statistical analysis of airport network of china through the study of airport network of china anc composed of 128 airports nodes and 1165 flights edges we show the topological structure of anc conveys two characteristics of small worlds a short average path length 2 067 and a high degree of clustering 0 733 the cumulative degree distributions of both directed and undirected anc obey two regime power laws with different exponents i e the so called double pareto law in degrees and out degrees of each airport have positive correlations whereas the undirected degrees of adjacent airports have significant linear anticorrelations it is demonstrated both weekly and daily cumulative distributions of flight weights frequencies of anc have power law tails besides the weight of any given flight is proportional to the degrees of both airports at the two ends of that flight it is also shown the diameter of each subcluster consisting of an airport and all those airports to which it is linked is inversely proportional to its density of connectivity efficiency of anc and of its subclusters is measured through a simple definition in terms of that the efficiency of anc s subclusters increases as the density of connectivity does anc is found to have an efficiency of 0 484

geographic coarse graining analysis of the railway network of china abstract we investigate the detailed empirical analysis of the statistical properties of the railway network of china rnc in space l and space g constructed by geographic coarse graining process the rnc exhibits similar properties in the cumulative distributions of degree and strength in two spaces and it presents the hierarchical structure small world behavior and assortativity areciprocal connection both in space l and space g we also investigate the path length that every train runs the distribution of the railroad length per degree and the optimal distribution of stations

high breakdown point and high efficiency robust estimates for regression a class of robust estimates for the linear model is introduced these estimates called mm estimates have simultaneously the following properties i they are highly efficient when the errors have a normal distribution and ii their breakdown point is 0 5 the mm estimates are defined by a three stage procedure in the first stage an initial regression estimate is computed which is consistent robust and with high breakdown point but not necessarily efficient in the second stage an m estimate of the errors scale is computed using residuals based on the initial estimate finally in the third stage an m estimate of the regression parameters based on a proper redescending psi function is computed consistency and asymptotical normality of the mm estimates assuming random carriers are proved a convergent iterative numerical algorithm is given finally the asymptotic biases under contamination of optimal bounded influence estimates and mm estimates are compared

pinning control of complex dynamical networks with general topology abstract recently the researches on pinning control of complex dynamical networks have mainly focused on such networks with very specific coupling schemes e g symmetric coupling uniform coupling and linear coupling however most real networks often consist of local units which interact with each other via asymmetric and heterogeneous connections in this paper pinning control of a continuous time complex dynamical network with general coupling topologies is studied some generic stability criteria based on master stability function msf are derived for such a general controlled network which guarantee that the whole network can be pinned to its equilibrium by placing feedback control only on a small fraction of nodes then these results are extended to discrete time case previous results about symmetric uniform or linear coupled networks in this area are included as special cases of the present work numerical simulations of directed networks with weighted coupling pinned by specifically selective pinning scheme are given for illustration and verification

a boundedness criterion for generalized calderon zygmund operators in 1965 a p calderon showed the l2 boundedness of the so called first calderon commutator this is one of the first examples of a non convolution operator associated to a kernel which satisfies certain size and smoothness properties comparable to those of the kernel of the hilbert transform these properties together with the l2 boundedness imply the lp boundedness for all p s in 1 oo many operators in analysis such as certain classes of pseudo differential operators and the cauchy integral operator on a curve are associated with kernels having these properties for these operators one of the major questions is if they are bounded on l2 we are going to give necessary and sufficient conditions for such an operator to be bounded on l2 they are essentially that the images of the function 1 under the actions of the operator and its adjoint both lie in bmo in the case of the aforementioned first commutator this can be checked by an integration by parts in the first section we present some basic notions and state the theorem which is proved in sections 2 and 3 in section 4 we show how to recover some classical results in sections 5 and 6 we construct a functional calculus for small perturbations of a and in section 7 we show a connection between the theory of calderon zygmund operators and kato s conjecture it is a pleasure to express our thanks to r r coifman and y meyer for suggesting many elegant simplifications in our proofs and most of the applications we also wish to thank stephen semmes for several pertinent remarks

self similarity and network perspective of the chinese fund market abstract by testing 88 different funds of the chinese fund market cfm we find fractal behavior and long range correlations in the return series which are insensitive to the kind of funds meanwhile a power law relationship between the deviation d of prices and the hurst exponent h has been obtained which may be useful for predicting the price time series in addition with funds being viewed as nodes and the connections among the funds being determined by the cross correlation coefficients using a winner takes all approach we investigate the topological properties of the fund network our analysis reveals that during different time periods the cumulative degree distributions of the fund network all obey the double power law format moreover the small world property is also found for the fund network

time series model specification in the presence of outliers abstract outliers are commonplace in data analysis time series analysis is no exception noting that the effect of outliers on model identification statistics could be serious this article is concerned with the problem of time series model specification in the presence of outliers an iterative procedure is proposed to identify the outliers to remove their effects and to specify a tentative model for the underlying process the procedure is essentially based on the iterative estimation procedure of chang and tiao 1983 and the extended sample autocorrelation function esacf model identification method of tsay and tiao 1984 an example is given properties of the proposed procedure are discussed

a topological phase transition between small worlds and fractal scaling in urban railway transportation networks abstract fractal and small worlds scaling laws are applied to study the growth of urban railway transportation networks using total length and total population as observational parameters in spite of the variety of populations and urban structures the variation of the total length of the railway network with the total population of conurbations follows similar patterns for large and middle metropolis diachronous analysis of data for urban transportation networks suggests that there is second order phase transition from small worlds behaviour to fractal scaling during their early stages of development

a directed network of greek and roman mythology abstract we construct a directed network using a dictionary of greek and roman mythology in which the nodes represent the entries listed in the dictionary and we make directional links from an entry to other entries that appear in its explanatory part we find that this network is clearly not a random network but a directed scale free network in which the distributions of out degree and in degree follow a power law with exponents out 3 0 and in 2 5 respectively also we measure several quantities which describe the topological properties of the network and compare it to that of other real networks

infinitesimal robustness for autoregressive processes we define the influence function and construct optimal robust estimators for autoregressive processes we show that the asymptotic bias caused by small contaminations of the marginals can be written as the integral of a certain function with respect to the contamination this function is called the influence function it is unique only up to an equivalence relation but there is a natural unique version which describes the limiting influence of an additional observation given the previous observations moreover with this version the asymptotic variance at the true model can be expressed in a simple form optimal robust estimators minimize this asymptotic variance under a constraint on the influence function as in the i i d case they are found by truncating a multiple of the influence function of the maximum likelihood estimator

robust estimation for arma models this paper introduces a new class of robust estimates for arma models they are m estimates but the residuals are computed so the effect of one outlier is limited to the period where it occurs these estimates are closely related to those based on a robust filter but they have two important advantages they are consistent and the asymptotic theory is tractable we perform a monte carlo where we show that these estimates compare favorably with respect to standard m estimates and to estimates based on a diagnostic procedure

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

existence theory for the isentropic euler equations we establish an existence theorem for entropy solutions to the euler equations modeling isentropic compressible fluids we develop a new approach for constructing mathematical entropies for the euler equations which are singular near the vacuum in particular we identify the optimal assumption required on the singular behavior on the pressure law at the vacuum in order to validate the two term asymptotic expansion of the entropy kernel we proposed earlier for more general pressure laws we introduce a new multiple term expansion based on the bessel functions with suitable exponents and we also identify the optimal assumption needed to validate the multiple term expansion and to establish the existence theory our results cover as a special example the density pressure law where and are arbitrary constants

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

a kinetic equation with kinetic entropy functions for scalar conservation laws we construct a nonlinear kinetic equation and prove that it is welladapted to describe general multidimensional scalar conservation laws in particular we prove that it is well posed uniformly in e the microscopic scale we also show that the proposed kinetic equation is equipped with a family of kinetic entropy functions analogous to boltzmann s microscopich function such that they recover krushkov type entropy inequality on the macroscopic scale finally we prove by both bv compactness arguments in the multidimensional case and by compensated compactness arguments in the one dimensional case that the local density of kinetic particles admits a continuum limit as it converges strongly with e 0 to the unique entropy solution of the corresponding conservation law

on the continuous benney equations abstract the continuous benney equations and its riemann invariants are studied the cauchy problem for these equations is solved by an analog of the inverse scattering problem method

bounded influence propagation tau estimation a new robust method for arma model estimation a new robust and statistically efficient estimator for arma models called the bounded influence propagation estimator is proposed the estimator incorporates an auxiliary model which prevents the propagation of outliers strong consistency and asymptotic normality of the estimator for arma models that are driven by independently and identically distributed iid innovations with symmetric distributions are established to analyze the infinitesimal effect of outliers on the estimator the influence function is derived and computed explicitly for an ar 1 model with additive outliers to obtain estimates for the ar p model a robust durbin levinson type and a forward backward algorithm are proposed an iterative algorithm to robustly obtain arma p q parameter estimates is also presented the problem of finding a robust initialization is addressed which for orders p q 2 is a nontrivial matter numerical experiments are conducted to compare the finite sample performance of the proposed estimator to existing robust methodologies for different types of outliers both in terms of average and of worst case performance as measured by the maximum bias curve to illustrate the practical applicability of the proposed estimator a real data example of outlier cleaning for r r interval plots derived from electrocardiographic data is considered the proposed estimator is not limited to biomedical applications but is also useful in any real world problem whose observations can be modeled as an arma process disturbed by outliers or impulsive noise

robust estimates for arma models abstract two new classes of robust estimates for arma models are introduced estimates based on residual autocovariances ra estimates and estimates based on truncated residual autocovariances tra estimates a heuristic derivation of the asymptotic normal distribution is given we also perform a monte carlo study to compare the robustness properties of these estimates with the least squares m and gm estimates in this study we consider observations that correspond to a gaussian model with additive outliers the monte carlo results show that ra and tra estimates compare favorably with respect to least squares m and gm estimates

comprehensive definitions of breakdown points for independent and dependent observations summary we provide a new definition of breakdown in finite samples with an extension to asymptotic breakdown previous definitions centre on defining a critical region for either the parameter or the objective function if for a particular outlier configuration the critical region is entered breakdown is said to occur in contrast with the traditional approach we leave the definition of the critical region implicit our proposal encompasses previous definitions of breakdown in linear and non linear regression settings in some cases it leads to a different and more intuitive notion of breakdown than other procedures that are available an important advantage of our new definition is that it also applies to models for dependent observations where current definitions of breakdown typically fail we illustrate our suggestion by using examples from linear and non linear regression and time series

enhancing robustness and immunization in geographical networks we find that different geographical structures of networks lead to varied percolation thresholds although these networks may have similar abstract topological structures thus strategies for enhancing robustness and immunization of a geographical network are proposed using the generating function formalism we obtain an explicit form of the percolation threshold q c for networks containing arbitrary order cycles for three cycles the dependence of q c on the clustering coefficients is ascertained the analysis substantiates the validity of the strategies with analytical evidence

scaling and correlations in three bus transport networks of china abstract we report the statistical properties of three bus transport networks btn in three different cities of china these networks are composed of a set of bus lines and stations serviced by these network properties including the degree distribution clustering and average path length are studied in different definitions of network topology we explore scaling laws and correlations that may govern intrinsic features of such networks besides we create a weighted network representation for btn with lines mapped to nodes and number of common stations to weights between lines in such a representation the distributions of degree strength and weight are investigated a linear behavior between strength and degree s k k is also observed

a spatial weighted network model based on optimal expected traffic abstract we propose a spatial weighted network model based on the optimal expected traffic the expected traffic represents the prediction of the flow created by two vertices and is calculated by the improved gravity equation the model maximizes the total expected traffic of the network by changing two parameters which control the fitness and the geographical constraints the model can vary its topology and give rise to a variety of statistical properties observed in the real world network notably our study shows that a linear and a nonlinear strength degree correlation can emerge when considering and neglecting the transport effect respectively

topology of technology graphs small world patterns in electronic circuits recent theoretical studies and extensive data analyses have revealed a common feature displayed by biological social and technological networks the presence of small world patterns here we analyze this problem by using several graphs obtained from one of the most common technological systems electronic circuits it is shown that both analogic and digital circuits exhibit small world behavior we conjecture that the small world pattern arises from the compact design in which many elements share a small close physical neighborhood plus the fact that the system must define a single connected component which requires shortcuts connecting different integrated clusters the degree distributions displayed are consistent with a conjecture concerning the sharp cutoffs associated to the presence of costly connections amaral et al proc natl acad sci usa 97 11 149 2000 thus providing a limit case for the classes of universality of small world patterns from real artificial networks the consequences for circuit design are outlined

compressible euler equations with general pressure law we study the hyperbolic system of euler equations for an isentropic compressible fluid governed by a general pressure law the existence and regularity of the entropy kernel that generates the family of weak entropies is established by solving a new euler poisson darboux equation which is highly singular when the density of the fluid vanishes new properties of cancellation of singularities in combinations of the entropy kernel and the associated entropy flux kernel are found

stability issues in the quasineutral limit of the one dimensional vlasov poisson equation this work is concerned with the quasineutral limit of the one dimensional vlasov poisson equation for initial data close to stationary homogeneous profiles our objective is threefold first we provide a proof of the fact that the formal limit does not hold for homogeneous profiles that satisfy the penrose instability criterion second we prove on the other hand that the limit is true for homogeneous profiles that satisfy some monotonicity condition together with a symmetry condition we handle the case of well prepared as well as ill prepared data last we study a stationary boundary value problem for the formal limit the so called quasineutral vlasov equation we show the existence of numerous stationary states with a lot of freedom in the construction compared to that of bgk waves for vlasov poisson this illustrates the degeneracy of the limit equation

a method of examining the structure and topological properties of public transport networks abstract this work presents a new method of examining the structure of public transport networks ptns and analyzes their topological properties through a combination of computer programming statistical data and large network analyses in order to automate the extraction processing and exporting of data a software program was developed allowing to extract the needed data from general transit feed specification thus overcoming difficulties occurring in accessing and collecting data the proposed method was applied to a real life ptn in auckland new zealand with the purpose of examining whether it showed characteristics of scale free networks and exhibited features of small world networks as a result new regression equations were derived analytically describing observed strong non linear relationships among the probabilities of randomly chosen stops in the ptn to be serviced by a given number of routes the established dependence is best fitted by an exponential rather than a power law function showing that the ptn examined is neither random nor scale free but a mixture of the two this finding explains the presence of hubs that are not typical of exponential networks and simultaneously not highly connected to the other nodes as is the case with scale free networks on the other hand the observed values of the topological properties of the network show that although it is highly clustered owing to its representation as a directed graph it differs slightly from small world networks which are characterized by strong clustering and a short average path length

dynamic weight evolution network with preferential attachment abstract a dynamic weight evolution network with preferential attachment is introduced the network includes two significant characteristics i topological growth triggered by newly added node with m links at each time step each new edge carries an initial weight growing nonlinearly with time ii weight dynamics the weight between two existing nodes experiences increasing or decreasing in a nonlinear way by using continuum theory and mean field method we study the strength the degree the weight and their distributions we find that the distributions exhibit a power law feature in particular the relationship between the degree and the strength is nonlinear and the power law exponents of the three are the same all the theoretical predictions are successfully contrasted with numerical simulations

stabilizing weighted complex networks real networks often consist of local units which interact with each other via asymmetric and heterogeneous connections in this paper the v stability problem is investigated for a class of asymmetric weighted coupled networks with nonidentical node dynamics which includes the unweighted network as a special case pinning control is suggested to stabilize such a coupled network the complicated stabilization problem is reduced to measuring the semi negative property of the characteristic matrix which embodies not only the network topology but also the node self dynamics and the control gains it is found that network stabilizability depends critically on the second largest eigenvalue of the characteristic matrix the smaller the second largest eigenvalue is the more the network is pinning controllable numerical simulations of two representative networks composed of non chaotic systems and chaotic systems respectively are shown for illustration and verification

from unweighted to weighted networks with local information abstract in this paper we analyze an evolving model with local information which can generate a class of networks by choosing different values of the parameter p the model introduced exhibits the transition from unweighted networks to weighted networks because the distribution of the edge weight can be widely tuned with the increase in the local information the degree correlation of the network transforms from assortative to disassortative we also study the distribution of the degree strength and edge weight which all show crossover between exponential and scale free finally an application of the proposed model to the study of the synchronization is considered it is concluded that the synchronizability is enhanced when the heterogeneity of the edge weight is reduced

stations trains and small world networks abstract the clustering coefficient path length and average vertex degree of two urban train line networks have been calculated the results are compared with theoretical predictions for appropriate random bipartite graphs they have also been compared with one another to investigate the effect of architecture on the small world properties

modeling the evolution of weighted networks we present a general model for the growth of weighted networks in which the structural growth is coupled with the edges weight dynamical evolution the model is based on a simple weight driven dynamics and a weights reinforcement mechanism coupled to the local network growth that coupling can be generalized in order to include the effect of additional randomness and nonlinearities which can be present in real world networks the model generates weighted graphs exhibiting the statistical properties observed in several real world systems in particular the model yields a nontrivial time evolution of vertices properties and scale free behavior with exponents depending on the microscopic parameters characterizing the coupling rules very interestingly the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices degree

visibility graph analysis of heart rate time series and bio marker of congestive heart failure abstract study of rr interval time series for congestive heart failure had been an area of study with different methods including non linear methods in this article the cardiac dynamics of heart beat are explored in the light of complex network analysis viz visibility graph method heart beat rr interval time series data taken from physionet database 46 47 belonging to two groups of subjects diseased congestive heart failure 29 in number and normal 54 in number are analyzed with the technique the overall results show that a quantitative parameter can significantly differentiate between the diseased subjects and the normal subjects as well as different stages of the disease further the data when split into periods of around 1 hour each and analyzed separately also shows the same consistent differences this quantitative parameter obtained using the visibility graph analysis thereby can be used as a potential bio marker as well as a subsequent alarm generation mechanism for predicting the onset of congestive heart failure

migration driven aggregate growth on scale free networks we study the kinetics of migration driven aggregate growth on completely connected scale free networks a reversible migration system is considered with the size dependent rate kernel k k l i j approximately k u i v lj v at which an i mer aggregate located on the node with j links gains one monomer from a k mer aggregate on the node with l links the results show that the evolution behavior of the aggregate size distribution is drastically different from that for the corresponding same system in normal space this model can be used to mimic some phenomena such as the distribution of city populations moreover we verify our analytic results in good agreement with the data of the population distributions of all u s counties

kinetic formulation of the isentropic gas dynamics and p systems we consider the 2 x 2 hyperbolic system of isentropic gas dynamics in both eulerian or lagrangian variables also called the p system we show that they can be reformulated as a kinetic equation using an additional kinetic variable such a formulation was first obtained by the authors in the case of multidimensio nal scalar conservation laws a new phenomenon occurs here namely that the advection velocity is now a combination of the macroscopic and kinetic velocities various applications are given we recover the invariant regions deduce new l estimates using moments lemma and prove l w stability for 7 3

analytic results for scaling function and moments for a different type of avalanche in the bak sneppen evolution model starting from the master equation for the hierarchical structure of avalanches of a different kind within the frame of the bak sneppen evolution model we derive the exact formula of the scaling function describing the probability distribution of avalanches the scaling function displays features required by the scaling ansatz and verified by simulations using the scaling function we investigate the avalanche moment denoted by s k ensuremath delta overline f it is found that for any non negative integer k s k ensuremath delta overline f diverges as ensuremath delta f ensuremath k which gives an infinite group of exact critical exponents simulation outcomes of avalanche moments with k 1 2 3 are found to be consistent with the corresponding analytical results

on optimality of sparse long range links in circulant consensus networks we consider spatially invariant consensus networks in which the directed graph describing the interconnection topology the link weights and the temporal dynamics are all characterized by circulant matrices we seek the best new links subject to budget constraints whose addition to the network maximally improves its rate of convergence to consensus motivated by small world networks we apply the optimal link creation problem to circulant networks with local communication links we observe that the optimal new links are sparse and long range and have an increasingly pronounced effect on the convergence rate of the network as its size grows to further investigate the properties of optimal links analytically we restrict attention to the creation of links with small weights referred to as weak links we employ perturbation methods to reformulate the problem of optimal weak link creation and uncover conditions on the network architecture which guarantee sparse and long range solutions to this optimization problem

resolution d equations d evolution quasilineaires en dimension n d espace a l aide d equations lineaires en dimension n 1 on montre que l on peut calculer les solutions de l equation d evolution quasi lineaire dans r n d t u div b u a u 0 u x t r x r n t 0 et en particulier de l equation d ordre 1 d t u div b u 0 u x t r x r n t 0 a l aide d une equation d evolution lineaire dans r n r

different hierarchy of avalanches observed in the bak sneppen evolution model a quantity overline f denoting the average fitness of an ecosystem is introduced in the bak sneppen model through this quantity a different hierarchy of avalanches f 0 avalanche is observed in the evolution of bak sneppen model an exact gap equation governing the self organization of the model is presented in terms of overline f it is found that self organized threshold f c can be exactly obtained two basic exponents of the new avalanche ensuremath tau avalanche distribution and d avalanche dimension are given through simulations of one and two dimensional bak sneppen models it is suggested that overline f may be a good quantity in determining the emergence of criticality

the pareto law of incomes an explanation and an extension abstract a stochastic model for the generation of observed income distributions is used to provide an explanation for the pareto law of incomes analysis of the model also yields a prediction of paretian power law behaviour in the lower tail of the distribution and this is shown to occur in a number of empirical distributions a tractable four parameter distribution is derived and shown to fit extremely well to a number of different empirical income distributions

a kinetic construction of global solutions of first order quasilinear equations on considere le probleme de cauchy pour des equations quasilineaires d ordre 1 de type conservation dans la region t 0 u t i 1 u a i u x i 0 u x o u o x ou x x 1 x n u u x t et a i i 1 n sont des fonctions continument differentiables a valeurs reelles d une seule variable reelle

kinetic semidiscretization of scalar conservation laws and convergence by using averaging lemmas we consider a time discrete kinetic scheme known as transport collapse method for the inviscid burgers equation partial t u partial x frac u 2 2 0 we prove the convergence of the scheme by using averaging lemmas without bounded variation estimate then the extension of this result to the kinetic model of brenier and corrias is discussed

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

statistical analysis of 22 public transport networks in poland public transport systems in 22 polish cities have been analyzed the sizes of these networks range from n 152 to 2881 depending on the assumed definition of network topology the degree distribution can follow a power law or can be described by an exponential function distributions of path lengths in all considered networks are given by asymmetric unimodal functions clustering assortativity and betweenness are studied all considered networks exhibit small world behavior and are hierarchically organized a transition between dissortative small networks n approximately or 500 is observed

asymptotic and spectral analysis of the gyrokinetic waterbag integro differential operator in toroidal geometry achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices the underlying equations are the vlasov poisson and vlasov maxwell vpm equations in three space variables three velocity variables and one time variable even in those somewhat academic cases where global equilibrium solutions are known studying their stability requires the analysis of the spectral properties of the linearized operator a daunting task we have identified a model for which not only equilibrium solutions can be constructed but many of their stability properties are amenable to rigorous analysis it uses a class of solution to the vpm equations or to their gyrokinetic approximations known as waterbag solutions which in particular are piecewise constant in phase space it also uses not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines but also an asymptotic approximation regarding the magnetic field induced anisotropy the s

mutual selection model for weighted networks for most networks the connection between two nodes is the result of their mutual affinity and attachment in this paper we propose a mutual selection model to characterize the weighted networks by introducing a general mechanism of mutual selection the model can produce power law distributions of degree weight and strength as confirmed in many real networks moreover we also obtained the nontrivial clustering coefficient c degree assortativity coefficient r and degree strength correlation depending on a single parameter m these results are supported by present empirical evidence studying the degree dependent average clustering coefficient c k and the degree dependent average nearest neighbors degree k nn k also provide us with a better description of the hierarchies and organizational architecture of weighted networks

degree distributions of evolving alphabetic bipartite networks and their projections many real world systems are modeled as evolving bipartite networks and their one mode projections in particular discrete combinatorial systems dcss which consist of a finite set of elementary units and different combinations of these units can be modeled by a subclass of bipartite networks known as alphabetic bipartite networks or a bins where the bottom partite set contains a fixed number of nodes the elementary units and the top partite set grows unboundedly with time through the addition of nodes the combinations the principal questions in the study of a bin evolution are to predict the degree distribution of the bottom set and that of the projection onto the bottom set the bottom projection from a knowledge of the bipartite growth dynamics in this paper we propose a realistic growth model for a bins where the degree distribution of the top set i e the distribution of the number of elementary units in the composite entities in the dcs can be any arbitrary distribution with finite first and second moments utilizing an exact correspondence between the preferential growth of a bins and the polya urn scheme we analytically solve the model to compute exact degree distributions of the bottom fixed set and the bottom projection to the best of our knowledge this is the first work which proposes and solves such a generalized growth model for a bins we also derive that the degree distributions of both the bottom set and the bottom projection suitably normalized with time converge to distributions that are invariant over time we also verify that this improved model can accurately explain the degree distributions of several real world dcss and their projections

a study on some urban bus transport networks abstract in this paper we present the empirical investigation results on the urban bus transport networks btns of four major cities in china in btn nodes are bus stops two nodes are connected by an edge when the stops are serviced by a common bus route the empirical results show that the degree distributions of btns take exponential function forms other two statistical properties of btns are also considered and they are suggested as the distributions of so called the number of stops in a bus route represented by s and the number of bus routes a stop joins by r the distributions of r also show exponential function forms while the distributions of s follow asymmetric unimodal functions to explain these empirical results and attempt to simulate a possible evolution process of btn we introduce a model by which the analytic and numerical result obtained agrees well with the empirical facts finally we also discuss some other possible evolution cases where the degree distribution shows a power law or an interpolation between the power law and the exponential decay

regularity of the moments of the solution of a transport equation let u u x v satisfy the transport equation u v xu f x rn v rnwhere f belongs to some space of type lp dx d v where is a positive bounded measure on rn we study the resulting regularity of the moment u x v d v in terms of fractional sobolev spaces for example counter examples are given in order to test the optimality of our results

exact equations and scaling relations for f0 avalanche in the bak sneppen evolution model an infinite hierarchy of exact equations is derived for the newly observed f0 avalanche in the bak sneppen model by solving the first order exact equation we find that the critical exponent gamma governing the divergence of the average avalanche size is exactly 1 for all dimensions which has been confirmed by extensive simulations solution of the gap equation yields another universal result rho 1 rho is the exponent of relaxation to attractor scaling relations are established among the critical exponents gamma tau d sigma and nu for the f0 avalanche

on the waterbag continuum the aim of this paper is to study the existence of a classical solution for the waterbag model with a continuum of waterbags which can been viewed as an infinite dimensional system of first order conservation laws the waterbag model which constitutes a special class of exact weak solution of the vlasov equation is well known in plasma physics and its applications in gyrokinetic theory and laser plasma interaction are very promising the proof of the existence of a continuum of regular waterbags relies on a generalized definition of hyperbolicity for an integrodifferential hyperbolic system of equations some results in singular integral operators theory and harmonic analysis riemann hilbert boundary value problems and energy estimates