temporal complexity of the order parameter at the phase transition we study a decision making model in a condition where it is equivalent to the two dimensional ising model and we show that at the onset of phase transition it generates temporal complexity namely nonstationary and nonergodic fluctuations we argue that this is a general property of criticality thereby opening the door to the application of the recently discovered phenomenon of complexity matching for an efficient transfer of information to occur a perturbing complex network must share the same temporal complexity as the perturbed complex network

growing scale free networks with tunable clustering we extend the standard scale free network model to include a triad formation step we analyze the geometric properties of networks generated by this algorithm both analytically and by numerical c

minimum time trajectory generation for constrained linear systems using flatness and b splines in this article we discuss minimum time trajectory generation for input and state constrained continuous time lti systems in the light of the notion of flatness and b splines parametrisation flat systems have the useful property that the input and the state trajectories can be completely characterised by the so called flat output we propose a splines parametrisation for the flat output and the corresponding parametrisations for the performance output the states and the inputs using this parametrisation the problem of minimum time constrained trajectory planning is cast into a feasibility search problem in the splines control point space in which the constraint region is characterised by a polytope a close approximation of the minimum time trajectory is obtained by systematically searching the end time that makes the constraint polytope to be minimally feasible

generalized bang bang control for feedforward constrained regulation in the behavioral framework for continuous time linear scalar systems simple sufficient conditions for the solution of the minimum time rest to rest feedforward constrained control problem are provided the investigation of the time optimal input output pair reveals that the input or the output saturates on the assigned constraints at all times except for a set of zero measure the resulting optimal input is composed of sequences of bang bang functions and linear combinations of the modes associated to the zero dynamics this signal behavior constitutes a generalized bang bang control that can be fruitfully exploited for feedforward constrained regulation using discretization an arbitrarily good approximation of the optimal generalized bang bang control is found by solving a sequence of linear programming problems numerical examples are included

nonlinear minimum time control with pre and post actuation this article studies the time optimal output transition problem to change the system output from an initial value y t y for all time t 0 to a final value y t y for all time t t for invertible nonlinear systems the main contribution of the article is to show that the use of pre and post actuation input outside the transition interval i t 0 t can reduce the transition time t beyond the standard bang bang type inputs for optimal state transition the advantage of using pre and post actuation is demonstrated with an illustrative nonlinear example

a comparison of two simple hazard ratio estimators based on the logrank test two hazard ratio estimators based on the logrank test are investigated using a simulation study the pike estimator ratio of relative death rates was shown to be consistently less biased than the peto 1 step estimator the latter has recently been advocated as the method of choice for point and interval estimation both estimators exhibited bias with increasing hazard ratios although the bias was minimal for effects less than 3 the confidence intervals also did not achieve the nominal coverage with increasing hazard ratios but again the pike estimator was superior the coverage could be improved by recalculation of the variance incorporating the point estimate for a hazard ratio of less than 3 we recommend the use of the pike estimator otherwise it is necessary to use a more complex method of estimation

kernel canonical correlation granger causality for multiple time series canonical correlation analysis as a multivariate statistical technique has been applied to multivariate granger causality analysis to infer information flow in complex systems it shows unique appeal and great superiority over the traditional vector autoregressive method due to the simplified procedure that detects causal interaction between multiple time series and the avoidance of potential model estimation problems however it is limited to the linear case here we extend the framework of canonical correlation to include the estimation of multivariate nonlinear granger causality for drawing inference about directed interaction its feasibility and effectiveness are verified on simulated data

estimating the relative risk with censored data abstract we investigate a class of nonparametric estimators of relative risk in the two sample case of the proportional hazards model for censored data the asymptotic distribution of these estimators is derived using influence functions the optimal estimator in this class has the same influence functions and the same asymptotic distribution as the maximum partial likelihood estimator of cox 1972 the behavior of the influence functions is discussed briefly and the last section presents two examples from the literature

some scale estimators and lack of fit tests for the censored two sample accelerated life model some new scale estimators for the censored two sample accelerated life model are introduced they are zeros of some integrated weighted difference between the two cumulative hazard estimators these estimators are asymptotically normal the weight is chosen to result in estimators whose asymptotic variances do not involve the destiny functions and can be easily estimated this provides a fast and simple means of statistical inference in the censored two sample accelerated life model through investigating the asymptotic relative efficiency at some important censoring submodels and the finite example behaviors in various numerical studies we obtain some estimators with very competitive performance from the new class of scale estimators some lack of fit tests for the accelerated life model are also derived these tests are related to gill schumacher type tests and require little extra computing time once the estimator is obtained the estimators and tests are illustrated in two applications for a vaginal cancer data set for rats the effect of pretreatment regime was found to be well described by the two sample accelerated life model for a data set on progression of ovarian cancer it was found that the effect of grade of disease could not be described either by the two sample proportional hazards model or the two sample accelerated life model

ising like dynamics in large scale functional brain networks brain rest is defined more or less unsuccessfully as the state in which there is no explicit brain input or output this work focuses on the question of whether such state can be comparable to any known dynamical state for that purpose correlation networks from human brain functional magnetic resonance imaging are contrasted with correlation networks extracted from numerical simulations of the ising model in two dimensions at different temperatures for the critical temperature tc striking similarities appear in the most relevant statistical properties making the two networks indistinguishable from each other these results are interpreted here as lending support to the conjecture that the dynamics of the functioning brain is near a critical point

small world and scale free organization of voxel based resting state functional connectivity in the human brain the brain is a complex dynamic system of functionally connected regions graph theory has been successfully used to describe the organization of such dynamic systems recent resting state fmri studies have suggested that inter regional functional connectivity shows a small world topology indicating an organization of the brain in highly clustered sub networks combined with a high level of global connectivity in addition a few studies have investigated a possible scale free topology of the human brain but the results of these studies have been inconclusive these studies have mainly focused on inter regional connectivity representing the brain as a network of brain regions requiring an arbitrary definition of such regions however using a voxel wise approach allows for the model free examination of both inter regional as well as intra regional connectivity and might reveal new information on network organization especially a voxel based study could give information about a possible scale free organization of functional connectivity in the human brain resting state 3 tesla fmri recordings of 28 healthy subjects were acquired and individual connectivity graphs were formed out of all cortical and sub cortical voxels with connections reflecting inter voxel functional connectivity graph characteristics from these connectivity networks were computed the clustering coefficient of these networks turned out to be much higher than the clustering coefficient of comparable random graphs together with a short average path length indicating a small world organization furthermore the connectivity distribution of the number of inter voxel connections followed a power law scaling with an exponent close to 2 suggesting a scale free network topology our findings suggest a combined small world and scale free organization of the functionally connected human brain the results are interpreted as evidence for a highly efficient organization of the functionally connected brain in which voxels are mostly connected with their direct neighbors forming clustered sub networks which are held together by a small number of highly connected hub voxels that ensure a high level of overall connectivity

distribution free methods of estimating location difference with censored paired data abstract nonparametric point and interval estimators of location difference in matched pairs data with arbitrary right censorship are proposed based on a generalized gehan gilbert test wei 1980 the point estimator is shown to be asymptotically normal and strongly consistent the limits of the corresponding interval estimator are readily computable an example is also provided to illustrate the techniques to problems in survival data analysis

estimation and testing in a two sample generalized odds rate model abstract the generalized odds ratio for a survival variable t is defined as t t c c 1 1 sc t sc t for c 0 and log s t for c 0 where s t pr t t this ratio coincides with the integrated hazard for c 0 and the odds ratio for c 1 when the distribution of t depends on a covariate vector we assume that conditionally on the covariates log t t c is linear in the covariates this model is a generalization of the proportional hazard model phm which has an interpretation both as a phm with random nuisance effects clayton and cuzick 1986 and as a proportional odds rate model with the odds rate defined from the response times of series systems harrington and fleming 1982 and bickel 1986a considered rank tests for this semiparametric model clayton and cuzick 1986 considered estimation we use the odds rate representation to define a class of estimates of the proportionality parameter in the two sample case we show that the estimates are consistent and asymptotica

generation of uncorrelated random scale free networks uncorrelated random scale free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks we propose and analyze a model capable of generating random uncorrelated scale free networks with no multiple and self connections the model is based on the classical configuration model with an additional restriction on the maximum possible degree of the vertices we check numerically that the proposed model indeed generates scale free networks with no two and three vertex correlations as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k respectively complex networks constitute a general framework for the topological characterization of many natural and technological systems whose complexity prevents a more detailed microscopic description f1 3g within this framework these systems are represented in terms of networks or graphs f4g in which vertices stand for the units composing the system while edges among vertices represent the interactions or relations between pairs of units the focus is thus shift to the topological characterization of the representative network a task which is largely more feasible and yields nevertheless a noticeable amount of information on the structure and properties of the original system the empirical analysis of many real complex networks has unveiled the presence of several typical properties widely found in systems belonging to a large variety of realms one of the most relevant is given by the scale free nature of the degree distribution pskd f1 3 5g defined as the probability that a randomly chosen vertex has degree k si e it is connected to other k verticesd in mathematical terms the scale free property translates into a power law function of the form psk d k g

estimation of the proportional hazard in two treatment group clinical trials two easily computed approximate methods of obtaining an estimate of the ratio of the hazard rates for two treatments in survival analysis are compared by simulation with the partial maximum likelihood cml estimator which assumes the cox model with no covariates the two methods studied are the mantel haenszel estimator and the o e method which employs the ratio of the relative death rates for the two treatments uncensored and censored cases are examined for both continuous and tied data with the assumption of either an underlying exponential distribution or a weibull distribution with shape parameter 2 the o e method is biased but within the range of values of the ratio of the hazard rates of interest in clinical trials it is more efficient in terms of mean square error than either cml or the mantel haenszel method for all but the largest trials the mantel haenszel method is minimally biased gives answers very close to those obtained using cml and may be used to provide satisfactory approximate confidence intervals

critical social networks abstract critical social ensembles are generated using a decision making model dmm consisting of a master equation with two state elements at the nodes of a two dimensional lattice the dynamics of the dmm undergo phase transitions to either a consensus state or another state composed of apparently statistically independent individuals as shown in an ensemble of calculations the critical social ensemble is entailed by the network elements nonlinearly interacting through imperfect social imitation on the backbone of a correlation network an information entropy measure of the difference between coherent and incoherent configurations in the critical social ensemble is constructed the entropy indicates a greater probability for the formation of either opposing groups or universal consensus above that of random disagreement

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

scale free brain functional networks functional magnetic resonance imaging is used to extract functional networks connecting correlated human brain sites analysis of the resulting networks in different tasks shows that a the distribution of functional connections and the probability of finding a link versus distance are both scale free b the characteristic path length is small and comparable with those of equivalent random networks and c the clustering coefficient is orders of magnitude larger than those of equivalent random networks all these properties typical of scale free small world networks reflect important functional information about brain states

estimation of the average hazard ratio summary simple estimators of the average hazard ratio are obtained for the two sample problem with censored failure time data these estimators are compared with estimators arising out of the partial likelihood within the proportional hazards class efficiency results are found to be generally quite favourable provided the hazard ratio is not too large some comments are made on extensions to the k sample problem

spectral decomposition of a fokker planck equation at criticality the mean field for a complex network consisting of a large but finite number of random two state elements m has been shown to satisfy a nonlinear langevin equation the noise intensity is inversely proportional to sqrt m in the limiting case m infty the solution to the langevin equation exhibits a transition from exponential to inverse power law relaxation as criticality is approached from above or below the critical point when m infty the inverse power law is truncated by an exponential decay with rate vargamma the evaluation of which is the main purpose of this article an analytic numeric approach is used to obtain the lowest order eigenvalues in the spectral decomposition of the solution to the corresponding fokker planck equation and its equivalent schrodinger equation representation

exactly solvable scale free network model we study a deterministic scale free network recently proposed by barabasi ravasz and vicsek we find that there are two types of nodes the hub and rim nodes which form a bipartite structure of the network we first derive the exact numbers p k of nodes with degree k for the hub and rim nodes in each generation of the network respectively using this we obtain the exact exponents of the distribution function p k of nodes with k degree in the asymptotic limit of k infinity we show that the degree distribution for the hub nodes exhibits the scale free nature p k proportional to k gamma with gamma ln 3 ln 2 1 584 962 while the degree distribution for the rim nodes is given by p k proportional to e gamma k with gamma ln 3 2 0 405 465 second we analytically calculate the second order average degree of nodes d third we numerically as well as analytically calculate the spectra of the adjacency matrix a for representing topology of the network we also analytically obtain the exact number of degeneracies at each eigenvalue in the network the density of states i e the distribution function of eigenvalues exhibits the fractal nature with respect to the degeneracy fourth we study the mathematical structure of the determinant of the eigenequation for the adjacency matrix fifth we study hidden symmetry zero modes and its index theorem in the deterministic scale free network finally we study the nature of the maximum eigenvalue in the spectrum of the deterministic scale free network we will prove several theorems for it using some mathematical theorems thus we show that most of all important quantities in the network theory can be analytically obtained in the deterministic scale free network model of barabasi ravasz and vicsek therefore we may call this network model the exactly solvable scale free network

mean field theory for clustering coefficients in barabasi albert networks we applied a mean field approach to study clustering coefficients in barabasi albert ba networks we found that the local clustering in ba networks depends on the node degree analytic results have been compared to extensive numerical simulations finding a very good agreement for nodes with low degrees clustering coefficient of a whole network calculated from our approach perfectly fits numerical data

non parametric analysis of treatment covariate interaction in the presence of censoring the demonstration of varying treatment efficacy among different subsets of patients is an important part of the analysis of clinical trials the paper commences by clarifying the meaning of interaction and by reviewing valid procedures of analysis in the presence of interaction suitable descriptive measures of treatment covariate interactions are ratios of hazard ratios to which generalized patel hoel tests for qualitative or ordinal categorical covariates are related both the hazard ratios and the tests are given in a formulation for use with different scoring systems such as u or e furthermore the procedures are related to common k sample tests and thus are suitable for proportional and for converging hazards a worked example is included

statistics of the occupation time of renewal processes we present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time according to the nature of the distribution of time intervals the probability density functions of these random variables have very different scalings in time we analyze successively the cases where this distribution is narrow where it is broad with index 1 and finally where it is broad with index 1 2 the methods introduced in this work provide a basis for the investigation of the statistics of the occupation time of more complex stochastic processes see joint paper by g de smedt c godreche and j m luck 26

time to consensus abstract the dynamics of a two state decision making model dmm with a tunable control parameter k is described on all to all ata networks the system undergoes a phase transition at a critical value of k c 1 scale free networks were also found to undergo phase transitions but the value of k c increases as the scale free exponent increases time to consensus is defined as a first passage time to a specified threshold of the global mean field which represents a level of majority for the network at criticality the time to consensus for sparse networks with broad degree distributions e g scale free networks approaches that of the ata networks although somewhat more cooperation higher k c is required

highly clustered scale free networks we propose a model for growing networks based on a finite memory of the nodes the model shows stylized features of real world networks power law distribution of degree linear preferential attachment of new links and a negative correlation between the age of a node and its link attachment rate notably the degree distribution is conserved even though only the most recently grown part of the network is considered as the network grows the clustering reaches an asymptotic value larger than that for regular lattices of the same average connectivity and similar to the one observed in the networks of movie actors coauthorship in science and word synonyms these highly clustered scale free networks indicate that memory effects are crucial for a correct description of the dynamics of growing networks

noise induced intermittency of a reflexive model with symmetry induced equilibrium manifold abstract we discuss a route to intermittency based on the concept of reflexivity namely on the interaction between observer and stochastic reality a simple model mirroring the essential aspects of this interaction is shown to generate perennial out of equilibrium condition intermittency and 1 f noise in the absence of noise the model yields a symmetry induced equilibrium manifold with two stable states noise makes this equilibrium manifold unstable with an escape rate becoming lower and lower upon time increase thereby generating an inverse power law distribution of waiting times the distribution of the times of permanence in the basin of attraction of the equilibrium manifold are analytically predicted through the adoption of a first passage time technique finally we discuss the possible extension of our approach to deal with the intermittency of complex systems in different fields

the estimation of average hazard ratios by weighted cox regression often the effect of at least one of the prognostic factors in a cox regression model changes over time which violates the proportional hazards assumption of this model as a consequence the average hazard ratio for such a prognostic factor is under or overestimated while there are several methods to appropriately cope with non proportional hazards in particular by including parameters for time dependent effects weighted estimation in cox regression is a parsimonious alternative without additional parameters the methodology which extends the weighted k sample logrank tests of the tarone ware scheme to models with multiple binary and continuous covariates has been introduced in the nineties of the last century and is further developed and re evaluated in this contribution the notion of an average hazard ratio is defined and its connection to the effect size measure p x y is emphasized the suggested approach accomplishes estimation of intuitively interpretable average hazard ratios and provides tools for inference a monte carlo study confirms the satisfactory performance advantages of the approach are exemplified by comparing standard and weighted analyses of an international lung cancer study sas and r programs facilitate application

weakly non ergodic statistical physics for weakly non ergodic systems the probability density function of a time average observable overline mathcal o is f alpha overline mathcal o 1 over pi lim epsilon to 0 mbox im sum j 1 l p mathrm eq j overline mathcal o mathcal o j i epsilon alpha 1 over sum j 1 l p mathrm eq j overline mathcal o mathcal o j i epsilon alpha where mathcal o j is the value of the observable when the system is in state j 1 l pjeq is the probability that a member of an ensemble of systems occupies state j in equilibrium for a particle undergoing a fractional diffusion process in a binding force field with thermal detailed balance conditions pjeq is boltzmann s canonical probability within the unbiased sub diffusive continuous time random walk model the exponent 0 1 is the anomalous diffusion exponent x2 t found for free boundary conditions when 1 ergodic statistical mechanics is recovered lim alpha to 1 f alpha overline mathcal o delta overline mathcal o langle mathcal o rangle we briefly discuss possible physical applications in single particle experiments

brief optimal noncausal set point regulation of scalar systems this paper presents a novel system inversion approach to the set point regulation of linear scalar minimum phase systems this approach uses closed form expressions of cause effect pairs that make possible an arbitrarily smooth transition between two given output set points the cause effect pairs are based on the introduced concept of transition polynomials simple optimization procedures are then proposed to solve the relevant optimal output synthesis and optimal input synthesis the potentiality of the method is highlighted by the examples presented namely a synthesis of elevator velocity profiles and the performance improving of a pid controller

using stable input output inversion for minimum time feedforward constrained regulation of scalar systems the paper approaches the feedforward minimum time smooth control of non minimum phase linear scalar systems for set point regulation the aim is to synthesize a bounded input subject to non saturating constraints on the input and its derivatives till a prespecified arbitrary order the provided solution relies on a stable input output dynamic inversion technique and an ad hoc parameterized family of output transition functions the synthesized minimum time input that exhibits pre and post actuation is determined by means of easily implementable closed form expressions examples are given to illustrate the methodology

scale free networks with an exponent less than two we study scale free simple graphs with an exponent of the degree distribution ensuremath gamma less than 2 generically one expects such extremely skewed networks which occur very frequently in systems of virtually or logically connected units to have different properties than those of scale free networks with ensuremath gamma g2 the number of links grows faster than the number of nodes and they naturally posses the small world property because the diameter increases by the logarithm of the size of the network and the clustering coefficient is finite we discuss a simple prototype model of such networks inspired by real world phenomena which exhibits these properties and allows for a detailed analytical investigation

functional scale free networks in the two dimensional abelian sandpile model recently the similarity of the functional network of the brain and the ising model was investigated by chialvo nat phys 6 744 2010 this similarity supports the idea that the brain is a self organized critical system in this study we derive a functional network of the two dimensional bak tang wiesenfeld sandpile model as a self organized critical model and compare its characteristics with those of the functional network of the brain obtained from functional magnetic resonance imaging

a tree like complex network model abstract we propose a new tree like network model our results indicate that the tree like model has a small world effect with a small average path length and large clustering coefficient strikingly our tree like model is scale free we also add weight to the links following the network structure with this adding weight method the weight of the nodes shows exponential growth which is ubiquitous in social networks

cooperation in neural systems bridging complexity and periodicity inverse power law distributions are generally interpreted as a manifestation of complexity and waiting time distributions with power index 2 reflect the occurrence of ergodicity breaking renewal events in this paper we show how to combine these properties with the apparently foreign clocklike nature of biological processes we use a two dimensional regular network of leaky integrate and fire neurons each of which is linked to its four nearest neighbors to show that both complexity and periodicity are generated by locality breakdown links of increasing strength have the effect of turning local interactions into long range interactions thereby generating time complexity followed by time periodicity increasing the density of neuron firings reduces the influence of periodicity thus creating a cooperation induced renewal condition that is distinctly non poissonian

distribution of first return times in correlated stationary signals we present an analytical expression for the first return time frt probability density function of a stationary correlated signal precisely we start by considering a stationary discrete time ornstein uhlenbeck ou process with exponential decaying correlation function the first return time distribution for this process is derived by adopting a well known formalism typically used in the study of the frt statistics for nonstationary diffusive processes then by a subordination approach we treat the case of a stationary process with power law tail correlation function and diverging correlation time we numerically test our findings obtaining in both cases a good agreement with the analytical results we notice that neither in the standard ou nor in the subordinated case a simple form of waiting time statistics like stretched exponential or similar can be obtained while it is apparent that long time transient may shadow the final asymptotic behavior

synchronization of two interacting populations of oscillators we analyze synchronization between two interacting populations of different phase oscillators for the important case of asymmetric coupling functions we find a much richer dynamical behavior compared to that of symmetrically coupled populations of identical oscillators it includes three types of bistabilities higher order entrainment and the existence of states with unusual stability properties all possible routes to synchronization of the populations are presented and some stability boundaries are obtained analytically the impact of these findings for neuroscience is discussed

renewal modulation and superstatistics in times series we consider two different approaches to which we refer to as renewal and modulation to generate time series with a nonexponential distribution of waiting times we show that different time series with the same waiting time distribution are not necessarily statistically equivalent and might generate different physical properties renewal generates aging and anomalous scaling while modulation yields no significant aging and either ordinary or anomalous diffusion according to the dynamic prescription adopted we show in fact that the physical realization of modulation generates two classes of events the events of the first class are determined by the persistent use of the same exponential time scale for an extended lapse of time and consequently are numerous the events of the second class are identified with the abrupt changes from one to another exponential prescription and consequently are rare the events of the second class although rare determine the scaling of the diffusion process and for this reason we term them as crucial events according to the prescription adopted to produce modulation the distribution density of the time distances between two consecutive crucial events might have or not a diverging second moment in the former case the resulting diffusion process although going through a transition regime very extended in time will eventually become anomalous in conclusion modulation rather than ruling out the action of renewal events produces crucial events hidden by clouds of exponential events thereby setting the challenge for their identification

linear response to perturbation of nonexponential renewal processes we study the linear response of a two state stochastic process obeying the renewal condition by means of a stochastic rate equation equivalent to a master equation with infinite memory we show that the condition of perennial aging makes the response to coherent perturbation vanish in the long time limit

a new measure of network efficiency a b s t r a c t we address the issue of the dynamical origin of scale free link distributions we study a two dimensional lattice of cooperatively interacting units although the units interact only with the four nearest neighbors a sufficiently large cooperation strength generates dynamically a scale free network with the power law index approaching 1 we explain this result by using a new definition of network efficiency determined by the euclidean distance between correlated units according to this definition the link distribution favoring long range connections makes efficiency increase we embed an ad hoc scale free network with power index 1 into a euclidean two dimensional space and show that the network efficiency becomes maximal as approaches 1 we therefore conclude that 1 emerging from the cooperative interaction of units may be a consequence of the principle of network maximal efficiency

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

complex intermittency blurred by noise theory and application to neural dynamics we propose a model for the passage between metastable states of mind dynamics as changing points we use the rapid transition processes simultaneously detectable in eeg signals related to different cortical areas our model consists of a non poissonian intermittent process which signals that the brain is in a condition of complexity upon which a poisson process is superimposed we provide an analytical solution for the waiting time distribution for the model which is well obeyed by physiological data although the role of the poisson process remains unexplained the model is able to reproduce many behaviors reported in literature although they seem contradictory

pseudofractal scale free web we find that scale free random networks are excellently modeled by simple deterministic graphs our graph has a discrete degree distribution degree is the number of connections of a vertex which is characterized by a power law with exponent gamma 1 ln 3 ln 2 properties of this compact structure are surprisingly close to those of growing random scale free networks with gamma in the most interesting region between 2 and 3 we succeed to find exactly and numerically with high precision all main characteristics of the graph in particular we obtain the exact shortest path length distribution for a large network ln n 1 the distribution tends to a gaussian of width approximately sqrt ln n centered at l approximately ln n we show that the eigenvalue spectrum of the adjacency matrix of the graph has a power law tail with exponent 2 gamma

estimating the clustering coefficient in scale free networks on lattices with local spatial correlation structure abstract when we study the architecture of networks of spatially extended systems the nodes in the network are subject to local correlation structures in this case we show that for scale free networks the traditional way to estimate the clustering coefficient may not be meaningful here we explain why and propose an approach that corrects this problem

correlation function and generalized master equation of arbitrary age we study a two state statistical process with a non poisson distribution of sojourn times in accordance with earlier work we find that this process is characterized by aging and we study three different ways to define the correlation function of arbitrary age of the corresponding dichotomous fluctuation these three methods yield exact expressions thus coinciding with the recent result by godreche and luck fj stat phys 104 489 s2001dg actually non poisson statistics yields infinite memory at the probability level thereby breaking any form of markovian approximation including the one adopted herein to find an approximated analytical formula for this reason we check the accuracy of this approximated formula by comparing it with the numerical treatment of the second of the three exact expressions we find that although not exact a simple analytical expression for the correlation function of arbitrary age is very accurate we establish a connection between the correlation function and a generalized master equation of the same age thus this formalism related to models used in glassy materials allows us to illustrate an approach to the statistical treatment of blinking quantum dots bypassing the limitations of the conventional liouville treatment

testing goodness of fit for proportional hazards model with censored observations abstract a numerical omnibus test of fit for the two sample proportional hazards model is proposed for randomly censored observations the test is derived from cox s partial likelihood and does not need a dummy time dependent covariate or any partition of the time axis consistency of the test is established examples are provided for illustration

asymptotically efficient two step estimators of the hazards ratio for follow up studies and survival data summary asymptotically efficient estimators of a common hazard rate ratio for follow up studies and the proportional hazards ratio for survival studies are obtained by a single iteration of the mantelhaenszel estimator appropriate for each setting estimators of their variance are also developed the two step estimator for survival data and its variance estimator are shown by simulation to be minimally biased and the estimator is shown to be efficient relative to the cox partial likelihood estimator in small samples

non parametric model selection for subject specific topological organization of resting state functional connectivity abstract in recent years graph theory has been successfully applied to study functional and anatomical connectivity networks in the human brain most of these networks have shown small world topological characteristics high efficiency in long distance communication between nodes combined with highly interconnected local clusters of nodes moreover functional studies performed at high resolutions have presented convincing evidence that resting state functional connectivity networks exhibits exponentially truncated scale free behavior such evidence however was mostly presented qualitatively in terms of linear regressions of the degree distributions on log log plots even when quantitative measures were given these were usually limited to the r 2 correlation coefficient however the r 2 statistic is not an optimal estimator of explained variance when dealing with truncated power law models recent developments in statistics have introduced new non parametric approaches based on the kolmogorov smirnov test for the problem of model selection in this work we have built on this idea to statistically tackle the issue of model selection for the degree distribution of functional connectivity at rest the analysis performed at voxel level and in a subject specific fashion confirmed the superiority of a truncated power law model showing high consistency across subjects moreover the most highly connected voxels were found to be consistently part of the default mode network our results provide statistically sound support to the evidence previously presented in literature for a truncated power law model of resting state functional connectivity

a new deterministic complex network model with hierarchical structure abstract we introduce a new simple pseudo tree like network model deterministic complex network dcn the proposed dcn model may simulate the hierarchical structure nature of real networks appropriately and have the unique property of skipping the levels which is ubiquitous in social networks our results indicate that the dcn model has a rather small average path length and large clustering coefficient leading to the small world effect strikingly our dcn model obeys a discrete power law degree distribution p k k with exponent approaching 1 0 we also discover that the relationship between the clustering coefficient and degree follows the scaling law c k k 1 which quantitatively determines the dcn s hierarchical structure

coupled three state oscillators abstract we investigate globally coupled stochastic three state oscillators which we consider as general models of stochastic excitable systems we compare two situations in the first case the transitions between the three states of each unit 1 2 3 1 are determined by poissonian waiting time distributions in the second case only transition 1 2 is poissonian whereas the others are deterministic with a fixed delay when coupled the second system shows coherent oscillations whereas the first remains in a stable stationary state we show that the coherent oscillations are due to a hopf bifurcation in the dynamics of the occupation probabilities of the discrete states and discuss the bifurcation diagram