abstract phase space networks describing reactive dynamics abstract an abstract network approach is proposed for the description of the dynamics in reactive processes the phase space of the variables concentrations in reactive systems is partitioned into a finite number of segments which constitute the nodes of the abstract network transitions between the nodes are dictated by the dynamics of the reactive process and provide the links between the nodes these are weighted networks since each link weight reflects the transition rate between the corresponding states nodes with this construction the network properties mirror the dynamics of the underlying process and one can investigate the system properties by studying the corresponding abstract network as a working example the lattice limit cycle llc model is used its corresponding abstract network is constructed and the transition matrix elements are computed via kinetic dynamic monte carlo simulations for this model it is shown that the degree distribution follows a power law with exponent 1 while the average clustering coefficient c n scales with the network size number of nodes n as c n n 1 46 the computed exponents classify the llc abstract reactive network into the scale free networks this conclusion corroborates earlier investigations demonstrating the formation of fractal spatial patterns in llc reactive dynamics due to stochasticity and to clustering of homologous species the present construction of abstract networks based on the partition of the phase space is generic and can be implemented with appropriate adjustments in many dynamical systems and in time series analysis

finite element analysis of transonic flows in highly staggered cascades a finite element method is employed in the solution of a full potential equation for analyzing steady transonic flows through highly staggered cascades convergence characteristics and efficiency of the developed numerical procedure are discussed accuracy of the mathematical model is investigated in terms of the employed computational grid in particular the importance of an accurate representation of the trailing edge together with the shock on the obtained flow results are studied numerical results include choked flows for cascades of naca 0012 and 8 circular arc airfoils with a pitch chord ratio of 1 and a stagger angle of 45 deg

on periodic waves for sine and sinh gordon equations abstract results of existence as well as orbital stability instability of periodic waves associated with sine gordon and sinh gordon equations will be treated in this manuscript the sine gordon equation is known to be completely integrable exactly solvable and it has several special solutions as soliton and breather solutions we obtain in both cases a periodic sign changed wave which is smooth when posed on whole real line the main tool used is the grillakis shatah and strauss theory

the expectation hypothesis of interest rates and network theory the case of brazil abstract this paper investigates the topological properties of the brazilian term structure of interest rates network we build the minimum spanning tree mst which is based on the concept of ultrametricity using the correlation matrix for interest rates of different maturities we show that the short term interest rate is the most important within the interest rates network which is in line with the expectation hypothesis of interest rates furthermore we find that the brazilian interest rates network forms clusters by maturity

generalizations of the clustering coefficient to weighted complex networks the recent high level of interest in weighted complex networks gives rise to a need to develop new measures and to generalize existing ones to take the weights of links into account here we focus on various generalizations of the clustering coefficient which is one of the central characteristics in the complex network theory we present a comparative study of the several suggestions introduced in the literature and point out their advantages and limitations the concepts are illustrated by simple examples as well as by empirical data of the world trade and weighted coauthorship networks

block structured solution scheme for analyzing three dimensional transonic potential flows le schema est base sur la resolution des equations d ecoulement potentiel pour des blocs individuels representant des sous volumes du champ d ecoulement

configuration model for correlation matrices preserving the node strength correlation matrices are a major type of multivariate data to examine properties of a given correlation matrix a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices such as those derived from random matrix theory that partially preserve properties of the original matrix we propose a model to generate such reference correlation and covariance matrices for the given matrix correlation matrices are often analyzed as networks which are heterogeneous across nodes in terms of the total connectivity to other nodes for each node given this background the present algorithm generates random networks that preserve the expectation of total connectivity of each node to other nodes akin to configuration models for conventional networks our algorithm is derived from the maximum entropy principle we will apply the proposed algorithm to measurement of clustering coefficients and community detection both of which require a null model to assess the statistical significance of the obtained results

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

finite element solutions of euler equations for lifting airfoils application d une formulation de clebsch des equations d euler aux ecoulements transsoniques autour de profils aerodynamiques

euler correction method for two and three dimensional transonic flows an euler correction method based on the clebsch formulation of the euler equations has been developed to improve shock calculations in full potential methods in the clebsch treatment of steady rotational flows the velocity is decomposed into potential and rotational components written in terms of scalar functions the potential part is computed from the continuity equation using a modified version of an existing finite volume full potential solver the rotational parts are determined analytically from the momentum equation based on small perturbation approximations the solutions obtained for airfoils and wing bodies are compared with those using the time marching euler methods the agreement between the results obtained using these two approaches is good

topological properties of hierarchical networks hierarchical networks are attracting a renewal interest for modeling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean field limitations here we consider the dyson hierarchical construction for ferromagnets neural networks and spin glasses recently analyzed from a statistical mechanics perspective and we focus on the topological properties of the underlying structures in particular we find that such structures are weighted graphs that exhibit a high degree of clustering and of modularity with a small spectral gap the robustness of such features with respect to the presence of thermal noise is also studied these outcomes are then discussed and related to the statistical mechanics scenario in full consistency last we look at these weighted graphs as markov chains and we show that in the limit of infinite size the emergence of ergodicity breakdown for the stochastic process mirrors the emergence of metastabilities in the corresponding statistical mechanical analysis

world trade web topological properties dynamics and evolution this paper studies the statistical properties of the web of import export relationships among world countries using a weighted network approach we analyze how the distributions of the most important network statistics measuring connectivity assortativity clustering and centrality have coevolved over time we show that all node statistic distributions and their correlation structure have remained surprisingly stable in the last 20 years and are likely to do so in the future conversely the distribution of positive link weights is slowly moving from a log normal density towards a power law we also characterize the autoregressive properties of network statistics dynamics we find that network statistics growth rates are well proxied by fat tailed densities like the laplace or the asymmetric exponential power finally we find that all our results are reasonably robust to a few alternative economically meaningful weighting schemes

synchrony and complexity in state related eeg networks an application of spectral graph theory the brain may be considered as a synchronized dynamic network with several coherent dynamical units however concerns remain whether synchronizability is a stable state in the brain networks if s

solitary wave solutions in double sinh gordon system two new classes of solitary wave solutions for the recently suggested double sinh gordon system have been obtained these solutions possess nice stability and asymptotic properties and are characterised by zero topological charge the existence and behaviour of these solutions in more than two space time dimensions and the properties of multisolitary waves have been studied in detail

complex networks in confined comminution the physical process of confined comminution is investigated within the framework of complex networks we first characterize the topology of the unweighted contact networks as generated by the confined comminution process we find this process gives rise to an ultimate contact network which exhibits a scale free degree distribution and small world properties in particular if viewed in the context of networks through which information travels along shortest paths we find that the global average of the node vulnerability decreases as the comminution process continues with individual node vulnerability correlating with grain size a possible application to the design of synthetic networks e g sensor networks is highlighted next we turn our attention to the physics of the granular comminution process and examine force transmission with respect to the weighted contact networks where each link is weighted by the inverse magnitude of the normal force acting at the associated contact we find that the strong forces i e force chains are transmitted along pathways in the network which are mainly following shortest path routing protocols as typically found for example in communication systems motivated by our earlier studies of the building blocks for self organization in dense granular systems we also explore the properties of the minimal contact cycles the distribution of the contact strain energy intensity of 4 cycle motifs in the ultimate state of the confined comminution process is shown to be consistent with a scale free distribution with infinite variance thereby suggesting that 4 cycle arrangements of grains are capable of storing vast amounts of energy in their contacts without breaking

numerical solution of transonic stream function equation the stream function equation in conservation form looks similar to the full potential equation and existing methods e g artificial compressibility can be readily applied rotational flows can be calculated once the vorticity due to shocks or nonuniformity is evaluated there are however two main difficulties first the density is not uniquely determined in terms of the flux there are two solutions the subsonic and the supersonic branch with a square root singularity at the sonic point methods to overcome this difficulty are studied and results are presented with some remarks on inviscid separation and closed stream lines second the need of two stream functions for three dimensional calculations is briefly discussed

probabilistic independent component analysis for functional magnetic resonance imaging we present an integrated approach to probabilistic independent component analysis ica for functional mri fmri data that allows for nonsquare mixing in the presence of gaussian noise in order to avoid overfitting we employ objective estimation of the amount of gaussian noise through bayesian analysis of the true dimensionality of the data i e the number of activation and non gaussian noise sources this enables us to carry out probabilistic modeling and achieves an asymptotically unique decomposition of the data it reduces problems of interpretation as each final independent component is now much more likely to be due to only one physical or physiological process we also describe other improvements to standard ica such as temporal prewhitening and variance normalization of timeseries the latter being particularly useful in the context of dimensionality reduction when weak activation is present we discuss the use of prior information about the spatiotemporal nature of the source processes and an alternative hypothesis testing approach for inference using gaussian mixture models the performance of our approach is illustrated and evaluated on real and artificial fmri data and compared to the spatio temporal accuracy of results obtained from classical ica and glm analyses

application of a finite element algorithm to the solution of steady transonic euler equations a finite element algorithm for the solution of two dimensional steady euler equations is presented which through a clebsch type transformation for the velocity vector solves the conservation of mass equation with one primary variable and two additional equations for the convection of two new variables the accuracy and efficiency of this scheme is discussed and the second order accuracy attained in the analysis of the convection of the vorticity is demonstrated together with the efficient treatment of rotational and irrotational flow subregions a sample problem is used to show the accuracy of the numerical scheme and its convergence characteristics

weight conserving characterization of complex functional brain networks complex functional brain networks are large networks of brain regions and functional brain connections statistical characterizations of these networks aim to quantify global and local properties of brain activity with a small number of network measures important functional network measures include measures of modularity measures of the goodness with which a network is optimally partitioned into functional subgroups and measures of centrality measures of the functional influence of individual brain regions characterizations of functional networks are increasing in popularity but are associated with several important methodological problems these problems include the inability to characterize densely connected and weighted functional networks the neglect of degenerate topologically distinct high modularity partitions of these networks and the absence of a network null model for testing hypotheses of association between observed nontrivial network properties and simple weighted connectivity properties in this study we describe a set of methods to overcome these problems specifically we generalize measures of modularity and centrality to fully connected and weighted complex networks describe the detection of degenerate high modularity partitions of these networks and introduce a weighted connectivity null model of these networks we illustrate our methods by demonstrating degenerate high modularity partitions and strong correlations between two complementary measures of centrality in resting state functional magnetic resonance imaging mri networks from the 1000 functional connectomes project an open access repository of resting state functional mri datasets our methods may allow more sound and reliable characterizations and comparisons of functional brain networks across conditions and subjects

clustering in complex directed networks many empirical networks display an inherent tendency to cluster i e to form circles of connected nodes this feature is typically measured by the clustering coefficient cc the cc originally introduced for binary undirected graphs has been recently generalized to weighted undirected networks here we extend the cc to the case of binary and weighted directed networks and we compute its expected value for random graphs we distinguish between ccs that count all directed triangles in the graph independently of the direction of their edges and ccs that only consider particular types of directed triangles e g cycles the main concepts are illustrated by employing empirical data on world trade flows

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

fast and robust fixed point algorithms for independent component analysis independent component analysis ica is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible we use a combination of two different approaches for linear ica comon s information theoretic approach and the projection pursuit approach using maximum entropy approximations of differential entropy we introduce a family of new contrast functions for ica these contrast functions enable both the estimation of the whole decomposition by minimizing mutual information and estimation of individual independent components as projection pursuit directions the statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model and it is shown how to choose contrast functions that are robust and or of minimum variance finally we introduce simple fixed point algorithms for practical optimization of the contrast functions

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

a mathematical analysis of the effects of hebbian learning rules on the dynamics and structure of discrete time random recurrent neural networks we present a mathematical analysis of the effects of hebbian learning in random recurrent neural networks with a generic hebbian learning rule including passive forgetting and different timescales for neuronal activity and learning dynamics previous numerical work has reported that hebbian learning drives the system from chaos to a steady state through a sequence of bifurcations here we interpret these results mathematically and show that these effects involving a complex coupling between neuronal dynamics and synaptic graph structure can be analyzed using jacobian matrices which introduce both a structural and a dynamical point of view on neural network evolution furthermore we show that sensitivity to a learned pattern is maximal when the largest lyapunov exponent is close to 0 we discuss how neural networks may take advantage of this regime of high functional interest

coupled intermittent maps modeling the statistics of genomic sequences a network approach the dynamics of coupled intermittent maps is used to model the correlated structure of genomic sequences the use of intermittent maps as opposed to other simple chaotic maps is particularly suited for the production of long range correlation features which are observed in the genomic sequences of higher eucaryotes a weighted network approach to symbolic sequences is introduced and it is shown that coupled intermittent polynomial maps produce degree and link size distributions with power law exponents similar to the ones observed in real genomes the proposed network approach to symbolic sequences is generic and can be applied to any symbol sequence artificial or natural

nonisentropic potential formulation for transonic flows a potential equation for nonisentropic transonic flows is formulated this procedure captures shock waves with rankine hugoniot strengths but retains the simplicity of the traditional potential equation numerical computations are presented that verify the efficiency of the present procedure it is also shown that crocco s theorem is not applicable to potential flows a new crocco s theorem valid for potential flows is derived and it is shown that transonic flows with nonconstant shock strengths can never be irrotational irrespective of whether the flow is isentropic or not

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

clustering coefficients of large networks abstract let g be a network with n nodes and eigenvalues 1 2 n then g is called an n d network if it is d regular and max 2 3 n it is shown that if g is an n d network and o d the average clustering coefficient c g of g satisfies c g d n for large d we show that this description also holds for strongly regular graphs and erd s renyi graphs although most real world networks are not constructed theoretically we find that many of them have c g close to d n and many close to 1 2 n d 1 d d 1 where d is the average degree of g and 2 is the average of the numbers of common neighbors over all non adjacent pairs of nodes

spatial network surrogates for disentangling complex system structure from spatial embedding of nodes networks with nodes embedded in a metric space have gained increasing interest in recent years the effects of spatial embedding on the networks structural characteristics however are rarely taken into account when studying their macroscopic properties here we propose a hierarchy of null models to generate random surrogates from a given spatially embedded network that can preserve certain global and local statistics associated with the nodes embedding in a metric space comparing the original network s and the resulting surrogates global characteristics allows one to quantify to what extent these characteristics are already predetermined by the spatial embedding of the nodes and links we apply our framework to various real world spatial networks and show that the proposed models capture macroscopic properties of the networks under study much better than standard random network models that do not account for the nodes spatial embedding depending on the actual performance of the proposed null models the networks are categorized into different classes since many real world complex networks are in fact spatial networks the proposed approach is relevant for disentangling the underlying complex system structure from spatial embedding of nodes in many fields ranging from social systems over infrastructure and neurophysiology to climatology

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

detecting network modules in fmri time series a weighted network analysis approach many network analyses of fmri data begin by defining a set of regions extracting the mean signal from each region and then analyzing the correlations between regions one essential question that has not been addressed in the literature is how to best define the network neighborhoods over which a signal is combined for network analyses here we present a novel unsupervised method for the identification of tightly interconnected voxels or modules from fmri data this approach weighted voxel coactivation network analysis wvcna is based on a method that was originally developed to find modules of genes in gene networks this approach differs from many of the standard network approaches in fmri in that connections between voxels are described by a continuous measure whereas typically voxels are considered to be either connected or not connected depending on whether the correlation between the two voxels survives a hard threshold value additionally instead of simply using pairwise correlations to describe the connection between two voxels wvcna relies on a measure of topological overlap which not only compares how correlated two voxels are but also the degree to which the pair of voxels is highly correlated with the same other voxels we demonstrate the use of wvcna to parcellate the brain into a set of modules that are reliably detected across data within the same subject and across subjects in addition we compare wvcna to ica and show that the wvcna modules have some of the same structure as the ica components but tend to be more spatially focused we also demonstrate the use of some of the wvcna network metrics for assessing a voxel s membership to a module and also how that voxel relates to other modules last we illustrate how wvcna modules can be used in a network analysis to find connections between regions of the brain and show that it produces reasonable results

statistical mechanics of double sinh gordon kinks abstract we study the classical thermodynamics of the double sinh gordon dshg theory in 1 1 dimensions this model theory has a double well potential v cosh2 n 2 when n thus allowing for the existence of kinks and antikinks though it is non integrable the dshg model is remarkably amenable to analysis below we obtain exact single kink and kink lattice solutions as well as the asymptotic kink antikink interaction in the continuum limit finding the classical partition function is equivalent to solving for the ground state of a schrodinger like equation obtained via the transfer integral method for the dshg model this equation turns out to be quasi exactly solvable we exploit this property to obtain exact energy eigenvalues and wavefunctions for several temperatures both above and below the symmetry breaking transition temperature provided n 1 2 6 the availability of exact results provides an excellent testing ground for large scale langevin simulations the probability distribution function pdf calculated from langevin dynamics is found to be in striking agreement with the exact pdf obtained from the ground state wavefunction this validation points to the utility of a pdf based computation of thermodynamics utilizing langevin methods in addition to the pdf field field and field fluctuation correlation functions were computed and also found to be in excellent agreement with the exact results

improved optimization for the robust and accurate linear registration and motion correction of brain images linear registration and motion correction are important components of structural and functional brain image analysis most modern methods optimize some intensity based cost function to determine the best registration to date little attention has been focused on the optimization method itself even though the success of most registration methods hinges on the quality of this optimization this paper examines the optimization process in detail and demonstrates that the commonly used multiresolution local optimization methods can and do get trapped in local minima to address this problem two approaches are taken 1 to apodize the cost function and 2 to employ a novel hybrid global local optimization method this new optimization method is specifically designed for registering whole brain images it substantially reduces the likelihood of producing misregistrations due to being trapped by local minima the increased robustness of the method compared to other commonly used methods is demonstrated by a consistency test in addition the accuracy of the registration is demonstrated by a series of experiments with motion correction these motion correction experiments also investigate how the results are affected by different cost functions and interpolation methods

beyond the power law uncovering stylized facts in interbank networks abstract we use daily data on bilateral interbank exposures and monthly bank balance sheets to study network characteristics of the russian interbank market over august 1998 october 2004 specifically we examine the distributions of un directed un weighted degree nodal attributes bank assets capital and capital to assets ratio and edge weights loan size and counterparty exposure we search for the theoretical distribution that fits the data best and report the best fit parameters we observe that all studied distributions are heavy tailed the fat tail typically contains 20 of the data and can be mostly described well by a truncated power law also the power law stretched exponential and log normal provide reasonably good fits to the tails of the data in most cases however separating the bulk and tail parts of the data is hard so we proceed to study the full range of the events we find that the stretched exponential and the log normal distributions fit the full range of the data best these conclusions are robust to 1 whether we aggregate the data over a week month quarter or year 2 whether we look at the growth versus maturity phases of interbank market development and 3 with minor exceptions whether we look at the normal versus crisis operation periods in line with prior research we find that the network topology changes greatly as the interbank market moves from a normal to a crisis operation period

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

block structured solution of euler equations for transonic flows a block structured solution scheme is developed for the solution of euler equations for steady three dimensional transonic flows the euler equations are expressed in terms of clebsch variables w v svn the resulting set of equations for conservation of mass entropy 5 and the clebsch variable j are solved using a block based relaxation scheme the flowfield is divided into a series of individual blocks representing local regions of the flowfield the employed grid generation scheme provides local refinement of each block yet ensures one to one matching of grid points on the surfaces of adjoining blocks for each of the blocks either potential or euler equations can be solved for every block the conservation of mass equation is solved to determine for blocks with rotationality two additional equations for determining s and t are solved in this paper the basic steps of the developed solution scheme are presented the computational considerations involved in utilizing the present scheme are demonstrated for several two dimensional sample problems

intensity and coherence of motifs in weighted complex networks the local structure of unweighted networks can be characterized by the number of times a subgraph appears in the network the clustering coefficient reflecting the local configuration of triangles can be seen as a special case of this approach in this paper we generalize this method for weighted networks we introduce subgraph intensity as the geometric mean of its link weights and coherence as the ratio of the geometric to the corresponding arithmetic mean using these measures motif scores and clustering coefficient can be generalized to weighted networks to demonstrate these concepts we apply them to financial and metabolic networks and find that inclusion of weights may considerably modify the conclusions obtained from the study of unweighted characteristics

comparison of different generalizations of clustering coefficient and local efficiency for weighted undirected graphs binary undirected graphs are well established but when these graphs are constructed often a threshold is applied to a parameter describing the connection between two nodes therefore the use of weighted graphs is more appropriate in this work we focus on weighted undirected graphs this implies that we have to incorporate edge weights in the graph measures which require generalizations of common graph metrics after reviewing existing generalizations of the clustering coefficient and the local efficiency we proposed new generalizations for these graph measures to be able to compare different generalizations a number of essential and useful properties were defined that ideally should be satisfied we applied the generalizations to two real world networks of different sizes as a result we found that not all existing generalizations satisfy all essential properties furthermore we determined the best generalization for the clustering coefficient and local efficiency based on their properties and the performance when applied to two networks we found that the best generalization of the clustering coefficient is defined in miyajima and sakuragawa 2014 while the best generalization of the local efficiency is proposed in this letter depending on the application and the relative importance of sensitivity and robustness to noise other generalizations may be selected on the basis of the properties investigated in this letter

network clustering and community detection using modulus of families of loops we study the structure of loops in networks using the notion of modulus of loop families we introduce an alternate measure of network clustering by quantifying the richness of families of simple loops modulus tries to minimize the expected overlap among loops by spreading the expected link usage optimally we propose weighting networks using these expected link usages to improve classical community detection algorithms we show that the proposed method enhances the performance of certain algorithms such as spectral partitioning and modularity maximization heuristics on standard benchmarks

on a penalty finite element cfd algorithm for high speed flow abstract the expanding interest in finite element discrete approximation techniques applied to high speed flow prediction has engendered derivation of many distinct theoretical statements quantization of algorithm robustness has focused on accuracy assessment for non smooth solutions i e those containing shocks and or contact discontinuities to reduced forms of the navier stokes equations specifically the euler equation system and the transonic potential flow equation this paper presents derivation of a penalty finite element algorithm applicable to both problem statements with penalty functional derived as a reduced form of a taylor galerkin weak statement numerical results for shocked transonic and euler solutions are cited to document aspects of accuracy convergence and stability

statistical properties of weighted complex networks characterized by metaweights abstract we propose several characterizations of weighted complex networks by incorporating the concept of metaweight into the clustering coefficient degree correlation and module decomposition these incorporations make it possible to describe weighted networks depending on how strongly we emphasize weights using some applications to real world weighted networks we demonstrate that the proposed approach provides rich information that was inaccessible by previous analyses such as the degree correlation for a specific magnitude of weights or the community structure under controlling the importance of roles of the topology and weights

characterizing pseudoperiodic time series through the complex network approach recently a new framework has been proposed to explore the dynamics of pseudoperiodic time series by constructing a complex network j zhang m small phys rev lett 96 2006 238701 essentially this is a transformation from the time domain to the network domain which allows for the dynamics of the time series to be studied via organization of the network in this paper we focus on the deterministic chaotic rossler time series and stochastic noisy periodic data that yield substantially different structures of networks in particular we test an extensive range of network topology statistics which have not been discussed in previous work but which are capable of providing a comprehensive statistical characterization of the dynamics from different angles our goal is to find out how they reflect and quantify different aspects of specific dynamics and how they can be used to distinguish different dynamical regimes for example we find that the joint degree distribution appears to fundamentally characterize spatial organizations of cycles in phase space and this is quantified via an assortativity coefficient we applied network statistics to electrocardiograms of a healthy individual and an arrythmia patient such time series are typically pseudoperiodic but are noisy and nonstationary and degrade traditional phase space based methods these time series are however better differentiated by our network based statistics

rotational compressible inverse design method for two dimensional internal flow configurations the development of a rotational inviscid compressible inverse design method for two dimensional internal flow configurations is described rotationality is due to incoming entropy gradient whereas total enthalpy is considered to be constant throughout the flowfield the method is based on the potential function stream function formulation the clebsch formulation is adopted to decompose the velocity vector into a potential and a rotational part the physical space on which the boundaries of the flowfield are sought is mapped onto the 0 v7 space via a body fitted coordinate transformation a novel procedure based on differential geometry arguments is employed to derive the governing equation for the velocity the velocity equation solved in conjunction with a transport equation for a thermal drift function provide the flowfield without any geometry feedback an auxiliary orthogonal computational grid adapted to the solution is employed geometry is determined by integrating frenet equations of the grid lines inverse calculation results are compared with results of direct reproduction calculations

maximal spanning trees asset graphs and random matrix denoising in the analysis of dynamics of financial networks abstract we study the time dependence of maximal spanning trees and asset graphs based on correlation matrices of stock returns in these networks the nodes represent companies and links are related to the correlation coefficients between them special emphasis is given to the comparison between ordinary and denoised correlation matrices the analysis of single and multi step survival ratios of the corresponding networks reveals that the ordinary correlation matrices are more stable in time than the denoised ones our study also shows that some information about the cluster structure of the companies is lost in the denoising procedure cluster structure that makes sense from an economic point of view exists and can easily be observed in networks based on denoised correlation matrices however this structure is somewhat clearer in the networks based on ordinary correlation matrices some technical aspects such as the random matrix denoising procedure are also presented