory argument the front propagation is standard fisher kolmogorov like even in presence of super or sub diffusion

on a general class of models for interaction this paper develops a class of probability models for configurations of interacting points in a domain the distributions depend on a function which may be viewed as giving the potential energy of the configurations examples include models for interaction in a spatial region and on lattices and graphs new models in the general class arise naturally an example being a spatial model for points of different categories some general methods including series expansions and a simulation method known from statistical mechanics can be useful for many of these models several applications of this kind are considered and some connections between the models and with the statistical mechanics are explored

infection dynamics on scale free networks we discuss properties of infection processes on scale free networks relating them to the node connectivity distribution that characterizes the network considering the epidemiologically important case of a disease that confers permanent immunity upon recovery we derive analytic expressions for the final size of an epidemic in an infinite closed population and for the dependence of infection probability on an individual s degree of connectivity within the population as in an earlier study r pastor satorras and a vesipignani phys rev lett 86 3200 2001 phys rev e 63 006117 2001 for an infection that did not confer immunity upon recovery the epidemic process in contrast with many traditional epidemiological models does not exhibit threshold behavior and we demonstrate that this is a consequence of the extreme heterogeneity in the connectivity distribution of a scale free network finally we discuss effects that arise from finite population sizes showing that networks of finite size do exhibit threshold effects infections cannot spread for arbitrarily low transmission probabilities

epidemic dynamics and endemic states in complex networks we study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks in networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null on the contrary on a wide range of scale free networks we observe the absence of an epidemic threshold and its associated critical behavior this implies that scale free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess these results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks

the emergence of scale free networks with a seceding mechanism in order to explore further the underlying mechanism of the scale free networks we study stochastic secession as a mechanism for the creation of complex networks in this evolution the network growth incorporates the addition of new links between existing nodes the deleting and rewiring of some existing links and the stochastic secession of nodes to random growing networks with preferential attachment the model yields scale free behavior for the degree distribution furthermore we get the analytical expression of the power law degree distribution with scaling exponent ranges from 1 1 to 9 the analytical expressions are in good agreement with the numerical simulation results

on the concepts of complex networks to quantify the difficulty in finding the way out of labyrinths abstract labyrinths have been a tradition and part of the imagination of the human kind for centuries and were probably built either as a challenge to make it difficult for someone to find the way out or for aesthetic purposes they are conventionally classified according to the country they were built to the style roman classic and contemporary or to the construction site in this study we show that labyrinths can be modeled as complex networks whose metrics can be used to classify them in terms of their difficulty to find the way out this is performed by calculating the absorption time defined as the time it takes for a particle on an internal node to reach an output node through a random walk the absorption time correlates well with the shortest paths and length of the networks as expected and has a very high correlation pearson coefficient of 0 97 with the betweenness therefore allowing one to quantify the level of complexity of any labyrinth it is shown that the conventional classification is inappropriate to distinguish between labyrinths because some with very similar properties exist in different countries or were built in distinct time periods a refined analysis in 77 famous labyrinths indicated that the majority were built for aesthetic purposes with relatively small absorption times furthermore with the expectation maximization algorithm we could combine the complex network metrics to identify four clusters of labyrinths that differ in terms of density and shape

ring structures and mean first passage time in networks in this paper we address the problem of the calculation of the mean first passage time on generic graphs we focus in particular on the mean first passage time on a node s for a random walker starting from a generic unknown node x we introduce an approximate scheme of calculation which maps the original process in a markov process in the space of the so called rings described by a transition matrix of size o ln n ln k ln n ln k where n is the size of the graph and k the average degree in the graph in this way one has a drastic reduction of degrees of freedom with respect to the size n of the transition matrix of the original process corresponding to an extremely low computational cost we first apply the method to the erdos renyi random graphs for which the method allows for almost perfect agreement with numerical simulations then we extend the approach to the barabasi albert graph as an example of scale free graph for which one obtains excellent results finally we test the method with two real world graphs internet and a network of the brain for which we obtain accurate results

rate equation approach for correlations in growing network models we propose a rate equation approach to compute two vertex correlations in scale free growing network models based on the preferential attachment mechanism the formalism based on previous work of szabo et al fphys rev e 67 056102 s2002dg for the clustering spectrum measuring three vertex correlations is based on a rate equation in the continuous degree and time approximation for the average degree of the nearest neighbors of vertices of degree k with an appropriate boundary condition we study the properties of both two and three vertex correlations for linear preferential attachment models and also for a model yielding a large clustering coefficient the expressions obtained are checked by means of extensive numerical simulations the rate equation proposed can be generalized to more sophisticated growing network models and also extended to deal with related correlation measures as an example we consider the case of a recently proposed model of weighted networks for which we are able to compute a weighted two vertex correlation function taking into account the strength of the interactions between connected vertices

real time dynamic substructuring in a coupled oscillator pendulum system real time dynamic substructuring is a powerful testing method which brings together analytical numerical and experimental tools for the study of complex structures it consists of replacing one part of the structure with a numerical model which is connected to the remainder of the physical structure the substructure by a transfer system in order to provide reliable results this hybrid system must remain stable during the whole test a primary mechanism for destabilization of these type of systems is the delays which are naturally present in the transfer system in this paper we apply the dynamic substructuring technique to a nonlinear system consisting of a pendulum attached to a mechanical oscillator the oscillator is modelled numerically and the transfer system is an actuator the system dynamics is governed by two coupled second order neutral delay differential equations we carry out local and global stability analyses of the system and identify the delay dependent stability boundaries for this type of system we then perform a series of hybrid experimental tests for a pendulum oscillator system the results give excellent qualitative and quantitative agreement when compared to the analytical stability results

decelerated spreading in degree correlated networks while degree correlations are known to play a crucial role for spreading phenomena in networks their impact on the propagation speed has hardly been understood here we investigate a tunable spreading model on scale free networks and show that the propagation becomes slow in positively negatively correlated networks if nodes with a high connectivity locally accelerate decelerate the propagation examining the efficient paths offers a coherent explanation for this result while the k core decomposition reveals the dependence of the nodal spreading efficiency on the correlation our findings should open new pathways to delicately control real world spreading processes

spreading dynamics in heterogeneous graphs beyond the assortativity coefficient abstract we study spreading dynamics of a reaction diffusion process in a special class of heterogeneous graphs with poissonian degree distribution and composed of both local and long range links the behavior of the spreading dynamics on such networks are investigated by relating them to the topological features of graphs we find that the degree of assortativity can give just some indication about the large scale behavior of the spreading dynamics while a detailed description of the process can be addressed by introducing new more appropriate topological quantities linked to the distance between nodes

identifying node spreading influence for tunable clustering coefficient networks abstract identifying the node spreading influence is of significant for information and innovation diffusion in this paper we argue that the spreading process should be taken into account for identifying the node spreading influence and investigate the effect of the network structure measured by the clustering coefficient on the performance of spreading dynamics firstly we generate a series of networks with tunable clustering coefficients then taking into account the spreading process we explore the performances among the dynamics sensitive ds index and the degree between closeness eigenvector indices comparing with the susceptible infective removed sir model the extensive results show that for different spreading time steps and clustering coefficients the ds centrality outperforms the performance 0 97 of degree betweenness closeness and eigenvector measures moreover the accuracy of closeness and eigenvector centrality is similar and conducts better in networks with larger spreading rate 0 20 0 93 as the clustering coefficient increases all the performances decrease but ds centrality with least percent of 1 16 at most under 0 10 and closeness with the largest percent of 9 75 under 0 05 this work suggests that the spreading influence not only depends on the network structure more importantly the spreading dynamic process also affect the performance greatly which should be taken into account simultaneously

effects of time delayed position feedback on a van der pol duffing oscillator abstract the mechanism for the action of time delay in a non autonomous system is investigated in this paper the original mathematical model under consideration is a van der pol duffing oscillator with excitation a delayed system is obtained by adding both linear and nonlinear time delayed position feedbacks to the original system functional analysis is used to change the delayed system into a functional differential equation fde the time delay is taken as a variable parameter to investigate its effect on the dynamics of the system such as the stability and bifurcation of an equilibrium point phase locked periodic and phase shifting solution period doubling quasi periodic motion and chaos a periodic solution expressed in the closed form with the aid of the center manifold and averaging theorem is found to be in good agreement with that obtained by numerical simulation two routes to chaos are found namely period doubling bifurcation and torus breaking the results obtained in this paper show that time delay may be used as a simple but efficient switch to control motions of a system either from order motion to chaos or from chaotic motion to order for different applications

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

network algorithmics and the emergence of information integration in cortical models an information theoretic framework known as integrated information theory iit has been introduced recently for the study of the emergence of consciousness in the brain d balduzzi and g tononi plos comput biol 4 e1000091 2008 iit purports that this phenomenon is to be equated with the generation of information by the brain surpassing the information that the brain s constituents already generate independently of one another iit is not fully plausible in its modeling assumptions nor is it testable due to severe combinatorial growth embedded in its key definitions here we introduce an alternative to iit which while inspired in similar information theoretic principles seeks to address some of iit s shortcomings to some extent our alternative framework uses the same network algorithmic cortical model we introduced earlier a nathan and v c barbosa phys rev e 81 021916 2010 and to allow for somewhat improved testability relative to iit adopts the well known notions of information gain and total correlation applied to a set of variables representing the reachability of neurons by messages in the model s dynamics we argue that these two quantities relate to each other in such a way that can be used to quantify the system s efficiency in generating information beyond that which does not depend on integration we give computational results on our cortical model and on variants thereof that are either structurally random in the sense of an erd s renyi random directed graph or structurally deterministic we have found that our cortical model stands out with respect to the others in the sense that many of its instances are capable of integrating information more efficiently than most of those others instances

analytical solutions for diffusion on fractal objects a generalization of the euclidean diffusion equation is proposed for diffusion on fractals on the basis of a scaling argument a renormalization group theory for the green s function and numerical tests conjectures on the applicability to natural fractals such as porous media are presented

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

dynamical features of reaction diffusion fronts in fractals the speed of front propagation in fractals is studied by using i the reduction of the reaction transport equation into a hamilton jacobi equation and ii the local equilibrium approach different equations proposed for describing transport in fractal media together with logistic reaction kinetics are considered finally we analyze the main features of wave fronts resulting from this dynamic process i e why they are accelerated and what is the exact form of this acceleration

solution of the delayed single degree of freedom system equation by exponential matrix method in this paper an exponential collocation method for the solution linear delay differential equations with constant delay is presented the utility of this matrix based method is that it is very systematic and by writing a maple program any type of second order linear differential delay equation can be solved easily the method is applied to three different types of delay equations linear oscillator with delay i in the restoring force term ii in the damping term and iii in the acceleration term time response curves have been plotted for each type and the effect of the parameters of the delay terms has been shown an error analysis based on residual function is carried out to show the accuracy of the results