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

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

weighted scale free networks with variable power law exponents abstract we present a weighted scale free network model in which the power law exponents can be controlled by the model parameters the network is generated through the weight driven preferential attachment of new nodes to existing nodes and the growth of the weights of existing links the simplicity of the model enables us to derive analytically the various statistical properties such as the distributions of degree strength and weight the degree strength and degree weight relationship and the dependencies of these power law exponents on the model parameters finally we demonstrate that networks of words coauthorship of researchers and collaboration of actor actresses are quantitatively well described by this model

robust noise region based active contour model via local similarity factor for image segmentation abstract image segmentation using a region based active contour model could present difficulties when its noise distribution is unknown to overcome this problem this paper proposes a novel region based model for the segmentation of objects or structures in images by introducing a local similarity factor which relies on the local spatial distance within a local window and local intensity difference to improve the segmentation results by using this local similarity factor the proposed method can accurately extract the object boundary while guaranteeing certain noise robustness furthermore the proposed algorithm completely avoids the pre processing steps typical of region based contour model segmentation resulting in a higher preservation of image details experiments performed on synthetic images and real word images demonstrate that the proposed algorithm as compared with the state of art algorithms is more efficient and robust to higher noise level manifestations in the images

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

return times of random walk on generalized random graphs random walks are used for modeling various dynamics in for example physical biological and social contexts furthermore their characteristics provide us with useful information on the phase transition and critical phenomena of even broader classes of related stochastic models abundant results are obtained for random walk on simple graphs such as the regular lattices and the cayley trees however random walks and related processes on more complex networks which are often more relevant in the real world are still open issues possibly yielding different characteristics in this paper we investigate the return times of random walks on random graphs with arbitrary vertex degree distributions we analytically derive the distributions of the return times the results are applied to some types of networks and compared with numerical data

can we neglect the multi layer structure of functional networks functional networks i e networks representing dynamic relationships between the components of a complex system have been instrumental for our understanding of among others the human brain due to limited data availability the multi layer nature of numerous functional networks has hitherto been neglected and nodes are endowed with a single type of links even when multiple relationships coexist at different physical levels a relevant problem is the assessment of the benefits yielded by studying a multi layer functional network against the simplicity guaranteed by the reconstruction and use of the corresponding single layer projection here i tackle this issue by using as a test case the functional network representing the dynamics of delay propagation through european airports neglecting the multi layer structure of a functional network has dramatic consequences on our understanding of the underlying system a fact to be taken into account when a projection is the only available information

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

branching annihilating random walk on random regular graphs the branching annihilating random walk is studied on a random graph whose sites have a uniform number of neighbors z the monte carlo simulations in agreement with the generalized mean field analysis indicate that the concentration decreases linearly with the branching rate for z 4 while the coefficient of the linear term becomes zero if z 3 these properties are described by a modified mean field theory taking explicitly into consideration the probability of mutual annihilation of the parent and its offspring particles using the returning features of a single walker on the same graph

dynamic analysis of traffic time series at different temporal scales a complex networks approach abstract the analysis of dynamics in traffic flow is an important step to achieve advanced traffic management and control in intelligent transportation system its complexity and periodicity are definitely two fundamental properties in traffic dynamics in this study we first measure the complexity of traffic flow data by lempel ziv algorithm at different temporal scales and the data are collected from loop detectors on freeway second to obtain more insight into the complexity and periodicity in traffic time series we then construct complex networks from traffic time series by considering each day as a cycle and each cycle as a single node the optimal threshold value of complex networks is estimated by the distribution of density and its derivative in addition the complex networks are subsequently analyzed in terms of some statistical properties such as average path length clustering coefficient density average degree and betweenness finally take 2 min aggregation data as example we use the correlation coefficient matrix adjacent matrix and closeness to exploit the periodicity of weekdays and weekends in traffic flow data the findings in this paper indicate that complex network is a practical tool for exploring dynamics in traffic time series

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

phase diagram for the eigen quasispecies theory with a truncated fitness landscape using methods of statistical physics we present rigorous theoretical calculations of eigen s quasispecies theory with the truncated fitness landscape which dramatically limits the available sequence space of information carriers as the mutation rate is increased from small values to large values one can observe three phases the first i selective also known as ferromagnetic phase the second ii intermediate phase with some residual order and the third iii completely randomized also known as paramagnetic phase we calculate the phase diagram for these phases and the concentration of information carriers in the master sequence also known as peak configuration x 0 and other classes of information carriers as the phase point moves across the boundary between phase i and phase ii x 0 changes continuously as the phase point moves across the boundary between phase ii and phase iii x 0 has a large change our results are applicable for the general case of a fitness landscape

geometric active contours without re initialization for image segmentation a geometric active contour model without re initialization that can be used for grey and color image segmentation is presented in this paper it combines directional information about edge location based on cumani operator as a part of driving force with the improved geodesic active contours containing bays error based statistical region information moreover an extra term that penalizes the deviation of the level set function from a signed distance function is also included in the model thus the costly re initialization procedure can be completely eliminated and all these measures are integrated in a unified frame experimental results on real grey and color images have shown that our model can precisely extract contours of images and its performance is much better and faster than the geodesic aided c v gacv model

betweenness centrality correlation in social networks scale free sf networks exhibiting a power law degree distribution can be grouped into the assortative dissortative and neutral networks according to the behavior of the degree degree correlation coefficient here we investigate the betweenness centrality bc correlation for each type of sf networks while the bc bc correlation coefficients behave similarly to the degree degree correlation coefficients for the dissortative and neutral networks the bc correlation is nontrivial for the assortative ones found mainly in social networks the mean bc of neighbors of a vertex with bc g i is almost independent of g i implying that each person is surrounded by almost the same influential environments of people no matter how influential the person may be

a multiphase level set framework for image segmentation using the mumford and shah model we propose a new multiphase level set framework for image segmentation using the mumford and shah model for piecewise constant and piecewise smooth optimal approximations the proposed method is also a generalization of an active contour model without edges based 2 phase segmentation developed by the authors earlier in t chan and l vese 1999 in scale space 99 m nilsen et al eds lncs vol 1682 pp 141 151 and t chan and l vese 2001 ieee ip 10 2 266 277 the multiphase level set formulation is new and of interest on its own by construction it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies including triple junctionss in the piecewise smooth case only two level set functions formally suffice to represent any partition based on the four color theorem finally we validate the proposed models by numerical results for signal and image denoising and segmentation implemented using the osher and sethian level set method

evolution equation of phenotype distribution general formulation and application to error catastrophe an equation describing the evolution of phenotypic distribution is derived using methods developed in statistical physics the equation is solved by using the singular perturbation method and assuming that the number of bases in the genetic sequence is large applying the equation to the mutation selection model by eigen provides the critical mutation rate for the error catastrophe phenotypic fluctuation of clones individuals sharing the same gene is introduced into this evolution equation with this formalism it is found that the critical mutation rate is sometimes increased by the phenotypic fluctuations i e noise can enhance robustness of a fitted state to mutation our formalism is systematic and general while approximations to derive more tractable evolution equations are also discussed

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

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

what is the real size of a sampled network the case of the internet internet mapping projects generally consist in sampling the network from a limited set of sources by usingtraceroute probes this methodology akin to the merging of spanning trees from the different sources to a set of destinations leads necessarily to a partial incomplete map of the internet accordingly determination of internet topology characteristics from such sampled maps is in part a problem of statistical inference our contribution begins with the observation that the inference of many of the most basic topological quantities including network size and degree characteristics fromtraceroute measurements is in fact a version of the so called species problem in statistics this obse rvation has important implications since species problems are often quite challenging we focus here on the most fundamental example of atraceroute internet species the number of nodes in a network specifica lly

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

solvable biological evolution models with general fitness functions and multiple mutations in parallel mutation selection scheme in a recent paper phys rev e 69 046121 2004 we used the suzuki trottere formalism to study a quasispecies biological evolution model in a parallel mutation selection scheme with a single peak fitness function and a point mutation in the present paper we extend such a study to evolution models with more general fitness functions or multiple mutations in the parallel mutation selection scheme we give some analytical equations to define the error thresholds for some general cases of mean field like or symmetric mutation schemes and fitness functions we derive some equations for the dynamics in the case of a point mutation and polynomial fitness functions we derive exact dynamics for two point mutations asymmetric mutations and the four value spin model with a single peak fitness function the same method is applied for the model with a royal road fitness function we derive the steady state distribution for the single peak fitness function

scale invariance in road networks we study the topological and geographic structure of the national road networks of the united states england and denmark by transforming these networks into their dual representation where roads are vertices and an edge connects two vertices if the corresponding roads ever intersect we show that they exhibit both topological and geographic scale invariance that is we show that for sufficiently large geographic areas the dual degree distribution follows a power law with exponent 2 2 or alpha or 2 4 and that journeys regardless of their length have a largely identical structure to explain these properties we introduce and analyze a simple fractal model of road placement that reproduces the observed structure and suggests a testable connection between the scaling exponent and the fractal dimensions governing the placement of roads and intersections

epidemic incidence in correlated complex networks a few years ago watts and strogatz 1 introduced a model able to produce networks with properties of both regu lar lattices and random graphs with small diameter their model soon led to a burst of activity in the field 2 3 further spurred by barabasi and co workers who found that many seemingly diverse systems share several topological proper ties such as a power law behavior in their connectivity dis tributions when represented as networks 4 these complex networks are formed by a set of many elements or nodes that are linked together through edges or links if they in teract directly empirical evidence supports that in notable networks such as metabolic or communication webs the probability p k that any node has k links to other nodes is distributed accordingly to a power law p k k 2g 5 7

quasispecies theory for multiple peak fitness landscapes we use a path integral representation to solve the eigen and crow kimura molecular evolution models for the case of multiple fitness peaks with arbitrary fitness and degradation functions in the general case we find that the solution to these molecular evolution models can be written as the optimum of a fitness function with constraints enforced by lagrange multipliers and with a term accounting for the entropy of the spreading population in sequence space the results for the eigen model are applied to consider virus or cancer proliferation under the control of drugs or the immune system

solvable biological evolution model with a parallel mutation selection scheme based on the connection between a quantum spin model and an asexual biological evolution model with a single peak fitness function in parallel mutation selection scheme we solve exactly both static and dynamics of the evolution model we find that relaxation in such a parallel scheme is faster than that in a connected scheme of eigen model our method can also be extended to other fitness functions

empirical analysis of the worldwide maritime transportation network abstract in this paper we present an empirical study of the worldwide maritime transportation network wmn in which the nodes are ports and links are container liners connecting the ports using the different representations of network topology the spaces l and p we study the statistical properties of wmn including degree distribution degree correlations weight distribution strength distribution average shortest path length line length distribution and centrality measures we find that wmn is a small world network with power law behavior important nodes are identified based on different centrality measures through analyzing weighted clustering coefficient and weighted average nearest neighbors degree we reveal the hierarchy structure and rich club phenomenon in the 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

scale free networks via attaching to random neighbors abstract preferential attachment is considered one of the key factors in the formation of scale free networks however complete random attachment without a preferential mechanism can also generate scale free networks in nature such as protein interaction networks in cells this article presents a new scale free network model that applies the following general mechanisms i networks expand continuously by the addition of new vertices and ii new vertices attach to random neighbors of random vertices that are already well connected the proposed model does not require global based preferential strategies and utilizes only the random attachment method theoretical analysis and numerical simulation results denote that the proposed model has steady scale free network characteristics and random attachment without a preferential mechanism may generate scale free networks

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

characterizing the topological and controllability features of u s power transmission networks understanding the controllability of complex networks continues to gain traction across disciplinary fields including the exploration of infrastructure systems such as power grids through topological principles this paper investigates the controllability features of an ensemble of 58 u s city level power transmission networks in seven u s states to perform structural controllability analyses the topological characteristics of the ensemble of networks are first quantified including degree shortest path length clustering coefficient meshedness and betweenness centrality as well as the uncertainty associated with these and related properties then the paper focuses on the controllability features of complex networks so as to detect the minimal sets of driver nodes to possibly control the networks given system linearity assumptions accordingly a node is critical intermittent or redundant if it acts as a driver node in all some or none of the potentially controllable system configurations moreover this paper constructs a new methodology to quantify the probability of being a driver node among the intermittent nodes and reveals the controllability importance of system components results show that a small proportion of driver nodes can provide the conditions for controlling the slow dynamics of entire power transmission networks from a topological perspective despite variations in network sizes and configurations this paper also reveals that the driver nodes tend to avoid high degree nodes and high triangulation sub graph nodes as well as high betweenness centrality nodes the identification of topological differences for different categories of nodes critical intermittent or redundant could help researchers and utilities understand the conditions for future functional controllability of power networks while improving their reliability and resilience as well as facilitating their transition into smart grid systems

rapid and brief communication gacv geodesic aided c v method a novel algorithm for image segmentation is proposed the proposed method incorporates geodesic curves and c v method to raise active contours performance on image segmentation moreover we extend our method to color images by practical experiments it is verified that our model obtains better results than original methods especially with respect to images within holes complex background weak edges and noise

cooperation in the noisy case prisoner s dilemma game on two types of regular random graphs we have studied an evolutionary prisoner s dilemma game with players located on two types of random regular graphs with a degree of 4 the analysis is focused on the effects of payoffs and noise temperature on the maintenance of cooperation when varying the noise level and or the highest payoff the system exhibits a second order phase transition from a mixed state of cooperators and defectors to an absorbing state where only defectors remain alive for the random regular graph and bethe lattice the behavior of the system is similar to those found previously on the square lattice with nearest neighbor interactions although the measure of cooperation is enhanced by the absence of loops in the connectivity structure for low noise the optimal connectivity structure is built up from randomly connected triangles

rise and fall of historic tram networks logistic approximation and discontinuous events abstract a logistic approximation was used to describe in terms of total length l and population h variables the growth and decay of historic transportation systems three successive stages separated for sharp discontinuities were detected for several european tramway and metro systems corresponding to a fast initial growth followed by an intermediate step of slow growth and a final stage of rapid decay a common generalized behaviour was obtained in the l h vs h variations relative to critical values of l and h parameters defined from the maximum in the l h ratio

statistical mechanics of eigen s evolution model the correspondence between eigen s model of macromolecular evolution and the equilibrium statistical mechanics of an inhomogeneous ising system is developed the free energy landscape of random ising systems with the hopfield hamiltonian as a special example is applied to the replication rate coefficient landscape the coupling constants are scaled with 1 l since the maxima of any landscape must not increase with the length of the macromolecules the calculated error threshold relation then agrees with eigen s expression which was derived in a different way it gives an explicit expression for the superiority parameter in terms of the parameters of the landscape the dynamics of selection and evolution is discussed

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

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

error threshold in simple landscapes we consider the quasispecies description of a population evolving in both the master sequence landscape where a single sequence is evolutionarily preferred over all others and the rem landscape where the fitness of different sequences is an independent identically distributed random variable we show that in both cases the error threshold is analogous to a first order thermodynamical transition where the overlap between the average genotype and the optimal one drops discontinuously to zero

epidemic dynamics behavior in some bus transport networks abstract we abstract bus transport networks btns to complex networks using the space p approach first we select three actual btns in three major cities in china namely beijing shanghai and hangzhou using the sis model we simulate and study the epidemic spreading in the three btns we obtain the density of infected vertices varying with time and the stationary density of infected vertices varying with infection rate second we simulate and study the epidemic spreading in a recently introduced btn evolution model the network properties of which correspond well with those of actual btns third we use mean field theory to analyze the epidemic dynamics behavior of the btn evolution model and obtain the theoretical epidemic threshold of this model the theoretical value agrees well with the simulation results based on the work in this paper we provide the following possible forecasts for epidemic dynamics in actual btns an actual btn should have a finite positive epidemic threshold if the effective infection rate is above this threshold the epidemic spread in the network and the density of infected vertices finally stabilizes in a balanced state below this threshold the number of infected vertices decays exponentially fast and the epidemic cannot spread on a large scale

large scale topological and dynamical properties of the internet we study the large scale topological and dynamical properties of real internet maps at the autonomous system level collected in a 3 yr time interval we find that the connectivity structure of the internet presents statistical distributions settled in a well defined stationary state the large scale properties are characterized by a scale free topology consistent with previous observations correlation functions and clustering coefficients exhibit a remarkable structure due to the underlying hierarchical organization of the internet the study of the internet time evolution shows a growth dynamics with aging features typical of recently proposed growing network models we compare the properties of growing network models with the present real internet data analysis

geographical networks evolving with an optimal policy in this article we propose a growing network model based on an optimal policy involving both topological and geographical measures in this model at each time step a new node having randomly assigned coordinates in a 1 1 square is added and connected to a previously existing node i which minimizes the quantity r 2 k where ri is the geographical distance ki the degree and a free parameter the degree distribution obeys a power law form when 1 and an exponential

a global minimization hybrid active contour model with applications to oil spill images active contour model is popularly and widely used in the field of image segmentation which is based on superior theoretical properties and efficient numerical methods nevertheless one of the prominent disadvantages of this kind of model is the existence of local minima in its functional energy in this paper we propose a novel global minimization hybrid active contour model this model effectively integrates the edge information the local region information and the global region information of the image which is relatively sufficient to extract the object boundaries furthermore we introduce an efficient and fast numerical approach to globally minimize the proposed model which is through a dual formulation of the minimization problem and easy to implement the proposed model is robust enough to the initial condition and does not need to initialize the contour in a distance function and re initialize it periodically during the evolution process specially we applied the proposed model to segment oil spill images in which there usually exist the noise blurry boundaries and intensity inhomogeneity compared with the state of the art models experiment results demonstrate the performance and effectiveness of the proposed model with applications to synthetical and real images especially for oil spill images

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

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

spin coherent state representation of the crow kimura and eigen models of quasispecies theory we present a spin coherent state representation of the crow kimura and eigen models of biological evolution we deal with quasispecies models where the fitness is a function of hamming distances from one or more reference sequences in the limit of large sequence length n we find exact expressions for the mean fitness and magnetization of the asymptotic quasispecies distribution in symmetric fitness landscapes the results are obtained by constructing a path integral for the propagator on the coset su 2 u 1 and taking the classical limit the classical limit gives a hamiltonian function on a circle for one reference sequence and on the product of 2m 1 circles for m reference sequences we apply our representation to study the schuster swetina phenomena where a wide lower peak is selected over a narrow higher peak the quadratic landscape with two reference sequences is also analyzed specifically and we present the phase diagram on the mutation fitness parameter phase space furthermore we use our method to investigate more biologically relevant system a model of escape from adaptive conflict through gene duplication and find three different phases for the asymptotic population distribution

universal scaling of distances in complex networks universal scaling of distances between vertices of erd ifmmode mbox h o else h o fi s r enyi random graphs scale free barab asi albert models science collaboration networks biological networks internet autonomous systems and public transport networks are observed a mean distance between two nodes of degrees k i and k j equals to l ij a ensuremath b phantom rule 0 2em 0ex mathrm log k i k j the scaling is valid over several decades a simple theory for the appearance of this scaling is presented parameters a and b depend on the mean value of a node degree k nn calculated for the nearest neighbors and on network clustering coefficients

harmony in the small world the small world phenomenon popularly known as six degrees of separation has been mathematically formalized by watts and strogatz in a study of the topological properties of a network small world networks are defined in terms of two quantities they have a high clustering coefficient c like regular lattices and a short characteristic path length l typical of random networks physical distances are of fundamental importance in applications to real cases nevertheless this basic ingredient is missing in the original formulation here we introduce a new concept the connectivity length d that gives harmony to the whole theory d can be evaluated on a global and on a local scale and plays in turn the role of l and 1 c moreover it can be computed for any metrical network and not only for the topological cases d has a precise meaning in terms of information propagation and describes in a unified way both the structural and the dynamical aspects of a network small worlds are defined by a small global and local d i e by a high efficiency in propagating information both on a local and global scale the neural system of the nematode c elegans the collaboration graph of film actors and the oldest us subway system can now be studied also as metrical networks and are shown to be small worlds

structural transitions in scale free networks real growing networks such as the world wide web or personal connection based networks are characterized by a high degree of clustering in addition to the small world property and the absence of a characteristic scale appropriate modifications of the barabasi albert preferential attachment network growth capture all these aspects we present a scaling theory to describe the behavior of the generalized models and the mean field rate equation for clustering this is solved for a specific case with the result c k approximately 1 k for the clustering of a node of degree k this mean field exponent agrees with simulations and reproduces the clustering of many real networks

research on the search ability of brownian particles on networks with an adaptive mechanism abstract in this paper we focus on the search ability of brownian particles with an adaptive mechanism in the adaptive mechanism nodes are allowed to be able to change their own accepting probability according to their congestion states two searching traffic models the static one in which nodes have fixed accepting probability to the incoming particles and the adaptive one in which nodes have adaptive accepting probability to the incoming particles are presented for testing the adaptive mechanism instead of number of hops we use the traveling time which includes not only the number of hops for a particle to jump from the source node to the destination but also the time that the particle stays in the queues of nodes to evaluate the search ability of brownian particles we apply two models to different networks the experiment results show that the adaptive mechanism can decrease the network congestion and the traveling time of the first arriving particle furthermore we investigate the influence of network topologies on the congestion of networks by addressing several main properties degree distribution average path length and clustering coefficient we show the reason why random topologies are more able to deal with congested traffic states than others we also propose an absorption strategy to deal with the additional brownian particles in networks the experiment results on barabasi albert ba scale free networks show that the absorption strategy can increase the probability of a successful search and decrease the average per node particles overhead for our models

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

negative edges and soft thresholding in complex network analysis of resting state functional connectivity data complex network analyses of functional connectivity have consistently revealed non random modular small world scale free like behavior of hard thresholded networks constructed from the right tail of the similarity histogram in the present study we determined network properties resulting from edges constrained to specific ranges across the full correlation histogram in particular the left negative most tail and their dependence on the confound signal removal strategy employed in the absence of global signal correction left tail networks comprised predominantly long range connections associated with weak correlations and were characterized by substantially reduced modularity and clustering negative assortativity and 1 deconvolution of specific confound signals white matter csf and motion resulted in the most robust within subject reproducibility of global network parameters iccs 0 5 global signal removal altered the network topology in the left tail with the clustering coefficient and assortativity converging to zero networks constructed from the absolute value of the correlation coefficient were thus compromised following global signal removal since the different right tail and left tail topologies were mixed these findings informed the construction of soft thresholded networks replacing the hard thresholding or binarization operation with a continuous mapping of all correlation values to edge weights suppressing rather than removing weaker connections and avoiding issues related to network fragmentation a power law adjacency function with 12 yielded modular networks whose parameters agreed well with corresponding hard thresholded values that were reproducible in repeated sessions across many months and evidenced small world like and scale free like properties

dynamics of the eigen and the crow kimura models for molecular evolution we introduce an alternative way to study molecular evolution within well established hamilton jacobi formalism showing that for a broad class of fitness landscapes it is possible to derive dynamics analytically within the 1n accuracy where n is the genome length for a smooth and monotonic fitness function this approach gives two dynamical phases smooth dynamics and discontinuous dynamics the latter phase arises naturally with no explicite singular fitness function counterintuitively the hamilton jacobi method yields straightforward analytical results for the models that utilize fitness as a function of hamming distance from a reference genome sequence we also show the way in which this method gives dynamical phase structure for multipeak fitness

topology and correlations in structured scale free networks we study a recently introduced class of scale free networks showing a high clustering coefficient and nontrivial connectivity correlations we find that the connectivity probability distribution strongly depends on the fine details of the model we solve exactly the case of low average connectivity providing also exact expressions for the clustering and degree correlation functions the model also exhibits a lack of small world properties in the whole parameter range we discuss the physical properties of these networks in the light of the present detailed analysis

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

eigen model as a quantum spin chain exact dynamics we map the eigen model of biological evolution naturwissenschaften 58 465 1971 into a quantum spin model with non hermitian hamiltonian based on such a connection we derive exact relaxation periods for the eigen model to approach static energy landscape from various initial conditions we also study a simple case of dynamic fitness function

scaling of distances in correlated complex networks abstract the influence of node node degree correlations on distances in complex networks has been studied we have found that even the presence of strong correlations in complex networks does not break a universal scaling of distances between vertices of such networks as science collaboration networks biological networks internet autonomous systems and public transport systems a mean distance between two nodes of degrees k i and k j in such networks equals to l ij a b log k i k j for a fixed value of the product k i k j the scaling is valid over several decades parameters a and b depend on the mean value of a node degree k nn calculated for the nearest neighbors we have found that extending our simple theory basing on a random branching tree by the first order node degree correlations improves theoretical predictions for parameters a and b in assortative networks while it fails in disassortative ones

diploid biological evolution models with general smooth fitness landscapes and recombination using a hamilton jacobi equation approach we obtain analytic equations for steady state population distributions and mean fitness functions for crow kimura and eigen type diploid biological evolution models with general smooth hypergeometric fitness landscapes our numerical solutions of diploid biological evolution models confirm the analytic equations obtained we also study the parallel diploid model for the simple case of recombination and calculate the variance of distribution which is consistent with numerical results

characterizing traffic time series based on complex network theory abstract a complex network is a powerful tool to research complex systems traffic flow being one of the most complex systems in this paper we use complex network theory to study traffic time series which provide a new insight into traffic flow analysis firstly the phase space which describes the evolution of the behavior of a nonlinear system is reconstructed using the delay embedding theorem secondly in order to convert the new time series into a complex network the critical threshold is estimated by the characteristics of a complex network which include degree distribution cumulative degree distribution and density and clustering coefficients we find that the degree distribution of associated complex network can be fitted with a gaussian function and the cumulative degree distribution can be fitted with an exponential function density and clustering coefficients are then researched to reflect the change of connections between nodes in complex network and the results are in accordance with the observation of the plot of an adjacent matrix consequently based on complex network analysis the proper range of the critical threshold is determined finally to mine the nodes with the closest relations in a complex network the modularity is calculated with the increase of critical threshold and the community structure is detected according to the optimal modularity the work in our paper provides a new way to understand the dynamics of traffic time series

biological evolution in a multidimensional fitness landscape we considered a multiblock molecular model of biological evolution in which fitness is a function of the mean types of alleles located at different parts blocks of the genome we formulated an infinite population model with selection and mutation and calculated the mean fitness for the case of recombination we formulated a model with a multidimensional fitness landscape the dimension of the space is equal to the number of blocks and derived a theorem about the dynamics of initially narrow distribution we also considered the case of lethal mutations we also formulated the finite population version of the model in the case of lethal mutations our models derived for the virus evolution are interesting also for the statistical mechanics and the hamilton jacobi equation as well

a new method for the solution of models of biological evolution derivation of exact steady state distributions we investigate well known models of biological evolution and address the open problem of how construct a correct continuous analog of mutations in discrete sequence space we deal with models where the fitness is a function of a hamming distance from the reference sequence the mutation selection master equation in the discrete sequence space is replaced by a hamilton jacobi equation for the logarithm of relative frequencies of different sequences the steady state distribution mean fitness and the variance of fitness are derived all our results are asymptotic in the large genome limit a variety of important biological and biochemical models can be solved by this new approach

rock scissors paper game on regular small world networks the spatial rock scissors paper game or cyclic lotka volterra system is extended to study how the spatiotemporal patterns are affected by the rewired host lattice providing uniform number of neighbours degree at each site on the square lattice this system exhibits a self organizing pattern with equal concentration of the competing strategies species if the quenched background is constructed by substituting random links for the nearest neighbour bonds of a square lattice then a limit cycle occurs when the portion of random links exceeds a threshold value this transition can also be observed if the standard link is replaced temporarily by a random one with a probability p at each step of iteration above a second threshold value of p the amplitude of global oscillation increases with time and finally the system reaches one of the homogeneous absorbing states in this case the results of monte carlo simulations are compared with the predictions of the dynamical cluster technique evaluating all the configuration probabilities on one two four and six site clusters

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved

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