The observation that real complex networks have internal structure has important implication for dynamic processes occurring on such topologies. Here we investigate the impact of community structure on a model of information transfer able to deal with both search and congestion simultaneously. We show that networks with fuzzy community structure are more efficient in terms of packet delivery than those with pronounced community structure. We also propose an alternative packet routing algorithm which takes advantage of the knowledge of communities to improve information transfer and show that in the context of the model an intermediate level of community structure is optimal. Finally, we show that in a hierarchical network setting, providing knowledge of communities at the level of highest modularity will improve network capacity by the largest amount.
Assessment of the thermal stability of anodic alumina membranes at high temperatures
L. Fernandez-Romero, J. M. Montero-Moreno, E. Pellicer, F. Peiro, A. Cornet, J. R. Morante, M. Sarret, C. Muller
MATERIALS CHEMISTRY AND PHYSICS
111
542 547
(2008)
abstract
The thermal stability of anodic alumina membranes (AAMs) annealed in air from 750 degrees C up to 1100 degrees C was investigated. AAMs were produced by single-step anodising of laminated AA1050 in 0.30M oxalic acid medium. The barrier layer provided thermal stability to the membranes, since it avoided or minimized bending and cracking phenomena. X-ray diffraction (XRD) analyses revealed that as-synthesized AAMs were amorphous and converted to polycrystalline after heat-treating above 750 degrees C. However, porous and barrier layers did not re-crystallize in the same way. The porous layer mainly crystallized in the gamma-Al2O3 phase within the range of 900-1100 degrees C, while the barrier layer was converted to the alpha-Al2O3 phase at 1100 degrees C. Different grain sizes were also estimated from Scherrer's formula. Scanning electron microscopy (SEM) images pointed out that cell wall dilation of the porous layer explained membrane cracking, which was avoided in presence of the barrier layer. (C) 2008 Elsevier B.V. All rights reserved.
Escape problem under stochastic volatility: The Heston model
Jaume Masoliver, Josep Perello
PHYSICAL REVIEW E
78
56104
(2008)
abstract
We solve the escape problem for the Heston random diffusion model from a finite interval of span L. We obtain exact expressions for the survival probability (which amounts to solving the complete escape problem) as well as for the mean exit time. We also average the volatility in order to work out the problem for the return alone regardless of volatility. We consider these results in terms of the dimensionless normal level of volatility-a ratio of the three parameters that appear in the Heston model-and analyze their form in several asymptotic limits. Thus, for instance, we show that the mean exit time grows quadratically with large spans while for small spans the growth is systematically slower, depending on the value of the normal level. We compare our results with those of the Wiener process and show that the assumption of stochastic volatility, in an apparently paradoxical way, increases survival and prolongs the escape time. We finally observe that the model is able to describe the main exit-time statistics of the Dow-Jones daily index.
Model for interevent times with long tails and multifractality in human communications: An application to financial trading
Josep Perello, Jaume Masoliver, Andrzej Kasprzak, Ryszard Kutner
PHYSICAL REVIEW E
78
36108
(2008)
abstract
Social, technological, and economic time series are divided by events which are usually assumed to be random, albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the Poissonian profile by being long-tailed distributed with resting and active periods interwoven. Understanding mechanisms generating consistent statistics has therefore become a central issue. The approach we present is taken from the continuous-time random-walk formalism and represents an analytical alternative to models of nontrivial priority that have been recently proposed. Our analysis also goes one step further by looking at the multifractal structure of the interevent times of human decisions. We here analyze the intertransaction time intervals of several financial markets. We observe that empirical data describe a subtle multifractal behavior. Our model explains this structure by taking the pausing-time density in the form of a superstatistics where the integral kernel quantifies the heterogeneous nature of the executed tasks. A stretched exponential kernel provides a multifractal profile valid for a certain limited range. A suggested heuristic analytical profile is capable of covering a broader region.
Option pricing under stochastic volatility: the exponential Ornstein-Uhlenbeck model
Josep Perello, Ronnie Sircar, Jaume Masoliver
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
P06010
(2008)
abstract
We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that takes a log-Brownian motion to describe price dynamics and an Ornstein-Uhlenbeck subordinated process describing the randomness of the log-volatility. We derive an approximate option price that is valid when ( i) the. uctuations of the volatility are larger than its normal level, ( ii) the volatility presents a slow driving force, toward its normal level and,finally, ( iii) the market price of risk is a linear function of the log-volatility. We study the resulting European call price and its implied volatility for a range of parameters consistent with daily Dow Jones index data.
Renewal equations for option pricing
M. Montero
EUROPEAN PHYSICAL JOURNAL B
65
295 306
(2008)
abstract
In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural to the issue because it is based in the use of renewal equations, and therefore it enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits.
A solvable model of the genesis of amino-acid sequences via coupled dynamics of folding and slow-genetic variation
S. Rabello, A. C. C. Coolen, Conrad J. Perez-Vicente, F. Fraternali
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
41
285004
(2008)
abstract
We study the coupled dynamics of primary and secondary structures formation (i.e. slow-genetic sequence selection and fast folding) in the context of a solvable microscopic model that includes both short-range steric forces and long-range polarity-driven forces. Our solution is based on the diagonalization of replicated transfer matrices, and leads in the thermodynamic limit to explicit predictions regarding phase transitions and phase diagrams at genetic equilibrium. The predicted phenomenology allows for natural physical interpretations, and finds satisfactory support in numerical simulations.
Spin models on random graphs with controlled topologies beyond degree constraints
Conrad J. Perez-Vicente, A. C. C. Coolen
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
41
255003
(2008)
abstract
We study Ising spin models on finitely connected random interaction graphs which are drawn from an ensemble in which not only the degree distribution p(k) can be chosen arbitrarily, but which allows for further fine tuning of the topology via preferential attachment of edges on the basis of an arbitrary function Q(k, k') of the degrees of the vertices involved. We solve these models using finite connectivity equilibrium replica theory, within the replica symmetric ansatz. In our ensemble of graphs, phase diagrams of the spin system are found to depend no longer only on the chosen degree distribution, but also on the choice made for Q(k, k'). The increased ability to control interaction topology in solvable models beyond prescribing only the degree distribution of the interaction graph enables a more accurate modeling of real-world interacting particle systems by spin systems on suitably defined random graphs.
Perpetual American options within CTRWs
Miquel Montero
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
387
3936 3941
(2008)
abstract
Continuous-time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution. We will apply this kind of market model to the valuation of perpetual American options: derivatives with no maturity that can be exercised at any time. Our approach leads to option prices that fulfill financial formulas when canonical assumptions on the dynamics governing the process are made, but it is still suitable for more exotic market conditions. (C) 2008 Elsevier B.V. All rights reserved.
Physics of Aesthetics: A meeting of science, art and thought in Barcelona
Josep Perello, Vicenc Altaio
LEONARDO
41
233 +
(2008)
abstract
The Physics of Aesthetics conference in Barcelona introduced the paradigms of the liveliest aspects of physics. One hundred years after Einstein's annus mirabilis, physics continues making progress, and the authors participated with internationally well-known scientists in drawing the outline of its more attractive face. Universal questions naturally arose, relating to the limits our perception, the design matter and the narrative of the complexity surrounding us. Local non-scientist personalities helped to distill aesthetics from the contemporary tendencies of this scientific discipline.
On cycles in AS relationships
Dimitropoulos, Xenofontas, M. Ángeles Serrano, Dmitri Krioukov
ACM SIGCOMM Computer Communication Review
38
103
(2008)
abstract
Why can the global Internet not have any AS relationship cycles? Why does it have to be a DAG (directed acyclic graph)? AS relationships emerge from business negotiations between pairs of ASs, while all relevant information is kept secret. In other words, local negotiations and interactions between AS pairs determine their relationships. Given the complexity of business agreements, it is quite unlikely that the local, independent, and diverse interactions between ASs yield a global, highly organized, and strictly hierarchical DAG structure.
Rich-club vs rich-multipolarization phenomena in weighted networks
M. Ángeles Serrano
Physical Review E
78
26101
(2008)
abstract
Large-scale hierarchies characterize complex networks in different domains. Elements at the top, usually the most central or influential, may show multipolarization or tend to club together, forming tightly interconnected communities. The rich-club phenomenon quantified this tendency based on unweighted network representations. Here, we define this metric for weighted networks and discuss the appropriate normalization which preserves the nodes' strengths and discounts structural strength-strength correlations if present. We find that in some real networks the results given by the weighted rich-club coefficient can be in sharp contrast to the ones in the unweighted approach. We also discuss the ability of the scanning of weighted subgraphs formed by the high-strength hubs to unveil features in contrast to the average: the formation of local alliances in multipolarized environments, or a lack of cohesion even in the presence of rich-club ordering. Beyond structure, this analysis matters for correct understanding of functionalities and dynamical processes relying on hub interconnectedness.
Structural Efficiency of Percolated Landscapes in Flow Networks
M. Ángeles Serrano, Paolo De Los Rios
PLOS ONE
3
e3654
(2008)
abstract
The large-scale structure of complex systems is intimately related to their functionality and evolution. In particular, global transport processes in flow networks rely on the presence of directed pathways from input to output nodes and edges, which organize in macroscopic connected components. However, the precise relation between such structures and functional or evolutionary aspects remains to be understood. Here, we investigate which are the constraints that the global structure of directed networks imposes on transport phenomena. We define quantitatively under minimal assumptions the structural efficiency of networks to determine how robust communication between the core and the peripheral components through interface edges could be. Furthermore, we assess that optimal topologies in terms of access to the core should look like "hairy balls'' so to minimize bottleneck effects and the sensitivity to failures. We illustrate our investigation with the analysis of three real networks with very different purposes and shaped by very different dynamics and time scales-the Internet customer provider set of relationships, the nervous system of the worm Caenorhabditis elegans, and the metabolism of the bacterium Escherichia coli. Our findings prove that different global connectivity structures result in different levels of structural efficiency. In particular, biological networks seem to be close to the optimal layout.
Approximating PageRank from in-degree
Fortunato, S; Marián Boguñá; Flammini, A; Menczer, F
ALGORITHMS AND MODELS FOR THE WEB-GRAPH. LECTURE NOTES IN COMPUTER SCIENCE
4936
59
(2008)
abstract
PageRank is a key element in the success of search engines, allowing to rank the most important hits in the top screen of results. One key aspect that distinguishes PageRank from other prestige measures such as in-degree is its global nature. From the information provider perspective, this makes it difficult or impossible to predict how their pages will be ranked. Consequently a market has emerged for the optimization of search engine results. Here we study the accuracy with which PageRank can be approximated by in-degree, a local measure made freely available by search engines. Theoretical and empirical analyses lead to conclude that given the weak degree correlations in the Web link graph, the approximation can be relatively accurate, giving service and information providers an effective new marketing tool.
Dynamical and spectral properties of complex networks
Juan Almendral A. Albert Diaz-Guilera
NEW JOURNAL OF PHYSICS
9
187
(2007)
abstract
Dynamical properties of complex networks are related to the spectral properties of the Laplacian matrix that describes the pattern of connectivity of the network. In particular we compute the synchronization time for different types of networks and different dynamics. We show that the main dependence of the synchronization time is on the smallest nonzero eigenvalue of the Laplacian matrix, in contrast to other proposals in terms of the spectrum of the adjacency matrix. Then, this topological property becomes the most relevant for the dynamics.
Synchronization and modularity in complex networks
Alex Arenas, Albert Diaz-Guilera
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
143
19 25
(2007)
abstract
We investigate the connection between the dynamics of synchronization and the modularity on complex networks. Simulating the Kuramoto's model in complex networks we determine patterns of meta-stability and calculate the modularity of the partition these patterns provide. The results indicate that the more stable the patterns are, the larger tends to be the modularity of the partition defined by them. This correlation works pretty well in homogeneous networks (all nodes have similar connectivity) but fails when networks contain hubs, mainly because the modularity is never improved where isolated nodes appear, whereas in the synchronization process the characteristic of hubs is to have a large stability when forming its own community.
Decoding the Structure of the WWW: A Comparative Analysis of Web Crawls
M. Angeles Serrano, Ana Maguitman, Marian Boguña, Santo Fortunato, A. Vespignani
ACM TRANSACTIONS ON THE WEB
1
10
(2007)
abstract
The understanding of the immense and intricate topological structure of the World Wide Web (WWW) is a major scientific and technological challenge. This has been recently tackled by characterizing the properties of its representative graphs, in which vertices and directed edges are identified with Web pages and hyperlinks, respectively. Data gathered in large-scale crawls have been analyzed by several groups resulting in a general picture of the WWW that encompasses many of the complex properties typical of rapidly evolving networks. In this article, we report a detailed statistical analysis of the topological properties of four different WWW graphs obtained with different crawlers. We find that, despite the very large size of the samples, the statistical measures characterizing these graphs differ quantitatively, and in some cases qualitatively, depending on the domain analyzed and the crawl used for gathering the data. This spurs the issue of the presence of sampling biases and structural differences of Web crawls that might induce properties not representative of the actual global underlying graph. In short, the stability of the widely accepted statistical description of the Web is called into question. In order to provide a more accurate characterization of the Web graph, we study statistical measures beyond the degree distribution, such as degree-degree correlation functions or the statistics of reciprocal connections. The latter appears to enclose the relevant correlations of the WWW graph and carry most of the topological information of the Web. The analysis of this quantity is also of major interest in relation to the navigability and searchability of the Web.
Extreme times for volatility processes
Jaume Masoliver, Josep Perello
PHYSICAL REVIEW E
75
46110
(2007)
abstract
Extreme times techniques, generally applied to nonequilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted from daily data of major indices seem to follow the same law regardless of the kind of index thus suggesting an universal pattern. The empirical mean first-passage time to a certain level L is fairly different from that of the Wiener process showing a dissimilar behavior depending on whether L is higher or lower than the average volatility. All of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value. We thus present the mean first-passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description. We discuss asymptotic approximations of these models and confront them to empirical results with a good agreement with the exponential Ornstein-Uhlenbeck model.
Volatility: A hidden Markov process in financial time series
Eisler, Zoltan Josep Perello, Jaume Masoliver
PHYSICAL REVIEW E
76
56105
(2007)
abstract
Volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, volatility is unobservable and only the price is known. Diffusion theory has many common points with the research on volatility, the key of the analogy being that volatility is a time-dependent diffusion coefficient of the random walk for the price return. We present a formal procedure to extract volatility from price data by assuming that it is described by a hidden Markov process which together with the price forms a two-dimensional diffusion process. We derive a maximum-likelihood estimate of the volatility path valid for a wide class of two-dimensional diffusion processes. The choice of the exponential Ornstein-Uhlenbeck (expOU) stochastic volatility model performs remarkably well in inferring the hidden state of volatility. The formalism is applied to the Dow Jones index. The main results are that (i) the distribution of estimated volatility is lognormal, which is consistent with the expOU model, (ii) the estimated volatility is related to trading volume by a power law of the form sigma proportional to V-0.55, and (iii) future returns are proportional to the current volatility, which suggests some degree of predictability for the size of future returns.
Nonindependent continuous-time random walks
Miquel Montero, Jaume Masoliver
PHYSICAL REVIEW E
76
61115
(2007)
abstract
The usual development of the continuous-time random walk (CTRW) assumes that jumps and time intervals are a two-dimensional set of independent and identically distributed random variables. In this paper, we address the theoretical setting of nonindependent CTRWs where consecutive jumps and/or time intervals are correlated. An exact solution to the problem is obtained for the special but relevant case in which the correlation solely depends on the signs of consecutive jumps. Even in this simple case, some interesting features arise, such as transitions from unimodal to bimodal distributions due to correlation. We also develop the necessary analytical techniques and approximations to handle more general situations that can appear in practice.
The CTRW in finance: Direct and inverse problems with some generalizations and extensions
Jaume Masoliver, Miquel Montero, Josep Perello, George H. Weiss
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
379
151 167
(2007)
abstract
We study financial distributions within the framework of the continuous time random walk (CTRW). We review earlier approaches and present new results related to overnight effects as well as the generalization of the formalism which embodies a non-Markovian formulation of the CTRW aimed to account for correlated increments of the return. (c) 2007 Elsevier B.V. All rights reserved.
Mean exit time and survival probability within the CTRW formalism
M. Montero, Jaume Masoliver
EUROPEAN PHYSICAL JOURNAL B
57
181 185
(2007)
abstract
An intense research on financial market microstructure is presently in progress. Continuous time random walks (CTRWs) are general models capable to capture the small-scale properties that high frequency data series show. The use of CTRW models in the analysis of financial problems is quite recent and their potentials have not been fully developed. Here we present two (closely related) applications of great interest in risk control. In the first place, we will review the problem of modelling the behaviour of the mean exit time (MET) of a process out of a given region of fixed size. The surveyed stochastic processes are the cumulative returns of asset prices. The link between the value of the MET and the timescale of the market fluctuations of a certain degree is crystal clear. In this sense, MET value may help, for instance, in deciding the optimal time horizon for the investment. The MET is, however, one among the statistics of a distribution of bigger interest: the survival probability (SP), the likelihood that after some lapse of time a process remains inside the given region without having crossed its boundaries. The final part of the manuscript is devoted to the study of this quantity. Note that the use of SPs may outperform the standard Value at Risk (VaR) method for two reasons: we can consider other market dynamics than the limited Wiener process and, even in this case, a risk level derived from the SP will ensure (within the desired quintile) that the quoted value of the portfolio will not leave the safety zone. We present some preliminary theoretical and applied results concerning this topic.
The global minima of the communicative energy of natural communication systems
Ramon Ferrer i Cancho, Albert Diaz-Guilera
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
P06009
(2007)
abstract
Until recently, models of communication have explicitly or implicitly assumed that the goal of a communication system is just maximizing the information transfer between signals and 'meanings'. Recently, it has been argued that a natural communication system not only has to maximize this quantity but also has to minimize the entropy of signals, which is a measure of the cognitive cost of using a word. The interplay between these two factors, i.e. maximization of the information transfer and minimization of the entropy, has been addressed previously using a Monte Carlo minimization procedure at zero temperature. Here we derive analytically the globally optimal communication systems that result from the interaction between these factors. We discuss the implications of our results for previous studies within this framework. In particular we prove that the emergence of Zipf's law using a Monte Carlo technique at zero temperature in previous studies indicates that the system had not reached the global optimum.
Downside risk analysis applied to the hedge funds universe
Josep Perello
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
383
480 496
(2007)
abstract
Hedge Funds are considered as one of the portfolio management sectors which shows a fastest growing for the past decade. An optimal Hedge Fund management requires an appropriate risk metrics. The classic CAPM theory and its Ratio Sharpe fail to capture some crucial aspects due to the strong non-Gaussian character of Hedge Funds statistics. A possible way out to this problem while keeping the CAPM simplicity is the so-called Downside Risk analysis. One important benefit lies in distinguishing between good and bad returns, that is: returns greater or lower than investor's goal. We revisit most popular Downside Risk indicators and provide new analytical results on them. We compute these measures by taking the Credit Suisse/Tremont Investable Hedge Fund Index Data and with the Gaussian case as a benchmark. In this way, an unusual transversal lecture of the existing Downside Risk measures is provided. (c) 2007 Elsevier B. V. All rights reserved.
Market memory and fat tail consequences in option pricing on the expOU stochastic volatility model
Josep Perello
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
382
213 218
(2007)
abstract
The expOU stochastic volatility model is capable of reproducing fairly well most important statistical properties of financial markets daily data. Among, them, the presence of multiple time scales in the volatility autocorrelation is perhaps the most relevant which makes appear fat tails in the return distributions. This paper wants to go further on with the expOU model we have studied in Ref. [J. Masoliver, J. Perello, Quant. Finance 6 (2006) 423] by exploring an aspect of practical interest. Having as a benchmark the parameters estimated from the Dow Jones daily data, we want to compute the price for the European option. This is actually done by Monte Carlo, running a large number of simulations. Our main interest is to see the effects of a long-range market memory from our expOU model in its subsequent European call option. We pay attention to the effects of the existence of a broad range of time scales in the volatility. We find that a richer set of time scales brings the price of the option higher. This appears in clear contrast to the presence of memory in the price itself which makes the price of the option cheaper. (C) 2007 Elsevier B.V. All rights reserved.
Volatility and dividend risk in perpetual American options
Miquel Montero
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
P04002
(2007)
abstract
American options are financial instruments that can be exercised at any time before expiration. In this paper we study the problem of pricing this kind of derivatives within a framework in which some of the properties - volatility and dividend policy - of the underlaying stock can change at a random instant of time, but in such a way that we can forecast their final values. Under this assumption we can model actual market conditions because some of the most relevant facts that may potentially a. ect a. rm will entail sharp predictable effects. We will analyse the consequences of this potential risk on perpetual American derivatives, a topic connected with a wide class of recurrent problems in physics: holders of American options must look for the fair price and the optimal exercise strategy at once, a typical question of free absorbing boundaries. We present explicit solutions to the most common contract specifications and derive analytical expressions concerning the mean and higher moments of the exercise time.
The role of time scale separation in a nonequilibrium roughening transition
M. Llas, Albert Diaz-Guilera, J. M. Lopez, P. M. Gleiser
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
374
289 292
(2007)
abstract
In this work we analyze the role of time scale separation between the external driving and the avalanche relaxation dynamics in a one-dimensional model of propagation of innovations among economic agents. When the time scales are separated the model presents a nonequilibrium roughening transition. We show that when avalanche overlapping is permitted, only a rough phase is observed. (c) 2006 Elsevier B.V. All rights reserved.
Complex fluctuations and robustness in stylized signalling networks
Albert Diaz-Guilera, A. A. Moreira, L. Guzman, L. A. N. Amaral
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
P01013
(2007)
abstract
Complex fluctuations with correlations involving multiple scales appear in many physical, social and biological systems. In particular, in physiological systems the degree of complexity, measured in terms of the exponent of the time correlations of the fluctuations, is altered with disease and ageing. Here, we show that correlated fluctuations characterized by 1/f scaling of their power spectra can emerge from networks of simple signalling units. We analyse networks of simple signalling units where the type of scaling of the fluctuations is associated with ( i) a complex topology with a discrete and sparse number of random links between units, ( ii) a restricted set of nonlinear interaction rules, and ( iii) the presence of noise. Furthermore, we find that changes in one or more of these properties leads to degradation of the correlation properties. Moreover, changes in the microscopic construction of the model do not produce qualitative changes in the dynamical behaviour, showing hence the robustness of our findings.
Correlations in complex networks
M. Ángeles Serrano, M Boguñá, Romualdo Pastor-Satorras, Alessandro Vespignani
Structure and Dynamics of Complex Networks. From Information Technology to Finance and Natural Science
World Scientific, Singapur
(2007)
abstract
In the following sections, we will focus on the characterization and modeling of correlations in undirected unweighted complex networks. In particular, we will devote our attention to the statistical characterization of these features in large scale networks. In the section, we review some important and useful general analytical results concerning the topological characterization of random networks. In the third section we recall a number of speci
Phase transition in the globalization of trade
M. Ángeles Serrano
Journal of Statistical Mechanics: Theory and Experiment
L01002
(2007)
abstract
Globalization processes are interwoven with economic structures on a worldwide scale, trade playing a central role as one of the elemental channels of interaction among countries. Despite the significance of such phenomena, measuring economic globalization still remains an open problem. More quantitative treatments could improve the understanding of globalization at the same time as helping to form a basis for comparative economic history. In this letter, we investigate the time evolution of the statistical properties of bilateral trade imbalances between countries in the trade system. We measure their cumulative probability distribution at different moments in time to discover a sudden transition around 1960 from a regime where the distribution was always represented by a steady characteristic function to a new state where the distribution dilates as time goes on. This suggests that the rule that was governing the statistical behaviour of bilateral trade imbalances until the 1960s abruptly changed to a new form persistent in the last decades. In the new regime, the figures for the different years collapse into a universal master curve when rescaled by the corresponding global value of gross domestic product. This coupling points to an increased interdependence of world economies and its onset corresponds in time with the start of the last wave of globalization.
Interfaces and the edge percolation map of random directed networks
M. Ángeles Serrano, Paolo De Los Rios
Physical Review E
76
56121
(2007)
abstract
The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in the strongly connected component and those in the in and out components. Formal equations for the relative sizes in the number of edges of these giant structures are derived for arbitrary joint degree distributions in the presence of local and two-point correlations. The uncorrelated null model is fully solved analytically and compared against simulations, finding an excellent agreement. Interfaces, and their particular conformations giving place from "hairy ball" percolation landscapes to bottleneck straits, could bring new light to the discussion of how a structure is interwoven with functionality in flow networks.
Patterns of dominant flows in the world trade web
M. Ángeles Serrano, Marián Boguñá, Alessandro Vespignani
Journal of Economic Interaction and Coordination
2
111
(2007)
abstract
The large-scale organization of the world economies is exhibiting increasing levels of local heterogeneity and global interdependency. Understanding the relation between local and global features calls for analytical tools able to uncover the global emerging organization of the international trade network. Here we analyze the world network of bilateral trade imbalances and characterize its overall flux organization, unraveling local and global high-flux pathways that define the backbone of the trade system. We develop a general procedure capable to progressively filter out in a consistent and quantitative way the dominant trade channels. This procedure is completely general and can be applied to any weighted network to detect the underlying structure of transport flows. The trade fluxes properties of the world trade web determine a ranking of trade partnerships that highlights global interdependencies, providing information not accessible by simple local analysis. The present work provides new quantitative tools for a dynamical approach to the propagation of economic crises.
On Local Estimations of PageRank: A Mean Field Approach
Santo Fortunato, Marián Boguñá, Alessandro Flammini, and Filippo Menczer
Internet Mathematics
4
245
(2007)
abstract
PageRank is a key element in the success of search engines, allowing the display of the most relevant hits in the first screen of results. One key aspect that distinguishes PageRank from other prestige measures such as in-degree is its global nature. From the information provider perspective, this makes it difficult or even impossible to predict how their pages will be ranked. Consequently, a market has emerged for the optimization of search engine results. Here we study the accuracy with which PageRank can be approximated by in-degree, a local measure made freely available by search engines. Theoretical and empirical analyses lead us to conclude that, given the weak degree of correlations in the Web link graph, the approximation can be relatively accurate, giving service and information providers an effective new marketing tool.
Synchronization reveals topological scales in complex networks
Alex Arenas, Albert Diaz-Guilera, Conrad J. Perez-Vicente
PHYSICAL REVIEW LETTERS
96
114102
(2006)
abstract
We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular structures corresponding to well-defined communities of nodes emerge in different time scales, ordered in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology, and spectral graph analysis.
Percolation and epidemic thresholds in clustered networks
M. Angeles Serrano, Marian Boguña
PHYSICAL REVIEW LETTERS
97
88701
(2006)
abstract
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant connected component, it cannot restore a finite percolation threshold. In turn, this implies the absence of an epidemic threshold in this class of networks, thus extending this result to a wide variety of real scale-free networks which shows a high level of transitivity. Our findings are in good agreement with numerical simulations.
Synchronization processes in complex networks
Alex Arenas, Albert Diaz-Guilera, Conrad J. Perez-Vicente
PHYSICA D-NONLINEAR PHENOMENA
224
27 34
(2006)
abstract
We present an extended analysis, based on the dynamics towards synchronization of a system of coupled oscillators, of the hierarchy of communities in complex networks. In the synchronization process, different structures corresponding to well defined communities of nodes appear in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology and spectral graph analysis. (c) 2006 Elsevier B.V. All rights reserved.
Numerical methods for the estimation of multifractal singularity spectra on sampled data: A comparative study
A. Turiel, Conrad J. Perez-Vicente, J. Grazzini
JOURNAL OF COMPUTATIONAL PHYSICS
216
362 390
(2006)
abstract
Physical variables in scale invariant systems often show chaotic, turbulent-like behavior, commonly associated to the existence of an underlying fractal or multifractal structure. However, the assessment of multifractality over experimental, discretized data requires of appropriate methods and to establish criteria to measure the confidence degree on the estimates. In this paper we have evaluated the quality of different techniques used for multifractal analysis. We have tested four different techniques: the moment (M) method, the wavelet transform modulus maxima (WTMM) method, the gradient modulus wavelet projection (GMWP) method and the gradient histogram (GH) method, which are used to estimate the singularity spectra of multifractal signals. The test consists in analyzing synthetic multifractal ID signals with given multifractal spectrum. We have compared the results, studying the sensibility of each method to the length of the series, size of the ensemble and type of spectrum. Our results show that GMWP method is the one attaining the best performance, providing reliable estimates which can be improved when the statistics is increased. All the other methods are affected by problems such as the linearization of the right tail of the spectrum, and some of them are very demanding in data. (c) 2005 Elsevier Inc. All rights reserved.
The effect of size heterogeneity on community identification in complex networks
Leon Danon, Albert Diaz-Guilera, Alex Arenas
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
P11010
(2006)
abstract
Identifying community structure can be used as a potent tool in the analysis and understanding of the structure of complex networks. Up to now, methods for evaluating the performance of identification algorithms have used ad hoc networks with communities of equal size. We show that inhomogeneities in community sizes can and do affect the performance of algorithms considerably, and propose an alternative method which takes these factors into account. Furthermore, we propose a simple modi. cation of the algorithm proposed by Newman for community detection (2004 Phys. Rev. E 69 066133) which treats communities of different sizes on an equal footing, and show that it outperforms the original algorithm while retaining its speed.
Clustering in complex networks. II. Percolation properties
M. Angeles Serrano, Marian Boguña
PHYSICAL REVIEW E
74
56115
(2006)
abstract
The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows us to find the critical threshold and the size of the giant component. Numerical simulations confirm the accuracy of our results. In more general terms, we show that weak clustering hinders the onset of the giant component whereas strong clustering favors its appearance. This is a direct consequence of the differences in the k-core structure of the networks, which are found to be totally different depending on the level of clustering. An empirical analysis of a real social network confirms our predictions.
Clustering in complex networks. I. General formalism
M. Angeles Serrano, Marian Boguña
PHYSICAL REVIEW E
74
56114
(2006)
abstract
We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in that it involves the properties of two-and not just one-vertices. The formalism is completed with the definition of a three-vertex correlation function, which is the fundamental quantity describing the properties of clustered networks. The formalism suggests different metrics that are able to thoroughly characterize transitive relations. A rigorous analysis of several real networks, which makes use of this formalism and the metrics, is also provided. It is also found that clustered networks can be classified into two main groups: the weak and the strong transitivity classes. In the first class, edge multiplicity is small, with triangles being disjoint. In the second class, edge multiplicity is high and so triangles share many edges. As we shall see in the following paper, the class a network belongs to has strong implications in its percolation properties.
Correlations in weighted networks
M. Angeles Serrano, Marian Boguña, Romualdo Pastor-Satorras
PHYSICAL REVIEW E
74
55101
(2006)
abstract
We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of structural constraints. We also introduce an algorithm for generating maximally random weighted networks with arbitrary P(k,s) to be used as null models. The application of our measures to real networks reveals the importance of weights in a correct understanding and modeling of these heterogeneous systems.
The continuous time random walk formalism in financial markets
Jaume Masoliver, Miquel Montero, Josep Perello, George H. Weiss
JOURNAL OF ECONOMIC BEHAVIOR & ORGANIZATION
61
577 598
(2006)
abstract
We adapt continuous time random walk (CTRW) formalism to describe asset price evolution and discuss some of the problems that can be treated using this approach. We basically focus on two aspects: (i) the derivation of the price distribution from high-frequency data, and (ii) the inverse problem, obtaining information on the market microstructure as reflected by high-frequency data knowing only the daily volatility. We apply the formalism to financial data to show that the CTRW offers alternative tools to deal with several complex issues of financial markets. (c) 2006 Elsevier B.V. All rights reserved.
Multiple time scales and the exponential Ornstein-Uhlenbeck stochastic volatility model
Jaume Masoliver, Josep Perello
QUANTITATIVE FINANCE
6
423 433
(2006)
abstract
We study the exponential Ornstein-Uhlenbeck stochastic volatility model and observe that the model shows a multiscale behaviour in the volatility autocorrelation. It also exhibits a leverage correlation and a probability profile for the stationary volatility which are consistent with market observations. All these features make the model quite appealing since it appears to be more complete than other stochastic volatility models also based on a two-dimensional diffusion. We finally present an approximate solution for the return probability density designed to capture the kurtosis and skewness effects.
Application of the microcanonical multifractal formalism to monofractal systems
Oriol Pont, A. Turiel, Conrad J. Perez-Vicente
PHYSICAL REVIEW E
74
61110
(2006)
abstract
The design of appropriate multifractal analysis algorithms, able to correctly characterize the scaling properties of multifractal systems from experimental, discretized data, is a major challenge in the study of such scale invariant systems. In the recent years, a growing interest for the application of the microcanonical formalism has taken place, as it allows a precise localization of the fractal components as well as a statistical characterization of the system. In this paper, we deal with the specific problems arising when systems that are strictly monofractal are analyzed using some standard microcanonical multifractal methods. We discuss the adaptations of these methods needed to give an appropriate treatment of monofractal systems.
Entropy of the Nordic electricity market: anomalous scaling, spikes, and mean-reversion
Josep Perello, Miquel Montero, L. Palatella, I. Simonsen, Jaume Masoliver
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
P11011
(2006)
abstract
The electricity market is a very peculiar market due to the large variety of phenomena that can affect the spot price. However, this market still shows many typical features of other speculative (commodity) markets like, for instance, data clustering and mean reversion. We apply the diffusion entropy analysis (DEA) to the Nordic spot electricity market (Nord Pool). We study the waiting time statistics between consecutive spot price spikes and find it to show anomalous scaling characterized by a decaying power law. The exponent observed in data follows a quite robust relationship with the one implied by the DEA analysis. In terms of the DEA we also revisit topics like clustering, mean-reversion and periodicities. We finally propose a GARCH inspired model but for the price itself. Models in the context of stochastic volatility processes appear under this scope to have a feasible description.
Performance of excitable small-world networks of Bonhoeffer-van der Pol-FitzHugh-Nagumo oscillators
I. Vragovic, E. Louis, Albert Diaz-Guilera
EUROPHYSICS LETTERS
76
780 786
(2006)
abstract
We investigate how performance (i.e. activity of the nodes and their subsequent synchronization) of excitable small-world networks depends on network topology. Network elements are described by Bonhoeffer-van der Pol-FitzHugh-Nagumo oscillators assumed to be close to the oscillating threshold. Global oscillations are induced by introducing a small amount of diversity. In homogeneous networks, it is found that the system performance is mainly determined by the average path length, no matter what the local properties are. The network undergoes a transition from low to high activity regimes at a critical path length. This transition, also found in regular networks, is shown to be caused by the dependence of the critical coupling strength between network units on the average path length.
Modeling the Internet
M. Angeles Serrano, Marian Boguña, Albert Diaz-Guilera
EUROPEAN PHYSICAL JOURNAL B
50
249 254
(2006)
abstract
We model the Internet as a network of interconnected Autonomous Systems which self-organize under an absolute lack of centralized control. Our aim is to capture how the Internet evolves by reproducing the assembly that has led to its actual structure and, to this end, we propose a growing weighted network model driven by competition for resources and adaptation to maintain functionality in a demand and supply balance. On the demand side, we consider the environment, a pool of users which need to transfer information and ask for service. On the supply side, ASs compete to gain users, but to be able to provide service efficiently, they must adapt their bandwidth as a function of their size. Hence, the Internet is not modeled as an isolated system but the environment, in the form of a pool of users, is also a fundamental part which must be taken into account. ASs compete for users and big and small come up, so that not all ASs are identical. New connections between ASs are made or old ones are reinforced according to the adaptation needs. Thus, the evolution of the Internet can not be fully understood if just described as a technological isolated system. A socio-economic perspective must also be considered.
Exact solutions and dynamics of globally coupled oscillators
Ll. Bonilla, Conrad J. Perez Vicente, F. Ritort, Soler, J.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
16
1919 1959
(2006)
abstract
We analyze mean-field models of synchronization of phase oscillators with singular couplings and subject to external random forces. They are related to the Kuramoto-Sakaguchi model. Their probability densities satisfy local partial differential equations similar to the porous medium, Burgers and extended Burgers systems depending on the degree of singularity of the coupling. We show that porous medium oscillators (the most singularly coupled) do not synchronize and that (transient) synchronization is possible only at zero temperature for Burgers oscillators. The extended Burgers oscillators have a nonlocal coupling first introduced by Daido and they may synchronize at any temperature. Exact expressions for their synchronized phases and for Daido's order function are given in terms of elliptic functions.
Detecting rich-club ordering in complex networks
Vittoria Colizza, Alessandro Flammini, M. Ángeles Serrano, Alessandro Vespignani
Nature Physics
2
110
(2006)
abstract
Uncovering the hidden regularities and organizational principles of networks arising in physical systems ranging from the molecular level to the scale of large communication infrastructures is the key issue in understanding their fabric and dynamical properties(1-5). The 'rich-club' phenomenon refers to the tendency of nodes with high centrality, the dominant elements of the system, to form tightly interconnected communities, and it is one of the crucial properties accounting for the formation of dominant communities in both computer and social sciences(4-8). Here, we provide the analytical expression and the correct null models that allow for a quantitative discussion of the rich-club phenomenon. The presented analysis enables the measurement of the rich-club ordering and its relation with the function and dynamics of networks in examples drawn from the biological, social and technological domains.
The Kuramoto model: A simple paradigm for synchronization phenomena
J.A. Acebron, Ll. Bonilla, Conrad J. Perez Vicente, F. Ritort, R. Spigler
REVIEWS OF MODERN PHYSICS
77
137 185
(2005)
abstract
Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model. A rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years are presented. Relevant applications of the model in different contexts are also included.