weighted network properties of chinese nature science basic research using the requisition papers of chinese nature science basic research in management and information department we construct the weighted network of research areas wnra in wnra two research areas which is represented by the subject codes are considered to be connected if they have been filled in one or more requisition papers the edge weight is defined as the number of requisition papers which have been filled in the same pairs of codes the node strength is defined as the number of requisition papers which have been filled in this code including the papers which have been filled in it alone here we study a variety of nonlocal statistics for wnra such as typical distance between research areas and measure of centrality such as betweenness these statistical characteristics can illuminate the global development trend of chinese scientific study it is also helpful to adjust the code system to reflect the real status more accurately finally we present a plausible model for the formation and structure of wnra with the observed properties

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

is the selected population the best random variables x i sim n theta i 1 i 1 2 cdots k are observed suppose x s is the largest observation if the inference theta s max i neq s theta i is made whenever x s max i neq s x i c then the probability of a false inference is maximized when two theta i are equal and the rest are infty equivalently the inference can be made whenever a two sample two sided test for difference of means based on the largest two observations would reject the hypothesis of no difference the result also holds in the case of unknown estimable common variance and in fact for location families with monotone likelihood ratio

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

on the lp spectrum of laplacians on graphs abstract we study the p independence of spectra of laplace operators on graphs arising from regular dirichlet forms on discrete spaces here a sufficient criterion is given solely by a uniform subexponential growth condition moreover under a mild assumption on the measure we show a one sided spectral inclusion without any further assumptions we study applications to normalized laplacians including symmetries of the spectrum and a characterization for positivity of the cheeger constant furthermore we consider laplacians on planar tessellations for which we relate the spectral p independence to assumptions on the curvature

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

lp independence of spectral bounds of feynman kac semigroups by continuous additive functionals abstract we establish conditions for the l p independence of spectral bounds of feynman kac semigroup by continuous additive functionals whose revuz measures are smooth measures of kato class having non negative order green tightness our continuous additive functionals do not necessarily admit bounded variation in general examples of cauchy principal value and hilbert transform of brownian local time and for relativistic symmetric stable processes are presented

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

empirical analysis of a scale free railway network in china abstract we present a detailed empirical analysis of the statistical properties of the china railway network crn consisting of 3915 nodes train stations and 22 259 edges railways based on this crn displays two explicit features already observed in numerous real world and artificial networks one feature the small world property has the fingerprint of a small characteristic shortest path length 3 5 accompanied by a high degree of clustering 0 835 another feature is characterized by the scale free distributions of both degrees and weighted degrees namely strengths correlations between strength and degree degree and degree and clustering coefficient and degree have been studied and the forms of such behaviors have been identified in addition we investigate distributions of clustering coefficients topological distances and spatial distances

multiple comparison procedures for steady state simulations suppose that there are k 2 different systems i e stochastic processes where each system has an unknown steady state mean performance and unknown asymptotic variance we allow for the asymptotic variances to be unequal and for the distributions of the k systems to be different we consider the problem of running independent single stage simulations to make multiple comparisons of the steady state means of the different systems we derive asymptotically valid as the run lengths of the simulations of the systems tend to infinity simultaneous confidence intervals for each of the following problems all pairwise comparisons of means all contrasts multiple comparisons with a control and multiple comparisons with the best our confidence intervals are based on standardized time series methods and we establish the asymptotic validity of each under the sole assumption that the stochastic processes representing the simulation output of the different systems satisfy a functional central limit theorem although simulation is the context of this paper the results naturally apply to asymptotically stationary time series

gaugeability and conditional gaugeability new kato classes are introduced for general transient borel right processes for which gauge and conditional gauge theorems hold these new classes are the genuine extensions of the green tight measures in the classical brownian motion case however the main focus of this paper is on establishing various equivalent conditions and consequences of gaugeability and conditional gaugeability we show that gaugeability conditional gaugeability and the subcriticality for the associated schrodinger operators are equivalent for transient borel right processes with strong duals analytic characterizations of gaugeability and conditional gaugeability are given for general symmetric markov processes these analytic characterizations are very useful in determining whether a process perturbed by a potential is gaugeable or conditionally gaugeable in concrete cases connections with the positivity of the spectral radii of the associated schrodinger operators are also established

analytic and geometric background of recurrence and non explosion of the brownian motion on riemannian manifolds we provide an overview of such properties of the brownian motion on complete non compact riemannian manifolds as recurrence and non explosion it is shown that both properties have various analytic characterizations in terms of the heat kernel green function liouville properties etc on the other hand we consider a number of geometric conditions such as the volume growth isoperimetric inequalities curvature bounds etc which are related to recurrence and non explosion

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

relativistic schrodinger operators asymptotic behavior of the eigenfunctions nonrelativistic schrodinger operators are perturbations of the negative laplacian and the connection with stochastic processes and brownian motion in particular is well known and usually goes under the name of feynman and kac we present a similar connection between a class of relativistic schrodinger operators and a class of processes with stationary independent increments in particular we investigate the decay of the eigenfunctions of these operators and we show that not only exponential decay but also polynomial decay can occur

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

schrodinger semigroups on manifolds abstract we derive uniform upper bounds for the transition density or parabolic kernel pv of the schrodinger operator 1 2 v on a riemannian manifold with ricci curvature bounded from below of the form p v t x y c m 1 2 b formula x m 1 2 b formula y formula or more suggestively of the form p v t x y p t x y e t where p denotes the heat kernel on the manifold and also similar lower bounds the assumptions on the potential v are very weak i e close to be necessary for instance on r d the assumptions for the upper and lower bound are satisfied by the highly singular oscillating potentials v x x k sin x k with arbitraryk 0 and v x exp 1 x sin exp l x we also admit to replace the functions v by signed measures in order to obtain estimates for the generalized schrodinger operators 1 2 for manifolds with nonnegative ricci curvature the number in our upper bound can be chosen arbitrarily close to the optimal value namely the l2 spectral bound in this case therefore the lp growth bound of schrodinger semigroups is independent of p 1 both assertions as well as the above bounds seem to be new even in the euclidean case in the euclidean case our estimates improve those of blanchard and ma derived under more restrictive assumptions on the potential which are not satisfied by the above examples for v 0 our bounds reduce to the heat kernel estimates of li and yau or more precisely to the improvements of these estimates by davies resp the author

subcriticality and gaugeability of the schrodinger operator we investigate a schrodinger operator 2 v in r d d 3 with a potential v in the class k d satisfying a similar kato condition at infinity and prove an equivalence theorem connecting various conditions on subcriticality strong positivity and gaugeability of the operator

progressive intrinsic ultracontractivity and heat kernel estimates for non local schrodinger operators abstract we study the long time asymptotic behaviour of semigroups generated by non local schrodinger operators of the form h l v the free operator l is the generator of a symmetric levy process in r d d 1 with non degenerate jump measure and v is a sufficiently regular confining potential we establish sharp two sided estimates of the corresponding heat kernels for large times and identify a new general regularity property which we call progressive intrinsic ultracontractivity to describe the large time evolution of the corresponding schrodinger semigroup we discuss various examples and applications of these estimates for instance we characterize the heat trace and heat content our examples cover a wide range of processes and we have to assume only mild restrictions on the growth resp decay of the potential and the jump intensity of the free process our approach is based on a combination of probabilistic and analytic methods our examples include fractional and quasi relativistic schrodinger operators

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

l p independence of spectral radius for generalized feynman kac semigroups under mild conditions on measures used in the perturbation we establish the l p independence of spectral radius for generalized feynman kac semigroups without assuming the irreducibility and the boundedness of the function appeared in the continuous additive functionals locally of zero energy in the framework of symmetric markov processes these results are obtained by using the gaugeability approach developed by the first named author as well as the recent progress on the irreducible decomposition for markov processes proved by the third author and on the analytic characterizations of gaugeability for generalized feynman kac functionals developed by the second and third authors

the randomly organized structure of urban ground bus transport networks in china in this paper the evolution dynamical properties of four topological urban ground bus transport networks btns in china are empirically researched as the statistical results of some common used measurements show that there are large fluctuations because of small sample sizes to induce some indistinct conclusions and there are even incorrect btn structure pictures as positive degree relation of the adjacent vertices in those btns though they are actually uncorrelated at all i e exhibiting pseudo positive connectivity correction thus in order to uncover the randomly organized architecture of btns new measurements of the average sum of the nearest neighbors degree degree correlation dnn k and the degree average edges among the nearest neighbors l k are proposed the obtained results of two new measurements do reflect that the considered btns are organized randomly in this point those empirical results provide one new framework for a more realistic btn model which will capture the underlying evolution principles of a btn in the geographical topology r 2007 elsevier b v all rights reserved

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

multiple comparisons with the best treatment abstract let 1 2 k be k 2 sources of observations treatments populations and suppose the goodness of treatment i is characterized by the size of an unknown real valued parameter i let k max1 i k i if i is preferred to j when i j the parameters i k i i 1 2 k reflect in an inverse sense the goodness of each treatment relative to the best treatment a general technique for obtaining simultaneous confidence intervals on the i is demonstrated with several examples this technique can be applied in any setting where comparison with control intervals can be computed regarding any j as the control these results have special importance in ranking and selection problems in that the process of generating upper bounds on the i generates traditional confidence statements of both the indifference zone and the subset selection schools simultaneously as established by hsu 1981

effects of accelerating growth on the evolution of weighted complex networks many real systems possess accelerating statistics where the total number of edges grows faster than the network size in this paper we propose a simple weighted network model with accelerating growth we derive analytical expressions for the evolutions and distributions for strength degree and weight which are relevant to accelerating growth we also find that accelerating growth determines the clustering coefficient of the networks interestingly the distributions for strength degree and weight display a transition from scale free to exponential form when the parameter with respect to accelerating growth increases from a small to large value all the theoretical predictions are successfully contrasted with numerical simulations

lp independence of spectral bounds of generalized non local feynman kac semigroups let x be a symmetric strong markov process on a luzin space in this paper we present criteria of the lp independence of spectral bounds for generalized non local feynman kac semigroups of x that involve continuous additive functionals of x having zero quadratic variations and discontinuous additive functionals of x

stepwise confidence intervals without multiplicity adjustment for dose response and toxicity studies abstract not all simultaneous inferences need multiplicity adjustment if the sequence of individual inferences is predefined and failure to achieve the desired inference at any step renders subsequent inferences unnecessary then multiplicity adjustment is not needed this can be justified using the closed testing principle to test appropriate hypotheses that are nested in sequence starting with the most restrictive one but what hypotheses are appropriate may not be obvious in some problems we give a fundamentally different confidence set based justification by partitioning the parameter space naturally and using the principle that exactly one member of the partition contains the true parameter in dose response studies designed to show superiority of treatments over a placebo negative control or a drug known to be efficacious active control the confidence set approach generates methods with meaningful guarantee against incorrect decision whereas previous applications of the closed testing app

on the emergence of scaling in weighted networks abstract general conditions for the appearance of the power law distribution of total weights concentrated in vertices of complex network systems are established by use of the rate equation approach for networks evolving by connectivity governed attachment of every new node to p 1 exiting nodes and by ascription to every new link a weight taken from algebraic distributions independent of network topologies it is shown that the distribution of the total weight w asymptotically follows the power law p w w with the exponent 0 2 the power law dependence of the weight distribution is also proved to hold for asymptotically large w in the case of networks in which a link between nodes i and j carries a load w ij determined by node degrees k i and k j at the final stage of the network growth according to the relation w ij k i k j with 1 0 for this class of networks the scaling exponent describing the weight distribution is found to satisfy the relationship 1 where is the scaling index characterizing the distribution of node degrees n k k

on the lp spectrum of uniformly elliptic operators on riemannian manifolds abstract we prove that the l p spectrum of uniformly elliptic divergence form operators on a complete riemannian manifold is independent of p 1 if the volume of the manifold grows uniformly subexponentially the latter condition is satisfied if the ricci curvature is bounded from below by a function k m r satisfying lim inf x k x 0 in particular if the ricci curvature is nonnegative on the other hand if we asume the existence of a globally defined volume density which grows exponentially in every direction then the l p spectrum depends on p this condition is satisfied if the manifold is simply connected and if the sectional curvature is bounded from above by a function k m r satisfying k 0 and lim sup x k x

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

ordered multiple comparisons with the best and their applications to dose response studies summary this article considers the problem of comparing several treatments dose levels interventions etc with the best where the best treatment is unknown and the treatments are ordered in some sense order relations among treatments often occur quite naturally in practice they may be ordered according to increasing risks such as tolerability or safety problems with increasing dose levels in a dose response study for example we tackle the problem of constructing a lower confidence bound for the smallest index of all treatments being at most marginally less effective than the best treatment having the largest effect such a bound ensures at confidence level 1 a that all treatments with lower indices are relevantly less effective than the best competitor we derive a multiple testing strategy that results in sharp confidence bounds the proposed lower confidence bound is compared with those derived from other testing strategies we further derive closed form expressions for power and sample size calculations finally we investigate several real data sets to illustrate various applications of our methods

age based model for weighted network with general assortative mixing abstract in this paper we propose an evolutionary model for weighted networks by introducing an age based mutual selection mechanism our model generates power law distributions of degree weight and strength which are confirmed by analytical predictions and are consistent with real observations the investigation of the relationship between clustering and the connectivity of nodes suggests hierarchical organization in the weighted networks furthermore both assortative and disassortative properties can be naturally obtained by tuning a parameter which controls the strength of age based preferential attachments since the age information of nodes is easier to acquire than the degree and strength of nodes and almost all empirically observed structural and weighted properties can be reproduced by the simple evolutionary regulation our model may reveal some underlying mechanisms that are key for the evolution of weighted complex networks

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

a probabilistic principle and generalized schrodinger perturbation abstract we present a probabilistic principle for an additive functional of certain markov processes its smallness with time is equivalent to its smalness with space and apply it to a perturbation problem for relativistic schrodinger operators

on δ equivalence with the best in k sample models in recent work we introduced a general a weak and a strong partitioning principles for the construction of multiple decision procedures as multiple testing or selection procedures partitioning principles can be viewed as natural extensions of the closure principle and sometimes yield more powerful decision procedures in this article we consider the problem of establishing equivalence with the best with respect to k treatment means where equivalence is defined in terms of a threshold value 0 we reformulate the original selection problem as a multiple testing problem and develop various step down and step up procedures by applying the closure principle and partitioning principles the new step down procedure is shown to provide a uniform improvement over procedures currently in use moreover we propose some projection methods that yield confidence intervals being compatible with stepwise tests and selection procedures

how to fit the degree distribution of the air network abstract we investigate three different approaches for fitting the degree distributions of china us and the composite china us air network in order to reveal the nature of such distributions and the potential theoretical background on which they are based our first approach is the fitting with q statistics probability distribution done separately in two regimes this yields acceptable outcomes but generates two sets of fitting parameters the second approach is an entire fitting to all data points with the formula proposed by tsallis et al so far this trial is not able to produce consistent results in the third approach we fit the data with two composite distributions which may lack theoretical support for the moment

the partitioning principle a powerful tool in multiple decision theory a first general principle and nowadays state of the art for the construction of powerful multiple test procedures controlling a multiple level a is the so called closure principle in this article we introduce another powerful tool for the construction of multiple decision procedures especially for the construction of multiple test procedures and selection procedures this tool is based on a partition of the parameter space and will be called partitioning principle pp in the first part of the paper we review basic concepts of multiple hypotheses testing and discuss a slight generalization of the current theory in the second part we present various variants of the pp for the construction of multiple test procedures these are a general pp gpp a weak pp wpp and a strong pp spp it will be shown that depending on the underlying decision problem a pp may lead to more powerful test procedures than a formal application of the closure principle fcp moreover the more complex spp may be more powerful than the wpp based on a duality between testing and selecting pps can also be applied for the construction of more powerful selection procedures in the third part of the paper fcp wpp and spp are applied and compared in some examples

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

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

lp independence of spectral bounds of schrodinger type semigroups let l be an m symmetric markov generator and a signed measure in the kato class we consider a schrodinger type operator h l on lp m we prove that under certain conditions for the markov semigroup generated by l and the potential the lp spectral bound of h is independent of p if and only if the l2 spectral bound is non positive

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

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

a variational formula for dirichlet forms and existence of ground states abstract let l be the generator of a symmetric markov process on a locally compact separable metric space and a certain measure in the kato class employing a variational formula for dirichlet forms we show the existence of a ground state of the time changed operator 1 l or the schrodinger type operator l

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

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

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

the exponential degree distribution in complex networks non equilibrium network theory numerical simulation and empirical data abstract the exponential degree distribution has been found in many real world complex networks based on which the random growing process has been introduced to analyze the formation principle of such kinds of networks inspired from the non equilibrium network theory we construct the network according to two mechanisms growing and adjacent random attachment by using the kolmogorov smirnov test kst for the same number of nodes and edges we find the simulation results are remarkably consistent with the predictions of the non equilibrium network theory and also surprisingly match the empirical databases such as the worldwide marine transportation network wmtn the email network of university at rovira i virgili enurv in spain and the north american power grid network napgn our work may shed light on interpreting the exponential degree distribution and the evolution mechanism of the complex networks

efficiency of informational transfer in regular and complex networks we analyze the process of informational exchange through complex networks by measuring network efficiencies aiming to study nonclustered systems we propose a modification of this measure on the local level we apply this method to an extension of the class of small worlds that includes declustered networks and show that they are locally quite efficient although their clustering coefficient is practically zero unweighted systems with small world and scale free topologies are shown to be both globally and locally efficient our method is also applied to characterize weighted networks in particular we examine the properties of underground transportation systems of madrid and barcelona and reinterpret the results obtained for the boston subway network

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

relationships between centrality measures of networks with diameter 2 abstract from an intuitive analysis of the betweeness of networks in which we detail its components not only the basic definition of the betweeness as the number of short paths through a node we propose a relationship between the betweeness the degree and the clustering coefficient of a node in networks with diameter 2 we verify the validity of this relationship on seven diameter 2 networks the global migration network the dual networks of the underground systems of barcelona tokyo london and three model networks we show also that the dependence of the closeness with the degree is an exact linear relation with slope equal to 1

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

an unbiased test for the bioequivalence problem it is shown that the standard two one sided tests procedure for bioequivalence is a biased test better tests exist in this paper an unbiased level test and other tests which are uniformly more powerful than the two one sided tests procedure are constructed its power can be noticeably larger than that of the level two one sided tests procedure

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

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

power law strength degree correlation from resource allocation dynamics on weighted networks many weighted scale free networks are known to have a power law correlation between strength and degree of nodes which however has not been well explained we investigate the dynamic behavior of resource traffic flow on scale free networks the dynamical system will evolve into a kinetic equilibrium state where the strength defined by the amount of resource or traffic load is correlated with the degree in a power law form with tunable exponent the analytical results agree well with simulations

country neighborhood network on territory and its geometrical model the country neighborhood network where nodes represent countries and two nodes are considered linked if the corresponding countries are neighbors on territory is created and its giant component the asia europe and africa aea cluster is carefully studied in this paper it is found that as common the degree distribution and the clustering function of the aea cluster are both compatible with scale free property besides the aea cluster presents a little disassortativity and its near power law country area degree relationship with the exponent close to 1 7 may imply a fractal dimension close to 1 2 of country borderlines in the aea continent it is also revealed that the average difference of population density between two countries obeys an approximately increasing function of the shortest path length between them which may suggest a gradual consensus of population density in the aea cluster a simple unity rule is then adopted to model the aea cluster and such model explains the aea cluster very well in most aspects e g power law domain area distribution and fractal domain borderlines etc except that the network derived by the model has stronger disassortativity which may be explained by the fact that in the evolution history of countries unbalanced neighbors are more likely to be united as one than balanced neighbors additionally the network evolving process can be divided into three periods defined as formation period growth period and combination period and there are indications that the aea cluster is in its third period

asymmetry between odd and even node weight in complex networks abstract phenomenon of asymmetry between odd and even node weight distribution in some complex networks such as public transportation networks and internet is presented reasons related to this phenomenon are summarized i e 1 edges are solid connections between nodes which are embedded in real geometric background and 2 preferential mechanism during the process of network formation incorporating these two points complex networks are constructed by self avoiding random walk on 2d grid and the simulation results are consistent well with that of empirical researches

the architecture of complex weighted networks networked structures arise in a wide array of different contexts such as technological and transportation infrastructures social phenomena and biological systems these highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity along with a complex topological structure real networks display a large heterogeneity in the capacity and intensity of the connections these features however have mainly not been considered in past studies where links are usually represented as binary states i e either present or absent here we study the scientific collaboration network and the world wide air transportation network which are representative examples of social and large infrastructure systems respectively in both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network we define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices this information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network these results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks

differentiability of spectral functions for symmetric alpha stable processes let be a signed radon measure in the kato class and define a schrodinger type operator h 1 2 2 on r d we show that its spectral bound c inf h is differentiable if d 2 and is green tight

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

dynamic fluctuation model of complex networks with weight scaling behavior and its application to airport networks abstract airport networks are a kind of complex systems that display significant fluctuations to describe this kind of phenomena a dynamical fluctuation model is proposed in this model the fluctuations in growth rates of weight are exponential there are two adjustable parameters the exponent and the creation probability p d of a new node characterizes the tendency to retain an optimal allocation of weights size of components for a given kind of networks p d reflects the interactive effect between the weight fluctuation and variation of nodes and links topological structure for each real network for airport networks the exponent is 0 4 and the creation probability p d is equal to 0 018 china 0 025 us 0 03 brazil and 0 04 europe this model quantitatively describes and reproduces these real airport networks

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

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

efficiency driven evolution of networks abstract a principle governing the evolution of network is proposed based on the consideration of improving the efficiency of a network by demanding that new connections should be added in the network to increase the transportation efficiency as much as possible it turns out that the added connections should be between two unconnected nodes with sum of their links maximum the evolution of some properties of the network is considered such as the degree distributions number of shortest paths with different distances and the moments of the spectrum distributions

the construction of upper confidence bounds on the range of several location parameters abstract this article considers the construction of an upper confidence bound on the range of a set of k location parameters such as the k treatment effects in a one way layout this confidence bound will be useful to the experimenter in assessing the equivalence of the location parameters some general theoretical results are presented and the case of normally distributed data is considered in detail with accompanying tables of confidence bounds some examples of the application of this new inference method are given

compatible simultaneous lower confidence bounds for the holm procedure and other bonferroni based closed tests we consider the problem of simultaneously testing multiple one sided null hypotheses single step procedures such as the bonferroni test are characterized by the fact that the rejection or non rejection of a null hypothesis does not take the decision for any other hypothesis into account for stepwise test procedures such as the holm procedure the rejection or non rejection of a null hypothesis may depend on the decision of other hypotheses it is well known that stepwise test procedures are by construction more powerful than their single step counterparts this power advantage however comes only at the cost of increased difficulties in constructing compatible simultaneous confidence intervals for the parameters of interest for example such simultaneous confidence intervals are easily obtained for the bonferroni method but surprisingly hard to derive for the holm procedure in this paper we discuss the inherent problems and show that ad hoc solutions used in practice typically do not control the pre specified simultaneous confidence level instead we derive simultaneous confidence intervals that are compatible with a certain class of closed test procedures using weighted bonferroni tests for each intersection hypothesis the class of multiple test procedures covered in this paper includes gatekeeping procedures based on bonferroni adjustments fixed sequence procedures the simple weighted or unweighted bonferroni procedure by holm and the fallback procedure we illustrate the results with a numerical example

on the relationship between stepwise decision procedures and confidence sets abstract this article considers the relationship between two standard methods of inference on a set of a unknown parameters namely stepwise decision procedures and the construction of simultaneous confidence intervals illustrative examples with k 2 are discussed for one sided step down and step up decision procedures and for a two sided step down decision procedure for these examples with normal distributional assumptions a set of confidence intervals associated with the decision procedure is constructed that provides additional information at no increase in the error rate the implication of this work is that commonly used stepwise decision procedures are per se not providing as complete an inference as is available the construction of new decision procedures and confidence sets designed specifically to meet an experimenter s particular requirements is also discussed

growing scale free small world networks with tunable assortative coefficient abstract in this paper we propose a simple rule that generates scale free small world networks with tunable assortative coefficient these networks are constructed by two stage adding process for each new node the model can reproduce scale free degree distributions and small world effect the simulation results are consistent with the theoretical predictions approximately interestingly we obtain the nontrivial clustering coefficient c and tunable degree assortativity r by adjusting the parameter the preferential exponent the model can unify the characterization of both assortative and disassortative networks

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

measuring edge importance to improve immunization performance the edge heterogeneity has a remarkable influence on disease spreading but it has seldom been considered in the disease controlling policies based on the gravity model we propose the edge importance index to describe the influence of edge heterogeneity on immunization strategies then the edge importance and contact weight are combined to calculate the infection rates on the i s infected susceptible edges in the complex network and the difference of the infection rates on strong and weak ties is analyzed simulation results show that edge heterogeneity has a significant influence on the performance of immunization strategies and better immunization efficiency is derived when the vaccination rate of the nodes in the weak i s edges is increased

optimal paths in complex networks with correlated weights the worldwide airport network we study complex networks with weights wij associated with each link connecting node i and j the weights are chosen to be correlated with the network topology in the form found in two real world examples a the worldwide airport network and b the e coli metabolic network here wijxijkikj where ki and kj are the degrees of nodes i and j xij is a random number and represents the strength of the correlations the case 0 represents correlation between weights and degree while 0 represents anticorrelation and the case 0 reduces to the case of no correlations we study the scaling of the lengths of the optimal paths opt with the system size n in strong disorder for scale free networks for different we find two different universality classes for opt in strong disorder depending on i if 0 then for 2 the scaling law optn 1 3 where is the power law exponent of the degree distribution of scale free networks and ii if 0 then opt nopt with opt identical to its value for the uncorrelated case 0 we calculate the robustness of correlated scale free networks with different and find the networks with 0 to be the most robust networks when compared to the other values of we propose an analytical method to study percolation phenomena on networks with this kind of correlation and our numerical results suggest that for scale free networks with 0 the percolation threshold pc is finite for 3 which belongs to the same universality class as 0 we compare our simulation results with the real worldwide airport network and we find good agreement

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

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