the role of network topology on extremism propagation with the relative agreement opinion dynamics abstract in deffuant et al j artif soc soc simulation 5 2002 4 we proposed a simple model of opinion dynamics which we used to simulate the influence of extremists in a population simulations were run without any specific interaction structure and varying the simulation parameters we observed different attractors such as predominance of centrism or of extremism we even observed in certain conditions that the whole population drifts to one extreme of the opinion even if initially there are an equal number of extremists at each extreme of the opinion axis in the present paper we study the influence of the social networks on the presence of such a dynamical behavior in particular we use small world networks with variable connectivity and randomness of the connections we find that the drift to a single extreme appears only beyond a critical level of connectivity which decreases when the randomness increases

phase correlation of foreign exchange time series abstract correlation of foreign exchange rates in currency markets is investigated based on the empirical data of usd dem and usd jpy exchange rates for a period from february 1 1986 to december 31 1996 the return of exchange time series is first decomposed into a number of intrinsic mode functions imfs by the empirical mode decomposition method the instantaneous phases of the resultant imfs calculated by the hilbert transform are then used to characterize the behaviors of pricing transmissions and the correlation is probed by measuring the phase differences between two imfs in the same order from the distribution of phase differences our results show explicitly that the correlations are stronger in daily time scale than in longer time scales the demonstration for the correlations in periods of 1986 1989 and 1990 1993 indicates two exchange rates in the former period were more correlated than in the latter period the result is consistent with the observations from the cross correlation calculation

combinatorial r matrices for a family of crystals b 1 n d 1 n a 2 2n and d 2 n 1 cases abstract for coherent families of crystals of affine lie algebras of type b 1 n d 1 n a 2 2 n and d 2 n 1 we describe the combinatorial r matrix using column insertion algorithms for b c d young tableaux this is a continuation of previous work by the authors 2000 in physical combinatorics m kashiwara and t miwa eds birkhauser boston

correlation patterns in foreign exchange markets abstract the value of an asset in a financial market is given in terms of another asset known as numeraire the dynamics of the value is non stationary and hence to quantify the relationships between different assets one requires convenient measures such as the means and covariances of the respective log returns here we develop transformation equations for these means and covariances when one changes the numeraire the results are verified by a thorough empirical analysis capturing the dynamics of numerous assets in a foreign exchange market we show that the partial correlations between pairs of assets are invariant under the change of the numeraire this observable quantifies the relationship between two assets while the influence of the rest is removed as such the partial correlations uncover intriguing observations which may not be easily noticed in the ordinary correlation analysis

clustering of tag induced subgraphs in complex networks abstract we study the behavior of the clustering coefficient in tagged networks the rich variety of tags associated with the nodes in the networks we considered provide additional relevant information about the entities represented by the nodes such specific features can be important for practical applications like searching in the networks here we examine how the clustering coefficient changes when narrowing the network to a subgraph associated with a given tag and how it correlates with various other properties of the subgraph a further question addressed in our paper is how the clustering coefficient of the individual nodes is affected by the tags on the node we argue that this kind of analysis can be useful when one is aimed at a detailed description of the structure of large complex systems

effects of attachment preferences on coevolution of opinions and networks abstract in the coevolution of network structures and opinion formation we investigate the effects of a mixed population with distinctive relinking preferences on both the convergence time and the network structures it has been found that a heterogeneous network structure is easier to be reached with more high degree preferential hdp nodes there exists high correlation between the convergence time and the network heterogeneity the heterogeneous degree distribution caused by preferential attachment accelerates the convergence to a consensus state and the shortened convergence time inhibits the occurrence of the following disquieting situation that occurs in a continuously evolving network with preferential attachment and long time evolvement most of the nodes would become separated and only a few leaders would have immediate neighbors analytical calculations based on mean field theory reveal that both the transition point p t r and the consensus time depend upon the standard deviation of the degree distribution d p t r increases while decreases with the rise of d functions of p t r k k 1 and a n k d 2 k are found theoretical analyses are in accordance with simulation data

the coupling analysis between stock market indices based on permutation measures abstract many information theoretic methods have been proposed for analyzing the coupling dependence between time series and it is significant to quantify the correlation relationship between financial sequences since the financial market is a complex evolved dynamic system recently we developed a new permutation based entropy called cross permutation entropy cpe to detect the coupling structures between two synchronous time series in this paper we extend the cpe method to weighted cross permutation entropy wcpe to address some of cpe s limitations mainly its inability to differentiate between distinct patterns of a certain motif and the sensitivity of patterns close to the noise floor it shows more stable and reliable results than cpe does when applied it to spiky data and ar 1 processes besides we adapt the cpe method to infer the complexity of short length time series by freely changing the time delay and test it with gaussian random series and random walks the modified method shows the advantages in reducing deviations of entropy estimation compared with the conventional one finally the weighted cross permutation entropy of eight important stock indices from the world financial markets is investigated and some useful and interesting empirical results are obtained

multifractality in the random parameter model for multivariate time series abstract the random parameter model was proposed to explain the structure of the covariance matrix in problems where most but not all of the eigenvalues of the covariance matrix can be explained by random matrix theory in this article we explore the scaling properties of the model as observed in the multifractal structure of the simulated time series we use the wavelet transform modulus maxima technique to obtain the multifractal spectrum dependence with the parameters of the model the model shows a scaling structure compatible with the stylized facts for a reasonable choice of the parameter values

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

multivariate markov chain modeling for stock markets abstract we study a multivariate markov chain model as a stochastic model of the price changes of portfolios in the framework of the mean field approximation the time series of price changes are coded into the sequences of up and down spins according to their signs we start with the discussion for small portfolios consisting of two stock issues the generalization of our model to arbitrary size of portfolio is constructed by a recurrence relation the resultant form of the joint probability of the stationary state coincides with gibbs measure assigned to each configuration of spin glass model through the analysis of actual portfolios it has been shown that the synchronization of the direction of the price changes is well described by the model

analytical calculation of fragmentation transitions in adaptive networks in adaptive networks fragmentation transitions have been observed in which the network breaks into disconnected components we present an analytical approach for calculating the transition point in general adaptive network models using the example of an adaptive voter model we demonstrate that the proposed approach yields good agreement with numerical results

a jump model for credit default swaps with hierarchical clustering abstract the return time series of credit default swaps cds display possibly the highest excess kurtosis and skewness of any asset class in capital markets capturing this requires a departure from classical modeling techniques here the premise is that cds prices jump and those jumps cluster initially a model is proposed that is driven by a diffusion and a hawkes process to reproduce the clustering of shocks the new element of the model is the use of hierarchical clustering to calibrate the distribution of the jumps partitioning the shocks identifies shifts in the volatility regime of the cds through time which are shown to consistently correspond to both systemic and idiosyncratic market events a piecewise definition of a double exponential distribution for the jumps corresponding to the identified clusters is employed to replicate the regime switching subsequently this demonstrably improves the accuracy of the calibration the model is fitted to all cds with more than 2000 closing prices from 2001 to 2014 a total of 1652 individual time series for each credit a peak over threshold approach is applied to the return series to separate the data into those returns that can broadly be classified as log normal and those that can be characterized as jumps by explicitly linking the results to market traded volumes the results indicate a clear split of the cds into liquid and illiquid names a key finding is that for the illiquid cds it is difficult to justify the continuous component of the model for the low liquidity names the hawkes process is shown to capture the price action without a diffusion a markov chain is then introduced into the simulation to replicate the clustering and regime switching

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

topology induced coarsening in language games we investigate how very large populations are able to reach a global consensus out of local microscopic interaction rules in the framework of a recently introduced class of models of semiotic dynamics the so called naming game we compare in particular the convergence mechanism for interacting agents embedded in a low dimensional lattice with respect to the mean field case we highlight that in low dimensions consensus is reached through a coarsening process that requires less cognitive effort of the agents with respect to the mean field case but takes longer to complete in one dimension the dynamics of the boundaries is mapped onto a truncated markov process from which we analytically computed the diffusion coefficient more generally we show that the convergence process requires a memory per agent scaling as n and lasts a time n 1 2 d in dimension d 4 the upper critical dimension while in mean field both memory and time scale as n 3 2 for a population of n agents we present analytical and numerical evidence supporting this picture

correlation structure and dynamics of international real estate securities markets a network perspective abstract in this paper we investigate the correlation structure and dynamics of international real estate securities markets by using daily returns of 20 national markets during the period 2006 2012 from a network perspective we construct the minimum spanning tree mst the hierarchical tree ht and the planar maximally filtered graph pmfg obtained from the correlation matrix computed by the daily returns during the investigated period and analyze the corresponding clustering structure hierarchical structure and community structure we also build the time varying mst and pmfg networks by a rolling window to examine the dynamics of correlation structure the empirical results show that 1 the distribution of correlation coefficients is asymmetric fat tailed and non gaussian 2 the distributions of the influence strength of the mst and pmfg networks obey a power law 3 two clusters i e the european and asia pacific clusters are found in the mst network three hierarchical clusters i e two like in the mst and the north american cluster in the ht and three communities in the pmfg network which shows that national markets are linked together according to their geographical distributions 4 the descriptive statistics of correlation coefficients and distances of the msts and pmfgs are time varying especially during periods of crisis they have a large fluctuation 5 a huge number of linkages between national markets survive from one time to the next and the long term stability of the correlation structure in international real estate securities markets descends as time goes on our obtained results are new insights in international real estate securities markets and have wide applications for investment portfolio and risk management

x m for symmetric powers author s schilling anne shimozono mark abstract the x m conjecture of hatayama et al asserts the equality between the one dimensional configuration sum x expressed as the generating function of crystal paths with energy statistics and the fermionic formula m for all affine kac moody algebra in this paper we prove the x m conjecture for tensor products of kirillov reshetikhin crystals b 1 s associated to symmetric powers for all nonexceptional affine algebras

dynamic scaling approach to study time series fluctuations we propose an approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface growth problem in this framework the fluctuation sampling time interval plays the role of time variable whereas the physical time is treated as the analog of spatial variable in this way we found that the fluctuations of many real world time series satisfy the analog of the family viscek dynamic scaling ansatz this finding permits us to use the powerful tools of kinetic roughening theory to classify model and forecast the fluctuations of real world time series

modelling gap size distribution of parked cars using random matrix theory abstract we apply the random matrix theory to the car parking problem for this purpose we adopt a coulomb gas model that associates the coordinates of the gas particles with the eigenvalues of a random matrix the nature of interaction between the particles is consistent with the tendency of the drivers to park their cars near to each other and in the same time keep a distance sufficient for manoeuvring we show that the recently measured gap size distribution of parked cars in a number of roads in central london is well represented by the spacing distribution of a gaussian unitary ensemble

quantization of branching coefficients for classical lie groups abstract we study natural quantizations k of branching coefficients corresponding to the restrictions of the classical lie groups to the levi subgroups of their standard parabolic subgroups the polynomials obtained can be regarded as generalizations of lusztig q analogues of weight multiplicities for gl n they coincide with poincare polynomials previously studied by shimozono and weyman they also appear in the hilbert series of the euler characteristic of certain graded virtual g modules and by a result of broer admit nonnegative coefficients providing that restrictive conditions are verified when the levi subgroup considered is isomorphic to a direct product of linear groups we prove that these polynomials admit a stable limit k which decomposes as nonnegative integer combination of poincare polynomials for a general levi subgroup it is conjectured that the polynomials k have nonnegative coefficients when they are parametrized by two partitions when g gl n the polynomials k can be interpreted as quantizations of the littlewood richardson coefficients we show that there also exists a duality between tensor product coefficients for types b c d defined as the analogues of the littlewood richardson coefficients and branching coefficients corresponding to the restriction of so 2 n to subgroups defined from orthogonal decompositions of the root system d n which are not levi subgroups these coefficients can also be quantified but the q analogues obtained may have negative coefficients given a tensor product of irreducible gl n modules we then introduce for each classical group g so n or sp n some q analogues d of the multiplicities obtained by decomposing into its g irreducible components we establish a duality between the polynomials d and k according to a conjecture by shimozono the stable one dimensional sums for nonexceptional affine crystals are expected to coincide with the polynomials d associated to a sequence of rectangular partitions of decreasing heights

scaling analysis of trends using dfa we study two aspects of the detrended uctuation analysis dfa method namely the scaling behavior of the leading terms of the best 0t polynomials and the detection of trends we show analytically and numerically that the standard deviation of the leading terms of the best 0t polynomials used in dfa displays scaling behavior furthermore we demonstrate that the distribution of these terms can be used to reveal the presence of trends in the data we also argue that this distribution can be used as a sensitive tool for identifying weak trends c 2001 elsevier science b v all rights reserved

coevolution of glauber like ising dynamics and topology we study the coevolution of a generalized glauber dynamics for ising spins with tunable threshold and of the graph topology where the dynamics takes place this simple coevolution dynamics generates a rich phase diagram in the space of the two parameters of the model the threshold and the rewiring probability the diagram displays phase transitions of different types spin ordering percolation and connectedness at variance with traditional coevolution models in which all spins of each connected component of the graph have equal value in the stationary state we find that for suitable choices of the parameters the system may converge to a state in which spins of opposite sign coexist in the same component organized in compact clusters of like signed spins mean field calculations enable one to estimate some features of the phase diagram

volatility and correlation based systemic risk measures in the us market this paper deals with the problem of how to use simple systemic risk measures to assess portfolio risk characteristics using three simple examples taken from previous literature one based on raw and partial correlations another based on the eigenvalue decomposition of the covariance matrix and the last one based on an eigenvalue entropy a granger causation analysis revealed some of them are not always a good measure of risk in the sp therefore in the sense of risk as volatility the indicators are not always suitable nevertheless their results towards returns are similar to previous works that accept them a deeper analysis has shown that any symmetric measure based on eigenvalue decomposition of correlation matrices however is not useful as a measure of correlation risk the empirical counterpart analysis of this proposition stated that negative correlations are usually small and therefore do not heavily distort the behavior of the indicator

detecting synchronization clusters in multivariate time series via coarse graining of markov chains synchronization cluster analysis is an approach to the detection of underlying structures in data sets of multivariate time series starting from a matrix r of bivariate synchronization indices a previous method utilized the eigenvectors of r for cluster identification analogous to several recent attempts at group identification using eigenvectors of the correlation matrix all of these approaches assumed a one to one correspondence of dominant eigenvectors and clusters which has however been shown to be wrong in important cases we clarify the usefulness of eigenvalue decomposition for synchronization cluster analysis by translating the problem into the language of stochastic processes and derive an enhanced clustering method harnessing recent insights from the coarse graining of finite state markov processes we illustrate the operation of our method using a simulated system of coupled lorenz oscillators and we demonstrate its superior performance over the previous approach finally we investigate the question of robustness of the algorithm against small sample size which is important with regard to field applications

naming games in two dimensional and small world connected random geometric networks we investigate a prototypical agent based model the naming game on two dimensional random geometric networks the naming game a baronchelli et al j stat mech theory exp 2006 p06014 is a minimal model employing local communications that captures the emergence of shared communication schemes languages in a population of autonomous semiotic agents implementing the naming games with local broadcasts on random geometric graphs serves as a model for agreement dynamics in large scale autonomously operating wireless sensor networks further it captures essential features of the scaling properties of the agreement process for spatiallyembedded autonomous agents among the relevant observables capturing the temporal properties of the agreement process we investigate the cluster size distribution and the distribution of the agreement times both exhibiting dynamic scaling we also present results for the case when a small density of long range communication links are added on top of the random geometric graph resulting in a small world like network and yielding a significantly reduced time to reach global agreement we construct a finite size scaling analysis for the agreement times in this case

effect of changing data size on eigenvalues in the korean and japanese stock markets abstract in this study we attempted to determine how eigenvalues change according to random matrix theory rmt in stock market data as the number of stocks comprising the correlation matrix changes specifically we tested for changes in the eigenvalue properties as a function of the number and type of stocks in the correlation matrix we determined that the value of the eigenvalue increases in proportion with the number of stocks furthermore we noted that the largest eigenvalue maintains its identical properties regardless of the number and type whereas other eigenvalues evidence different features

a new approach to quantify power law cross correlation and its application to commodity markets abstract we proposed a new method detrended moving average cross correlation analysis dmca to detect the power law cross correlation between two correlated non stationary time series by combining detrended cross correlation analysis dcca and detrended moving average dma in order to compare the performance of dmca and dcca in the detection of cross correlation and to estimate the influence of periodic trend we generate two cross correlated time series x i and y i by a periodic two component fractionally autoregressive integrated moving average arfima process then we apply both methods to quantify the cross correlations of the generated series whose theoretical values are already known to us by comparing the results we obtained we find that the performance of this new approach is comparable to dcca with less calculating amounts our method can also reduce the impact of trends furthermore dmca for background and forward moving average case outperforms dcca in more accurate estimation when the analyzed times series are short in length to provide an example we also apply this new method to the time series of the real world data from brent and wti crude oil spot markets to investigate the complex cross market correlation between these commodity markets in all our method is another practical choice to detect the cross correlation between two short period non stationary time series and has potential application to real world problems

schensted type correspondence plactic monoid and jeu de taquin for type cn we use kashiwara s theory of crystal bases to study the plactic monoid for uq sp2n then we describe the corresponding insertion and sliding algorithms the sliding algorithm is essentially the symplectic jeu de taquin defined by sheats and our construction gives the proof of its compatibility with plactic relations

crystal graphs for representations of the q analogue of classical lie algebras the explicit form of the crystal graphs for the finite dimensional representations of the q analogue of the universal enveloping algebras of type a b c and d is given in terms of semi standard tableaux and its analogues

universal and nonuniversal properties of cross correlations in financial time series we use methods of random matrix theory to analyze the cross correlation matrix c of stock price changes of the largest 1000 u s companies for the 2 year period 1994 1995 we find that the statistics of most of the eigenvalues in the spectrum of c agree with the predictions of random matrix theory but there are deviations for a few of the largest eigenvalues we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices furthermore we analyze the eigenvectors of c through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum a situation reminiscent of localization theory results

affine crystals one dimensional sums and parabolic lusztig q analogues this paper is concerned with one dimensional sums in classical affine types we prove a conjecture of shimozono and zabrocki j algebra 299 33 61 2006 by showing they all decompose in terms of one dimensional sums related to affine type a provided the rank of the root system considered is sufficiently large as a consequence any one dimensional sum associated to a classical affine root system with sufficiently large rank can be regarded as a parabolic lusztig q analogue

comparison of voter and glauber ordering dynamics on networks we study numerically the ordering process of two very simple dynamical models for a two state variable on several topologies with increasing levels of heterogeneity in the degree distribution we find that the zero temperature glauber dynamics for the ising model may get trapped in sets of partially ordered metastable states even for finite system size and this becomes more probable as the size increases voter dynamics instead always converges to full order on finite networks even if this does not occur via coherent growth of domains the time needed for order to be reached diverges with the system size in both cases the ordering process is rather insensitive to the variation of the degreee distribution from sharply peaked to scale free

stable rigged configurations for quantum affine algebras of nonexceptional types for an affine algebra of nonexceptional type in the large rank we show the fermionic formula depends only on the attachment of the node 0 of the dynkin diagram to the rest and the fermionic formula of not type a can be expressed as a sum of that of type a with littlewood richardson coefficients combining this result with kirillov et al 2002 13 and lecouvey et al 2011 18 we settle the x m conjecture under the large rank hypothesis

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

correlation network analysis for multi dimensional data in stocks market this paper shows how the concept of vector correlation can appropriately measure the similarity among multivariate time series in stocks network the motivation of this paper is i to apply the rv coefficient to define the network among stocks where each of them is represented by a multivariate time series ii to analyze that network in terms of topological structure of the stocks of all minimum spanning trees and iii to compare the network topology between univariate correlation based on r and multivariate correlation network based on rv coefficient

economic fluctuations and statistical physics quantifying extremely rare and less rare events in finance one challenge of economics is that the systems treated by these sciences have no perfect metronome in time and no perfect spatial architecture crystalline or otherwise nonetheless as if by magic out of nothing but randomness one finds remarkably fine tuned processes in time we present an overview of recent research joining practitioners of economic theory and statistical physics to try to better understand puzzles regarding economic fluctuations one of these puzzles is how to describe outliers phenomena that lie outside of patterns of statistical regularity we review evidence consistent with the possibility that such outliers may not exist this possibility is supported by recent analysis of databases containing information about each trade of every stock r 2007 elsevier b v all rights reserved

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

consensus formation on coevolving networks groups formation and structure we study the effect of adaptivity on a social model of opinion dynamics and consensus formation we analyse how the adaptivity of the network of contacts between agents to the underlying social dynamics affects the size and topological properties of groups and the convergence time to the stable final state we find that while on static networks these properties are determined by percolation phenomena on adaptive networks the rewiring process leads to different behaviors adaptive rewiring fosters group formation by enhancing communication between agents of similar opinion though it also makes possible the division of clusters we show how the convergence time is determined by the characteristic time of link rearrangement we finally investigate how the adaptivity yields nontrivial correlations between the internal topology and the size of the groups of agreeing agents

visibility graph analysis on quarterly macroeconomic series of china based on complex network theory abstract the visibility graph approach and complex network theory provide a new insight into time series analysis the inheritance of the visibility graph from the original time series was further explored in the paper we found that degree distributions of visibility graphs extracted from pseudo brownian motion series obtained by the frequency domain algorithm exhibit exponential behaviors in which the exponential exponent is a binomial function of the hurst index inherited in the time series our simulations presented that the quantitative relations between the hurst indexes and the exponents of degree distribution function are different for different series and the visibility graph inherits some important features of the original time series further we convert some quarterly macroeconomic series including the growth rates of value added of three industry series and the growth rates of gross domestic product series of china to graphs by the visibility algorithm and explore the topological properties of graphs associated from the four macroeconomic series namely the degree distribution and correlations the clustering coefficient the average path length and community structure based on complex network analysis we find degree distributions of associated networks from the growth rates of value added of three industry series are almost exponential and the degree distributions of associated networks from the growth rates of gdp series are scale free we also discussed the assortativity and disassortativity of the four associated networks as they are related to the evolutionary process of the original macroeconomic series all the constructed networks have small world features the community structures of associated networks suggest dynamic changes of the original macroeconomic series we also detected the relationship among government policy changes community structures of associated networks and macroeconomic dynamics we find great influences of government policies in china on the changes of dynamics of gdp and the three industries adjustment the work in our paper provides a new way to understand the dynamics of economic development

fragmentation transitions in multistate voter models adaptive models of opinion formation among humans can display a fragmentation transition where a social network breaks into disconnected components here we investigate this transition in a class of models with arbitrary number of opinions in contrast to previous work we do not assume that opinions are equidistant or arranged on a one dimensional conceptual axis our investigation reveals detailed analytical results on fragmentations in a three opinion model which are confirmed by agent based simulations furthermore we show that in certain models the number of opinions can be reduced without affecting the fragmentation points

hierarchy and polysynchrony in an adaptive network we describe a simple adaptive network of coupled chaotic maps the network reaches a stationary state frozen topology for all values of the coupling parameter although the dynamics of the maps at the nodes of the network can be nontrivial the structure of the network shows interesting hierarchical properties and in certain parameter regions the dynamics is polysynchronous nodes can be divided in differently synchronized classes but contrary to cluster synchronization nodes in the same class need not be connected to each other these complicated synchrony patterns have been conjectured to play roles in systems biology and circuits the adaptive system we study describes ways whereby this behavior can evolve from undifferentiated nodes

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

lusztig s q analogue of weight multiplicity and one dimensional sums for affine root systems abstract in this paper we complete the proof of the x k conjecture that for every family of nonexceptional affine algebras the graded multiplicities of tensor products of symmetric power kirillov reshetikhin modules known as one dimensional sums have a large rank stable limit x that has a simple expression called the k polynomial as nonnegative integer combination of kostka foulkes polynomials we consider a subfamily of lusztig s q analogues of weight multiplicity which we call stable kl polynomials and denote by kl we give a type independent proof that k kl this proves that x kl the family of stable one dimensional sums coincides with family of stable kl polynomials our result generalizes the theorem of nakayashiki and yamada which establishes the above equality in the case of one dimensional sums of affine type a and the lusztig q analogue of type a where both are kostka foulkes polynomials

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

random matrix approach to categorical data analysis correlation and similarity measures are widely used in all the areas of sciences and social sciences often the variables are not numbers but are instead qualitative descriptors called categorical data we define and study similarity matrix as a measure of similarity for the case of categorical data this is of interest due to a deluge of categorical data such as movie ratings top 10 rankings and data from social media in the public domain that require analysis we show that the statistical properties of the spectra of similarity matrices constructed from categorical data follow random matrix predictions with the dominant eigenvalue being an exception we demonstrate this approach by applying it to the data for indian general elections and sea level pressures in the north atlantic ocean

localized short range correlations in the spectrum of the equal time correlation matrix we suggest a procedure to identify those parts of the spectrum of the equal time correlation matrix mathbf c where relevant information about correlations of a multivariate time series is induced using an ensemble average over each of the distances between eigenvalues all nearest neighbor distributions can be calculated individually we present numerical examples where a information about cross correlations is found in the so called bulk of eigenvalues which generally is thought to contain only random correlations and where b the information extracted from the lower edge of the spectrum of mathbf c is statistically more significant than that extracted from the upper edge we apply the analysis to electroencephalographic recordings with epileptic events

voter model dynamics in complex networks role of dimensionality disorder and degree distribution we analyze the ordering dynamics of the voter model in different classes of complex networks we observe that whether the voter dynamics orders the system depends on the effective dimensionality of the interaction networks we also find that when there is no ordering in the system the average survival time of metastable states in finite networks decreases with network disorder and degree heterogeneity the existence of hubs i e highly connected nodes in the network modifies the linear system size scaling law of the survival time the size of an ordered domain is sensitive to the network disorder and the average degree decreasing with both however it seems not to depend on network size and on the heterogeneity of the degree distribution

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

developments in random matrix theory in this introduction to the journal of physics a special issue on random matrix theory we give a review of the main historical developments in random matrix theory a short summary of the papers that appear in this special issue is also given

time scales involved in emergent market coherence abstract in addressing the question of the time scales characteristic for the market formation we analyze high frequency tick by tick data from the nyse and from the german market by using returns on various time scales ranging from seconds or minutes up to 2 days we compare magnitude of the largest eigenvalue of the correlation matrix for the same set of securities but for different time scales for various sets of stocks of different capitalization and the average trading frequency we observe a significant elevation of the largest eigenvalue with increasing time scale our results from the correlation matrix study can be considered as a manifestation of the so called epps effect there is no unique explanation of this effect and it seems that many different factors play a role here one of such factors is randomness in transaction moments for different stocks another interesting conclusion to be drawn from our results is that in the contemporary markets the emergence of significant correlations occurs on time scales much smaller than in the more distant history

complexity of major uk companies between 2006 and 2010 hierarchical structure method approach abstract this study reports on topology of the top 40 uk companies that have been analysed for predictive verification of markets for the period 2006 2010 applying the concept of minimal spanning tree and hierarchical tree ht analysis construction of the minimal spanning tree mst and the hierarchical tree ht is confined to a brief description of the methodology and a definition of the correlation function between a pair of companies based on the london stock exchange lse index in order to quantify synchronization between the companies a derivation of hierarchical organization and the construction of minimal spanning and hierarchical trees for the 2006 2008 and 2008 2010 periods have been used and the results validate the predictive verification of applied semantics the trees are known as useful tools to perceive and detect the global structure taxonomy and hierarchy in financial data from these trees two different clusters of companies in 2006 were detected they also show three clusters in 2008 and two between 2008 and 2010 according to their proximity the clusters match each other as regards their common production activities or their strong interrelationship the key companies are generally given by major economic activities as expected this work gives a comparative approach between mst and ht methods from statistical physics and information theory with analysis of financial markets that may give new valuable and useful information of the financial market dynamics

the coevolution of individual economic characteristics and socioeconomic networks abstract the dynamics of individual characteristics of economic agents is modeled with the link structure influenced by this dynamics links between agents with similar characteristics are more stable than those between agents with vastly different characteristics a simple scaling law describes the number of distinct surviving characteristic realizations as a function of the number of agents and the number of possible distinct characteristics realizations with the chosen specification the investigated properties do not essentially differ from those found for analogous sociophysics models with a fixed network structure

self organization of complex networks as a dynamical system to understand the dynamics of real world networks we investigate a mathematical model of the interplay between the dynamics of random walkers on a weighted network and the link weights driven by a resource carried by the walkers our numerical studies reveal that under suitable conditions the co evolving dynamics lead to the emergence of stationary power law distributions of the resource and link weights while the resource quantity at each node ceaselessly changes with time we analyze the network organization as a deterministic dynamical system and find that the system exhibits multistability with numerous fixed points limit cycles and chaotic states the chaotic behavior of the system leads to the continual changes in the microscopic network dynamics in the absence of any external random noises we conclude that the intrinsic interplay between the states of the nodes and network reformation constitutes a major factor in the vicissitudes of real world networks

consensus formation on adaptive networks the structure of a network can significantly influence the properties of the dynamical processes that take place on them while many studies have been paid to this influence much less attention has been devoted to the interplay and feedback mechanisms between dynamical processes and network topology on adaptive networks adaptive rewiring of links can happen in real life systems such as acquaintance networks where people are more likely to maintain a social connection if their views and values are similar in our study we consider different variants of a model for consensus formation our investigations reveal that the adaptation of the network topology fosters cluster formation by enhancing communication between agents of similar opinion although it also promotes the division of these clusters the temporal behavior is also strongly affected by adaptivity while on static networks it is influenced by percolation properties on adaptive networks both the early and late time evolutions of the system are determined by the rewiring process the investigation of a variant of the model reveals that the scenarios of transitions between consensus and polarized states are more robust on adaptive networks

deformed universal characters for classical and affine algebras abstract creation operators are given for the three distinguished bases of the type bcd universal character ring of koike and terada yielding an elegant way of treating computations for all three types in a unified manner deformed versions of these operators create symmetric function bases whose expansion in the universal character basis has polynomial coefficients in q with nonnegative integer coefficients we conjecture that these polynomials are one dimensional sums associated with crystal bases of finite dimensional modules over quantized affine algebras for all nonexceptional affine types these polynomials satisfy a macdonald type duality

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

detection and characterization of changes of the correlation structure in multivariate time series we propose a method based on the equal time correlation matrix as a sensitive detector for phase shape correlations in multivariate data sets the key point of the method is that changes of the degree of synchronization between time series provoke level repulsions between eigenstates at both edges of the spectrum of the correlation matrix consequently detailed information about the correlation structure of the multivariate data set is imprinted into the dynamics of the eigenvalues and into the structure of the corresponding eigenvectors the performance of the technique is demonstrated by application to n f tori autoregressive models and coupled chaotic systems the high sensitivity the comparatively small computational effort and the excellent time resolution of the method recommend it for application to the analysis of complex spatially extended nonstationary systems

multifractal detrended cross correlation analysis of gold price and sensex abstract this paper studies the variation of autocorrelation and cross correlation coefficients of gold price and sensex fluctuations with time the paper uses mfdfa and mfdxa methodologies sensex plays a more dominant role in the variation of cross correlations it is observed that the cross correlation coefficients can be linked with the stability of the market the market is most stable when the two series are most correlated

a model of the effects of authority on consensus formation in adaptive networks impact on network topology and robustness abstract opinions of individuals in real social networks are arguably strongly influenced by external determinants such as the opinions of those perceived to have the highest levels of authority in order to model this we have extended an existing model of consensus formation in an adaptive network by the introduction of a parameter representing each agent s level of authority based on their opinion relative to the overall opinion distribution we found that introducing this model along with a randomly varying opinion convergence factor significantly impacts the final state of converged opinions and the number of interactions required to reach that state we also determined the relationship between initial and final network topologies for this model and whether the final topology is robust to node removals our results indicate firstly that the process of consensus formation with a model of authority consistently transforms the network from an arbitrary initial topology to one with distinct measurements in mean shortest path clustering coefficient and degree distribution secondly we found that subsequent to the consensus formation process the mean shortest path and clustering coefficient are less affected by both random and targeted node disconnection speculation on the relevance of these results to real world applications is provided

dynamics of majority rule in two state interacting spin systems we introduce a two state opinion dynamics model where agents evolve by majority rule in each update a group of agents is specified whose members then all adopt the local majority state in the mean field limit where a group consists of randomly selected agents consensus is reached in a time that scales ln n where n is the number of agents on finite dimensional lattices where a group is a contiguous cluster the consensus time fluctuates strongly between realizations and grows as a dimension dependent power of n the upper critical dimension appears to be larger than 4 the final opinion always equals that of the initial majority except in one dimension

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

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

collective behavior of stock price movements a random matrix theory approach we review recent work on quantifying collective behavior among stocks by applying the conceptual framework of random matrix theory rmt developed in physics to describe the energy levels ofcomplex systems rmt makes predictions f universal properties that do not depend on the interactions between the elements comprising the system deviations from rmt provide clues regarding system speci c properties we compare the statistics ofthe cross correlation matrix c whose elements cij are the correlation coe cients ofprice uctuations ofstock i and j against a random matrix having the same symmetry properties it is found that rmt methods can distinguish random and non random parts of c the non random part of c which deviates from rmt results provides information regarding genuine collective behavior among stocks c 2001 published by elsevier science b v

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

quantifying economic fluctuations abstract this manuscript is a brief summary of a talk designed to address the question of whether two of the pillars of the field of phase transitions and critical phenomena scale invariance and universality can be useful in guiding research on interpreting empirical data on economic fluctuations using this conceptual framework as a guide we empirically quantify the relation between trading activity measured by the number of transactions n and the price change g t for a given stock over a time interval t t t we relate the time dependent standard deviation of price changes volatility to two microscopic quantities the number of transactions n t in t and the variance w2 t of the price changes for all transactions in t we find that the long ranged volatility correlations are largely due to those of n we then argue that the tail exponent of the distribution of n is insufficient to account for the tail exponent of p g x since n and w display only weak inter dependency our results show that the fat tails of the distribution p g x arises from w finally we review recent work on quantifying collective behavior among stocks by applying the conceptual framework of random matrix theory rmt rmt makes predictions for universal properties that do not depend on the interactions between the elements comprising the system and deviations from rmt provide clues regarding system specific properties we compare the statistics of the cross correlation matrix c whose elements cij are the correlation coefficients of price fluctuations of stock i and j against a random matrix having the same symmetry properties it is found that rmt methods can distinguish random and non random parts of c the non random part of c which deviates from rmt results provides information regarding genuine collective behavior among stocks we also discuss results that are reminiscent of phase transitions in spin systems where the divergent behavior of the response function at the critical point zero magnetic field leads to large fluctuations and we discuss a curious symmetry breaking a feature qualitatively identical to the behavior of the probability density of the magnetization for fixed values of the inverse temperature

deffuant model of opinion formation in one dimensional multiplex networks complex systems in the real world often operate through multiple kinds of links connecting their constituents in this paper we propose an opinion formation model under bounded confidence over multiplex networks consisting of edges at different topological and temporal scales we determine rigorously the critical confidence threshold by exploiting probability theory and network science when the nodes are arranged on the integers evolving in continuous time it is found that the existence of multiplexity impedes the convergence and that working with the aggregated or summarized simplex network is inaccurate since it misses vital information analytical calculations are confirmed by extensive numerical simulations

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

early fragmentation in the adaptive voter model on directed networks we consider voter dynamics on a directed adaptive network with fixed out degree distribution a transition between an active phase and a fragmented phase is observed this transition is similar to the undirected case if the networks are sufficiently dense and have a narrow out degree distribution however if a significant number of nodes with low out degree is present then fragmentation can occur even far below the estimated critical point due to the formation of self stabilizing structures that nucleate fragmentation this process may be relevant for fragmentation in current political opinion formation processes

similarities between stock price correlation networks and co main product networks threshold scenarios abstract because of the high yields and high risks associated with the stock market investors can hold diversified portfolios with low relativity of stocks to reduce unsystematic risk the current literature analyzes single factors affecting the relativity of stocks but in this paper we analyze the correlations between different factors to provide multiple perspectives of and about investment portfolios this study analyzes the relationships between the similarities of the main products of listed companies and the varying degrees of correlations of stock price by examining different threshold scenarios of the energy industry between 2012 and 2016 and then constructing stock price correlation threshold networks and co main product networks to analyze the similarities in their structures the results indicate that two factors are significantly correlated in 97 5 of the scenarios and that these factors are the most strongly correlated when the threshold is between 0 5 and 0 7 the two networks exhibit a high degree of similarity in degree weighted degree and community division main product similarity used as supplementary information for stock relativity research plays a role similar to stock price correlations in certain scenarios furthermore compared with stock price correlations the similarity of main products is simpler and more intuitive this paper proposes a new method to study stock relativity based on different threshold scenarios thus it could serve as a reference for investors when developing portfolio strategies from multiple perspectives

graph fission in an evolving voter model we consider a simplified model of a social network in which individuals have one of two opinions called 0 and 1 and their opinions and the network connections coevolve edges are picked at random if the two connected individuals hold different opinions then with probability 1 one imitates the opinion of the other otherwise i e with probability the link between them is broken and one of them makes a new connection to an individual chosen at random i from those with the same opinion or ii from the network as a whole the evolution of the system stops when there are no longer any discordant edges connecting individuals with different opinions letting be the fraction of voters holding the minority opinion after the evolution stops we are interested in how depends on and the initial fraction u of voters with opinion 1 in case i there is a critical value c which does not depend on u with u for c and 0 for c u u but for c u we have u 1 2 using simulations and approximate calculations we explain why these two nearly identical models have such dramatically different phase transitions

an analysis of cross correlations in an emerging market abstract we apply random matrix theory to compare correlation matrix estimators c obtained from emerging market data the correlation matrices are constructed from 10 years of daily data for stocks listed on the johannesburg stock exchange jse from january 1993 to december 2002 we test the spectral properties of c against random matrix predictions and find some agreement between the distributions of eigenvalues nearest neighbour spacings distributions of eigenvector components and the inverse participation ratios for eigenvectors we show that interpolating both missing data and illiquid trading days with a zero order hold increases agreement with rmt predictions for the more realistic estimation of correlations in an emerging market we suggest a pairwise measured data correlation matrix for the data set used this approach suggests greater temporal stability for the leading eigenvectors an interpretation of eigenvectors in terms of trading strategies is given as opposed to classification by economic sectors

record statistics for multiple random walks we study the statistics of the number of records r n n for n identical and independent symmetric discrete time random walks of n steps in one dimension all starting at the origin at step 0 at each time step each walker jumps by a random length drawn independently from a symmetric and continuous distribution we consider two cases i when the variance ensuremath sigma 2 of the jump distribution is finite and ii when ensuremath sigma 2 is divergent as in the case of l evy flights with index 0l ensuremath mu l2 in both cases we find that the mean record number ensuremath langle r n n ensuremath rangle grows universally as ensuremath sim ensuremath alpha n sqrt n for large n but with a very different behavior of the amplitude ensuremath alpha n for ng1 in the two cases we find that for large n ensuremath alpha n ensuremath approx 2 sqrt mathrm ln n independently of ensuremath sigma 2 in case i in contrast in case ii the amplitude approaches to an n independent constant for large n ensuremath alpha n ensuremath approx 4 sqrt ensuremath pi independently of 0l ensuremath mu l2 for finite ensuremath sigma 2 we argue and this is confirmed by our numerical simulations that the full distribution of r n n sqrt n ensuremath 2 sqrt mathrm ln n sqrt mathrm ln n converges to a gumbel law as n ensuremath rightarrow ensuremath infty and n ensuremath rightarrow ensuremath infty in case ii our numerical simulations indicate that the distribution of r n n sqrt n converges for n ensuremath rightarrow ensuremath infty and n ensuremath rightarrow ensuremath infty to a universal nontrivial distribution independently of ensuremath mu we discuss the applications of our results to the study of the record statistics of 366 daily stock prices from the standard poor s 500 index

multiopinion coevolving voter model with infinitely many phase transitions we consider an idealized model in which individuals changing opinions and their social network coevolve with disagreements between neighbors in the network resolved either through one imitating the opinion of the other or by reassignment of the discordant edge specifically an interaction between x and one of its neighbors y leads to x imitating y with probability 1 and otherwise i e with probability x cutting its tie to y in order to instead connect to a randomly chosen individual building on previous work about the two opinion case we study the multiple opinion situation finding that the model has infinitely many phase transitions in the large graph limit with infinitely many initial opinions moreover the formulas describing the end states of these processes are remarkably simple when expressed as a function of 1

network trending leadership followership and neutrality among companies a random matrix approach abstract in this article we analyze the cross correlation between returns of different stocks to answer the following important questions the first one is if there exists collective behavior in a financial market how could we detect it and the second question is is there a particular company among the companies of a market as the leader of the collective behavior or is there no specified leadership governing the system similar to some complex systems we use the method of random matrix theory to answer the mentioned questions cross correlation matrix of index returns of four different markets is analyzed the participation ratio quantity related to each matrices eigenvectors and the eigenvalue spectrum is calculated we introduce shuffled matrix created of cross correlation matrix in such a way that the elements of the later one are displaced randomly comparing the participation ratio quantities obtained from a correlation matrix of a market and its related shuffled one on the bulk distribution region of the eigenvalues we detect a meaningful deviation between the mentioned quantities indicating the collective behavior of the companies forming the market by calculating the relative deviation of participation ratios we obtain a measure to compare the markets according to their collective behavior answering the second question we show there are three groups of companies the first group having higher impact on the market trend called leaders the second group is followers and the third one is the companies who have not a considerable role in the trend the results can be utilized in portfolio construction