identification of influential nodes in complex networks method from spreading probability viewpoint abstract the problem of identifying influential nodes in complex networks has attracted much attention owing to its wide applications including how to maximize the information diffusion boost product promotion in a viral marketing campaign prevent a large scale epidemic and so on from spreading viewpoint the probability of one node propagating its information to one other node is closely related to the shortest distance between them the number of shortest paths and the transmission rate however it is difficult to obtain the values of transmission rates for different cases to overcome such a difficulty we use the reciprocal of average degree to approximate the transmission rate then a semi local centrality index is proposed to incorporate the shortest distance the number of shortest paths and the reciprocal of average degree simultaneously by implementing simulations in real networks as well as synthetic networks we verify that our proposed centrality can outperform well known centralities such as degree centrality betweenness centrality closeness centrality k shell centrality and nonbacktracking centrality in particular our findings indicate that the performance of our method is the most significant when the transmission rate nears to the epidemic threshold which is the most meaningful region for the identification of influential nodes

empirical likelihood for regression discontinuity design this paper proposes empirical likelihood based inference methods for causal effects identified from regression discontinuity designs we consider both the sharp and fuzzy regression discontinuity designs and treat the regression functions as nonparametric the proposed inference procedures do not require asymptotic variance estimation and the confidence sets have natural shapes unlike the conventional wald type method these features are illustrated by simulations and an empirical example which evaluates the effect of class size on pupils scholastic achievements furthermore for the sharp regression discontinuity design we show that the empirical likelihood statistic admits a higher order refinement so called the bartlett correction bandwidth selection methods are also discussed

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

exact solution for mean first passage time on a pseudofractal scale free web the explicit determinations of the mean first passage time mfpt for trapping problem are limited to some simple structure e g regular lattices and regular geometrical fractals and determining mfpt for random walks on other media especially complex real networks is a theoretical challenge in this paper we investigate a simple random walk on the the pseudofractal scale free web psfw with a perfect trap located at a node with the highest degree which simultaneously exhibits the remarkable scale free and small world properties observed in real networks we obtain the exact solution for the mfpt that is calculated through the recurrence relations derived from the structure of psfw the rigorous solution exhibits that the mfpt approximately increases as a power law function of the number of nodes with the exponent less than 1 we confirm the closed form solution by direct numerical calculations we show that the structure of psfw can improve the efficiency of transport by diffusion compared with some other structure such as regular lattices sierpinski fractals and t graph the analytical method can be applied to other deterministic networks making the accurate computation of mfpt possible

scaling of the average weighted receiving time on a family of double weighted hierarchical networks abstract in this paper we introduce a family of double weighted hierarchical networks which is depended on the initial complete bipartite graph and two weight factors r w 0 r 1 0 w 1 then we consider the biased walk in the double weighted hierarchical networks what is more we define two weighted times the mean weighted first passing time mwfpt and the average weighted receiving time awrt according to the definition we calculate the exact expressions of the mwfpt and the awrt on the double weighted hierarchical networks the expressions we obtain in this paper illustrate that the awrt tends to a constant when the size of the networks increases while if n 2 4 n 1 n 2 1 w 2 where n 1 and n 2 denote the number of nodes in initial complete bipartite graph and n n 1 n 2 holds the awrt grows as a power law function of network order with the exponent denoted by log n n k

global partial likelihood for nonparametric proportional hazards models as an alternative to the local partial likelihood method of tibshirani and hastie and fan gijbels and king a global partial likelihood method is proposed to estimate the covariate effect in a nonparametric proportional hazards model t x exp x 0 t the estimator x reduces to the cox partial likelihood estimator if the covariate is discrete the estimator is shown to be consistent and semiparametrically efficient for linear functionals of x moreover breslow type estimation of the cumulative baseline hazard function using the proposed estimator x is proved to be efficient the asymptotic bias and variance are derived under regularity conditions computation of the estimator involves an iterative but simple algorithm extensive simulation studies provide evidence supporting the theory the method is illustrated with the stanford heart transplant data set the proposed global approach is also extended to a partially linear proportional hazards model and found to provide efficien

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

pseudo likelihood methods for community detection in large sparse networks many algorithms have been proposed for fitting network models with communities but most of them do not scale well to large networks and often fail on sparse networks here we propose a new fast pseudo likelihood method for fitting the stochastic block model for networks as well as a variant that allows for an arbitrary degree distribution by conditioning on degrees we show that the algorithms perform well under a range of settings including on very sparse networks and illustrate on the example of a network of political blogs we also propose spectral clustering with perturbations a method of independent interest which works well on sparse networks where regular spectral clustering fails and use it to provide an initial value for pseudo likelihood we prove that pseudo likelihood provides consistent estimates of the communities under a mild condition on the starting value for the case of a block model with two communities

message passing approach for recurrent state epidemic models on networks epidemic processes are common out of equilibrium phenomena of broad interdisciplinary interest recently dynamic message passing dmp has been proposed as an efficient algorithm for simulating epidemic models on networks and in particular for estimating the probability that a given node will become infectious at a particular time to date dmp has been applied exclusively to models with one way state changes as opposed to models like sis and sirs where nodes can return to previously inhabited states because many real world epidemics can exhibit such recurrent dynamics we propose a dmp algorithm for complex recurrent epidemic models on networks our approach takes correlations between neighboring nodes into account while preventing causal signals from backtracking to their immediate source and thus avoids echo chamber effects where a pair of adjacent nodes each amplify the probability that the other is infectious we demonstrate that this approach well approximates results obtained from monte carlo simulation and that its accuracy is often superior to the pair approximation which also takes second order correlations into account moreover our approach is more computationally efficient than the pair approximation especially for complex epidemic models the number of variables in our dmp approach grows as 2mk where m is the number of edges and k is the number of states as opposed to mk 2 for the pair approximation we suspect that the resulting reduction in computational effort as well as the conceptual simplicity of dmp will make it a useful tool in epidemic modeling especially for high dimensional inference tasks

predicting epidemic threshold of correlated networks a comparison of methods abstract being able to theoretically predict the outbreak threshold of an epidemic is essential in disease control real world correlated networks are ubiquitous and their topological structure strongly affects the prediction accuracy of present day theoretical methods quantifying their accuracy and fitness in predicting outbreak thresholds of correlated networks is thus essential we use a susceptible infected removed sir model to examine four widely used theoretical methods the heterogeneous mean field h m f quenched mean field q m f dynamical message passing d m p and connectivity matrix c m methods to predict the outbreak threshold of a correlated network the potential topological structure of correlated network impacts on prediction accuracy of these four methods we emphasize that the quantitative changes of degree correlation degree distribution exponent and network size strongly affect the outbreak of sir spreading dynamics and compare the simulation results with the theoretical ones obtained from these four methods the extensive experiments in synthetic networks show that a the increasing degree correlation coefficients reduce outbreak threshold and suppress outbreak size b the increasing degree distribution exponents raise outbreak threshold but suppress outbreak size c the increasing network sizes decrease outbreak threshold but do not affect outbreak size d as for four theoretical methods c m and d m p are more likely to precisely predict outbreak threshold because they to some extent incorporate network topology with dynamical correlations the experimental results in 50 real world networks also prove the above conclusions

multifractal analysis and topological properties of a new family of weighted koch networks abstract weighted complex networks especially scale free networks which characterize real life systems better than non weighted networks have attracted considerable interest in recent years studies on the multifractality of weighted complex networks are still to be undertaken in this paper inspired by the concepts of koch networks and koch island we propose a new family of weighted koch networks and investigate their multifractal behavior and topological properties we find some key topological properties of the new networks their vertex cumulative strength has a power law distribution there is a power law relationship between their topological degree and weight strength the networks have a high weighted clustering coefficient of 0 41004 which is independent of the scaling factor c in the limit of large generation t the second smallest eigenvalue 2 and the maximum eigenvalue n are approximated by quartic polynomials of the scaling factor c for the general laplacian operator while 2 is approximately a quartic polynomial of c and n 1 5 for the normalized laplacian operator then we find that weighted koch networks are both fractal and multifractal their fractal dimension is influenced by the scaling factor c we also apply these analyses to six real world networks and find that the multifractality in three of them are strong

local partial likelihood estimation in proportional hazards regression fan gijbels and king ann statist 25 1997 1661 1690 considered the estimation of the risk function x in the proportional hazards model their proposed estimator is based on integrating the estimated derivative function obtained through a local version of the partial likelihood they proved the large sample properties of the derivative function but the large sample properties of the estimator for the risk function itself were not established in this paper we consider direct estimation of the relative risk function x 2 x 1 for any location normalization point x 1 the main novelty in our approach is that we select observations in shrinking neighborhoods of both x 1 and x 2 when constructing a local version of the partial likelihood whereas fan gijbels and king ann statist 25 1997 1661 1690 only concentrated on a single neighborhood resulting in the cancellation of the risk function in the local likelihood function the asymptotic properties of our estimator are rigorously established and the variance of the estimator is easily estimated the idea behind our approach is extended to estimate the differences between groups a simulation study is carried out

the statistical analysis of failure time data preface 1 introduction 1 1 failure time data 1 2 failure time distributions 1 3 time origins censoring and truncation 1 4 estimation of the survivor function 1 5 comparison of survival curves 1 6 generalizations to accommodate delayed entry 1 7 counting process notation bibliographic notes exercises and complements 2 failure time models 2 1 introduction 2 2 some continuous parametric failure time models 2 3 regression models 2 4 discrete failure time models bibliographic notes exercises and complements 3 inference in parametric models and related topics 3 1 introduction 3 2 censoring mechanisms 3 3 censored samples from an exponential distribution 3 4 large sample likelihood theory 3 5 exponential regression 3 6 estimation in log linear regression models 3 7 illustrations in more complex data sets 3 8 discrimination among parametric models 3 9 inference with interval censoring 3 10 discussion bibliographic notes exercises and complements 4 relative risk cox regression models 4 1 introduction 4 2 estimation of beta 4 3 estimation of the baseline hazard or survivor function 4 4 inclusion of strata 4 5 illustrations 4 6 counting process formulas 4 7 related topics on the cox model 4 8 sampling from discrete models bibliographic notes exercises and complements 5 counting processes and asymptotic theory 5 1 introduction 5 2 counting processes and intensity functions 5 3 martingales 5 4 vector valued martingales 5 5 martingale central limit theorem 5 6 asymptotics associated with chapter 1 5 7 asymptotic results for the cox model 5 8 asymptotic results for parametric models 5 9 efficiency of the cox model estimator 5 10 partial likelihood filtration bibliographic notes exercises and complements 6 likelihood construction and further results 6 1 introduction 6 2 likelihood construction in parametric models 6 3 time dependent covariates and further remarks on likelihood construction 6 4 time dependence in the relative risk model 6 5 nonnested conditioning events 6 6 residuals and model checking for the cox model bibliographic notes exercises and complements 7 rank regression and the accelerated failure time model 7 1 introduction 7 2 linear rank tests 7 3 development and properties of linear rank tests 7 4 estimation in the accelerated failure time model 7 5 some related regression models bibliographic notes exercises and complements 8 competing risks and multistate models 8 1 introduction 8 2 competing risks 8 3 life history processes bibliographic notes exercises and complements 9 modeling and analysis of recurrent event data 9 1 introduction 9 2 intensity processes for recurrent events 9 3 overall intensity process modeling and estimation 9 4 mean process modeling and estimation 9 5 conditioning on aspects of the counting process history bibliographic notes exercises and complements 10 analysis of correlated failure time data 10 1 introduction 10 2 regression models for correlated failure time data 10 3 representation and estimation of the bivariate survivor function 10 4 pairwise dependency estimation 10 5 illustration australian twin data 10 6 approaches to nonparametric estimation of the bivariate survivor function 10 7 survivor function estimation in higher dimensions bibliographic notes exercises and complements 11 additional failure time data topics 11 1 introduction 11 2 stratified bivariate failure time analysis 11 3 fixed study period survival studies 11 4 cohort sampling and case control studies 11 5 missing covariate data 11 6 mismeasured covariate data 11 7 sequential testing with failure time endpoints 11 8 bayesian analysis of the proportional hazards model 11 9 some analyses of a particular data set bibliographic notes exercises and complements glossary of notation appendix a some sets of data appendix b supporting technical material bibliography author index subject index

mean first passage times for two biased walks on the weighted rose networks abstract compared with traditional random walk biased walks have been studied extensively over the past decade especially in the transport and communication networks in this paper we first introduce the weighted rose networks then for the weighted rose networks we focus on two biased walks maximal entropy walk and weight dependent walk and obtain the exact expressions of their stationary distributions and mean first passage times finally we find that the average receiving time for maximal entropy walk is a quadratic function of the weight parameter r while the average receiving time for weighted dependent walk is a linear function of the weight parameter r meanwhile for the maximal entropy walk the smaller the value of r is the more efficient the trapping process is for the weighted dependent walk the larger the value of r r r 0 2 6 is the more efficient for the weighted dependent walk the smaller the value of r r r 0 2 6 is the more efficient for the weight dependent walk

spectra of random graphs with given expected degrees in the study of the spectra of power law graphs there are basically two competing approaches one is to prove analogues of wigner s semicircle law whereas the other predicts that the eigenvalues follow a power law distribution although the semicircle law and the power law have nothing in common we will show that both approaches are essentially correct if one considers the appropriate matrices we will prove that under certain mild conditions the eigenvalues of the normalized laplacian of a random power law graph follow the semicircle law whereas the spectrum of the adjacency matrix of a power law graph obeys the power law our results are based on the analysis of random graphs with given expected degrees and their relations to several key invariants of interest are a number of new values for the exponent where phase transitions for eigenvalue distributions occur the spectrum distributions have direct implications to numerous graph algorithms such as for example randomized algorithms that involve rapidly mixing markov chains

normal numbers and finite automata we give an elementary and direct proof of the following theorem a real number is normal to a given integer base if and only if its expansion in that base is incompressible by lossless finite state compressors these are finite automata augmented with an output transition function such that the automata input output behaviour is injective they are also known as injective finite state transducers as a corollary we obtain v n agafonov s theorem on the preservation of normality on subsequences selected by finite automata

finite state dimension classical hausdorff dimension sometimes called fractal dimension was recently effectivized using gales betting strategies that generalize martingales thereby endowing various complexity classes with dimension structure and also defining the constructive dimensions of individual binary infinite sequences in this paper we use gales computed by multi account finite state gamblers to develop the finite state dimensions of sets of binary sequences and individual binary sequences the theorem of eggleston quart j math oxford ser 20 1949 31 36 relating hausdorff dimension to entropy is shown to hold for finite state dimension both in the space of all sequences and in the space of all rational sequences binary expansions of rational numbers every rational sequence has finite state dimension 0 but every rational number in 0 1 is the finite state dimension of a sequence in the low level complexity class ac0 our main theorem shows that the finite state dimension of a sequence is precisely the infimum of all compression ratios achievable on the sequence by information lossless finite state compressors

scaling of average weighted shortest path and average receiving time on weighted hierarchical networks abstract recent work on the networks has focused on the weighted hierarchical networks that are significantly different from the un weighted hierarchical networks in this paper we study a family of weighted hierarchical networks which are recursively defined from an initial uncompleted graph in which the weights of edges have been assigned to different values with certain scale firstly we study analytically the average weighted shortest path awsp on the weighted hierarchical networks using a recursive method we determine explicitly the awsp the obtained rigorous solution shows that the networks grow unbounded but with the logarithm of the network size while the weighted shortest paths stay bounded then depending on a biased random walk we research the mean first passage time mfpt between a hub node and any peripheral node finally we deduce the analytical expression of the average of mfpts for a random walker originating from any node to first visit to a hub node which is named as the average receiving time art the obtained result shows that art is bounded or grows sublinearly with the network order relating to the number of initial nodes and the weighted factor or grows quadratically with the iteration

time delayed feedback control of a flashing ratchet closed loop or feedback control ratchets use information about the state of the system to operate with the aim of maximizing the performance of the system in this paper we investigate the effects of a time delay in the feedback for a protocol that performs an instantaneous maximization of the center of mass velocity for the one and the few particle cases the flux decreases with increasing delay as an effect of the decorrelation of the present state of the system with the information that the controller uses but the delayed closed loop protocol succeeds to perform better than its open loop counterpart provided the delays are smaller than the characteristic times of the brownian ratchet for the many particle case we also show that for small delays the center of mass velocity decreases for increasing delays however for large delays we find the surprising result that the presence of the delay can improve the performance of the nondelayed feedback ratchet and the flux can attain the maximum value obtained with the optimal periodic protocol this phenomenon is the result of the emergence of a dynamical regime where the presence of the delayed feedback stabilizes one quasiperiodic solution or several multistability which resemble the solutions obtained in the so called threshold protocol our analytical and numerical results point towards the feasibility of an experimental implementation of a feedback controlled ratchet that performs equal or better than its optimal open loop version

spacing ratio characterization of the spectra of directed random networks previous literature on random matrix and network science has traditionally employed measures derived from nearest neighbor level spacing distributions to characterize the eigenvalue statistics of random matrices this approach however depends crucially on eigenvalue unfolding procedures which in many situations represent a major hindrance due to constraints in the calculation especially in the case of complex spectra here we study the spectra of directed networks using the recently introduced ratios between nearest and next to nearest eigenvalue spacing thus circumventing the shortcomings imposed by spectral unfolding specifically we characterize the eigenvalue statistics of directed erd ifmmode mbox h o else h o fi s r enyi er random networks by means of two adjacency matrix representations namely 1 weighted non hermitian random matrices and 2 a transformation on non hermitian adjacency matrices which produces weighted hermitian matrices for both representations we find that the distribution of spacing ratios becomes universal for a fixed average degree in accordance with undirected random networks furthermore by calculating the average spacing ratio as a function of the average degree we show that the spectral statistics of directed er random networks undergoes a transition from poisson to ginibre statistics for model 1 and from poisson to gaussian unitary ensemble statistics for model 2 eigenvector delocalization effects of directed networks are also discussed

nonbacktracking expansion of finite graphs message passing equations yield a sharp percolation transition in finite graphs as an artifact of the locally treelike approximation for an arbitrary finite connected undirected graph we construct an infinite tree having the same local structural properties as this finite graph when observed by a nonbacktracking walker formally excluding the boundary this infinite tree is a generalization of the bethe lattice we indicate an infinite locally treelike random network whose local structure is exactly given by this infinite tree message passing equations for various cooperative models on this construction are the same as for the original finite graph but here they provide the exact solutions of the corresponding cooperative problems these solutions are good approximations to observables for the models on the original graph when it is sufficiently large and not strongly correlated we show how to express these solutions in the critical region in terms of the principal eigenvector components of the nonbacktracking matrix as representative examples we formulate the problems of the random and optimal destruction of a connected graph in terms of our construction the nonbacktracking expansion we analyze the limitations and the accuracy of the message passing algorithms for different classes of networks and compare the complexity of the message passing calculations to that of direct numerical simulations notably in a range of important cases simulations turn out to be more efficient computationally than the message passing

leveraging percolation theory to single out influential spreaders in networks among the consequences of the disordered interaction topology underlying many social technological and biological systems a particularly important one is that some nodes just because of their position in the network may have a disproportionate effect on dynamical processes mediated by the complex interaction pattern for example the early adoption of a commercial product by an opinion leader in a social network may change its fate or just a few superspreaders may determine the virality of a meme in social media despite many recent efforts the formulation of an accurate method to optimally identify influential nodes in complex network topologies remains an unsolved challenge here we present the exact solution of the problem for the specific but highly relevant case of the susceptible infected removed sir model for epidemic spreading at criticality by exploiting the mapping between bond percolation and the static properties of the sir model we prove that the recently introduced nonbacktracking centrality is the optimal criterion for the identification of influential spreaders in locally tree like networks at criticality by means of simulations on synthetic networks and on a very extensive set of real world networks we show that the nonbacktracking centrality is a highly reliable metric to identify top influential spreaders also in generic graphs not embedded in space and for noncritical spreading

on the effect of bias estimation on coverage accuracy in nonparametric inference abstractnonparametric methods play a central role in modern empirical work while they provide inference procedures that are more robust to parametric misspecification bias they may be quite sensitive to tuning parameter choices we study the effects of bias correction on confidence interval coverage in the context of kernel density and local polynomial regression estimation and prove that bias correction can be preferred to undersmoothing for minimizing coverage error and increasing robustness to tuning parameter choice this is achieved using a novel yet simple studentization which leads to a new way of constructing kernel based bias corrected confidence intervals in addition for practical cases we derive coverage error optimal bandwidths and discuss easy to implement bandwidth selectors for interior points we show that the mse optimal bandwidth for the original point estimator before bias correction delivers the fastest coverage error decay rate after bias correction when second order equi

inference on causal effects in a generalized regression kink design we consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known deterministic but kinked function of an observed assignment variable we characterize a broad class of models in which a sharp regression kink design rkd or rk design identifies a readily interpretable treatment on the treated parameter florens heckman meghir and vytlacil 2008 we also introduce a fuzzy regression kink design generalization that allows for omitted variables in the assignment rule noncompliance and certain types of measurement errors in the observed values of the assignment variable and the policy variable our identifying assumptions give rise to testable restrictions on the distributions of the assignment variable and predetermined covariates around the kink point similar to the restrictions delivered by lee 2008 for the regression discontinuity design using a kink in the unemployment benefit formula we apply a fuzzy rkd to empirically estimate the effect of benefit rates on unemployment durations in austria

the equivalence problem for single valued two way transducers on npdtol languages is decidable the equivalence problem for deterministic two way transducers was a longstanding problem finally shown decidable by e m gurari we show a generalization of this result namely that it is decidable whether two single valued two way transducers are equivalent on an npdtol language we obtain this result by showing that it is even decidable whether a two way transducer is single valued on an npdtol language our solution is based on the compactness property of the systems of equations over a finitely generated free monoid shown recently by j lawrence and m albert and also v s guba this was a longstanding open problem known as the ehrenfeucht conjecture our approach also shows that for one way transducers their single valuedness on a given hdtol language can be tested and thus the equivalence of two single valued one way transducers on an hdtol language is decidable too our results imply the decidability of the hdol and hdtol sequence equivalence problems also longstanding open problems solved rece

the modified box dimension and average weighted receiving time of the weighted hierarchical graph abstract in this paper we study the weighted hierarchical graph which is generated from bipartite graph with n n 1 n 2 vertices in which the weights of edges have been assigned to different values with certain scale firstly we introduce the definition of the modified box dimension then for the weighted hierarchical graph we deduce the modified box dimension dim m b g n n n log r n depending on the weighted factor r and the number n of copies secondly we mainly study their two average weighted receiving times awrts t i n and t ii n of the weighted hierarchical graph on random walk we discuss two cases in the case of n 1 n 2 r n 2 n 1 we deduce both awrts grow as a power law function of the network size v g n with the postive exponent represented by log n n n 1 n 2 or log n r 1 dim m b g n n n which means that the bigger the value of the modified box dimension is the slower the process of receiving information is in the case of n 1 n 2 r n 2 n 1 both awrts tend to constant if n n 1 n 2 the awrts grow with increasing order as log n v g n if n n 1 n 2 and both awrts grow as a power law function of the network size v g n with the exponent represented by log n n n 1 n 2 0 if n n 1 n 2

predicting percolation thresholds in networks we consider different methods which do not rely on numerical simulations of the percolation process to approximate percolation thresholds in networks we perform a systematic analysis on synthetic graphs and a collection of 109 real networks to quantify their effectiveness and reliability as prediction tools our study reveals that the inverse of the largest eigenvalue of the nonbacktracking matrix of the graph often provides a tight lower bound for true percolation threshold however in more than 40 of the cases this indicator is less predictive than the naive expectation value based solely on the moments of the degree distribution we find that the performance of all indicators becomes worse as the value of the true percolation threshold grows thus none of them represents a good proxy for the robustness of extremely fragile networks

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

the equivalence problem for deterministic two way sequential transducers is decidable the equivalence problem for deterministic two way sequential transducers is a long time open problem which is known to be decidable for some restricted cases here the problem is shown to be decidable also for the general case in fact the result holds even when the devices are allowed to make some finite number of nondeterministic moves

a zero inflated ordered probit model with an application to modelling tobacco consumption abstract data for discrete ordered dependent variables are often characterised by excessive zero observations which may relate to two distinct data generating processes traditional ordered probit models have limited capacity in explaining this preponderance of zero observations we propose a zero inflated ordered probit model using a double hurdle combination of a split probit model and an ordered probit model monte carlo results show favourable performance in finite samples the model is applied to a consumer choice problem of tobacco consumption indicating that policy recommendations could be misleading if the splitting process is ignored

regression and time series model selection in small samples summary a bias correction to the akaike information criterion aic is derived for regression and autoregressive time series models the correction is of particular use when the sample size is small or when the number of fitted parameters is a moderate to large fraction of the sample size the corrected method called aicc is asymptotically efficient if the true model is infinite dimensional furthermore when the true model is of finite dimension aicc is found to provide better model order choices than any other asymptotically efficient method applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed

average receiving scaling of the weighted polygon koch networks with the weight dependent walk based on the weighted koch networks and the self similarity of fractals we present a family of weighted polygon koch networks with a weight factor r 0 r 1 we study the average receiving time art on weight dependent walk i e the walker moves to any of its neighbors with probability proportional to the weight of edge linking them whose key step is to calculate the sum of mean first passage times mfpts for all nodes absorpt at a hub node we use a recursive division method to divide the weighted polygon koch networks in order to calculate the art scaling more conveniently we show that the art scaling exhibits a sublinear or linear dependence on network order thus the weighted polygon koch networks are more efficient than expended koch networks in receiving information finally compared with other previous studies results i e koch networks weighted koch networks we find out that our models are more general

normality and two way automata we prove that two way transducers both deterministic and non deterministic cannot compress normal numbers to achieve this we first show that it is possible to generalize compressibility from one way transducers to two way transducers these results extend a known result normal infinite words are exactly those that cannot be compressed by lossless finite state transducers and more generally by bounded to one non deterministic finite state transducers we also argue that such a generalization cannot be extended to two way transducers with unbounded memory even in the simple form of a single counter

spectra of random graphs with arbitrary expected degrees we study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices we give a complete prescription for calculating the spectra that is exact in the limit of large network size and large vertex degrees we also study the effect on the spectra of hubs in the network vertices of unusually high degree and show that these produce isolated eigenvalues outside the main spectral band akin to impurity states in condensed matter systems with accompanying eigenvectors that are strongly localized around the hubs we give numerical results that confirm our analytic expressions

local likelihood and local partial likelihood in hazard regression in survival analysis the relationship between a survival time and a covariate is conveniently modeled with the proportional hazards regression model this model usually assumes that the covariate has a log linear effect on the hazard function in this paper we consider the proportional hazards regression model with a nonparametric risk effect we discuss estimation of the risk function and its derivatives in two cases when the baseline hazard function is parametrized and when it is not parametrized in the case of a parametric baseline hazard function inference is based on a local version of the likelihood function while in the case of a nonparametric baseline hazard we use a local version of the partial likelihood this results in maximum local likelihood estimators and maximum local partial likelihood estimators respectively we establish the asymptotic normality of the estimators it turns out that both methods have the same asymptotic bias and variance in a common situation even though the local likelihood method uses information about the baseline hazard function

non parametric identification and estimation of the number of components in multivariate mixtures this article analyzes the identiability of the number of components in k variate mcomponent nite mixture models in which each component distribution has independent marginals including models in latent class analysis without making parametric assumptions on the component distributions we investigate how one can identify the number of components from the distribution function of the observed data when k 2 a lower bound on the number of components m is nonparametrically identiable from the rank of a matrix constructed from the distribution function of the observed variables building on this identication condition we develop a procedure to consistently estimate a lower bound on the number of components

bayesian analysis of the ordered probit model with endogenous selection this paper presents a bayesian analysis of an ordered probit model with endogenous selection the model can be applied when analyzing ordered outcomes that depend on endogenous covariates that are discrete choice indicators modeled by a multinomial probit model the model is illustrated by analyzing the effects of different types of medical insurance plans on the level of hospital utilization allowing for potential endogeneity of insurance status the estimation is performed using the markov chain monte carlo mcmc methods to approximate the posterior distribution of the parameters in the model

on the α nonbacktracking centrality for complex networks existence and limit cases abstract nonbactracking centrality was introduced as an attempt to correct some deficiencies of eigenvector centrality in this work the nonbacktracking centrality is introduced as an extension that interpolates between the nonbacktracking centrality of the edges of a directed network and the eigenvector centrality of the corresponding directed line graph the existence of this new nonbacktracking centrality is proved in terms of the connectivity of the original network we prove that the limit of the nonbacktracking centrality when decreases to zero exists and is well defined moreover it coincides with the nonbacktracking centrality when this measure is defined with the same techniques we also prove the convergence of pagerank vectors to the eigenvector centrality vector when the damping factor tends to 1

robust nonparametric confidence intervals for regression discontinuity designs in the regression discontinuity rd design units are assigned to treatment based on whether their value of an observed covariate exceeds a known cutoff in this design local polynomial estimators are now routinely employed to construct confidence intervals for treatment effects the performance of these confidence intervals in applications however may be seriously hampered by their sensitivity to the specific bandwidth employed available bandwidth selectors typically yield a large bandwidth leading to data driven confidence intervals that may be biased with empirical coverage well below their nominal target we propose new theory based more robust confidence interval estimators for average treatment effects at the cutoff in sharp rd sharp kink rd fuzzy rd and fuzzy kink rd designs our proposed confidence intervals are constructed using a bias corrected rd estimator together with a novel standard error estimator for practical implementation we discuss mean squared error optimal bandwidths which are by construction not valid for conventional confidence intervals but are valid with our robust approach and consistent standard error estimators based on our new variance formulas in a special case of practical interest our procedure amounts to running a quadratic instead of a linear local regression more generally our results give a formal justification to simple inference procedures based on increasing the order of the local polynomial estimator employed we find in a simulation study that our confidence intervals exhibit close to correct empirical coverage and good empirical interval length on average remarkably improving upon the alternatives available in the literature all results are readily available in r and stata using our companion software packages described in calonico cattaneo and titiunik 2014d 2014b

diagnostic checking in arma models with uncorrelated errors we consider tests for lack of fit in arma models with nonindependent innovations in this framework the standard box pierce and ljung box portmanteau tests can perform poorly specifically the usual text book formulas for asymptotic distributions are based on strong assumptions and should not be applied without careful consideration in this article we derive the asymptotic covariance matrix of a vector of autocorrelations for residuals of arma models under weak assumptions on the noise the asymptotic distribution of the portmanteau statistics follows a consistent estimator of and a modification of the portmanteau tests are proposed this allows us to construct valid asymptotic significance limits for the residual autocorrelations and asymptotically valid goodness of fit tests when the underlying noise process is assumed to be noncorrelated rather than independent or a martingale difference a set of monte carlo experiments and an application to the standard poor 500 returns illustrate the p

analysis of the dynamics and topology dependencies of small perturbations in electric transmission grids we study the phase dynamics in power grids in response to small disturbances and how this depends on the grid topology to this end we consider the swing equations in linear order in phase disturbances and solve the resulting linear wave equation deriving the eigenmodes of the weighted graph laplacian a linear response expression for the deviation of frequency is given in terms of these eigenvalues and eigenvectors which it is argued to be the basis for future power system stabilizers and other control measures in power systems as an example we present results for random networks based on the watts strogatz model where we observe a transition to localized eigenstates as the randomness in the degree distribution grows moreover it is found that localization leads to faster decay rates thereby disturbances are found to remain localized on a few nodes where they decay faster finally we also consider the german transmission grid topology where the eigenstate of the lowest eigenfrequency the fiedler vector is found to be extended with large intensities at the northwestern and southern boundaries

scale free and small world properties of sierpinski networks abstract in this paper we construct the evolving networks from sierpinski carpet using the encoding approach in fractal geometry we consider the small similar copies of unit square as nodes of network where two nodes are neighbors if and only if their corresponding copies have common surface for our networks we check their scale free and small world effect by the self similar structures the exponent of power law on degree distribution is log 3 8 which is the hausdorff dimension of the carpet

weighted fractal networks abstract in this paper we define a new class of weighted complex networks sharing several properties with fractal sets and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension general networks with fractal or hierarchical structures can be set in the proposed framework that moreover could be used to provide some answers to the widespread emergence of fractal structures in nature

scaling of average weighted shortest path and average receiving time on the weighted cayley networks abstract in this paper we mainly study two important properties of weighted cayley networks depending on a weight factor r the weight factor makes it more difficult to calculate the topological characteristics such as average weighted shortest path awsp and average receiving time art of the networks we first calculate some basic network measurements such as average degree and average node strength then we derive the expression for awsp and show that it stays bounded with network order growing 0 r 1 in the limit of large network order at last we focus on random walks and trapping issue on the networks that is we calculate the art in more detail for 0 r 1 2 the art grows with increasing size n t as ln n t for r 1 2 the art grows with increasing size n t as ln 2 n t for 1 2 r 1 the art grows sublinearly with the network size n t for r 1 the art grows linearly with the network size n t

average weighted receiving time on the non homogeneous double weighted fractal networks abstract in this paper based on actual road networks a model of the non homogeneous double weighted fractal networks is introduced depending on the number of copies s and two kinds of weight factors w i r i i 1 2 s the double weights represent the capacity flowing weights and the cost traveling weights respectively denote by w i j f the capacity flowing weight connecting the nodes i and j and denote by w i j c the cost traveling weight connecting the nodes i and j let w i j f be related to the weight factors w 1 w 2 w s and let w i j c be related to the weight factors r 1 r 2 r s assuming that the walker at each step starting from its current node moves to any of its neighbors with probability proportional to the capacity flowing weight of edge linking them the weighted time for two adjacency nodes is the cost traveling weight connecting the two nodes the average weighted receiving time awrt is defined on the non homogeneous double weighted fractal networks awrt depends on the relationships of the number of copies s and two kinds of weight factors w i r i i 1 2 s the obtained remarkable results display that in the large network the awrt grows as a power law function of the network size n g with the exponent represented by log s w 1 r 1 w 2 r 2 w s r s 1 when w 1 r 1 w 2 r 2 w s r s 1 which means that the smaller the value of w 1 r 1 w 2 r 2 w s r s is the more efficient the process of receiving information is especially when w 1 r 1 w 2 r 2 w s r s 1 awrt grows with increasing order n g as log n g or log n g 2 in the classic fractal networks the average receiving time art grows with linearly with the network size n g thus the non homogeneous double weighted fractal networks are more efficient than classic fractal networks in term of receiving information

scaling of average receiving time and average weighted shortest path on weighted koch networks abstract in this paper we present weighted koch networks based on classic koch networks a new method is used to determine the average receiving time art whose key step is to write the sum of mean first passage times mfpts for all nodes to absorption at the trap located at a hub node as a recursive relation we show that the art exhibits a sublinear or linear dependence on network order thus the weighted koch networks are more efficient than classic koch networks in receiving information moreover average weighted shortest path awsp is calculated in the infinite network order limit the awsp depends on the scaling factor the weighted koch network grows unbounded but with the logarithm of the network size while the weighted shortest paths stay bounded

fractal models for diffusion controlled aggregation a two dimensional fractal model is constructed for diffusion controlled deposition on a surface the fractal geometry of the deposit and the power law behaviour of the quantities characterising the non equilibrium cluster size distribution are shown to be consequences of the competition generally present in a nonlinear growth process a qualitative agreement with previous numerical results is found and the scaling laws for the critical exponents of the problem are shown to be satisfied exactly

monte carlo tests with nuisance parameters a general approach to finite sample inference and nonstandard asymptotics abstract the technique of monte carlo mc tests dwass 1957 annals of mathematical statistics 28 181 187 barnard 1963 journal of the royal statistical society series b 25 294 provides a simple method for building exact tests from statistics whose finite sample distribution is intractable but can be simulated when no nuisance parameter is involved we extend this method in two ways first by allowing for mc tests based on exchangeable possibly discrete test statistics second by generalizing it to statistics whose null distribution involves nuisance parameters maximized mc mmc tests simplified asymptotically justified versions of the mmc method are also proposed these provide a simple way of improving standard asymptotics and dealing with nonstandard asymptotics

the relations between network operation and topological property in a scale free and small world network with community structure abstract it is always an open demanding and difficult task for generating available model to simulate dynamical functions and reveal inner principles from complex systems and networks in this article due to lots of real life and artificial networks are built from series of simple and small groups components we discuss some interesting and helpful network operation to generate more realistic network models in view of community structure modular topology we present a class of sparse network models n t m at the moment we capture the fact the n t 4 has not only scale free feature which means that the probability that a randomly selected vertex with degree k decays as a power law following p k k where is the degree exponent but also small world property which indicates that the typical distance between two uniform randomly chosen vertices grows proportionally to logarithm of the order of n t 4 namely relatively shorter diameter and lower average path length simultaneously displays higher clustering coefficient next as a new topological parameter correlating to reliability synchronization capability and diffusion properties of networks the number of spanning trees over a network is studied in more detail an exact analytical solution for the number of spanning trees of the n t 4 is obtained based on the network operation part hub vertex linking with each other will be helpful for structuring various network models and investigating the rules related with real life networks

modified wald tests under nonregular conditions abstract under nonregular conditions wald tests are known to have incorrect size even asymptotically in part of the parameter space modifications are discussed which ensure an asymptotic 2 distribution of the wald statistic under h0 as an example wald tests for multi step causality are considered a variable yt is h step causal for another variable xt if the information in yt helps improving the j step forecasts of xt for some j 1 2 h if more than two variables are involved and are generated by a finite order vector autoregressive var process this type of multi step noncausality implies a set of highly nonlinear restrictions on the var coefficient matrices for this type of nonlinear restrictions standard wald tests fail to have limiting 2 distributions in general

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

scaling of weighted spectral distribution in deterministic scale free networks abstract scale free networks are abundant in the real world in this paper we investigate the scaling properties of the weighted spectral distribution in several deterministic and stochastic models of evolving scale free networks first we construct a new deterministic scale free model whose node degrees have a unified format using graph structure features we derive a precise formula for the spectral metric in this model this formula verifies that the spectral metric grows sublinearly as network size i e the number of nodes grows additionally the mathematical reasoning of the precise formula theoretically provides detailed explanations for this scaling property finally we validate the scaling properties of the spectral metric using some stochastic models the experimental results show that this scaling property can be retained regardless of local world node deleting and assortativity adjustment

a semi nonparametric estimator of regression discontinuity design with discrete duration outcomes abstract we consider the regression discontinuity rd design with the duration outcome which has discrete support the parameters of policy interest are treatment effects on unconditional duration effect and conditional hazard effect exiting probabilities for each discrete level we propose a novel semi nonparametric estimator which exploits a flexible separability structure of the underlying continuous time duration process simultaneous inference over discrete levels is nonstandard since the asymptotic variance matrix is singular with unknown rank the peculiarity is delivered by the nature of the rd estimand and we provide solutions random censoring and competing risks can also be allowed in our framework

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

a permutation test for the regression kink design the regression kink rk design is an increasingly popular empirical method for estimating causal effects of policies such as the effect of unemployment benefits on unemployment duration using si

asymptotics for semiparametric econometric models via stochastic equicontinuity this paper provides a general framework for proving the square root of t consistency and asymptotic normality of a wide variety of semiparametric estimators the class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator the method of proof exploits results concerning the stochastic equicontinuity of stochastic processes the results are applied to the problem of semiparametric weighted least squares estimation of partially parametric regression models primitive conditions are given for square root of t consistency and asymptotic normality of this estimator copyright 1994 by the econometric society

localization of eigenvector centrality in networks with a cut vertex we show that eigenvector centrality exhibits localization phenomena on networks that can be easily partitioned by the removal of a vertex cut set the most extreme example being networks with a cut vertex three distinct types of localization are identified in these structures one is related to the well established hub node localization phenomenon and the other two are introduced and characterized here we gain insights into these problems by deriving the relationship between eigenvector centrality and katz centrality this leads to an interpretation of the principal eigenvector as an approximation to more robust centrality measures which exist in the full span of an eigenbasis of the adjacency matrix

modularity and extreme edges of the internet we study the spectral properties of a diffusion process taking place on the internet network focusing on the slowest decaying modes these modes identify an underlying modular structure roughly corresponding to individual countries for instance in the slowest decaying mode the diffusion current flows from russia to u s military sites quantitatively the modular structure manifests itself in a 10 times larger participation ratio of its slow decaying modes compared to a random scale free network we propose to use the fraction of nodes participating in slow decaying modes as a general measure of the modularity of a network for the 100 slowest decaying modes of the internet this fraction is 30 finally we suggest that the degree of isolation of an individual module can be assessed by comparing its participation in different diffusion modes

on the exponential generating function for non backtracking walks we derive an explicit formula for the exponential generating function associated with non backtracking walks around a graph we study both undirected and directed graphs our results allow us to derive computable expressions for non backtracking versions of network centrality measures based on the matrix exponential we find that eliminating backtracking walks in this context does not significantly increase the computational expense we show how the new measures may be interpreted in terms of standard exponential centrality computation on a certain multilayer network insights from this block matrix interpretation also allow us to characterize centrality measures arising from general matrix functions rigorous analysis on the star graph illustrates the effect of non backtracking and shows that unwanted localization effects can be eliminated when we restrict to non backtracking walks we also investigate the localization issue on synthetic networks

identification and estimation of treatment effects with a regression discontinuity design the regression discontinuity rd data design is a quasi experimental design with the defining characteristic that the probability of receiving treatment changes discontinuously as a function of one or more underlying variables this data design arises frequently in economic and other applications but is only infrequently exploited as a source of identifying information in evaluating effects of a treatment in the first application and discussion of the rd method thistlethwaite and campbell 1960 study the effect of student scholarships on career aspirations using the fact that awards are only made if a test score exceeds a threshold more recently van der klaauw 1997 estimates the effect of financial aid offers on students decisions to attend a particular college taking into account administrative rules that set the aid amount partly on the basis of a discontinuous function of the students grade point average and sat score angrist and lavy 1999 estimate the effect of class size on student test scores taking advantage of a rule stipulating that another classroom be added when the average class size exceeds a threshold level finally black 1999 uses an rd approach to estimate parents willingness to pay for higher quality schools by comparing housing prices near geographic school attendance boundaries regression discontinuity methods have potentially broad applicability in economic research because geographic boundaries or rules governing programs often create discontinuities in the treatment assignment mechanism that can be exploited under the method although there have been several discussions and applications of rd methods in the literature important questions still remain concerning sources of identification and ways of estimating treatment effects under minimal parametric restrictions here we show that identifying conditions invoked in previous applications of rd methods are often overly strong and that treatment effects can be nonparametrically identified under an rd design by a weak functional form restriction the restriction is unusual in that it requires imposing continuity assumptions in order to take advantage of the known discontinuity in the treatment assignment mechanism we also propose a way of nonparametrically estimating treatment effects and offer an interpretation of the wald estimator as an rd estimator

wanna get away regression discontinuity estimation of exam school effects away from the cutoff in regression discontinuity rd studies exploiting an award or admissions cutoff causal effects are nonparametrically identified for those near the cutoff the effect of treatment on inframarginal applicants is also of interest but identification of such effects requires stronger assumptions than those required for identification at the cutoff this article discusses rd identification and estimation away from the cutoff our identification strategy exploits the availability of dependent variable predictors other than the running variable conditional on these predictors the running variable is assumed to be ignorable this identification strategy is used to study effects of boston exam schools for inframarginal applicants identification based on the conditional independence assumptions imposed in our framework yields reasonably precise and surprisingly robust estimates of the effects of exam school attendance on inframarginal applicants these estimates suggest that the causal effects of exam school

localization and centrality in networks eigenvector centrality is a common measure of the importance of nodes in a network here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to concentrate on a small number of nodes in the network in this regime the measure is no longer useful for distinguishing among the remaining nodes and its efficacy as a network metric is impaired as a remedy we propose an alternative centrality measure based on the nonbacktracking matrix which gives results closely similar to the standard eigenvector centrality in dense networks where the latter is well behaved but avoids localization and gives useful results in regimes where the standard centrality fails

mean field diffusive dynamics on weighted networks diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks here we introduce a general formalism that allows to easily write down mean field equations for any diffusive dynamics on weighted networks we also propose the concept of annealed weighted networks in which such equations become exact we show the validity of our approach addressing the problem of the random walk process pointing out a strong departure of the behavior observed in quenched real scale free networks from the mean field predictions additionally we show how to employ our formalism for more complex dynamics our work sheds light on mean field theory on weighted networks and on its range of validity and warns about the reliability of mean field results for complex dynamics

generalisations and randomisation of the plane koch curve the koch curve evolves from a base equilateral triangle by the trisection of each side and the replication of the original triangle on the mid section the process being repeated ad infinitum by the addition of sets of successively smaller triangles the process is generalised to replace the trisectioning by 2k 1 sectioning it is shown that a square is the only other regular polygon on which the 2k 1 sectioning procedure can be implemented the koch curves thus generated are strictly self similar their fractal dimensions being similarity dimensions and enclose simply connected areas randomisation of the generating procedure is also discussed

average geodesic distance of skeleton networks of sierpinski tetrahedron abstract the average distance is concerned in the research of complex networks and is related to wiener sum which is a topological invariant in chemical graph theory in this paper we study the skeleton networks of the sierpinski tetrahedron an important self similar fractal and obtain their asymptotic formula for average distances to provide the formula we develop some technique named finite patterns of integral of geodesic distance on self similar measure for the sierpinski tetrahedron