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

estimated correlation matrices and portfolio optimization abstract correlations of returns on various assets play a central role in financial theory and also in many practical applications from a theoretical point of view the main interest lies in the proper description of the structure and dynamics of correlations whereas for the practitioner the emphasis is on the ability of the models to provide adequate inputs for the numerous portfolio and risk management procedures used in the financial industry the theory of portfolios initiated by markowitz has suffered from the curse of dimensions from the very outset over the past decades a large number of different techniques have been developed to tackle this problem and reduce the effective dimension of large bank portfolios but the efficiency and reliability of these procedures are extremely hard to assess or compare in this paper we propose a model simulation based approach which can be used for the systematical testing of all these dimensional reduction techniques to illustrate the usefulness of our framework we develop several toy models that display some of the main characteristic features of empirical correlations and generate artificial time series from them then we regard these time series as empirical data and reconstruct the corresponding correlation matrices which will inevitably contain a certain amount of noise due to the finiteness of the time series next we apply several correlation matrix estimators and dimension reduction techniques introduced in the literature and or applied in practice as in our artificial world the only source of error is the finite length of the time series and in addition the true model hence also the true correlation matrix are precisely known therefore in sharp contrast with empirical studies we can precisely compare the performance of the various noise reduction techniques one of our recurrent observations is that the recently introduced filtering technique based on random matrix theory performs consistently well in all the investigated cases based on this experience we believe that our simulation based approach can also be useful for the systematic investigation of several related problems of current interest in finance

correlation study of the athens stock exchange we study the year after year properties of three different portfolios traded in the athens stock exchange ase for the time period 1987 2004 we use the minimum spanning tree mst technique and the random matrix theory rmt which make it possible to examine at the same time the temporal evolution of the portfolios and of the market as a whole the first four moments of the distribution of correlations and the normalized tree lengths of the mst show a similar behaviour for all three portfolios however by studying topological properties of the mst such as the node degree k we are able to identify changes to the mst associated to each portfolio that are due to a crisis in the market like the one that happened during the period 1999 2001 we also see that while the effect of the market to the information content of the correlation matrix for all three portfolios is almost the same the market is affected differently by different economic sectors at different time periods r 2007 elsevier b v all rights reserved

fuzzy linear regression with fuzzy intervals abstract in this paper we introduce a new class of fuzzy linear regression models based on tanaka s approach unlike in the tanaka model here all training data influence the estimated interval the crisp lp of tanaka s approach is generalized to a fuzzy linear programming problem with the proposed model an adaptation of the fuzzy regression equation to new data becomes possible

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

accelerated growth in outgoing links in evolving networks deterministic versus stochastic picture in several real world networks such as the internet world wide web etc the number of links grow in time in a nonlinear fashion we consider growing networks in which the number of outgoing links is a nonlinear function of time but new links between older nodes are forbidden the attachments are made using a preferential attachment scheme in the deterministic picture the number of outgoing links m t at any time t is taken as n t ensuremath theta where n t is the number of nodes present at that time the continuum theory predicts a power law decay of the degree distribution p k ensuremath propto k ensuremath 1 ensuremath 2 1 ensuremath ensuremath theta while the degree of the node introduced at time t i is given by k t i t t i ensuremath theta phantom rule 0 2em 0ex t t i 1 ensuremath theta 2 when the network is evolved till time t numerical results show a growth in the degree distribution for small k values at any nonzero ensuremath theta in the stochastic picture m t is a random variable as long as m t is independent of time the network shows a behavior similar to the barab asi albert ba model different results are obtained when m t is time dependent e g when m t follows a distribution p m ensuremath propto m ensuremath ensuremath lambda the behavior of p k changes significantly as ensuremath lambda is varied for ensuremath lambda g3 the network has a scale free distribution belonging to the ba class as predicted by the mean field theory for smaller values of ensuremath lambda it shows different behavior characteristic features of the clustering coefficients in both models have also been discussed

a study of causality structure and dynamics in industrial electricity consumption based on granger network abstract based on industrial electricity consumption we model industrial networks by granger causality method and mst minimum spanning tree and then further stick onto an industrial coupling mechanism from energy consumption perspective first we construct granger causality networks of five provinces in south china of gd gx gz hn and yn based on their industrial electricity consumption data and we demonstrate from a network topology perspective the distribution of weight of links of all industrial electricity consumption granger causality networks approximately follows power law distribution revealing a phenomenon that few industries may bring a tremendous influence on the rest moreover correlation analysis between weight and degree of a node shows that in most granger causality networks both span and strength of influence of a given industry will significantly increase further we analyze the relationship between the thresholds of granger causality significance and density of corresponding networks results show gd and hn could be classified into a group with relatively greater global differentiation in industries and unbalanced industrial development however gx gz and yn are grouped as second cluster with relatively balanced industrial development furthermore using chu liu edmonds mst algorithm we extract graphs of msts or maximal cliques from industrial electricity consumption granger causality networks and research on energy transmission structure feedback loop and bootstrap reliability by analyzing msts we find that only gd gx and yn can be extracted with mst graphs and capture the probable transmission routes of key nodes besides we illustrate all three mst graphs are involved with feedback loops structures with various characteristics gx has complete feed forward section feed back section and feedback loop section yn has only feed forward section and feedback loop section gd has multiple feedback loops section finally we conduct bootstrap reliability tests on msts results show branches of reliability of gd gx and yn are decentralized while those feedback loops sections are only concentrated on highly reliable branches as neither hn nor gz can be extracted with mst graphs we characterize them by maximal cliques it is demonstrated that both industrial systems of hn and gz are significantly grouped into two independent branches and those internal industries inside independent branches are highly correlated however from perspectives of whole south china the causal relationship is only converged on a few of industries for regions without mst graphs like hn and gz the reliability of links is also greater than that of gd gx and yn

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

possibilistic linear systems and their application to the linear regression model abstract it is the purpose of this paper to illustrate possibilistic linear systems based on possibility measure and to formulate a linear regression analysis by possibilistic linear models linear regression by a possibilistic model is called possibilistic linear regression this is a new interpretation of fuzzy linear regression and also includes a new method by which interval analysis can be done in fuzzy numbers

noise dressing of financial correlation matrices we show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series the central result of the present study which focuses on the case of financial price fluctuations is the remarkable agreement between the theoretical prediction based on the assumption that the correlation matrix is random and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the s 500 or other major markets in particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management

how are rescaled range analyses affected by different memory and distributional properties a monte carlo study abstract financial data has been extensively studied for correlations using pearson s cross correlation coefficient as the point of departure we employ an estimator based on recurrence plots the correlation of probability of recurrence c p r to analyze connections between nine stock indices spread worldwide we suggest a slight modification of the c p r approach in order to get more robust results we examine trends in c p r for an approximately 19 month window moved along the time series and compare them to trends in binning c p r into three levels of connectedness strong moderate and weak we extract the trends in number of connections in each bin over time we also look at the behavior of c p r during the dot com bubble by shifting the time series to align their peaks c p r mainly uncovers that the markets move in and out of periods of strong connectivity erratically instead of moving monotonically towards increasing global connectivity this is in contrast to which gives a picture of ever increasing correlation c p r also exhibits that time shifted markets have high connectivity around the dot com bubble of 2000 we use significance tests using twin surrogates to interpret all the measures estimated in the study

fuzzy linear regression and its applications to forecasting in uncertain environment abstract linear regression has been used for many years in developing mathematical models for application in marketing management and sales forecasting in this paper two different sales forecasting techniques are discussed the first technique involves non fuzzy abstract methods of linear regression and econometrics a study of the international market sales of cameras done in 1968 by john scott armstrong utilized these non fuzzy forecasting techniques the second sales forecasting technique uses fuzzy linear regression introduced by h tanaka s uejima and k asai in 1980 in this paper a study of the computer and peripheral equipment sales in the united states is discussed using fuzzy linear regression moreover fuzzy linear regression is applied to forecasting in an uncertain environment finally some possible improvements and suggestions for further study are mentioned

visualization of a stock market correlation matrix abstract this paper presents a novel application of neighbor net a clustering algorithm developed for constructing a phylogenetic network in the field of evolutionary biology to visualizing a correlation matrix we apply neighbor net as implemented in the splitstree software package to 48 stocks listed on the new zealand stock exchange we show that by visualizing the correlation matrix using a neighbor net splits graph and its associated circular ordering of the stocks that some of the problems associated with understanding the large number of correlations between the individual stocks can be overcome we compare the visualization of neighbor net with that provided by hierarchical clustering trees and minimum spanning trees the use of neighbor net networks or splits graphs yields greater insight into how closely individual stocks are related to each other in terms of their correlations and suggests new avenues of research into how to construct small diversified stock portfolios

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

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

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

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

weighted network analysis of high frequency cross correlation measures in this paper we implement a fourier method to estimate high frequency correlation matrices from small data sets the fourier estimates are shown to be considerably less noisy than the standard pearson correlation measures and thus capable of detecting subtle changes in correlation matrices with just a month of data the evolution of correlation at different time scales is analyzed from the full correlation matrix and its minimum spanning tree representation the analysis is performed by implementing measures from the theory of random weighted networks

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

hierarchical structures of fuzzy ratings in the analysis of strategic goals of enterprises abstract analysis of strategic goals of enterprises involves simultaneous consideration of various goals subgoals and strategies which are changed according to situations and problems and it is a complex unstructured ill defined process incorporating multiattribute comparisons and impreciseness of the data to cope with this analysis a methodology integrating the analytic hierarchy process ahp procedure what if analysis fuzzy sets and fuzzy arithmetic is proposed in this paper

least squares model fitting to fuzzy vector data abstract we consider model fitting problems in which the mathematical model of an observed event is a system of equations involving model parameters and observables and in which the data are fuzzy vectors such problems naturally arise in applications when data are scarce and information is vague about distributions of variances that are contained in the observations then it may only be possible to obtain estimates of membership functions of the data a model can be fitted to such data by maximizing the membership values of the adjusted observations we achieve this by minimizing the sum of squares of the deviations of the membership values from one the optimization problem simplifies significantly if the membership functions of the fuzzy vectors belong to a class of conical functions which are defined in terms of an elliptic norm properties of these functions are discussed and a membership propagation formula derived which component wise obeys the extension principle the least squares model fitting to the described fuzzy vector data deviates in important aspects from ordinary least squares one obtains as a solution a fuzzy model parameter vector and a number of indicators which describe the quality of the fit viz the grade of compatibility between data and model their discord and dilators of model and data membership functions these new concepts are illustrated and discussed in the context of an example from a terminal ballistics problem

minimum spanning tree filtering of correlations for varying time scales and size of fluctuations based on a recently proposed q dependent detrended cross correlation coefficient ensuremath rho q j kwapie ifmmode acute n else n fi p o ifmmode acute s else s fi wi ifmmode mbox k e else k e fi cimka and s dro ifmmode dot z else z fi d ifmmode dot z else z fi phys rev e 92 052815 2015 we generalize the concept of the minimum spanning tree mst by introducing a family of q dependent minimum spanning trees q mathrm mst mathrm s that are selective to cross correlations between different fluctuation amplitudes and different time scales of multivariate data they inherit this ability directly from the coefficients ensuremath rho q which are processed here to construct a distance matrix being the input to the mst constructing kruskal s algorithm the conventional mst with detrending corresponds in this context to q 2 in order to illustrate their performance we apply the q mathrm msts to sample empirical data from the american stock market and discuss the results we show that the q mathrm mst graphs can complement ensuremath rho q in disentangling hidden correlations that cannot be observed in the mst graphs based on ensuremath rho mathrm dcca and therefore they can be useful in many areas where the multivariate cross correlations are of interest as an example we apply this method to empirical data from the stock market and show that by constructing the q mathrm msts for a spectrum of q values we obtain more information about the correlation structure of the data than by using q 2 only more specifically we show that two sets of signals that differ from each other statistically can give comparable trees for q 2 while only by using the trees for q ensuremath ne 2 do we become able to distinguish between these sets we also show that a family of q mathrm msts for a range of q expresses the diversity of correlations in a manner resembling the multifractal analysis where one computes a spectrum of the generalized fractal dimensions the generalized hurst exponents or the multifractal singularity spectra the more diverse the correlations are the more variable the tree topology is for different q s as regards the correlation structure of the stock market our analysis exhibits that the stocks belonging to the same or similar industrial sectors are correlated via the fluctuations of moderate amplitudes while the largest fluctuations often happen to synchronize in those stocks that do not necessarily belong to the same industry

evolution of worldwide stock markets correlation structure and correlation based graphs we investigate the daily correlation present among market indices of stock exchanges located all over the world in the time period january 1996 to july 2009 we discover that the correlation among market indices presents both a fast and a slow dynamics the slow dynamics reflects the development and consolidation of globalization the fast dynamics is associated with critical events that originate in a specific country or region of the world and rapidly affect the global system we provide evidence that the short term time scale of correlation among market indices is less than 3 trading months about 60 trading days the average values of the nondiagonal elements of the correlation matrix correlation based graphs and the spectral properties of the largest eigenvalues and eigenvectors of the correlation matrix are carrying information about the fast and slow dynamics of the correlation of market indices we introduce a measure of mutual information based on link co occurrence in networks in order to detect the fast dynamics of successive changes of correlation based graphs in a quantitative way

growing network with local rules preferential attachment clustering hierarchy and degree correlations the linear preferential attachment hypothesis has been shown to be quite successful in explaining the existence of networks with power law degree distributions it is then quite important to determine if this mechanism is the consequence of a general principle based on local rules in this work it is claimed that an effective linear preferential attachment is the natural outcome of growing network models based on local rules it is also shown that the local models offer an explanation for other properties like the clustering hierarchy and degree correlations recently observed in complex networks these conclusions are based on both analytical and numerical results for different local rules including some models already proposed in the literature

topological properties of stock networks based on minimal spanning tree and random matrix theory in financial time series abstract we investigated the topological properties of stock networks constructed by a minimal spanning tree we compared the original stock network with the estimated network the original network is obtained by the actual stock returns while the estimated network is the correlation matrix created by random matrix theory we found that the consistency between the two networks increases as more eigenvalues are considered in addition we suggested that the largest eigenvalue has a significant influence on the formation of stock networks

dynamic asset trees and black monday abstract the minimum spanning tree based on the concept of ultrametricity is constructed from the correlation matrix of stock returns the dynamics of this asset tree can be characterised by its normalised length and the mean occupation layer as measured from an appropriately chosen centre called the central node we show how the tree length shrinks during a stock market crisis black monday in this case and how a strong reconfiguration takes place resulting in topological shrinking of the tree

topology of correlation based minimal spanning trees in real and model markets we compare the topological properties of the minimal spanning tree obtained from a large group of stocks traded at the new york stock exchange during a 12 year trading period with the one obtained from surrogated data simulated by using simple market models we find that the empirical tree has features of a complex network that cannot be reproduced even as a first approximation by a random market model and by the widespread one factor model

on assessing the h value in fuzzy linear regression abstract there are certain circumstances under which the application of statistical regression is not appropriate or even feasible because it makes rigid assumptions about the statistical properties of the model fuzzy regression a nonparametric method can be quite useful in estimating the relationships among variables where the available data are very limited and imprecise and variables are interacting in an uncertain qualitative and fuzzy way thus it may have considerable practical applications in many management and engineering problems in this paper the relationship among the h value membership function shape and spreads of fuzzy parameters in fuzzy linear regression is determined and the sensitivity of the spread with respect to the h value and membership function shape is examined the spread of a fuzzy parameter increases as a higher value of h and or a decreasingly concave or increasingly convex membership function is employed by utilizing the relationship among the h value membership function and spreads of the fuzzy parameters a systematic approach to assessing a proper h parameter value is also developed the approach developed and illustrated enables a decision maker s beliefs regarding the shape and range of the possibility distribution of the model to be reflected more systematically and consequently should yield more reliable and realistic results from fuzzy regression the resulging regressing equations could for example also be used as constraints in a fuzzy mathematical optimization model such as in quality function deployment

evaluation of design alternatives in mechanical engineering abstract the paper gives a description of a structure dedicated to evaluation of design alternatives in mechanical engineering a list of particular features of the system such as its ability to cope with fuzziness and a uniform way of treating various criteria involved in design processes is given and discussed in length special attention is focused on empirical engineering oriented aspects of membership functions estimation with a particular emphasis on expressing achieved precision the paper re analyzes some existing methods of multiobjective decision making some original contributions of the study to this area are focussed on developing new indices significantly facilitating interpretation of results of ranking such as e g specificity of different alternatives as well as strength of dominance observed among them an illustration of the performance of the system is completed with the aid of an evaluation of different types of joints found in hydraulic cylinders

interest rates hierarchical structure we propose a general method to study the hierarchical organization of financial data the statistical geometrical and topological properties of such data are analyzed by embedding the structure of their correlations in metric graphs in multi dimensional spaces we show an application to two dierent sets of interest rates data in this case we construct triangular embeddings on the sphere the resulting graph contains the minimum spanning tree as sub graph and it preserves its hierarchical structure this results in a clear cluster dierentiation

identification of clusters of companies in stock indices via potts super paramagnetic transitions the clustering of companies within a specic stock market index is studied by means of super paramagnetic transitions of an appropriate q state potts model where the spins correspond to companies and the interactions are functions of the correlation coecients determined from the time dependence of the companies individual stock prices the method is a generalization of the clustering algorithm by domany et al to the case of anti ferromagnetic interactions corresponding to anti correlations for the dow jones industrial average where no anti correlations were observed in the investigated time period the previous results obtained by dierent tools were well reproduced for the standard poor s 500 where anti correlations occur repulsion between stocks modify the cluster structure c 2000 elsevier science b v all rights reserved stock market indices like the dow jones dj or standard poor s 500 s p 500 are used as indicators of the status of the markets they are averaged values of a dierent number of selected companies indicative of the economy of a given market it is of both theoretical and practical importance to analyze how individual contributions to the average behave the customary approach in the nancial literature focuses on the investigation of the properties of the covariance matrix here we take a dierent approach aiming to identify the presence of a hierarchical structure inside the set of stocks simultaneously traded in a market the identication of the hierarchy of clusters is of central importance both from the point of view of understanding the dynamics of

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

topology of the correlation networks among major currencies using hierarchical structure methods abstract we studied the topology of correlation networks among 34 major currencies using the concept of a minimal spanning tree and hierarchical tree for the full years of 2007 2008 when major economic turbulence occurred we used the usd us dollar and the tl turkish lira as numeraires in which the usd was the major currency and the tl was the minor currency we derived a hierarchical organization and constructed minimal spanning trees msts and hierarchical trees hts for the full years of 2007 2008 and for the 2007 2008 period we performed a technique to associate a value of reliability to the links of msts and hts by using bootstrap replicas of data we also used the average linkage cluster analysis for obtaining the hierarchical trees in the case of the tl as the numeraire these trees are useful tools for understanding and detecting the global structure taxonomy and hierarchy in financial data we illustrated how the minimal spanning trees and their related hierarchical trees developed over a period of time from these trees we identified different clusters of currencies according to their proximity and economic ties the clustered structure of the currencies and the key currency in each cluster were obtained and we found that the clusters matched nicely with the geographical regions of corresponding countries in the world such as asia or europe as expected the key currencies were generally those showing major economic activity

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

from unweighted to weighted networks with local information abstract in this paper we analyze an evolving model with local information which can generate a class of networks by choosing different values of the parameter p the model introduced exhibits the transition from unweighted networks to weighted networks because the distribution of the edge weight can be widely tuned with the increase in the local information the degree correlation of the network transforms from assortative to disassortative we also study the distribution of the degree strength and edge weight which all show crossover between exponential and scale free finally an application of the proposed model to the study of the synchronization is considered it is concluded that the synchronizability is enhanced when the heterogeneity of the edge weight is reduced

generalized local world models for weighted networks based on the weighted scale free network model proposed by barrat barth elemy and vespignani phys rev lett 92 228701 2004 and enlightened by our local world concept li and chen physica a 328 274 2003 we propose two generalized local world glw models for weighted complex networks theoretical analysis and numerical simulations show that the glw models generate weighted networks as a crossover between exponential and scale free weighted networks and exhibit an alteration from assortative networks to disassortative networks

pruning a minimum spanning tree abstract this work employs various techniques in order to filter random noise from the information provided by minimum spanning trees obtained from the correlation matrices of international stock market indices prior to and during times of crisis the first technique establishes a threshold above which connections are considered affected by noise based on the study of random networks with the same probability density distribution of the original data the second technique is to judge the strength of a connection by its survival rate which is the amount of time a connection between two stock market indices endures the idea is that true connections will survive for longer periods of time and that random connections will not that information is then combined with the information obtained from the first technique in order to create a smaller network in which most of the connections are either strong or enduring in time

fuzzy data analysis by possibilistic linear models abstract since fuzzy data can be regarded as distribution of possibility fuzzy data analysis by possibilistic linear models is proposed in this paper possibilistic linear systems are defined by the extension principle fuzzy parameter estimations are discussed in possibilistic linear systems and possibilistic linear models are employed for fuzzy data analysis with non fuzzy inputs and fuzzy outputs defined by fuzzy numbers the estimated possibilistic linear system can be obtained by solving a linear programming problem this approach can be regarded as fuzzy interval analysis

structural and topological phase transitions on the german stock exchange abstract we find numerical and empirical evidence for dynamical structural and topological phase transitions on the german frankfurt stock exchange fse in the temporal vicinity of the worldwide financial crash using the minimal spanning tree mst technique a particularly useful canonical tool of the graph theory two transitions of the topology of a complex network representing the fse were found the first transition is from a hierarchical scale free mst representing the stock market before the recent worldwide financial crash to a superstar like mst decorated by a scale free hierarchy of trees representing the market s state for the period containing the crash subsequently a transition is observed from this transient meta stable state of the crash to a hierarchical scale free mst decorated by several star like trees after the worldwide financial crash the phase transitions observed are analogous to the ones we obtained earlier for the warsaw stock exchange and more pronounced than those found by onnela chakraborti kaski kertesz for the s p 500 index in the vicinity of black monday october 19 1987 and also in the vicinity of january 1 1998 our results provide an empirical foundation for the future theory of dynamical structural and topological phase transitions on financial markets

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

stock market networks the dynamic conditional correlation approach we demonstrate the economic relevance of minimum spanning trees msts constructed from dynamic conditional correlations dcc for a sample of s p 100 constituents an empirical comparison of mst properties shows that using the standard approach of rolling or sliding window correlations yields trees that are more robust have higher densities and exhibit higher industry clustering than msts based on dcc our results suggest that these properties are achieved at the expense of the smoothing of market dynamics which is better preserved by dcc the dcc approach offers a new perspective for the analysis of complex systems such as stock markets

modeling the evolution of weighted networks we present a general model for the growth of weighted networks in which the structural growth is coupled with the edges weight dynamical evolution the model is based on a simple weight driven dynamics and a weights reinforcement mechanism coupled to the local network growth that coupling can be generalized in order to include the effect of additional randomness and nonlinearities which can be present in real world networks the model generates weighted graphs exhibiting the statistical properties observed in several real world systems in particular the model yields a nontrivial time evolution of vertices properties and scale free behavior with exponents depending on the microscopic parameters characterizing the coupling rules very interestingly the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices degree

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

correlation and network analysis of global financial indices random matrix theory rmt and network methods are applied to investigate the correlation and network properties of 20 financial indices the results are compared before and during the financial crisis of 2008 in the rmt method the components of eigenvectors corresponding to the second largest eigenvalue form two clusters of indices in the positive and negative directions the components of these two clusters switch in opposite directions during the crisis the network analysis uses the fruchterman reingold layout to find clusters in the network of indices at different thresholds at a threshold of 0 6 before the crisis financial indices corresponding to the americas europe and asia pacific form separate clusters on the other hand during the crisis at the same threshold the american and european indices combine together to form a strongly linked cluster while the asia pacific indices form a separate weakly linked cluster if the value of the threshold is further increased to 0 9 then the european indices france germany and the united kingdom are found to be the most tightly linked indices the structure of the minimum spanning tree of financial indices is more starlike before the crisis and it changes to become more chainlike during the crisis the average linkage hierarchical clustering algorithm is used to find a clearer cluster structure in the network of financial indices the cophenetic correlation coefficients are calculated and found to increase significantly which indicates that the hierarchy increases during the financial crisis these results show that there is substantial change in the structure of the organization of financial indices during a financial crisis

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

fuzzy linear regression models for assessing risks of cumulative trauma disorders abstract cumulative trauma disorders ctds are a major problem in industry and today s office environments especially for keyboard users since comprehensive knowledge about individual or a combination of risk factors contributing to ctds of the hand and forearm is still lacking developing methodologies to quantify relationships of risk factors is greatly needed the purpose of this research was to build fuzzy linear regression models to reveal the relationship of ctd risk factors to predict the injuries and to evaluate risk levels of individuals twenty seven keyboard users twenty two for model building and five for model validation and three ctd experts participated in the model building four fuzzy models were built corresponding to four risk categories and a final fuzzy linear model was established using ahp pairwise comparisons multicolinearity effects were addressed and a partial standard deviation scaling method was used to eliminate the effects from a methodological point of view fuzzy linear regression models provide useful insight into risk factors ctd relationship

fuzzy regression in hydrology a general methodology for fuzzy regression is developed and illustrated by an actual hydrological case study fuzzy regression may be used whenever a relationship between variables is imprecise and or data are inaccurate and or sample sizes are insufficient in such cases fuzzy regression may be used as a complement or an alternative to statistical regression analysis in fuzzy regression several goodness of fit criteria may be used such as the maximum average vagueness criterion and the prediction vagueness criterion the technique is illustrated by means of a case study involving the relationship between soil electrical resistivity and hydraulic permeability this relationship is imprecise and based on only a few data points in the present case a curvilinear relationship is fitted using fuzzy regression with six calculated resistivities and six measured permeabilities prediction vagueness criteria appears to yield a more robust fuzzy regression than the maximum average vagueness criteria potential application areas of fuzzy regression in hydrology are discussed further the methodology is relatively simple and the results can be interpreted to provide a valuable hydrological decision making aid

a study of hierarchical structure on south china industrial electricity consumption correlation abstract based on industrial electricity consumption data of five southern provinces of china from 2005 to 2013 we study the industrial correlation mechanism with mst minimal spanning tree and ht hierarchical tree models first we comparatively analyze the industrial electricity consumption correlation structure in pre crisis and after crisis period using mst model and bootstrap technique of statistical reliability test of links results exhibit that all industrial electricity consumption trees of five southern provinces of china in pre crisis and after crisis time are in formation of chain and the center periphery structure of those chain like trees is consistent with industrial specialization in classical industrial chain theory additionally the industrial structure of some provinces is reorganized and transferred in pre crisis and after crisis time further the comparative analysis with hierarchical tree and bootstrap technique demonstrates that as for both observations of gd and overall nf the industrial electricity consumption correlation is non significant clustered in pre crisis period whereas it turns significant clustered in after crisis time therefore we propose that in perspective of electricity consumption their industrial structures are directed to optimized organization and global correlation finally the analysis of distance of hts verifies that industrial reorganization and development may strengthen market integration coordination and correlation of industrial production except gz other four provinces have a shorter distance of industrial electricity consumption correlation in after crisis period revealing a better performance of regional specialization and integration

the effect of a market factor on information flow between stocks using the minimal spanning tree abstract we empirically investigated the effects of market factors on the information flow created from n n 1 2 linkage relationships among stocks we also examined the possibility of employing the minimal spanning tree mst method which is capable of reducing the number of links to n 1 we determined that market factors carry important information value regarding information flow among stocks moreover the information flow among stocks showed time varying properties according to the changes in market status in particular we noted that the information flow increased dramatically during periods of market crises finally we confirmed via the mst method that the information flow among stocks could be assessed effectively with the reduced linkage relationships among all links among stocks from the perspective of the overall market

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

sector analysis for a ftse portfolio of stocks abstract using a portfolio of stocks from the london stock exchange ftse100 index ftse we study both the time dependence of their correlations and the normalized tree length of the associated minimal spanning tree mst the first four moments of the distribution of correlations and lengths of the tree are examined in detail and differences in behavior noted for different economic groups and industries clustering is evident however comparing the classification used prior to 2006 with that introduced in january 2006 it is clear that the new classification apart from one or two notable exceptions is much more compatible with the clustering obtained by the mst analysis we finally compare the mst for real data with that obtained for a synthetic random market the latter tree would seem more like the structure found by coronnello et al for trees based on high frequency data

how many zeros of a random polynomial are real we provide an elementary geometric derivation of the kac integral formula for the expected number of real zeros of a random polynomial with independent standard normally distributed coefficients we show that the expected number of real zeros is simply the length of the moment curve 1 t tn projected onto the surface of the unit sphere divided by the probability density of the real zeros is proportional to how fast this curve is traced out we then relax kac s assumptions by considering a variety of random sums series and distributions and we also illustrate such ideas as integral geometry and the fubini study metric

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

renyi indices of financial minimum spanning trees abstract the renyi index is used here to describe topological structures of minimum spanning trees msts of financial markets we categorize the topological structures of msts as dragon star and super star types the mst based on geometric brownian motion is of dragon type the mst constructed by one factor model is super star type and most msts based on real market data belong to the star type the renyi index of the mst corresponding to s p500 is evaluated and the result shows that the renyi index varies significantly in different time periods in particular it rose during crises and dropped when the s p500 index rose significantly a comparison study between the csi300 index of the chinese market and the s p500 index shows that the mst structure of the csi300 index varies more dramatically than the mst structure of the s p500

correlations in commodity markets abstract in this paper we analyzed dependencies in commodity markets investigating correlations of future contracts for commodities over the period 1998 09 01 2007 12 14 we constructed a minimal spanning tree based on the correlation matrix the tree provides evidence for sector clusterization of investigated contracts we also studied dynamical properties of commodity dependencies it turned out that the market was constantly getting more correlated within the investigated period although the increase of correlation was distributed non uniformly among all contracts and depended on contracts branches

degree stability of a minimum spanning tree of price return and volatility we investigate the time series of the degree of minimum spanning trees msts obtained by using a correlation based clustering procedure which starts from i asset return and ii volatility time series the mst is obtained at different times by computing correlation among time series over a time window of fixed length t we find that the mst of asset return is characterized by stock degree values which are more stable in time than the ones obtained by analyzing a mst computed starting from volatility time series our analysis also shows that the degree of stocks has a very slow dynamics with a time scale of several years in both cases

a method for detection of abrupt changes in the financial market combining wavelet decomposition and correlation graphs abstract the objective of this work is to propose a new methodology to detect the imminence of abrupt changes in the stock market by combining a numerical indicator based on the wavelet decomposition technique with a measure of the interdependency of the markets using graph theory while the indicator based on wavelet decomposition is based on a single time series an approach based on network representation can provide information on the interdependency of the various markets more specifically the stock market indices are associated with nodes of a network and the correlation between pairs of nodes with links results from the theory of graphs can then be used to indicate numerically the connectivity of this network experimentations with a variety of financial time series shows that the connectivity varies as trends of the financial time series varies combining the indicator based on the wavelet decomposition with the proposed measure of the connectivity of the network it was possible to refine the authors previous results in terms of detecting abrupt changes in the stock market in order to illustrate the methodology a case study involving twelve stock market indices was presented

on the location of the zero free half plane of a random epstein zeta function in this note we study for a random lattice l of large dimension n the supremum of the real parts of the zeros of the epstein zeta function e n l s and prove that this random variable scaled by n 1 has a limit distribution which we give explicitly this limit distribution is studied in some detail in particular we give an explicit formula for its distribution function furthermore we obtain a limit distribution for the frequency of zeros of e n l s in vertical strips contained in the half plane mathfrak r s frac n 2

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

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

dynamics of market correlations taxonomy and portfolio analysis the time dependence of the recently introduced minimum spanning tree description of correlations between stocks called the asset tree has been studied in order to reflect the financial market taxonomy the nodes of the tree are identified with stocks and the distance between them is a unique function of the corresponding element of the correlation matrix by using the concept of a central vertex chosen as the most strongly connected node of the tree an important characteristic is defined by the mean occupation layer during crashes due to the strong global correlation in the market the tree shrinks topologically and this is shown by a low value of the mean occupation layer the tree seems to have a scale free structure where the scaling exponent of the degree distribution is different for business as usual and crash periods the basic structure of the tree topology is very robust with respect to time we also point out that the diversification aspect of portfolio optimization results in the fact that the assets of the classic markowitz portfolio are always located on the outer leaves of the tree technical aspects such as the window size dependence of the investigated quantities are also discussed

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

fuzzy least squares abstract several models for simple least squares fitting of fuzzy valued data are developed criteria are given for when fuzzy data sets can be fitted to the models and analogues of the normal equations are derived

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

the effects of node exclusion on the centrality measures in graph models of interacting economic agents abstract this work concerns the study of the effects felt by a network as a whole when a specific node is perturbed many real world systems can be described by network models in which the interactions of the various agents can be represented as an edge of a graph with a graph model in hand it is possible to evaluate the effect of deleting some of its edges on the architecture and values of nodes of the network eventually a node may end up isolated from the rest of the network and an interesting problem is to have a quantitative measure of the impact of such an event for instance in the field of finance the network models are very popular and the proposed methodology allows to carry out what if tests in terms of weakening the links between the economic agents represented as nodes the two main concepts employed in the proposed methodology are i the vibrational ic information centrality which can provide a measure of the relative importance of a particular node in a network and ii autocatalytic networks that can indicate the evolutionary trends of the network although these concepts were originally proposed in the context of other fields of knowledge they were also found to be useful in analyzing financial networks in order to illustrate the applicability of the proposed methodology a case of study using the actual data comprising stock market indices of 12 countries is presented

weighted assortative and disassortative networks model abstract real world networks process structured connections since they have non trivial vertex degree correlation and clustering here we propose a toy model of structure formation in real world weighted network in our model a network evolves by topological growth as well as by weight change in addition we introduce the weighted assortativity coefficient which generalizes the assortativity coefficient of a topological network to measure the tendency of having a high weighted link between two vertices of similar degrees network generated by our model exhibits scale free behavior with a tunable exponent besides a few non trivial features found in real world networks are reproduced by varying the parameter ruling the speed of weight evolution most importantly by studying the weighted assortativity coefficient we found that both topologically assortative and disassortative networks generated by our model are in fact weighted assortative

clustering of casablanca stock market based on hurst exponent estimates abstract this paper deals with the problem of casablanca stock exchange cse topology modeling as a complex network during three different market regimes general trend characterized by ups and downs increasing trend and decreasing trend in particular a set of seven different hurst exponent estimates are used to characterize long range dependence in each industrial sector generating process they are employed in conjunction with hierarchical clustering approach to examine the co movements of the casablanca stock exchange industrial sectors the purpose is to investigate whether cluster structures are similar across variable increasing and decreasing regimes it is observed that the general structure of the cse topology has been considerably changed over 2009 variable regime 2010 increasing regime and 2011 decreasing regime time periods the most important findings follow first in general a high value of hurst exponent is associated to a variable regime and a small one to a decreasing regime in addition hurst estimates during increasing regime are higher than those of a decreasing regime second correlations between estimated hurst exponent vectors of industrial sectors increase when casablanca stock exchange follows an upward regime whilst they decrease when the overall market follows a downward regime

on the zero distribution of epstein zeta functions we prove that the mean value of the real parts of the nontrivial zeros of the epstein zeta function open image in new window associated with a positive definite quadratic form open image in new window in n variables is equal to open image in new window furthermore we show that epstein zeta functions in general have an asymmetric zero distribution with respect to the critical line re open image in new window

to lag or not to lag how to compare indices of stock markets that operate on different times abstract financial markets worldwide do not have the same working hours as a consequence the study of correlation or causality between financial market indices becomes dependent on whether we should use all indices on the same day or lagged indices in computations of correlation matrices the answer this article proposes is that we should consider both by representing original and lagged indices in the same network we then obtain a better understanding of how indices that operate on different hours relate to each other we use a diverse range of 79 stock market indices from around the world and study their correlation structure the eigenvalues and eigenvectors of their correlations under different time periods and volatility as well as the differences between the working hours of the stock exchanges in order to analyze the possible time zone effects and suggest ways to remove them we also analyze the enlarged correlation matrix obtained from original and lagged indices and examine a network structure derived from it thus showing connections between lagged and original indices that could not be well represented before

evolution of correlation structure of industrial indices of u s equity markets we investigate the dynamics of correlations present between pairs of industry indices of u s stocks traded in u s markets by studying correlation based networks and spectral properties of the correlation matrix the study is performed by using 49 industry index time series computed by k french and e fama during the time period from july 1969 to december 2011 which spans more than 40 years we show that the correlation between industry indices presents both a fast and a slow dynamics the slow dynamics has a time scale longer than 5 years showing that a different degree of diversification of the investment is possible in different periods of time moreover we also detect a fast dynamics associated with exogenous or endogenous events the fast time scale we use is a monthly time scale and the evaluation time period is a 3 month time period by investigating the correlation dynamics monthly we are able to detect two examples of fast variations in the first and second eigenvalue of the correlation matrix the first occurs during the dot com bubble from march 1999 to april 2001 and the second occurs during the period of highest impact of the subprime crisis from august 2008 to august 2009

on the poisson distribution of lengths of lattice vectors in a random lattice we prove that the volumes determined by the lengths of the non zero vectors x in a random lattice l of covolume 1 define a stochastic process that as the dimension n tends to infinity converg

market structure explained by pairwise interactions financial markets are a typical example of complex systems where interactions between constituents lead to many remarkable features here we give empirical evidence by making as few assumptions as possible that the market microstructure capturing almost all of the available information in the data of stock markets does not involve higher order than pairwise interactions we give an economic interpretation of this pairwise model we show that it accurately recovers the empirical correlation coefficients thus the collective behaviors are quantitatively described by models that capture the observed pairwise correlations but no higher order interactions furthermore we show that an order disorder transition occurs as predicted by the pairwise model last we make the link with the graph theoretic description of stock markets recovering the non random and scale free topology shrinking length during crashes and meaningful clustering features as expected