scaling properties of random walks on small world networks using both numerical simulations and scaling arguments we study the behavior of a random walker on a one dimensional small world network for the properties we study we find that the random walk obeys a characteristic scaling form these properties include the average number of distinct sites visited by the random walker the mean square displacement of the walker and the distribution of first return times the scaling form has three characteristic time regimes at short times the walker does not see the small world shortcuts and effectively probes an ordinary euclidean network in d dimensions at intermediate times the properties of the walker shows scaling behavior characteristic of an infinite small world network finally at long times the finite size of the network becomes important and many of the properties of the walker saturate we propose general analytical forms for the scaling properties in all three regimes and show that these analytical forms are consistent with our numerical simulations

algebraic quantization of the closed bosonic string the gauge invariant observables of the closed bosonic string are quantized in four space time dimensions by constructing their quantum algebra in a manifestly covariant approach respecting all symmetries of the classical observables the quantum algebra is the kernel of a derivation on the universal enveloping algebra of an infinite dimensional lie algebra the search for hilbert space representations of this algebra is separated from its construction and postponed

scale free property of local world networks and their community structures abstract the scale free property and community structures of complex networks formed by local events have been studied theoretically numerically and empirically we showed analytically and numerically that the degree distribution function p k of the local world evolving network exhibits a crossover from an exponential to power law form by increasing the local world size m for m much larger than the crossover local world size m co the distribution function p k has a power law form for any degree k 1 below m co however p k obeys a power law for 1 k k co and decays exponentially for k k co the crossover size m co and the crossover degree k co have been also elucidated in addition we constructed the drug prescription network dpn as a real local world network in which the local world subsets are definitely specified to reveal how the local world nature affects properties of real world networks we found that the community structure of the dpn strongly correlates with the local worlds

the invariant charges of the nambu goto string and canonical quantization it is shown that the algebra of diffeomorphism invariant charges of the nambu goto string cannot be quantized in the framework of canonical quantization the argument is shown to be independent of the dimension of the underlying minkowski space

scattering states of plektons particles with braid group statistics in 2 1 dimensional quantum field theory a haag ruelle scattering theory for particles with braid group statistics is developed and the arising structure of the hilbert space of multiparticle states is analyzed

analysis of weighted networks the connections in many networks are not merely binary entities either present or not but have associated weights that record their strengths relative to one another recent studies of networks have by and large steered clear of such weighted networks which are often perceived as being harder to analyze than their unweighted counterparts here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph allowing us to apply standard techniques for unweighted graphs to weighted ones as well we give a number of examples of the method including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum flow minimum cut theorem

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

uncovering the detailed structure of the algebra formed by the invariant charges of closed bosonic strings moving in 1 2 dimensional minkowski space for the nambu goto theory of closed bosonic strings moving in three space time dimensions generating relations of degree 6 for the poisson algebra of the infinitesimal generators of observable symmetry transformations have been computed these computations result in a deeper insight into the structure of the symmetry algebra in addition a parametrization of the quantum corrections for the generating relations of degree 3 is given

weighted self similar networks under preferential attachment abstract we introduce an abstract evolutionary formalism that generates weighted networks whose growth under stochastic preferential attachment triggers unrestricted weight rearrangements in existing links the class of resulting algorithms for different parameter values includes the barabasi albert and barrat barthelemy vespignani models as special cases we solve the recursions that describe the average growth to derive exact solutions for the expected degree and strength distribution the individual strength and weight development and the joint distribution of neighboring degrees we find that the network exhibits a particular form of self similarity namely every sufficiently interconnected node has on average the same constitution of small degree neighbors as any other node of large degree finally we suggest potential applications in several fields of interest

a schwarz alternating procedure using spline collocation methods a collocation method is described which obtains an approximate solution to poisson s equation u f on an l shaped region the l shaped region is viewed as the union of two overlapping rectangles the schwarz alternating procedure may be employed to reduce the problem to one in which collocation techniques are used on each rectangle the convergence of the alternating scheme depends upon a discrete maximum principle for collocation methods several sample problems are presented to illustrate the order of convergence of this method and to compare it with several existing numerical methods for the l shaped region

community detection in complex networks using extremal optimization we propose a method to find the community structure in complex networks based on an extremal optimization of the value of modularity the method outperforms the optimal modularity found by the existing algorithms in the literature giving a better understanding of the community structure we present the results of the algorithm for computer simulated and real networks and compare them with other approaches the efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks

constrained markovian dynamics of random graphs we introduce a statistical mechanics formalism for the study of constrained graph evolution as a markovian stochastic process in analogy with that available for spin systems deriving its basic properties and highlighting the role of the mobility the number of allowed moves for any given graph as an application of the general theory we analyze the properties of degree preserving markov chains based on elementary edge switchings we give an exact yet simple formula for the mobility in terms of the graph s adjacency matrix and its spectrum this formula allows us to define acceptance probabilities for edge switchings such that the markov chains become controlled glauber type detailed balance processes designed to evolve to any required invariant measure representing the asymptotic frequencies with which the allowed graphs are visited during the process as a corollary we also derive a condition in terms of simple degree statistics sufficient to guarantee that in the limit where the number of nodes diverges even for state independent acceptance probabilities of proposed moves the invariant measure of the process will be uniform we test our theory on synthetic graphs and on realistic larger graphs as studied in cellular biology showing explicitly that for instances where the simple edge swap dynamics fails to converge to the uniform measure a suitably modified markov chain instead generates the correct phase space sampling

string localized quantum fields and modular localization we study free covariant quantum bose fields that are associated with irreducible representations of the poincare group and localized in semi infinite strings extending to spacelike infinity among these are fields that generate the irreducible representations of mass zero and infinite spin that are known to be incompatible with point like localized fields for the massive representations and the massless representations of finite helicity all string localized free fields can be written as an integral along the string of point localized tensor or spinor fields as a special case we discuss the string localized vector fields associated with the point like electromagnetic field and their relation to the axial gauge condition in the usual setting

random matrix analysis of localization properties of gene coexpression network we analyze gene coexpression network under the random matrix theory framework the nearest neighbor spacing distribution of the adjacency matrix of this network follows gaussian orthogonal statistics of random matrix theory rmt spectral rigidity test follows random matrix prediction for a certain range and deviates afterwards eigenvector analysis of the network using inverse participation ratio suggests that the statistics of bulk of the eigenvalues of network is consistent with those of the real symmetric random matrix whereas few eigenvalues are localized based on these ipr calculations we can divide eigenvalues in three sets a the nondegenerate part that follows rmt b the nondegenerate part at both ends and at intermediate eigenvalues which deviates from rmt and expected to contain information about important nodes in the network c the degenerate part with zero eigenvalue which fluctuates around rmt predicted value we identify nodes corresponding to the dominant modes of the corresponding eigenvectors and analyze their structural properties

a jost schroer theorem for string fields it is shown that the truncated wightman functions of three or more string localized fields vanish if they are solutions of a klein gordon equation in each variable as an application it is shown that a string field is a free field if its two point functions are those of a free field another application to perturbation theory is pointed out

the effective theory of strings we show that the nambu goto string and its higher dimensional generalizations can be quantized in the sense of an effective theory in any dimension of the target space the crucial point is to consider expansions around classical string configurations we are using tools from perturbative algebraic quantum field theory quantum field theory on curved spacetimes and the batalin vilkovisky formalism our model has some similarities with the luscher weisz string but we allow for arbitrary classical background string configurations and keep the diffeomorphism invariance

string and brane localized causal fields in a strongly nonlocal model we study a weakly local but nonlocal model in spacetime dimension d 2 and prove that it is maximally nonlocal in a certain specific quantitative sense nevertheless depending on the number of dimensions d it has string localized or brane localized operators which commute at spatial distances in two spacetime dimensions the model even comprises a covariant and local subnet of operators localized in bounded subsets of minkowski space which has a nontrivial scattering matrix the model thus exemplifies the algebraic construction of local operators from algebras associated with nonlocal fields

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

a class of improved algorithms for detecting communities in complex networks abstract detecting communities in complex networks is of considerable importance for understanding both the structure and function of the networks here we propose a class of improved algorithms for community detection by combining the betweenness algorithm of girvan and newman with the edge weight defined by the edge clustering coefficient the improved algorithms are tested on some artificial and real world networks and the results show that they can detect communities of networks more effectively in both unweighted and weighted cases in addition the technique for improving the betweenness algorithm in this paper thanks to its compatibility can directly be applied to various detection algorithms

finding local community structure in networks although the inference of global community structure in networks has recently become a topic of great interest in the physics community all such algorithms require that the graph be completely known here we define both a measure of local community structure and an algorithm that infers the hierarchy of communities that enclose a given vertex by exploring the graph one vertex at a time this algorithm runs in time o k2d for general graphs when d is the mean degree and k is the number of vertices to be explored for graphs where exploring a new vertex is time consuming the running time is linear o k we show that on computer generated graphs the average behavior of this technique approximates that of algorithms that require global knowledge as an application we use this algorithm to extract meaningful local clustering information in the large recommender network of an online retailer

maximum principle and convergence analysis for the meshfree point collocation method the discrete laplacian operator is considered in the sense of the meshfree point collocation method which will be called the strong meshfree laplacian operator to define the strong meshfree laplacian operator we use the fast version of the generalized moving least square approximation which can calculate the approximated derivatives of shape functions some types of the locally layered node distribution are defined in this paper and two specific domains are constructed onto which we can distribute locally layered nodes at such nodes the discrete maximum principle can be shown to hold through the representation formula for the strong meshfree laplacian operator the discrete maximum principle together with the reproducing property of the meshfree approximations results in an a priori estimate for the strong meshfree laplacian operator in the nodal solution space furthermore the a priori estimate we have obtained guarantees the existence and the uniqueness of the numerical solution and plays a central role in achieving converged results for the poisson problem with dirichlet boundary conditions in the nodal solution space the order of convergence of the nodal solutions can be raised up to o h2 at the proposed type of nodes in specific domains for generally shaped domains immersed in the previously mentioned domains we can obtain the first order convergence result of o h

construction of quantum field theories with factorizing s matrices the subject of this thesis is a novel construction method for interacting relativistic quantum field theories on two dimensional minkowski space employing the algebraic framework of quantum field theory it is shown under which conditions an algebra of observables localized in a wedge shaped region of spacetime can be used to construct model theories a crucial input in this context is the modular nuclearity condition for wedge algebras which implies the existence of local observables as an application of the new method a rigorous construction of a large family of models with factorizing s matrices is obtained in an inverse scattering approach a given factorizing scattering operator is used to define certain semi localized wightman fields associated to it with the help of these fields a wedge algebra can be defined which determines the local observable content of a well defined quantum field theory in this approach the modular nuclearity condition translates to certain analyticity and boundedness conditions on the formfactors of wedge local observables these conditions are shown to hold for a large class of underlying s matrices including the scattering operators of the sinh gordon model and the scaling ising model as special examples the so constructed models are investigated with respect to their scattering properties they are shown to solve the inverse scattering problem for the underlying s matrices and a proof of asymptotic completeness for these models is given

locality in free string field theory free string field operators are constructed for the open bosonic string in the light cone gauge in any dimension these are naturally localized by the center of mass coordinate relative to this localization they are shown to have a causal commutator provided there are no tachyons for the critical string in d 26 the result still holds if the tachyon is suppressed we also show a causal commutator relative to the string light cone

causal independence and the energy level density of states in local quantum field theory within the general framework of local quantum field theory a physically motivated condition on the energy level density of well localized states is proposed and discussed it is shown that any model satisfying this condition obeys a strong form of the principle of causal statistical independence which manifests itself in a specific algebraic structure of the local algebras split property it is also shown that the proposed condition holds in a free field theory

detection of community structures in networks via global optimization abstract we present an analysis of communality structure in networks based on the application of simulated annealing techniques in this case we use as cost function the already introduced modularity q 1 which is based on the relative number of links within a commune against the number of links that would correspond in case the links were distributed randomly we compare the results of our approach against other methodologies based on betweenness analysis and show that in all cases a better community structure can be attained

the invariant charges of the nambu goto theory in wkb approximation renormalization we discuss the one loop renormalization of the reparametrization invariant non local conserved charges of the nambu goto string theory in addition we show the stability of a special well known state under the corresponding infinitesimal symmetry transformations at least in the wkb approximation

finding community structure in very large networks the discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community but most methods proposed so far are unsuitable for very large networks because of their computational cost here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms its running time on a network with n vertices and m edges is o md phantom rule 0 2em 0ex mathrm log phantom rule 0 2em 0ex n where d is the depth of the dendrogram describing the community structure many real world networks are sparse and hierarchical with m ensuremath sim n and d ensuremath sim mathrm log phantom rule 0 2em 0ex n in which case our algorithm runs in essentially linear time o n phantom rule 0 2em 0ex mathrm log 2 phantom rule 0 2em 0ex n as an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on line retailer items in the network being linked if they are frequently purchased by the same buyer the network has more than 400 000 vertices and 2 ifmmode times else texttimes fi 10 6 edges we show that our algorithm can extract meaningful communities from this network revealing large scale patterns present in the purchasing habits of customers

algebraic properties of the invariant charges of the nambu goto theory we analyse the infinite dimensional algebra of observable non local integrals of motion of the nambu goto string theory

sufficient conditions for a discrete maximum principle for high order collocation methods abstract the purpose of this work is to extend earlier results concerning a discrete maximum principle for collocation methods to higher order piecewise polynomial approximations the techniques of this paper use a different set of basis elements for the piecewise polynomial space than that employed in the earlier work for the cubic and quartic cases

stability of shortest paths in complex networks with random edge weights we study shortest paths and spanning trees of complex networks with random edge weights edges which do not belong to the spanning tree are inactive in a transport process within the network the introduction of quenched disorder modifies the spanning tree such that some edges are activated and the network diameter is increased with analytic random walk mappings and numerical analysis we find that the spanning tree is unstable to the introduction of disorder and displays a phase transitionlike behavior at zero disorder strength epsilon 0 in the infinite network size limit n infinity we obtain a continuous transition with the density of activated edges phi growing like phi approximately epsilon 1 and with the diameter expansion coefficient upsilon growing like upsilon approximately epsilon 2 in the regular network and first order transitions with discontinuous jumps in phi and upsilon at epsilon 0 for the small world sw network and the barabasi albert scale free sf network the asymptotic scaling behavior sets in when n n c where the crossover size scales as n c approximately epsilon 2 for the regular network n c approximately exp alpha epsilon 2 for the sw network and n c approximately exp alpha ln epsilon epsilon 2 for the sf network in a transient regime with n n c there is an infinite order transition with phi approximately upsilon approximately exp alpha epsilon 2 ln n for the sw network and approximately exp alpha epsilon 2 ln n ln ln n for the sf network it shows that the transport pattern is practically most stable in the sf network

detecting communities in large networks we develop an algorithm to detect community structure in complex networks the algorithm is based on spectral methods and takes into account weights and link orientation since the method detects efficiently clustered nodes in large networks even when these are not sharply partitioned it turns to be specially suitable for the analysis of social and information networks we test the algorithm on a large scale data set from a psychological experiment of word association in this case it proves to be successful both in clustering words and in uncovering mental association patterns

finding modules and hierarchy in weighted financial network using transfer entropy we study the modular structure of financial network based on the transfer entropy te from the comparison with the obtained modular structure using the cross correlation cc we find that te and cc both provide well organized modular structure and the hierarchical relationship between each industrial group when the time scale of the measurement is less than one month however when the time scale of the measurement becomes larger than one month we find that the modular structure from cc cannot correctly reflect the known industrial classification and their hierarchy in addition the measured maximum modularity qmax for te is always larger than that for cc which indicates that te is a better weight measure than cc for the system with asymmetric relationship

a discrete maximum principle for collocation methods abstract a discrete maximum principle for collocation approximations is formulated for the cases of piecewise cubic and piecewise quartic c 1 approximations suffiecient conditions for the placement of the collocation points are derived which ensure that the resulting collocation approximations satisfy the discrete maximum principle

on discrete maximum principles for discontinuous galerkin methods the aim of this work is to propose a monotonicity preserving method for discontinuous galerkin dg approximations of convection diffusion problems to do so a novel definition of discrete maximum principle dmp is proposed using the discrete variational setting of the problem and we show that the fulfilment of this dmp implies that the minimum maximum depending on the sign of the forcing term is on the boundary for multidimensional problems then an artificial viscosity av technique is designed for convection dominant problems that satisfies the above mentioned dmp the noncomplete stabilized interior penalty dg method is proved to fulfil the dmp property for the one dimensional linear case when adding such av with certain parameters the benchmarks for the constant values to satisfy the dmp are calculated and tested in the numerical experiments section finally the method is applied to different test problems in one and two dimensions to show its performance

statistical ensembles for economic networks economic networks share with other social networks the fundamental property of sparsity it is well known that the maximum entropy techniques usually employed to estimate or simulate weighted networks produce unrealistic dense topologies at the same time strengths should not be neglected since they are related to core economic variables like supply and demand to overcome this limitation the exponential bosonic model has been previously extended in order to obtain ensembles where the average degree and strength sequences are simultaneously fixed conditional geometric model in this paper a new exponential model which is the network equivalent of boltzmann ideal systems is introduced and then extended to the case of joint degree strength constraints conditional poisson model finally the fitness of these alternative models is tested against a number of networks while the conditional geometric model generally provides a better goodness of fit in terms of log likelihoods the conditional poisson model could nevertheless be preferred whenever it provides a higher similarity with original data if we are interested instead only in topological properties the simple bernoulli model appears to be preferable to the correlated topologies of the two more complex models

heterogeneous bond percolation on multitype networks with an application to epidemic dynamics considerable attention has been paid in recent years to the use of networks in modeling complex real world systems among the many dynamical processes involving networks propagation processes in which the final state can be obtained by studying the underlying network percolation properties have raised formidable interest in this paper we present a bond percolation model of multitype networks with an arbitrary joint degree distribution that allows heterogeneity in the edge occupation probability as previously demonstrated the multitype approach allows many nontrivial mixing patterns such as assortativity and clustering between nodes we derive a number of useful statistical properties of multitype networks as well as a general phase transition criterion we also demonstrate that a number of previous models based on probability generating functions are special cases of the proposed formalism we further show that the multitype approach by naturally allowing heterogeneity in the bond occupation probability overcomes some of the correlation issues encountered by previous models we illustrate this point in the context of contact network epidemiology

spectral analysis of deformed random networks we study spectral behavior of sparsely connected random networks under the random matrix framework subnetworks without any connection among them form a network having perfect community structure as connections among the subnetworks are introduced the spacing distribution shows a transition from the poisson statistics to the gaussian orthogonal ensemble statistics of random matrix theory the eigenvalue density distribution shows a transition to the wigner s semicircular behavior for a completely deformed network the range for which spectral rigidity measured by the dyson mehta ensuremath delta 3 statistics follows the gaussian orthogonal ensemble statistics depends upon the deformation of the network from the perfect community structure the spacing distribution is particularly useful to track very slight deformations of the network from a perfect community structure whereas the density distribution and the ensuremath delta 3 statistics remain identical to the undeformed network on the other hand the ensuremath delta 3 statistics is useful for the larger deformation strengths finally we analyze the spectrum of a protein protein interaction network for helicobacter and compare the spectral behavior with those of the model networks

dynamics of cluster structures in a financial market network abstract in the course of recent fifteen years the network analysis has become a powerful tool for studying financial markets in this work we analyze stock markets of the usa and sweden we study cluster structures of a market network constructed from a correlation matrix of returns of the stocks traded in each of these markets such cluster structures are obtained by means of the p median problem pmp whose objective is to maximize the total correlation between a set of stocks called medians of size p and other stocks every cluster structure is an undirected disconnected weighted graph in which every connected component cluster is a star or a tree with one central node called a median and several leaf nodes connected with the median by weighted edges our main observation is that in non crisis periods of time cluster structures change more chaotically while during crises they show more stable behavior and fewer changes thus an increasing stability of a market graph cluster structure obtained via the pmp could be used as an indicator of a coming crisis

differential equations as a tool for community identification we consider the task of identification of a cluster structure in random networks the results of two methods are presented i the newman algorithm m e j newman and m girvan phys rev e 69 026113 2004 and ii our method based on differential equations a series of computer experiments is performed to check if in applying these methods we are able to determine the structure of the network the trial networks consist initially of well defined clusters and are disturbed by introducing noise into their connectivity matrices further we show that an improvement of the previous version of our method is possible by an appropriate choice of the threshold parameter beta with this change the results obtained by the two methods above are similar and our method works better for all the computer experiments we have done

the invariant charges of the nambu goto theory their geometric origin and their completeness we give an alternative construction of the reparametrization invariant non local conserved charges of the nambu goto theory which elucidates their geometric nature and their completeness property

the poisson algebra of the invariant charges of the nambu goto theory casimir elements the reparametrization invariant non local conserved charges of the nambu goto theory form an algebra under poisson bracket operation the center of the formal closure of this algebra is determined the relation of the central elements to the constraints of the nambu goto theory is clarified

a kind of collaboration competition networks abstract we propose describing a kind of cooperation competition systems by node weighted bipartite graphs in such systems the nodes can be divided into two types one expresses a kind of activities organizations or events named acts and another expresses the actors participating in some acts in each act the actors basically show collaboration relationship with each other however they play different roles in the cooperation usually every actor tries to play the most important role therefore the role difference can be regarded as a kind of competition the node weight usually signifies the role or importance degree of each actor we propose using some statistical properties for the description of such kind of systems the properties without considering node weight can describe the cooperation situation and configuration the properties with node weight may describe the competition results two example systems are reported to show the description method and the corresponding empirical investigation results one is the undergraduate elective network and another the library network of yangzhou university the description method may be effective for the similar systems in different fields

discrete maximum principle for higher order finite elements in 1d we formulate a sufficient condition on the mesh under which we prove the discrete maximum principle dmp for the one dimensional poisson equation with dirichlet boundary conditions discretized by the hp fem the dmp holds if a relative length of every element k in the mesh is bounded by a value h rel p 0 9 1 where p 1 is the polynomial degree of the element k the values h rel p are calculated for 1 p 100

deformations of quantum field theories and integrable models deformations of quantum field theories which preserve poincare covariance and localization in wedges are a novel tool in the analysis and construction of model theories here a general scenario for such deformations is discussed and an infinite class of explicit examples is constructed on the borchers uhlmann algebra underlying wightman quantum field theory these deformations exist independently of the space time dimension and contain the recently studied warped convolution deformation as a special case in the special case of two dimensional minkowski space they can be used to deform free field theories to integrable models with non trivial s matrix

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

a modified evidential methodology of identifying influential nodes in weighted networks abstract how to identify influential nodes in complex networks is still an open hot issue in the existing evidential centrality evc node degree distribution in complex networks is not taken into consideration in addition the global structure information has also been neglected in this paper a new evidential semi local centrality esc is proposed by modifying evc in two aspects firstly the basic probability assignment bpa of degree generated by evc is modified according to the actual degree distribution rather than just following uniform distribution bpa is the generation of probability in order to model uncertainty secondly semi local centrality combined with modified evc is extended to be applied in weighted networks numerical examples are used to illustrate the efficiency of the proposed method

the algebra formed by the invariant charges of the nambu goto theory identification of a maximal abelian subalgebra continuing the analysis of the algebraic structure of the invariant charges of the nambu goto theory we identify a complete set of commuting observables for the bosonic strings

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