official web page
Jan 29, 2010:
We are quite busy, so we didn't have time to write a paper in Nature! Meanwhile, here it is the link to the journal:
Here you can find a complete list of our publications, which are ordered by year and type of publication (regular papers, popular science papers and conference proceedings). They are fully downloadable and any comment/suggestion is welcome.
[1] 
R. SevillaEscoboza, I. Sendiña Nadal, I. Leyva, R. Gutiérrez, J. M.
Buldú, and S. Boccaletti, “Interlayer synchronization in multiplex
networks.” 2015, 1510.07498.
[ bib 
DOI 
arXiv 
html ]
Interlayer synchronization is a distinctive process of multiplex networks whereby each node in a given layer undergoes a synchronous evolution with all its replicas in other layers, irrespective of whether or not it is synchronized with the other units of the same layer. We analytically derive the necessary conditions for the existence and stability of interlayer synchronization, and verify numerically the analytical predictions in several cases where such a state emerges. We inspect the impact of the layer topology on the robustness of such a state against a progressive demultiplexing of the network. Finally, we provide experimental evidence by means of multiplexes of nonlinear electronic circuits, showing the stability of the synchronized manifold despite the intrinsic noise and parameter mismatch in the experiment.

[1] 
I. Sendiña Nadal, M. M. Danziger, Z. Wang, S. Havlin, and S. Boccaletti,
“Assortativity and leadership emerge from antipreferential attachment in
heterogeneous networks,” Scientific Reports, vol. 6, p. 21297, Feb.
2016, 1508.03528.
[ bib 
DOI 
arXiv 
html ]
Many realworld networks exhibit degreeassortativity, with nodes of similar degree more likely to link to one another. Particularly in social networks, the contribution to the total assortativity varies with degree, featuring a distinctive peak slightly past the average degree. The way traditional models imprint assortativity on top of predefined topologies is via degreepreserving link permutations, which however destroy the particular graph's hierarchical traits of clustering. Here, we propose the first generative model which creates heterogeneous networks with scalefreelike properties and tunable realistic assortativity. In our approach, two distinct populations of nodes are added to an initial network seed: one (the followers) that abides by usual preferential rules, and one (the potential leaders) connecting via antipreferential attachments, i.e. selecting lower degree nodes for their initial links. The latter nodes come to develop a higher average degree, and convert eventually into the final hubs. Examining the evolution of links in Facebook, we present empirical validation for the connection between the initial antipreferential attachment and long term high degree. Thus, our work sheds new light on the structure and evolution of social networks.

[2]  J. Buldu, R. SevillaEscoboza, J. Aguirre, D. Papo, and R. Gutierrez, “Interconnecting networks: the role of connector links,” in Interconnected Networks (A. Garas, ed.), refereed 10, pp. 6177, New York: Springer, 2016. [ bib  pdf ] 
[3] 
R. SevillaEscoboza, J. M. Buldú, S. Boccaletti, D. Papo, D. U. Hwang,
G. HuertaCuellar, and R. Gutiérrez, “Experimental implementation of
maximally synchronizable networks,” Physica A, vol. 448, pp. 17,
2016, 1507.02551.
[ bib 
DOI 
arXiv 
html ]
Maximally synchronizable networks (MSNs) are acyclic directed networks that maximize synchronizability. In this paper, we investigate the feasibility of transforming networks of coupled oscillators into their corresponding MSNs. By tuning the weights of any given network so as to reach the lowest possible eigenratio $lambda_N/lambda_2$, the synchronized state is guaranteed to be maintained across the longest possible range of coupling strengths. We check the robustness of the resulting MSNs with an experimental implementation of a network of nonlinear electronic oscillators and study the propagation of the synchronization errors through the network. Importantly, a method to study the effects of topological uncertainties on the synchronizability is proposed and explored both theoretically and experimentally.

[4]  V. Makarov, a.a. Koronovskii, V. Maksimenko, a.E. Hramov, O. Moskalenko, J. Buldú, and S. Boccaletti, “Emergence of a multilayer structure in adaptive networks of phase oscillators,” Chaos, Solitons & Fractals, vol. 84, pp. 2330, 2016. [ bib  DOI  html ] 
[5]  D. Papo, M. Zanin, J. H. Martínez, and J. M. Buldú, “Beware of the Smallworld neuroscientist !,” vol. 10, no. March, pp. 14, 2016. [ bib  DOI ] 
[1] 
A. Navas, J. A. VillacortaAtienza, I. Leyva, J. A. Almendral,
I. SendinaNadal, and S. Boccaletti, “Effective centrality and explosive
synchronization in complex networks,” Physical Review E, vol. 92,
p. 062820, Dec. 2015, 1503.00954.
[ bib 
DOI 
arXiv 
pdf ]
Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. For non identical elements, the lack of quantitative tools has hampered so far a systematic study of the mechanisms behind such a collective behavior. We here propose an effective network whose topological properties reflect the interplay between the topology and dynamics of the original network. On that basis, we are able to introduce the "synchronization centrality", a measure which quantifies the role and importance of each network's node in the synchronization process. In particular, we use such a measure to assess the propensity of a graph to synchronize explosively, thus indicating a unified framework for most of the different models proposed so far for such an irreversible transition. Taking advantage of the predicting power of this measure, we furthermore discuss a strategy to induce the explosive behavior in a generic network, by acting only upon a small fraction of its nodes.

[2] 
P. Ariza, E. SolesioJofre, J. H. Martinez, J. a. PinedaPardo, G. Niso,
F. Maestu, and J. M. Buldu, “Evaluating the effect of aging on interference
resolution with timevarying complex networks analysis,” Frontiers in
Human Neuroscience, vol. 9, no. May, p. Article 255, 2015.
[ bib 
DOI 
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In this study we used graph theory analysis to investigate agerelated reorganization of functional networks during the active maintenance of information that is interrupted by external interference. Additionally, we sought to investigate network differences before and after averaging network parameters between both maintenance and interference windows. We compared young and older adults by measuring their magnetoencephalographic recordings during an interferencebased working memory task restricted to successful recognitions. Data analysis focused on the topology/temporal evolution of functional networks during both the maintenance and interference windows. We observed that: (a) Older adults require higher synchronization between cortical brain sites in order to achieve a successful recognition, (b) The main differences between age groups arise during the interference window, (c) Older adults show reduced ability to reorganize network topology when interference is introduced, and (d) Averaging network parameters leads to a loss of sensitivity to detect age differences.

[3] 
D. Malagarriga, M. a. GarcíaVellisca, A. E. P. Villa, J. M. Buldú,
J. GarcíaOjalvo, and A. J. Pons, “Synchronizationbased computation
through networks of coupled oscillators,” Frontiers in Computational
Neuroscience, vol. 9, no. August, pp. 113, 2015.
[ bib 
DOI 
html ]
The mesoscopic activity of the brain is strongly dynamical, while at the same time exhibits remarkable computational capabilities. In order to examine how these two features coexist, here we show that the patterns of synchronized oscillations displayed by networks of neural mass models, representing cortical columns, can be used as substrates for Booleanlike computations. Our results reveal that the same neural mass network may process different combinations of dynamical inputs as different logical operations or combinations of them. This dynamical feature of the network allows it to process complex inputs in a very sophisticated manner. The results are reproduced experimentally with electronic circuits of coupled Chua oscillators, showing the robustness of this kind of computation to the intrinsic noise and parameter mismatch of the coupled oscillators. We also show that the informationprocessing capabilities of coupled oscillations go beyond the simple juxtaposition of logic gates.

[4] 
R. SevillaEscoboza, R. Gutierrez, G. HuertaCuellar, S. Boccaletti,
J. GomezGardenes, a. Arenas, and J. M. Buldu, “Enhancing the stability of
the synchronization of multivariable coupled oscillators,” Physical
Review E  Statistical, Nonlinear, and Soft Matter Physics, vol. 92, no. 3,
pp. 17, 2015, 1508.06887.
[ bib 
DOI 
arXiv 
pdf ]
Synchronization processes in populations of identical networked oscillators are in the focus of intense studies in physical, biological, technological and social systems. Here we analyze the stability of the synchronization of a network of oscillators coupled through different variables. Under the assumption of an equal topology of connections for all variables, the master stability function formalism allows assessing and quantifying the stability properties of the synchronization manifold when the coupling is transferred from one variable to another. We report on the existence of an optimal coupling transference that maximizes the stability of the synchronous state in a network of R"osslerlike oscillators. Finally, we design an experimental implementation (using nonlinear electronic circuits) which grounds the robustness of the theoretical predictions against parameter mismatches, as well as against intrinsic noise of the system.

[5] 
G. Tirabassi, R. SevillaEscoboza, J. M. Buldú, and C. Masoller,
“Inferring the connectivity of coupled oscillators from timeseries
statistical similarity analysis,” Scientific Reports, vol. 5,
p. 10829, 2015.
[ bib 
DOI 
html ]
A system composed by interacting dynamical elements can be represented by a network, where the nodes represent the elements that constitute the system, and the links account for their interactions, which arise due to a variety of mechanisms, and which are often unknown. A popular method for inferring the system connectivity (i.e., the set of links among pairs of nodes) is by performing a statistical similarity analysis of the timeseries collected from the dynamics of the nodes. Here, by considering two systems of coupled oscillators (Kuramoto phase oscillators and Rössler chaotic electronic oscillators) with known and controllable coupling conditions, we aim at testing the performance of this inference method, by using linear and non linear statistical similarity measures. We find that, under adequate conditions, the network links can be perfectly inferred, i.e., no mistakes are made regarding the presence or absence of links. These conditions for perfect inference require: i) an appropriated choice of the observed variable to be analysed, ii) an appropriated interaction strength, and iii) an adequate thresholding of the similarity matrix. For the dynamical units considered here we find that the linear statistical similarity measure performs, in general, better than the nonlinear ones.

[6]  B. Podobnik, D. Horvatic, T. Lipic, M. Perc, J. M. Buldú, and H. E. Stanley, “The cost of attack in competing networks,” Journal of The Royal Society Interface, vol. 12, no. 112, p. 20150770, 2015, 1501.04348. [ bib  DOI  arXiv  pdf  html ] 
[7] 
J. H. Martinez, P. Ariza, M. Zanin, D. Papo, F. Maestu, J. M. Pastor, R. Bajo,
S. Boccaletti, and J. M. Buldu, “Anomalous consistency in mild cognitive
impairment: A complex networks approach,” Chaos Solitons & Fractals,
vol. 70, pp. 144155, 2015.
[ bib 
DOI 
pdf 
html ]
Increased variability in performance has been associated with the emergence of several neurological and psychiatric pathologies. However, whether and how consistency of neuronal activity may also be indicative of an underlying pathology is still poorly understood. Here we propose a novel method for evaluating consistency from noninvasive brain recordings. We evaluate the consistency of the cortical activity recorded with magnetoencephalography in a group of subjects diagnosed with Mild Cognitive Impairment (MCI), a condition sometimes prodromal of dementia, during the execution of a memory task. We use metrics coming from nonlinear dynamics to evaluate the consistency of cortical regions. A representation known as parenclitic networks is constructed, where atypical features are endowed with a network structure, the topological properties of which can be studied at various scales. Pathological conditions correspond to strongly heterogeneous networks, whereas typical or normative conditions are characterized by sparsely connected networks with homogeneous nodes. The analysis of this kind of networks allows identifying the extent to which consistency is affected in the MCI group and the focal points where MCI is especially severe. To the best of our knowledge, these results represent the first attempt at evaluating the consistency of brain functional activity using complex networks theory. (C) 2014 Elsevier Ltd. All rights reserved.

[8] 
R. SevillaEscoboza, J. M. Buldu, A. N. Pisarchik, S. Boccaletti, and
R. Gutierrez, “Synchronization of intermittent behavior in ensembles of
multistable dynamical systems,” Physical Review E, vol. 91, no. 3,
2015.
[ bib 
DOI 
pdf 
html ]
We propose a methodology to analyze synchronization in an ensemble of diffusively coupled multistable systems. First, we study how two bidirectionally coupled multistable oscillators synchronize and demonstrate the high complexity of the basins of attraction of coexisting synchronous states. Then, we propose the use of the master stability function (MSF) for multistable systems to describe synchronizability, even during intermittent behavior, of a network of multistable oscillators, regardless of both the number of coupled oscillators and the interaction structure. In particular, we show that a network of multistable elements is synchronizable for a given range of topology spectra and coupling strengths, irrespective of specific attractor dynamics to which different oscillators are locked, and even in the presence of intermittency. Finally, we experimentally demonstrate the feasibility and robustness of the MSF approach with a network of multistable electronic circuits.

[9] 
D. de SantosSierra, I. SendiñaNadal, I. Leyva, J. a. Almendral, A. Ayali,
S. Anava, C. SanchezAvila, and S. Boccaletti, “Graphbased unsupervised
segmentation algorithm for cultured neuronal networks' structure
characterization and modeling,” Cytometry Part A, vol. 87, no. 6,
pp. 513523, 2015.
[ bib 
DOI 
pdf 
html ]
Large scale phasecontrast images taken at high resolution through the life of a cultured neuronal network are analyzed by a graphbased unsupervised segmentation algorithm with a very low computational cost, scaling linearly with the image size. The processing automatically retrieves the whole network structure, an object whose mathematical representation is a matrix in which nodes are identified neurons or neurons' clusters, and links are the reconstructed connections between them. The algorithm is also able to extract any other relevant morphological information characterizing neurons and neurites. More importantly, and at variance with other segmentation methods that require fluorescence imaging from immunocytochemistry techniques, our non invasive measures entitle us to perform a longitudinal analysis during the maturation of a single culture. Such an analysis furnishes the way of individuating the main physical processes underlying the selforganization of the neurons' ensemble into a complex network, and drives the formulation of a phenomenological model yet able to describe qualitatively the overall scenario observed during the culture growth. Â© 2014 International Society for Advancement of Cytometry.

[10] 
I. Sendiña Nadal, I. Leyva, A. Navas, J. A. VillacortaAtienza, J. A.
Almendral, Z. Wang, and S. Boccaletti, “Effects of degree correlations on
the explosive synchronization of scalefree networks,” Phys. Rev. E,
vol. 91, p. 032811, 2015.
[ bib 
DOI 
pdf 
html ]
We study the organization of finitesize, large ensembles of phase oscillators networking via scalefree topologies in the presence of a positive correlation between the oscillators' natural frequencies and the network's degrees. Under those circumstances, abrupt transitions to synchronization are known to occur in growing scalefree networks, while the transition has a completely different nature for static random configurations preserving the same structuredynamics correlation. We show that the further presence of degreedegree correlations in the network structure has important consequences on the nature of the phase transition characterizing the passage from the phaseincoherent to the phasecoherent network state. While high levels of positive and negative mixing consistently induce a secondorder phase transition, moderate values of assortative mixing, such as those ubiquitously characterizing social networks in the real world, greatly enhance the irreversible nature of explosive synchronization in scalefree networks. The latter effect corresponds to a maximization of the area and of the width of the hysteretic loop that differentiates the forward and backward transitions to synchronization

[11] 
A. Navas, D. Papo, S. Boccaletti, F. DelPozo, R. Bajo, F. Maestú, J. H.
Martínez, P. Gil, I. SendiñaNadal, and J. M. Buldú, “Functional
hubs in mild cognitive impairment,” International Journal of
Bifurcation and Chaos, vol. 25, no. 03, p. 1550034, 2015.
[ bib 
DOI 
pdf 
html ]
We investigate how hubs of functional brain networks are modified as a result of mild cognitive impairment (MCI), a condition causing a slight but noticeable decline in cognitive abilities, which sometimes precedes the onset of Alzheimer's disease. We used magnetoencephalography (MEG) to investigate the functional brain networks of a group of patients suffering from MCI and a control group of healthy subjects, during the execution of a shortterm memory task. Couplings between brain sites were evaluated using synchronization likelihood, from which a network of functional interdependencies was constructed and the centrality, i.e. importance, of their nodes was quantified. The results showed that, with respect to healthy controls, MCI patients were associated with decreases and increases in hub centrality respectively in occipital and central scalp regions, supporting the hypothesis that MCI modifies functional brain network topology, leading to more random structures.

[1]  D. Papo, J. Buldu, and S. Boccaletti, “Network theory in neuroscience,” in Encyclopedia of Computational Neuroscience (A. Garas, ed.), refereed 10, pp. 121, New York: Springer, 2014. [ bib  DOI  pdf ] 
[2] 
J. Aguirre, R. SevillaEscoboza, R. Gutierrez, D. Papo, and J. M. Buldu,
“Synchronization of interconnected networks: The role of connector nodes,”
Physical Review Letters, vol. 112, no. 24, 2014.
[ bib 
DOI 
pdf 
html ]
In this Letter we identify the general rules that determine the synchronization properties of interconnected networks. We study analytically, numerically, and experimentally how the degree of the nodes through which two networks are connected influences the ability of the whole system to synchronize. We show that connecting the highdegree (lowdegree) nodes of each network turns out to be the most (least) effective strategy to achieve synchronization. We find the functional relation between synchronizability and size for a given network of networks, and report the existence of the optimal connector link weights for the different interconnection strategies. Finally, we perform an electronic experiment with two coupled star networks and conclude that the analytical results are indeed valid in the presence of noise and parameter mismatches.

[3]  D. Papo, J. M. Buldu, S. Boccaletti, and E. T. Bullmore, “Complex network theory and the brain,” Philosophical Transactions of the Royal Society BBiological Sciences, vol. 369, no. 1653, 2014. [ bib  DOI  pdf  html ] 
[4] 
D. Papo, M. Zanin, J. Angel PinedaPardo, S. Boccaletti, and J. M. Buldu,
“Functional brain networks: great expectations, hard times and the big leap
forward,” Philosophical Transactions of the Royal Society BBiological
Sciences, vol. 369, no. 1653, 2014.
[ bib 
DOI 
pdf 
html ]
Many physical and biological systems can be studied using complex network theory, a new statistical physics understanding of graph theory. The recent application of complex network theory to the study of functional brain networks has generated great enthusiasm as it allows addressing hitherto nonstandard issues in the field, such as efficiency of brain functioning or vulnerability to damage. However, in spite of its high degree of generality, the theory was originally designed to describe systems profoundly different from the brain. We discuss some important caveats in the wholesale application of existing tools and concepts to a field they were not originally designed to describe. At the same time, we argue that complex network theory has not yet been taken full advantage of, as many of its important aspects are yet to make their appearance in the neuroscience literature. Finally, we propose that, rather than simply borrowing from an existing theory, functional neural networks can inspire a fundamental reformulation of complex network theory, to account for its exquisitely complex functioning mode.

[5]  D. Papo, M. Zanin, and J. M. Buldu, “Reconstructing functional brain networks: have we got the basics right?,” Frontiers in Human Neuroscience, vol. 8, 2014. [ bib  DOI  html ] 
[6] 
S. Boccaletti, G. Bianconi, R. Criado, C. I. del Genio, J. GomezGardeñes,
M. Romance, I. SendiñaNadal, Z. Wang, and M. Zanin, “The structure and
dynamics of multilayer networks,” Physics Reports, vol. 544, no. 1,
pp. 1122, 2014.
[ bib 
DOI 
html ]
In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal or contextrelated properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of realworld systems, and explicitly considered the timevarying and multilayer nature of networks. We offer here a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics. (C) 2014 Elsevier B.V. All rights reserved.

[7] 
D. de SantosSierra, I. SendiñaNadal, I. Leyva, J. A. Almendral, S. Anava,
A. Ayali, D. Papo, and S. Boccaletti, “Emergence of smallworld anatomical
networks in selforganizing clustered neuronal cultures,” Plos One,
vol. 9, no. 1, 2014.
[ bib 
DOI 
pdf 
html ]
In vitro primary cultures of dissociated invertebrate neurons from locust ganglia are used to experimentally investigate the morphological evolution of assemblies of living neurons, as they selforganize from collections of separated cells into elaborated, clustered, networks. At all the different stages of the culture's development, identification of neurons' and neurites' location by means of a dedicated software allows to ultimately extract an adjacency matrix from each image of the culture. In turn, a systematic statistical analysis of a group of topological observables grants us the possibility of quantifying and tracking the progression of the main network's characteristics during the selforganization process of the culture. Our results point to the existence of a particular state corresponding to a smallworld network configuration, in which several relevant graph's microand mesoscale properties emerge. Finally, we identify the main physical processes ruling the culture's morphological transformations, and embed them into a simplified growth model qualitatively reproducing the overall set of experimental observations.

[8] 
D. de SantosSierra, I. SendiñaNadal, I. Leyva, J. A. Almendral, A. Ayali,
S. Anava, C. SánchezÁvila, and S. Boccaletti, “Graphbased unsupervised
segmentation algorithm for cultured neuronal networks' structure
characterization and modeling,” Cytometry Part A, 2014.
DOI: 10.1002/cyto.a.22591.
[ bib 
DOI 
pdf 
html ]
Large scale phasecontrast images taken at high resolution through the life of a cultured neuronal network are analyzed by a graphbased unsupervised segmentation algorithm with a very low computational cost, scaling linearly with the image size. The processing automatically retrieves the whole network structure, an object whose mathematical representation is a matrix in which nodes are identified neurons or neurons' clusters, and links are the reconstructed connections between them. The algorithm is also able to extract any other relevant morphological information characterizing neurons and neurites. More importantly, and at variance with other segmentation methods that require fluorescence imaging from immunocytochemistry techniques, our non invasive measures entitle us to perform a longitudinal analysis during the maturation of a single culture. Such an analysis furnishes the way of individuating the main physical processes underlying the selforganization of the neurons' ensemble into a complex network, and drives the formulation of a phenomenological model yet able to describe qualitatively the overall scenario observed during the culture growth. Â© 2014 International Society for Advancement of Cytometry

[1] 
R. Gutierrez, R. SevillaEscoboza, P. Piedrahita, C. Finke, U. Feudel, J. M.
Buldu, G. HuertaCuellar, R. JaimesReategui, Y. Moreno, and S. Boccaletti,
“Generalized synchronization in relay systems with instantaneous coupling,”
Phys. Rev. E, vol. 88, no. 5, 2013.
[ bib 
DOI 
pdf ]
We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the socalled relay systems. Specifically, we analyze the Lyapunov spectrum of the full system to elucidate when complete and generalized synchronization appear. We show that once a critical coupling strength is achieved, complete synchronization emerges between the systems to be synchronized, and at the same point, generalized synchronization with the relay system also arises. Next, we use two nonlinear measures based on the distance between phasespace neighbors to quantify the generalized synchronization in discretized time series. Finally, we experimentally show the robustness of the phenomenon and of the theoretical tools here proposed to characterize it.

[2] 
J. Aguirre, D. Papo, and J. M. Buldu, “Successful strategies for competing
networks,” Nat. Phys., vol. 9, no. 4, pp. 230234, 2013.
[ bib 
DOI ]
Competitive interactions represent one of the driving forces behind evolution and natural selection in biological and sociological systems(1,2). For example, animals in an ecosystem may vie for food or mates; in a market economy, firms may compete over the same group of customers; sensory stimuli may compete for limited neural resources to enter the focus of attention. Here, we derive rules based on the spectral properties of the network governing the competitive interactions between groups of agents organized in networks. In the scenario studied here the winner of the competition, and the time needed to prevail, essentially depend on the way a given network connects to its competitors and on its internal structure. Our results allow assessment of the extent to which real networks optimize the outcome of their interaction, but also provide strategies through which competing networks can improve on their situation. The proposed approach is applicable to a wide range of systems that can be modelled as networks(3).

[3] 
I. Leyva, I. SendinaNadal, J. A. Almendral, A. Navas, S. Olmi, and
S. Boccaletti, “Explosive synchronization in weighted complex networks,”
Phys. Rev. E, vol. 88, no. 4, 2013.
[ bib 
DOI 
pdf ]
The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. Given a set of phase oscillators networking with a generic wiring of connections and displaying a generic frequency distribution, we show how combining dynamical local information on frequency mismatches and global information on the graph topology suggests a judicious and yet practical weighting procedure which is able to induce and enhance explosive, irreversible, transitions to synchronization. We report extensive numerical and analytical evidence of the validity and scalability of such a procedure for different initial frequency distributions, for both homogeneous and heterogeneous networks, as well as for both linear and nonlinear weighting functions. We furthermore report on the possibility of parametrically controlling the width and extent of the hysteretic region of coexistence of the unsynchronized and synchronized states.

[4] 
I. Leyva, A. Navas, I. SendinaNadal, J. A. Almendral, J. M. Buldu, M. Zanin,
D. Papo, and S. Boccaletti, “Explosive transitions to synchronization in
networks of phase oscillators,” Sci. Rep., vol. 3, 2013.
[ bib 
DOI 
pdf ]
The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. The occurrence of a firstorder phase transition to synchronization of an ensemble of networked phase oscillators was reported, so far, for very particular network architectures. Here, we show how a sharp, discontinuous transition can occur, instead, as a generic feature of networks of phase oscillators. Precisely, we set conditions for the transition from unsynchronized to synchronized states to be firstorder, and demonstrate how these conditions can be attained in a very wide spectrum of situations. We then show how the occurrence of such transitions is always accompanied by the spontaneous setting of frequencydegree correlation features. Third, we show that the conditions for abrupt transitions can be even softened in several cases. Finally, we discuss, as a possible application, the use of this phenomenon to express magneticlike states of synchronization.

[1] 
V. Avalos Gaytán, J. Almendral, D. Papo, S. Schaeffer, and S. Boccaletti,
“Assortative and modular networks are shaped by adaptive synchronization
processes,” Physical Review E  Rapid Communication, vol. (R)86,
p. 015101, 2012.
[ bib 
DOI 
pdf ]
Modular organization and degreedegree correlations are ubiquitous in the connectivity structure of biological, technological, and social interacting systems. So far most studies have concentrated on unveiling both features in real world networks, but a model that succeeds in generating them simultaneously is needed. We consider a network of interacting phase oscillators, and an adaptation mechanism for the coupling that promotes the connection strengths between those elements that are dynamically correlated. We show that, under these circumstances, the dynamical organization of the oscillators shapes the topology of the graph in such a way that modularity and assortativity features emerge spontaneously and simultaneously. In turn, we prove that such an emergent structure is associated with an asymptotic arrangement of the collective dynamical state of the network into cluster synchronization.

[2]  M. Zanin, R. Gutierrez, R. Bajo, J. M. Buldu, D. Papo, and S. Boccaletti, “THEME SECTION: Dynamics and Processes of Complex Networks,” Int. J. of Bifurcat. and Chaos, vol. 22, no. 7, 2012. [ bib  DOI ] 
[3] 
E. F. Lavia, A. Chernomoretz, J. M. Buldu, M. Zanin, and P. Balenzuela,
“Modeling the evolution of item rating netwokrs using timedomain
preferential attachment,” Int. J. of Bifurcat. and Chaos, vol. 22,
no. 7, 2012.
[ bib 
DOI ]
The understanding of the structure and dynamics of the intricate network of connections among people that consumes products through Internet appears as an extremely useful asset in order to study emergent properties related to social behavior. This knowledge could be useful, for example, to improve the performance of personal recommendation algorithms. In this contribution, we analyzed fiveyear records of movierating transactions provided by Netflix, a movie rental platform where users rate movies from an online catalog. This dataset can be studied as a bipartite useritem network whose structure evolves in time. Even though several topological properties from subsets of this bipartite network have been reported with a model that combines random and preferential attachment mechanisms [Beguerisse Diaz et al., 2010], there are still many aspects worth to be explored, as they are connected to relevant phenomena underlying the evolution of the network. In this work, we test the hypothesis that bursty human behavior is essential in order to describe how a bipartite useritem network evolves in time. To that end, we propose a novel model that combines, for user nodes, a network growth prescription based on a preferential attachment mechanism acting not only in the topological domain (i.e. based on node degrees) but also in time domain. In the case of items, the model mixes degree preferential attachment and random selection. With these ingredients, the model is not only able to reproduce the asymptotic degree distribution, but also shows an excellent agreement with the Netflix data in several timedependent topological properties.

[4] 
J. M. Buldu, I. SendinaNadal, I. Leyva, J. A. Almendral, M. Zanin, and
S. Boccaletti, “Nonlocal analysis of modular roles,” Int. J. of
Bifurc. and Chaos, vol. 22, no. 7, 2012.
[ bib 
DOI 
pdf ]
We introduce a new methodology to characterize the role that a given node plays inside the community structure of a complex network. Our method relies on the ability of the links to reduce the number of steps between two nodes in the network, which is measured by the number of shortest paths crossing each link, and its impact on the node proximity. In this way, we use node closeness to quantify the importance of a node inside its community. At the same time, we define a participation coefficient that depends on the shortest paths contained in the links that connect two communities. The combination of both parameters allows to identify the role played by the nodes in the network, following the same guidelines introduced by Guimera et al. [Guimera & Amaral, 2005] but, in this case, considering global information about the network. Finally, we give some examples of the hub characterization in real networks and compare our results with the parameters most used in the literature.

[5] 
I. Leyva, S.E. R., J. M. Buldú, I. SendiñaNadal,
J. GómezGardeñes, A. A., M. Y., G. S., J.R. R., and B. S.,
“Explosive firstorder transition to synchrony in networked chaotic
oscillators,” Phys. Rev. Lett., vol. 108, p. 168702, 2012.
[ bib 
DOI 
pdf ]
Critical phenomena in complex networks, and the emergence of dynamical abrupt transitions in the macroscopic state of the system are currently a subject of the outmost interest. We report evidence of an explosive phase synchronization in networks of chaotic units. Namely, by means of both extensive simulations of networks made up of chaotic units, and validation with an experiment of electronic circuits in a star configuration, we demonstrate the existence of a firstorder transition towards synchronization of the phases of the networked units. Our findings constitute the first prove of this kind of synchronization in practice, thus opening the path to its use in realworld applications.

[6] 
A. A. Rad, I. SendiñaNadal, D. Papo, M. Zanin, J. M. Buldu, F. del Pozo,
and S. Boccaletti, “Topological measure locating the effective crossover
between segregation and integration in a modular network,” Phys. Rev.
Lett., vol. 108, no. 21, 2012.
[ bib 
DOI 
pdf ]
We introduce an easily computable topological measure which locates the effective crossover between segregation and integration in a modular network. Segregation corresponds to the degree of network modularity, while integration is expressed in terms of the algebraic connectivity of an associated hypergraph. The rigorous treatment of the simplified case of cliques of equal size that are gradually rewired until they become completely merged, allows us to show that this topological crossover can be made to coincide with a dynamical crossover from cluster to global synchronization of a system of coupled phase oscillators. The dynamical crossover is signaled by a peak in the product of the measures of intracluster and global synchronization, which we propose as a dynamical measure of complexity. This quantity is much easier to compute than the entropy (of the average frequencies of the oscillators), and displays a behavior which closely mimics that of the dynamical complexity index based on the latter. The proposed topological measure simultaneously provides information on the dynamical behavior, sheds light on the interplay between modularity and total integration, and shows how this affects the capability of the network to perform both local and distributed dynamical tasks.

[7] 
R. Gutierrez, I. SendiñaNadal, M. Zanin, D. Papo, and S. Boccaletti,
“Targeting the dynamics of complex networks,” Sci. Rep., vol. 2,
2012.
[ bib 
DOI 
pdf ]
We report on a generic procedure to steer (target) a network's dynamics towards a given, desired evolution. The problem is here tackled through a Master Stability Function approach, assessing the stability of the aimed dynamics, and through a selection of nodes to be targeted. We show that the degree of a node is a crucial element in this selection process, and that the targeting mechanism is most effective in heterogeneous scalefree architectures. This makes the proposed approach applicable to the large majority of natural and manmade networked systems.

[1] 
J. Almendral, R. Criado, I. Leyva, J. Buldú, and I. SendiñaNadal,
“Mesoscales in complex networks,” Chaos, vol. 21, p. 016101, 2011.
[ bib 
DOI 
pdf ]
Although the functioning of real complex networks is greatly determined by modularity, the majority of articles have focused, until recently, on either their local scale structure or their macroscopical properties. However, neither of these descriptions can adequately describe the important features that complex networks exhibit due to their organization in modules. This Focus Issue precisely presents the state of the art on the study of complex networks at that intermediate level. The reader will find out why this mesoscale level has become an important topic of research through the latest advances carried out to improve our understanding of the dynamical behavior of modular networks. The contributions presented here have been chosen to cover, from different viewpoints, the many open questions in the field as different aspects of community definition and detection algorithms, moduli overlapping, dynamics on modular networks, interplay between scales, and applications to biological, social, and technological fields.

[2] 
J. M. Buldú, R. Bajo, F. Maestu, N. Castellanos, I. Leyva, P. Gil,
I. SendiñaNadal, J. A. Almendral, A. Nevado, F. del Pozo, and
S. Boccaletti, “Reorganization of functional networks in mild cognitive
impairment,” PLoS ONE, vol. 6, p. e19584, 2011.
[ bib 
pdf ]
Whether the balance between integration and segregation of information in the brain is damaged in Mild Cognitive Impairment (MCI) subjects is still a matter of debate. Here we characterize the functional network architecture of MCI subjects by means of complex networks analysis. Magnetoencephalograms (MEG) time series obtained during a memory task were evaluated by synchronization likelihood (SL), to quantify the statistical dependence between MEG signals and to obtain the functional networks. Graphs from MCI subjects show an enhancement of the strength of connections, together with an increase in the outreach parameter, suggesting that memory processing in MCI subjects is associated with higher energy expenditure and a tendency toward random structure, which breaks the balance between integration and segregation. All features are reproduced by an evolutionary network model that simulates the degenerative process of a healthy functional network to that associated with MCI. Due to the high rate of conversion from MCI to Alzheimer Disease (AD), these results show that the analysis of functional networks could be an appropriate tool for the early detection of both MCI and AD.

[3] 
I. Leyva, A. Navas, I. SendiñaNadal, J. M. Buldú, J. A. Almendral, and
S. Boccaletti, “Synchronization waves in geometric networks,” Physical
Review E, vol. 84, pp. 0651011(R), 2011.
[ bib 
DOI 
pdf ]
We report synchronization of networked excitable nodes embedded in a metric space, where the connectivity properties are mostly determined by the distance between units. Such a high clustered structure, combined with the lack of longrange connections, prevents full synchronization and yields instead the emergence of synchronization waves. We show that this regime is optimal for information transmission through the system, as it enhances the options of reconstructing the topology from the dynamics. Measurements of topological and functional centralities reveal that the wavesynchronization state allows detection of the most structurally relevant nodes from a single observation of the dynamics, without any a priori information on the model equations ruling the evolution of the ensemble

[4] 
N. P. Castellanos, I. Leyva, J. M. Buldú, R. Bajo, N. Paúl, P. Cuesta,
V. E. Ordóñez, C. L. Pascua, S. Boccaletti, F. Maestú, and F. del Pozo,
“Principles of recovery from traumatic brain injury: Reorganization of
functional networks,” NeuroImage, vol. 55, pp. 11891199, 2011.
[ bib 
DOI 
pdf ]
Recovery after brain injury is an excellent platform to study the mechanism underlying brain plasticity, the reorganization of networks. Do complex network measures capture the physiological and cognitive alterations that occurred after a traumatic brain injury and its recovery? Patients as well as control subjects underwent restingstate MEG recording following injury and after neurorehabilitation. Next, network measures such as network strength, path length, efficiency, clustering and energetic cost were calculated. We show that these parameters restore, in many cases, to control ones after recovery, specifically in delta and alpha bands, and we design a model that gives some hints about how the functional networks modify their weights in the recovery process. Positive correlations between complex network measures and some of the general index of the WAISIII test were found: changes in deltabased pathlength and those in Performance IQ score, and alphabased normalized global efficiency and Perceptual Organization Index. These results indicate that: 1) the principle of recovery depends on the spectral band, 2) the structure of the functional networks evolves in parallel to brain recovery with correlations with neuropsychological scales, and 3) energetic cost reveals an optimal principle of recovery.

[5] 
M. Zanin, D. Papo, I. SendiñaNadal, and S. Boccaletti, “Computation as an
emergent feature of adaptive synchronization,” Phys. Rev. E, vol. 84,
no. 6, 1, 2011.
[ bib 
DOI 
pdf ]
We report on the spontaneous emergence of computation from adaptive synchronization of networked dynamical systems. The fundamentals are nonlinear elements, interacting in a directed graph via a coupling that adapts itself to the synchronization level between two input signals. These units can emulate different Boolean logics, and perform any computational task in a Turing sense, each specific operation being associated with a given network's motif. The resilience of the computation against noise is proven, and the general applicability is demonstrated with regard to periodic and chaotic oscillators, and excitable systems mimicking neural dynamics.

[6] 
I. SendiñaNadal, J. M. Buldú and, I. Leyva, R. Bajo, J. A. Almendral,
and F. del Pozo, “Integration versus segregation in functional brain
networks,” Biomedical Engineering, IEEE Transactions on, vol. 58,
no. 10, pp. 3004 3007, 2011.
[ bib 
DOI 
pdf ]
We propose a new methodology to evaluate the balance between segregation and integration in functional brain networks by using singular value decomposition techniques. By means of magnetoencephalography, we obtain the brain activity of a control group of 19 individuals during a memory task. Next, we project the nodetonode correlations into a complex network that is analyzed from the perspective of its modular structure encoded in the contribution matrix. In this way, we are able to study the role that nodes play I/O its community and to identify connector and local hubs. At the mesoscale level, the analysis of the contribution matrix allows us to measure the degree of overlapping between communities and quantify how far the functional networks are from the configuration that better balances the integrated and segregated activity.

[7] 
I. SendiñaNadal, Y. Ofran, J. A. Almendral, J. Buldú, I. Leyva, D. Li,
S. Havlin, and S. Boccaletti, “Unveiling protein functions through the
dynamics of the interaction network,” PLoS ONE, vol. 6, no. 3,
p. e17679, 2011.
[ bib 
DOI ]
Protein interaction networks have become a tool to study biological processes, either for predicting molecular functions or for designing proper new drugs to regulate the main biological interactions. Furthermore, such networks are known to be organized in subnetworks of proteins contributing to the same cellular function. However, the protein function prediction is not accurate and each protein has traditionally been assigned to only one function by the network formalism. By considering the network of the physical interactions between proteins of the yeast together with a manual and single functional classification scheme, we introduce a method able to reveal important information on protein function, at both micro and macroscale. In particular, the inspection of the properties of oscillatory dynamics on top of the protein interaction network leads to the identification of misclassification problems in protein function assignments, as well as to unveil correct identification of protein functions. We also demonstrate that our approach can give a network representation of the metaorganization of biological processes by unraveling the interactions between different functional classes.

[1] 
J. Almendral, I. Leyva, L. Daqing, I. SendiñaNadal, H. Shlomo, and
S. Boccaletti, “Dynamics of overlapping structures in modular networks,”
Physical Review E, vol. 82, p. 016115, 2010.
[ bib 
DOI 
pdf ]
Modularity is a fundamental feature of real networks, being intimately bounded to their functionality, i.e., to their capability of performing parallel tasks in a coordinated way. Although the modular structure of real graphs has been intensively studied, very little is known on the interactions between functional modules of a graph. Here, we present a general method based on synchronization of networking oscillators, that is able to detect overlapping structures in multimodular environments. We furthermore report the full analytical and theoretical description on the relationship between the overlapping dynamics and the underlying network topology. The method is illustrated by means of a series of applications.

[2] 
J. Almendral, I. Leyva, I. SendiñaNadal, and S. Boccaletti, “Interacting
oscillators in complex networks: synchronization and the emergence of
scalefree topologies,” International Journal of Bifurcacion and
Chaos, vol. 20, pp. 111, 2010.
[ bib 
DOI 
pdf ]
In natural systems, many processes can be represented as the result of the interaction of self sustained oscillators on top of complex topological wirings of connections. We review some of the main results on the setting of collective (synchronized) behaviors in globally and locally identical coupled oscillators, and then discuss in more detail the main formalism that gives the necessary condition for the stability of a synchronous motion. Finally, we also briefly describe a case of a growing network of nonidentical oscillators, where the growth process is entirely guided by dynamical rules, and where the final synchronized state is accompanied with the emergence of a specific statistical feature (the scalefree property) in the network's degree distribution.

[3] 
M. Zanin, J. M. Buldú, and S. Boccaletti, “Networks of springs: a
practical approach,” Int. J. of Bifurcation and Chaos, vol. 3, p. 827,
2010.
[ bib 
pdf ]
In the current work, we study the propagation of perturbations through networks of springs which are spatially distributed on a plane.We show that the topological properties of the network are related to the dissipation of energy within the system. By varying the rewiring parameter of the graph, and thus going from a regular to a random structure, we obtain a lower energy output, due to the fact that the initial (linear) perturbation is transformed into oscillations around each node. The results obtained are related to the transmission of information through a complex structure with potential applications to the design of more efficient damping systems.

[4] 
J. TianaAlsina, J. M. Buldú, M. C. Torrent, and J. GarcíaOjalvo,
“Quantifying stochasticity in the dynamics of delaycoupled semiconductor
lasers via forbidden patterns,” Phil. Trans. R. Soc. A, vol. 368,
p. 367, 2010.
[ bib 
pdf ]
We quantify the level of stochasticity in the dynamics of two mutually coupled semiconductor lasers. Specifically, we concentrate on a regime in which the lasers synchronize their dynamics with a nonzero lag time, and the leader and laggard roles alternate irregularly between the lasers. We analyse this switching dynamics in terms of the number of forbidden patterns of the alternate time series. The results reveal that the system operates in a stochastic regime, with the level of stochasticity decreasing as the lasers are pumped further away from their lasing threshold. This behaviour is similar to that exhibited by a single semiconductor laser subject to external optical feedback, as its dynamics shifts from the regime of lowfrequency fluctuations to coherence collapse.

[5] 
I. Leyva, I SendiñaNadal, J. Almendral, J. Buldú, D. Li, S. Havlin,
and S. Boccaletti, “Entrainment competition in complex networks,”
International Journal of Bifurcations and Chaos, vol. 20, pp. 827833,
2010.
[ bib 
DOI 
pdf ]
The response of a random and modular network to the simultaneous presence of two frequencies is considered. The competition for controlling the dynamics of the network results in different behaviors, such as frequency changes or permanent synchronization frustration, which can be directly related to the network structure. From these observations, we propose a new method for detecting overlapping communities in structured networks.

[1] 
J. Almendral, I. SendiñaNadal, I. Leyva, D. Yu, and S. Boccaletti,
“Regulating synchronous states of complex networks by pinning interaction
with an external node,” Physical Review E, vol. 80, p. 066111, 2009.
[ bib 
DOI 
pdf ]
To shed light on how biological and technological systems can establish or maintain a synchronous functioning, we address the problem of how to engi neer an external pinning action on a network of dynamical units. In particular, we study the regulation of a network towards a synchronized behavior by means of a bidirectional interaction with an external node that leaves unchanged its inner parameters and architecture. We demonstrate that ther e are two classes of networks susceptible of being regulated into a synchronous motion, and provide a simple method, for each one of them, to proper ly design a pinning sequence to achieve regulation. We also discuss how the obtained sequence can be compared with a topological ranking of the network nodes.

[2] 
J. Almendral, I. Leyva, and I. SendiñaNadal, “Enhancing network
synchronization by sparse repulsive couplings,” International Journal
of Bifurcation and Chaos, vol. 19(2), pp. 711717, 2009.
[ bib 
pdf ]
In a smallworld network of mainly attractively coupled nonidentical neurons, we show that a small fraction of phaserepulsive couplings is able to strongly improve synchronization for certain values of the link strength, and longrange connection probability. By means of a spectral analysis we relate the observed dynamical behavior with the structural properties of the network.

[3] 
J. Aguirre, J. M. Buldú, and S. C. Manrubia, “Evolutionary dynamics on
networks of selectively neutral genotypes: Effects of topology and sequence
stability,” Physical Review E, vol. 80, p. 066112, 2009.
[ bib 
pdf ]
Networks of selectively neutral genotypes underlie the evolution of populations of replicators in constant environments. Previous theoretical analysis predicted that such populations will evolve toward highly connected regions of the genome space. We first study the evolution of populations of replicators on simple networks and quantify how the transient time to equilibrium depends on the initial distribution of sequences on the neutral network, on the topological properties of the latter, and on the mutation rate. Second, network neutrality is broken through the introduction of an energy for each sequence. This allows to study the competition between two features (neutrality and energetic stability) relevant for survival and subjected to different selective pressures. In cases where the two features are negatively correlated, the population experiences sudden migrations in the genome space for values of the relevant parameters that we calculate. The numerical study of larger networks indicates that the qualitative behavior to be expected in more realistic cases is already seen in representative examples of small networks.

[4] 
A. Wagemakers, J. M. Buldú, M. A. F. Sanjuan, O. de Luis, A. Izquierdo, and
A. Coloma, “Entraining synthetic genetic oscillators,” Chaos,
vol. 19, p. 0033139, 2009.
[ bib 
pdf ]
We propose a new approach for synchronizing a population of synthetic genetic oscillators, which consists in the entrainment of a colony of repressilators by external modulation. We present a model where the repressilator dynamics is affected by periodic changes in temperature. We introduce an additional plasmid in the bacteria in order to correlate the temperature variations with the enhancement of the transcription rate of a certain gene. This can be done by introducing a promoter that is related to the heat shock response. This way, the expression of that gene results in a protein that enhances the overall oscillations. Numerical results show coherent oscillations of the population for a certain range of the external frequency, which is in turn related to the natural oscillation frequency of the modified repressilator. Finally we study the transient times related with the loss of synchronization and we discuss possible applications in biotechnology of largescale production coupled to synchronization events induced by heat shock.

[5] 
M. Zanin, P. Cano, J. M. Buldú, and O. Celma, “Preferential attachment,
aging and weights in recommendation systems,” International Journal of
Bifurcation and Chaos, vol. 19, p. 755, 2009.
[ bib 
pdf ]
In the present work, algorithms based on complex network theory are applied to Recommendation Systems in order to improve their quality of predictions. We show how some networks are grown under the influence of trendy forces, and how this can be used to enhance the results of a recommendation system, i.e. increase their percentage of right predictions. After defining a base algorithm, we create recommendation networks which are based on a histogram of user ratings, using therefore an underlying principle of preferential attachment. We show the influence of data aging in the prediction of user habits and how the exact moment of the prediction influences the recommendation. Finally, we design weighted networks that take into account the age of the information used to generate the links. In this way, we obtain a better approximation to evaluate the usersâ€™ tastes.

[6] 
K. Staliunas, G. J. Valcarcel, J. M. Buldú, and J. GarcíaOjalvo,
“Noiseinduced phase bistability via stochastic rocking,” Phys. Rev.
Lett., vol. 102, p. 010601, 2009.
[ bib 
pdf ]
We study the effect of a randomly modulated harmonic driving on the phase behavior of a nonlinear oscillator. A multiplescale analysis shows that the system is formally equivalent to a rocked oscillator, in which a modulated harmonic driving locks the system at one of two phases, both of which are in quadrature with that of the driving. This theoretically predicted noiseinduced bistable phase locking is reproduced with numerical simulations of a stochastic StuartLandau model, and verified experimentally in a nonlinear electronic circuit.

[7] 
I. Leyva, I SendiñaNadal, J. Buldú, J. Almendral, and S. Boccaletti,
“Generation of scalefree topology in complex networks by phase
entrainment,” International Journal of Systems Science, vol. 40,
pp. 923930, 2009.
[ bib 
DOI 
pdf ]
A collection of connected phase oscillators, initially unsynchronised, are subjected to a growing process. In such a process, pacemaker oscillators attach to the original network following an exclusively dynamical criterion oriented to entrain the network. Under these conditions, we show that successful entrainment always corresponds to the generation of a scalefree topology in the original graph.

[8] 
I. SendiñaNadal, I. Leyva, J. Buldú, J. A. Almendral, and
S. Boccaletti, “Entraining the topology and the dynamics of a network of
phase oscillators,” Phys. Rev. E, vol. 79, p. 046105, 2009.
[ bib 
DOI 
pdf ]
We show that the topology and dynamics of a network of unsynchronized Kuramoto oscillators can be simultaneously controlled by means of a forcing mechanism which yields a phase locking of the oscillators to that of an external pacemaker in connection with the reshaping of the network's degree distribution. The entrainment mechanism is based on the addition, at regular time intervals, of unidirectional links from oscillators that follow the dynamics of a pacemaker to oscillators in the pristine graph whose phases hold a prescribed phase relationship. Such a dynamically based rule in the attachment process leads to the emergence of a powerlaw shape in the final degree distribution of the graph whenever the network is entrained to the dynamics of the pacemaker. We show that the arousal of a scalefree distribution in connection with the success of the entrainment process is a robust feature, characterizing different network's initial configurations and parameters.

[1] 
T. Teitelbaum, P. Balenzuela, P. Cano, and J. M. Buldú, “Community
structures and role detection in music networks,” Chaos, vol. 18,
p. 043105, 2008.
[ bib 
pdf ]
We analyze the existence of community structures in two different social networks using data obtained from similarity and collaborative features between musical artists. Our analysis reveals some characteristic organizational patterns and provides information about the driving forces behind the growth of the networks. In the similarity network, we find a strong correlation between clusters of artists and musical genres. On the other hand, the collaboration network shows two different kinds of communities: rather small structures related to music bands and geographic zones, and much bigger communities built upon collaborative clusters with a high number of participants related through the period the artists were active. Finally, we detect the leading artists inside their corresponding communities and analyze their roles in the network by looking at a few topological properties of the nodes.

[2] 
M. Zanin, J. M. Buldú, P. Cano, and S. Boccaletti, “Disorder and decision
cost in spatial networks,” Chaos, vol. 18, p. 023103, 2008.
[ bib 
pdf ]
We introduce the concept of decision cost of a spatial graph, which measures the disorder of a given network taking into account not only the connections between nodes but their position in a twodimensional map. The influence of the network size is evaluated and we show that normalization of the decision cost allows us to compare the degree of disorder of networks of different sizes. Under this framework, we measure the disorder of the connections between airports of two different countries and obtain some conclusions about which of them is more disordered. The introduced concepts (decision cost and disorder of spatial networks) can easily be extended to Euclidean networks of higher dimensions, and also to networks whose nodes have a certain fitness property (i.e., onedimensional).

[3] 
A. Wagemakers, J. M. Buldú, and M. A. F. Sanjuan, “Experimental
demonstration of bidirectional chaotic communication by means of isochronal
synchronization,” Europhysics Letters, vol. 81, p. 40005, 2008.
[ bib 
pdf ]
We give the first experimental demonstration of simultaneous bidirectional communication through chaotic carriers thanks to the phenomenon of isochronal synchronization. Two MackeyGlass electronic circuits with chaotic behaviour exchange their signals through a coupling line with delay. When the internal feedback of the circuits and the coupling are accurately matched, isochronal synchronization arises. Under this dynamical regime, we introduce a binary message at both outputs and recover it at the opposite circuit. Finally, we discuss the security of this kind of communication system by analyzing the message recovered by a potential eavesdropper.

[4] 
D. Li, I. Leyva, J. Almendral, I. SendiñaNadal, J. Buldú, S. Havlin,
and S. Boccaletti, “Synchronization interfaces and overlapping communities
in complex networks,” Phys. Rev. Lett., vol. 101, p. 168701, 2008.
[ bib 
DOI 
pdf ]
We show that a complex network of phase oscillators may display interfaces between domains (clusters) of synchronized oscillations. The emergence and dynamics of these interfaces are studied for graphs composed of either dynamical domains (influenced by different forcing processes), or structural domains (modular networks). The obtained results allow to give a functional definition of overlapping structures in modular networks, and suggest a practical method able to give information on overlapping clusters in both artificially constructed and real world modular networks.

[5] 
N. Sungar, E. Allaria, I. Leyva, and F. Arecchi, “Comparison of single neuron
models in terms of synchronization propensity,” Chaos, vol. 18,
p. 033108, 2008.
Also selected paper in Virtual Journal of Biological Physics Research
16, 3 (2008).
[ bib 
DOI 
pdf ]
A plausible model for coherent perception is the synchronization of chaotically distributed neural spike trains over wide cortical areas. A recently introduced propensity criterion provides a tool for a quantitative comparison of different neuron models in terms of their ability to synchronize to an applied perturbation. We explore the propensity of several systems and indicate the requirements to be satisfied by a plausible candidate for modeling neuronal activity. Our results show that the conflicting requirements of stability and sensitivity leading to high propensity to synchronization can be satisfied by a strongly nonuniform attractor made of two distinct regions: a saddle focus plus a sufficiently separated saddle node.

[6] 
K. Al Naimee, I. Leyva, I. PerezMarino, and F. Arecchi, “Noise effects in
intrinsic laser polarization switching,” Physical Review A, vol. 77,
p. 063803, 2008.
[ bib 
DOI 
pdf ]
A quasiisotropic CO2 laser near the resonant condition can present bistability in the polarization state, with spontaneous flips between two orthogonal linear polarization eigenmodes. In this work, we explore the role of the pump and noise on the polarization dynamics, showing a transition from stable to bistable states and the presence of coherent resonance.

[7] 
I. SendiñaNadal, J. Buldú, I. Leyva, and S. Boccaletti, “Phase
locking induces scalefree topologies in networks of coupled oscillators,”
PLoS ONE, vol. 3, 2008.
[ bib 
DOI 
pdf ]
An initial unsynchronized ensemble of networking phase oscillators is further subjected to a growing process where a set of forcing oscillators, each one of them following the dynamics of a frequency pacemaker, are added to the pristine graph. Linking rules based on dynamical criteria are followed in the attachment process to force phase locking of the network with the external pacemaker. We show that the eventual locking occurs in correspondence to the arousal of a scalefree degree distribution in the original graph.

[8] 
V. Beato, I. SendiñaNadal, I. Gerdes, and H. Engel, “Coherence resonance
in a chemical excitable system driven by coloured noise,” Philosophical
Transactions Of The Royal Society A, vol. 366, pp. 381395, 2008.
[ bib 
DOI 
pdf ]
We investigate how the temporal correlation in excitable systems driven by external noise affects the coherence of the system's response. The coupling to the fluctuating environment is introduced via fluctuations of a bifurcation parameter that controls the local dynamics of the lightsensitive Belousov Zhabotinsky reaction and of its numerical description, the Oregonator model. Both systems are brought from a highly incoherent regime to a coherent one by an appropriate choice of the correlation time and keeping noise variance constant. This effect has been found both for an Ornstein Uhlenbeck process and for a dichotomous telegraph signal. In the latter case, we are able to connect the optimal correlation time, for which the system behaviour is most coherent, with a characteristic time scale of the system.

[1] 
J. Almendral, J. Oliveira, L. Lopez, M. Sanjuan, and J. Mendes, “The interplay
of universities and industry through the fp5 network,” New Journal Of
Physics, vol. 9, 2007.
[ bib 
pdf ]
To improve the quality of life in a modern society it is essential to reduce the distance between basic research and applications, whose crucial roles in shaping today's society prompt us to seek their understanding. Existing studies on this subject, however, have neglected the network character of the interaction between universities and industry. Here we use stateoftheart network theory methods to analyse this interplay in the socalled Framework Programme (FP)an initiative which sets out the priorities for the European Union's research and technological development. In particular we study in the 5th FP (FP5) the role played by companies and scientific institutions and how they contribute to enhance the relationship between research and industry. Our approach provides quantitative evidence that while firms are size hierarchically organized, universities and research organizations keep the network from falling into pieces, paving the way for an effective knowledge transfer.

[2] 
J. Almendral and A. DiazGuilera, “Dynamical and spectral properties of
complex networks,” New Journal Of Physics, vol. 9, 2007.
[ bib 
pdf ]
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.

[3] 
J. Almendral, J. Oliveira, L. Lopez, J. Mendes, and M. Sanjuan, “The network
of scientific collaborations within the european framework programme,”
Physica AStatistical Mechanics And Its Applications, vol. 384,
pp. 675683, 2007.
[ bib 
pdf ]
We use the emergent field of complex networks to analyze the network of scientific collaborations between entities (universities, research organizations, industry related companies....) which collaborate in the context of the socalled framework programme. We demonstrate here that it is a scalefree network with an accelerated growth, which implies that the creation of new collaborations is encouraged. Moreover, these collaborations possess hierarchical modularity. Likewise, we find that the information flow depends on the size of the participants but not on geographical constraints. (C) 2007 Elsevier B.V. All rights reserved.

[4] 
A. Wagemakers, J. M. Buldú, and M. A. F. Sanjuan, “Isochronous
synchronization in mutually coupled chaotic circuits,” Chaos, vol. 17,
2007.
[ bib 
pdf ]
This paper examines the robustness of isochronous synchronization in simple arrays of bidirectionally coupled systems. First, the achronal synchronization of two mutually chaotic circuits, which are coupled with delay, is analyzed. Next, a third chaotic circuit acting as a relay between the previous two circuits is introduced. We observe that, despite the delay in the coupling path, the outer dynamical systems show isochronous synchronization of their outputs, i.e., display the same dynamics at exactly the same moment. Finally, we give here the first experimental evidence that the central relaying system is not required to be of the same kind of its outer counterparts.(c) 2007 American Institute of Physics.

[5] 
J. M. Buldú, P. Cano, M. Koppenberger, J. A. Almendral, and S. Boccaletti,
“The complex network of musical tastes,” New Journal Of Physics,
vol. 9, 2007.
[ bib 
pdf ]
We present an empirical study of the evolution of a social network constructed under the influence of musical tastes. The network is obtained thanks to the selfless effort of a broad community of users who share playlists of their favourite songs with other users. When two songs cooccur in a playlist a link is created between them, leading to a complex network where songs are the fundamental nodes. In this representation, songs in the same playlist could belong to different musical genres, but they are prone to be linked by a certain musical taste (e.g. if songs A and B cooccur in several playlists, an user who likes A will probably like also B). Indeed, playlist collections such as the one under study are the basic material that feeds some commercial music recommendation engines. Since playlists have an input date, we are able to evaluate the topology of this particular complex network from scratch, observing how its characteristic parameters evolve in time. We compare our results with those obtained from an artificial network defined by means of a null model. This comparison yields some insight on the evolution and structure of such a network, which could be used as ground data for the development of proper models. Finally, we gather information that can be useful for the development of music recommendation engines and give some hints about how tophits appear.

[6] 
J. M. Buldu, M. C. Torrent, and J. GarciaOjalvo, “Synchronization in
semiconductor laser rings,” Journal Of Lightwave Technology, vol. 25,
pp. 15491554, 2007.
[ bib 
pdf ]
We examine the dynamics of semiconductor lasers coupled in a ring configuration. The lasers, which have stable output intensity when isolated, behave chaotically when coupled unidirectionally in a closed chain. In this way, we show that neither feedback nor bidirectional coupling is necessary to induce chaotic dynamics at the laser output. We study the synchronization phenomena arising in this particular coupling architecture and discuss its possible application to chaosbased communications. Next, we extend the study to bidirectional coupling and propose an appropriate technique to optical chaos encryption/decryption in closed chains of mutually coupled semiconductor lasers.

[7]  J. M. Buldu, A. Wagemakers, M. A. F. Sanjuan, and J. GarciaOjalvo, “Electronic design of synthetic genetic networks,” International Journal of Bifurcation and Chaos, vol. 17, pp. 35073511, 2007. [ bib  pdf ] 
[8] 
X. Vidal, P. Balenzuela, J. M. Buldu, J. Martorell, and J. GarciaOjalvo,
“Coincidence detection of inharmonic pulses in a nonlinear crystal.,”
Phys Rev E Stat Nonlin Soft Matter Phys, vol. 75, p. 012902, 2007.
[ bib 
pdf ]
Two trains of light pulses at periods that are equally shifted from the harmonics of a missing fundamental are combined in a nonlinear crystal. As a result of a noncollinear phasematched secondorder nonlinear generation, a new train of pulses is obtained. When the temporal width of the input pulses is large, the frequency of the resulting pulse train follows the observations from classical experiments on the perception of virtual pitch by the brain. On the other hand, when the width of the input pulses is small, the generated pulse train exhibits much lower frequencies, analogous to those observed in the motor neural system. Our experimental setup allows us to explore, systematically and continuously, the transition between these two regimes, while at the same time to demonstrate that the functionalities that have been observed in the nervous system are similar to the ones we observe from coincidence detection in quadratic nonlinear systems.

[9] 
C. M. Gonzalez, J. M. Buldu, M. C. Torrent, and J. GarciaOjalvo, “Processing
distributed inputs in coupled excitable lasers,” Physical Review A,
vol. 76, 2007.
[ bib 
pdf ]
In many instances, networks of dynamical elements are subject to distributed input signals that enter the network through different nodes. In these cases, processing of the input signals may be mediated by coupling, in what constitutes an emerging property of the network. Here we study experimentally this effect in two mutually injected semiconductor lasers with optical feedback, operating in an excitable regime. The lasers are subject to different periodic input signals in their pump current, with distinct frequencies. Our results show that when the signals are harmonics of an absent fundamental, the laser array is able to process these signals and respond at the missing fundamental frequency. When the input frequencies are rigidly shifted from their harmonic values, the response frequency follows a simple law derived from a linear sum of the inputs, even though the array integrates the electrical inputs after having transduced them optically. The results are reproduced numerically with a dynamical model of the laser array.

[10] 
S. Boccaletti, J. M. Buldu, R. Criado, J. Flores, V. Latora, J. Pello, and
M. Romance, “Multiscale vulnerability of complex networks.,” Chaos,
vol. 17, p. 043110, 2007.
[ bib 
pdf ]
We present a novel approach to quantify the vulnerability of a complex network, i.e., the capacity of a graph to maintain its functional performance under random damages or malicious attacks. The proposed measure represents a multiscale evaluation of vulnerability, and makes use of combined powers of the links' betweenness. We show that the proposed approach is able to properly describe some cases for which earlier measures of vulnerability fail. The relevant applications of our method for technological network design are outlined.

[11] 
J. Park, O. Celma, M. Koppenberger, P. Cano, and J. M. Buldu, “The social
network of contemporary popular musicians,” International Journal Of
Bifurcation And Chaos, vol. 17, pp. 22812288, 2007.
[ bib 
pdf ]
In this paper, we analyze two social network datasets of contemporary musicians constructed from allmusic.com (AMG), a music and artists' information database: one is the collaboration network in which two musicians are connected if they have performed or produced an album together, and the other is the similarity network in which they are connected if they were musically similar according to the music experts. We find that, while both networks exhibit typical features of social networks such as high transitivity (clustering), we find that they differ significantly in some key network features such as the degree and the betweenness distributions. We believe that this highlights the fundamental differences in the construction mechanism (selforganized collaboration and humanperceived similarity) of the new networks.

[12] 
O.U. Kheowan, E. Mihaliuk, B. Blasius, I. SendiñaNadal, and K. Showalter,
“Wave mediated synchronization of nonuniform oscillatory media,” Phys
Rev Lett, vol. 98, p. 074101, 2007.
[ bib 
DOI 
pdf ]
We characterize the spatiotemporal evolution of a photosensitive BelousovZhabotinsky medium that is made up of coupled oscillatory cells with randomly distributed frequencies. The medium evolves from an initial state of multiple wave sources to a synchronized state governed by a single wave source. The synchronization occurs via a competition between the sources, which arises when the oscillators are not identical but have slightly different natural frequencies. The evolution of each cell is monitored to demonstrate frequency and phase synchronization of the inhomogeneous cellular medium, and a simple kinematic description for the advance of the phasediffusion wave is presented.

[1] 
P. Balenzuela, J. M. Buldu, M. Casanova, and J. GarciaOjalvo, “Episodic
synchronization in dynamically driven neurons.,” Phys Rev E Stat Nonlin
Soft Matter Phys, vol. 74, p. 061910, 2006.
[ bib 
pdf ]
We examine the response of type II excitable neurons to trains of synaptic pulses, as a function of the pulse frequency and amplitude. Similarly to the case of harmonic inputs, these neurons exhibit a resonant behavior also for pulsed inputs. We interpret this phenomenon in terms of the subthreshold response of the neuron. In the presence of dynamical trains of input pulses whose frequency varies continuously in time, the receiving neuron synchronizes episodically to the input pulses, whenever the pulse frequency lies within the neuron's locking range. The results are obtained both in numerical simulations of the MorrisLecar model and in an electronic implementation of the FitzHughNagumo system, evidencing the robustness of the phenomenon.

[2] 
J. M. Buldu, K. Staliunas, J. Casals, and J. GarciaOjalvo, “Bistable phase
control via rocking in a nonlinear electronic oscillator,” Chaos,
vol. 16, 2006.
[ bib 
pdf ]
We experimentally demonstrate the effective rocking [de Valcarcel and Staliunas, Phys. Rev. E 67, 026604 (2003)] of a nonlinear electronic circuit operating in a periodic regime. Namely, we show that by driving a Chua circuit with a periodic signal, whose phase alternates (also periodically) in time, we lock the oscillation frequency of the circuit to that of the driving signal, and its phase to one of two possible values shifted by pi, and lying between the alternating phases of the input signal. In this way, we show that a rocked nonlinear oscillator displays phase bistability. We interpret the experimental results via a theoretical analysis of rocking on a simple oscillator model, based on a normal form description (complex Landau equation) of the rocked Hopf bifurcation. (c) 2006 American Institute of Physics.

[3] 
J. M. Buldu, T. Heil, I. Fischer, M. c. Torrent, and J. GarciaOjalvo,
“Episodic synchronization via dynamic injection.,” Phys Rev Lett,
vol. 96, p. 024102, 2006.
[ bib 
pdf ]
We report the occurrence of spontaneous synchronizing events between two semiconductor lasers, when the emission of a frequency and intensitychaotic driving laser is unidirectionally coupled into a second stable response laser. The driving laser is driven chaotic by delayed optical feedback, the response laser is a deviceidentical solitary laser. We demonstrate the onset of an episodic synchronization regime when the two lasers are spectrally detuned with respect to each other. By a joint experimental and modeling analysis we can attribute the onset and the duration of the episodes to properties of spectral overlap of both lasers. This effect can even give rise to seemingly anticorrelated intensity behavior. We expect episodic synchronization to be a generic scenario for the loss of synchronization of chaotic oscillators exhibiting frequency cycles.

[4] 
P. Cano, O. Celma, M. Koppenberger, and J. Buldu, “Topology of music
recommendation networks,” Chaos, vol. 16, 2006.
[ bib 
pdf ]
We study the topology of several music recommendation networks, which arise from relationships between artist, cooccurrence of songs in play lists or experts' recommendation. The analysis uncovers the emergence of complex network phenomena in these kinds of recommendation networks, built considering artists as nodes and their resemblance as links. We observe structural properties that provide some hints on navigation and possible optimizations on the design of music recommendation systems. Finally, the analysis derived from existing music knowledge sources provides a deeper understanding of the human music similarity perception. (C) 2006 American Institute of Physics.

[5] 
I. Da Silva, J. Buldu, C. Mirasso, and J. GarciaOjalvo, “Synchronization by
dynamical relaying in electronic circuit arrays,” Chaos, vol. 16,
2006.
[ bib 
pdf ]
We experimentally study the synchronization of two chaotic electronic circuits whose dynamics is relayed by a third parametermatched circuit, to which they are coupled bidirectionally in a linear chain configuration. In a wide range of operating parameters, this setup leads to synchronization between the outer circuits, while the relaying element remains unsynchronized. The specifics of the synchronization differ with the coupling level: for low couplings a state of intermittent synchronization between the outer circuits coexists with one of antiphase synchronization. Synchronization becomes in phase for moderate couplings, and for strong coupling identical synchronization is observed between the outer elements, which are themselves synchronized in a generalized way with the relaying element. In the latter situation, the middle element displays a triplescroll attractor that is not possible to obtain when the chaotic oscillator is isolated. (c) 2006 American Institute of Physics.

[6] 
I. Fischer, R. Vicente, J. M. Buldu, M. Peil, C. R. Mirasso, M. c. Torrent, and
J. GarciaOjalvo, “Zerolag longrange synchronization via dynamical
relaying.,” Phys Rev Lett, vol. 97, p. 123902, 2006.
[ bib 
pdf ]
We show that isochronous synchronization between two delaycoupled oscillators can be achieved by relaying the dynamics via a third mediating element, which surprisingly lags behind the synchronized outer elements. The zerolag synchronization thus obtained is robust over a considerable parameter range. We substantiate our claims with experimental and numerical evidence of such synchronization solutions in a chain of three coupled semiconductor lasers with long interelement coupling delays. The generality of the mechanism is validated in a neuronal model with the same coupling architecture. Thus, our results show that zerolag synchronized chaotic dynamical states can occur over long distances through relaying, without restriction by the amount of delay.

[7] 
A. Lopera, J. M. Buldu, M. c. Torrent, D. R. Chialvo, and J. GarciaOjalvo,
“Ghost stochastic resonance with distributed inputs in pulsecoupled
electronic neurons.,” Phys Rev E Stat Nonlin Soft Matter Phys,
vol. 73, p. 021101, 2006.
[ bib 
pdf ]
We study experimentally the phenomenon of ghost stochastic resonance in pulsecoupled excitable systems, for input signals distributed among different elements. Specifically, two excitable electronic circuits are driven by different sinusoidal signals that produce periodic spikes at distinct frequencies. Their outputs are sent to a third circuit that processes these spiking signals and is additionally perturbed by noise. When the input signals are harmonics of a certain fundamental (that is not present in the inputs) the processing circuit exhibits, for an optimal amount of noise, a resonant response at the frequency of the missing fundamental (ghost frequency). In contrast with the standard case in which the signals being directly integrated are sinusoidal, this behavior relies here on a coincidencedetection mechanism. When the input signals are homogeneously shifted in frequency, the processing circuit responds with pulse packages composed of spikes at a frequency that depends linearly on the frequency shift. Expressions for the dependence of the package period and duration on the frequency shift and spike width, respectively, are obtained. These results provide an experimental verification of a recently proposed mechanism of binaural pitch perception.

[8] 
A. Wagemakers, J. Buldu, J. GarciaOjalvo, and M. Sanjuan, “Synchronization of
electronic genetic networks,” Chaos, vol. 16, 2006.
[ bib 
pdf ]
We describe a simple analog electronic circuit that mimics the behavior of a wellknown synthetic gene oscillator, the repressilator, which represents a set of three genes repressing one another. Synchronization of a population of such units is thoroughly studied, with the aim to compare the role of global coupling with that of global forcing on the population. Our results show that coupling is much more efficient than forcing in leading the gene population to synchronized oscillations. Furthermore, a modification of the proposed analog circuit leads to a simple electronic version of a genetic toggle switch, which is a simple network of two mutual repressor genes, where control by external forcing is also analyzed. (C) 2006 American Institute of Physics.

[9] 
I. Leyva, I. SendinaNadal, J. Almendral, and M. Sanjuan, “Sparse repulsive
coupling enhances synchronization in complex networks,” Physical Review
E, vol. 74, p. 056112(7), 2006.
Also selected paper in Virtual Journal of Biological Physics Research
12, 41 (2006).
[ bib 
DOI 
pdf ]
Through the last years, different strategies to enhance synchronization in complex networks have been proposed. In this work, we show that synchronization of nonidentical dynamical units that are attractively coupled in a smallworld network is strongly improved by just making phaserepulsive a tiny fraction of the couplings. By a purely topological analysis that does not depend on the dynamical model, we link the emerging dynamical behavior with the structural properties of the sparsely coupled repulsive network.

[10] 
R. Meucci, F. Salvadori, I. Leyva, I. Marino, K. Al Naimee, and M. Capo,
“Polarization selection by optical feedback,” Optics Communications,
vol. 268, pp. 169173, 2006.
[ bib 
pdf ]
We present experimental and numerical evidence of polarization selection in an isotropic CO2 laser achieved by means of an unpolarized optical feedback. This mechanism can be applied in situations where the direction of polarization plays a crucial role, including polarization coding. (c) 2006 Elsevier B.V. All rights reserved.

[11] 
S. Zambrano, E. Allaria, S. Brugioni, I. Leyva, R. Meucci, M. Sanjuan, and
F. Arecchi, “Numerical and experimental exploration of phase control of
chaos,” Chaos, vol. 16, 2006.
[ bib 
pdf ]
A wellknown method to suppress chaos in a periodically forced chaotic system is to add a harmonic perturbation. The phase control of chaos scheme uses the phase difference between a small added harmonic perturbation and the main driving to suppress chaos, leading the system to different periodic orbits. Using the Duffing oscillator as a paradigm, we present here an indepth study of this technique. A thorough numerical exploration has been made focused in the important role played by the phase, from which new interesting patterns in parameter space have appeared. On the other hand, our novel experimental implementation of phase control in an electronic circuit confirms both the wellknown features of this method and the new ones detected numerically. All this may help in future implementations of phase control of chaos, which is globally confirmed here to be robust and easy to implement experimentally. (C) 2006 American Institute of Physics.

[12] 
I. SendiñaNadal, M. decastro, and M. GomezGesteira, “Kinematic
description of wave propagation through a chemical diode,” Chaos,
vol. 16, 2006.
[ bib 
DOI 
pdf ]
The geometry of an active medium can cause wave blocking and induce unidirectional propagation. This well established phenomenon was studied in a previous paper within the framework of the photosensitive BelousovZhabotinsky reaction and the associated Oregonator model. In the present paper, as an extension of that study, the main factors that influence this phenomenon are interpreted in terms of a kinematic model. (c) 2006 American Institute of Physics.

[1] 
J. Almendral, L. Lopez, V. Cholvi, and M. Sanjuan, “Congestion schemes and
nash equilibrium in complex networks,” Physica AStatistical Mechanics
And Its Applications, vol. 355, pp. 602618, 2005.
[ bib 
pdf ]
Whenever a common resource is scarce, a set of rules are needed to share it in a fairly way. However, most control schemes assume that users will behave in a cooperative way, without taking care of guaranteeing that they will not act in a selfish manner. Then, a fundamental issue is to evaluate the impact of cheating. From the point of view of game theory, a Nash equilibrium implies that nobody can take advantage by unilaterally deviating from this stable state, even in the presence of selfish users. In this paper we prove that any efficient Nash equilibrium strongly depends on the number of users, if the control scheme policy does not record their previous behavior. Since this is a common pattern in real situations, this implies that the system would be always out of equilibrium. Consequently, this result proves that, in practice, oblivious control schemes must be improved to cope with selfish users. (c) 2005 Elsevier B.V. All rights reserved.

[2] 
J. Buldu, J. GarciaOjalvo, and M. Torrent, “Demultiplexing chaos from
multimode semiconductor lasers,” Ieee Journal Of Quantum Electronics,
vol. 41, pp. 164170, 2005.
[ bib 
pdf ]
We show numerically that the injection of two chaotic modes of a multimode semiconductor laser with optical feedback into two singlemode standalone semiconductor lasers leads to chaotic synchronization between the respective intensities. The effect of parameter mismatch between the transmitter and receiver lasers is examined, and it is concluded that the observed synchronization is a consequence of injection locking. Under these conditions, the possibility of using this demultiplexing scheme for message transmission is examined.

[3] 
J. Buldu, C. Gonzalez, J. Trull, M. Torrent, and J. GarciaOjalvo,
“Couplingmediated ghost resonance in mutually injected lasers,”
Chaos, vol. 15, 2005.
[ bib 
pdf ]
We experimentally and numerically study the phenomenon of ghost resonance in coupled nonlinear systems. Two mutually injected semiconductor lasers are externally perturbed in their pump currents by two respective periodic signals of different frequencies f(1) and f(2). For small amplitudes of the external modulations, the two laser intensities display synchronized optical pulses, in the form of dropout events occurring at irregular times. By adjusting the amplitude and frequencies of the driving signals, the system exhibits a ghost resonance in the dropout appearance at a frequency f(r) not present in the distributed inputs. (C) 2005 American Institute of Physics.

[4] 
V. Beato, I. SendiñaNadal, I. Gerdes, and H. Engel, “Noiseinduced wave
nucleations in an excitable chemical reaction,” Phys Rev E, vol. 71,
p. 035204R, 2005.
[ bib 
DOI 
pdf ]
We study both experimentally and numerically the temporal coherence of noiseinduced wave nucleations in excitable media subjected to external fluctuations with finite correlation time. The experiments are performed with the lightsensitive variant of the BelousovZhabotinsky (BZ) reaction forced by an exponentially correlated dichotomous fluctuating illumination. We find that there exists an optimal correlation time for which nucleations coherence reaches a maximum. The same behavior is obtained in numerical simulations with a stochastic Oregonator model, modified to describe the lightsensitive BZ reaction.

[1] 
J. Almendral, L. Fernandez, V. Cholvi, and M. Sanjuan, “Oblivious router
policies and nash equilibrium,” Iscc2004: Ninth International Symposium
On Computers And, pp. 736741, 2004.
[ bib 
pdf ]
Most of congestion control schemes require users to behave in a cooperative way, so that they respect some "social responsible" rules. However, without forcing end users to adopt a centralized mandated algorithm controlling their behavior (which is not advisable), it is not possible to guarantee that they will not act in a selfish manner. Consequently, a fundamental issue is to evaluate the impact of having users that act in such a manner. In such a scenario, having a Nash equilibrium guarantees that no selfish user has incentive to unilaterally deviate from its current state (i.e., it guarantees that we are in a stable state in the presence of selfish users). However, here we formally prove that an efficient Nash equilibrium can not be reached in practice for any oblivious control policy.

[2] 
J. Buldu, J. GarciaOjalvo, M. Torrent, J. Sancho, C. Mirasso, and D. Chialvo,
“External noise in semiconductor lasers,” Fluctuations And Noise In
Photonics And Quantum Optics Ii, vol. 5468, pp. 118132, 2004.
[ bib 
pdf ]
In the present work we review recent results concerning stochastic phenomena in semiconductor lasers with optical feedback which operate in the lowfrequency fluctuation (LFF) regime. Under these conditions the output intensity of the laser shows an irregular pulsated behavior in the form of sudden intensity dropouts. In the first two sections we show numerically the existence of stochastic and coherence resonance in the dropout appearance. These resonances are caused by the help of external colored noise introduced through the pumping current of the laser. In the third section we describe a recently reported new type of stochastic resonance, where a nonlinear system shows a resonance at a frequency not present neither at its internal time scales nor at any external perturbation. This phenomenon, known as ghost resonance, is reported both numerically and experimentally.

[3] 
J. Buldu, C. Gonzalez, J. GarciaOjalvo, M. Torrent, J. Trull, C. Mirasso, and
D. Chialvo, “Ghost resonance in coupled lasers,” Experimental Chaos,
vol. 742, pp. 247252, 2004.
[ bib 
pdf ]
We study the phenomenon of ghost resonance in a system of two bidirectionally coupled nonlinear oscillators. Ghost resonance was reported recently in an excitable system when perturbed by two periodic signals of different frequencies. Under these circumstances and with the help of noise, the system is able to resonate at a frequency not present in the external perturbations but related with them. In the current work, we give the first experimental evidence of ghost resonance in a coupled system which consists on two bidirectionally coupled semiconductor lasers.

[4] 
J. Buldu, J. GarciaOjalvo, and M. Torrent, “Multimode synchronization and
communication using unidirectionally coupled semiconductor lasers,”
Ieee Journal Of Quantum Electronics, vol. 40, pp. 640650, 2004.
[ bib 
pdf ]
We study numerically the synchronization of two multimode semiconductor lasers unidirectionally coupled in an openloop configuration, focusing on the comparison with the results obtained in the singlemode case. Anticipative and isochronous synchronization, and their range of validity, are analyzed from the point of view of the total lasing output, and the synchronization between individual modes is studied. Selective injection is also examined and compared with global injection. In light of these results, message encoding and decoding via multimode synchronization is analyzed.

[5] 
J. m. Buldu, J. GarciaOjalvo, and M. c. Torrent, “Delayinduced resonances in
an optical system with feedback.,” Phys Rev E Stat Nonlin Soft Matter
Phys, vol. 69, p. 046207, 2004.
[ bib 
pdf ]
We study the influence of the delay time in the response of a delayed feedback system to external periodic driving. The nonlinear system we consider is a semiconductor laser with optical feedback operating in the lowfrequency fluctuation regime. We numerically examine the consequences of varying the external cavity length of the system when a weak modulation is introduced through the laser's pump current. The harmonic modulation is seen to lead to a partial periodic entrainment of power dropouts, and the distribution of time intervals between the dropouts exhibits resonances with certain delay times. In other words, the response of the system to the external modulation is enhanced for particular values of the external cavity length. The same effect can be observed in the presence of noise, indicating that stochastic resonance can be enhanced or degraded depending on the feedback time.

[6] 
M. s. Baptista, S. Boccaletti, K. Josic, and I. Leyva, “Irrational phase
synchronization.,” Phys Rev E Stat Nonlin Soft Matter Phys, vol. 69,
p. 056228, 2004.
[ bib 
pdf ]
We study the occurrence of physically observable phase locked states between chaotic oscillators and rotors in which the frequencies of the coupled systems are irrationally related. For two chaotic oscillators, the phenomenon occurs as a result of a coupling term which breaks the 2 pi invariance in the phase equations. In the case of rotors, a coupling term in the angular velocities results in very long times during which the coupled systems exhibit alternatively irrational phase synchronization and random phase diffusion. The range of parameters for which the phenomenon occurs contains an open set, and is thus physically observable.

[7]  I. Leyva, E. Allaria, and R. Meucci, “Polarization dynamics in a co2 laser,” Focus On Lasers And ElectroOptics Research, pp. 149167, 2004. [ bib  pdf ] 
[8] 
R. Meucci, I. Leyva, and E. Allaria, “Polarization instabilities in a
quasiisotropic co2 laser,” Free And Guided Optical Beams,
pp. 185191, 2004.
[ bib 
pdf ]
In this work we present experimental and theoretical results for the polarization competition dynamics in the transient state of a quasiisotropic lowpressure CO2 laser. We show that the polarization dynamics during the switchon is well described by means of a model including optical coherences (intrinsic anisotropy) and extrinsic linear anisotropies. Furthermore, the experiment provides a numerical assignment for the decay rate of the coherence term for a CO2 laser. These results extend a previous work in which competition is interpreted in a phenomenological way as a parametric cross coupling between the matter polarization and electric fields.

[9] 
I. Leyva, E. Allaria, S. Boccaletti, and F. Arecchi, “In phase and antiphase
synchronization of coupled homoclinic chaotic oscillators,” Chaos,
vol. 14, pp. 118122, 2004.
[ bib 
pdf ]
We numerically investigate the dynamics of a closed chain of unidirectionally coupled oscillators in a regime of homoclinic chaos. The emerging synchronization regimes show analogies with the experimental behavior of a single chaotic laser subjected to a delayed feedback. (C) 2004 American Institute of Physics.

[1] 
J. Almendral, L. Lopez, and M. Sanjuan, “Information flow in generalized
hierarchical networks,” Physica AStatistical Mechanics And Its
Applications, vol. 324, pp. 424429, 2003.
[ bib 
pdf ]
The theory of complex networks is used to study different aspects of a topology that we propose to describe the relationships between members of a social group. This model is a generalized hierarchical model since relations between members of the same group are also considered.. We derive the existence of a natural limit in the size of a group, and besides, an insight into hierarchical networks is given, which explains why they are so spread despite its global inefficiency. (C) 2003 Elsevier Science B.V. All rights reserved.

[2] 
J. Almendral and M. Sanjuan, “Integrability and symmetries for the helmholtz
oscillator with friction,” Journal Of Physics AMathematical And
General, vol. 36, pp. 695710, 2003.
[ bib 
pdf ]
This paper deals with the Helmholtz oscillator, which is a simple nonlinear oscillator whose equation presents a quadratic nonlinearity and the possibility of escape. When a periodic external force is introduced, the width of the stochastic layer, which is a region around the separatrix where orbits may exhibit transient chaos, is calculated. In the absence of friction and external force, it is well known that analytical solutions exist since it is completely integrable. When only friction is included, there is no analytical solution for all parameter values. However, by means of the Lie theory for differential equations we find a relation between parameters for which the oscillator is integrable. This is related to the fact that the system possesses a symmetry group and the corresponding symmetries are computed. Finally, the analytical explicit solutions are shown and related to the basins of attraction.

[3] 
L. Lopez, J. Almendral, and M. Sanjuan, “Complex networks and the www
market,” Physica AStatistical Mechanics And Its Applications,
vol. 324, pp. 754758, 2003.
[ bib 
pdf ]
This paper presents a model for the competition dynamics in the World Wide Web market. We show that this problem is suitable to be analyzed in the framework of the theory of complex networks, representing each site by a vertex in a graph and each competitive interaction as an edge. Once the topology of the interaction network has been defined, we evaluate the dynamical evolution of the fraction of the market controlled by the sites through a set of differential equations based on the LotkaVolterra equations. We show that, under these assumptions, some interesting and novel nonlinear effects emerge in this kind of markets. (C) 2002 Elsevier Science B.V. All rights reserved.

[4]  J. Buldu, D. Chialvo, C. Mirasso, M. Torrent, and J. GarciaOjalvo, “Ghost resonance in a semiconductor laser with optical feedback,” Europhysics Letters, vol. 64, pp. 178184, 2003. [ bib  pdf ] 
[5] 
J. Buldu, J. GarciaOjalvo, M. Torrent, R. Vicente, T. Perez, and C. Mirasso,
“Entrainment of optical lowfrequency fluctuations is enhanced by
coupling,” Fluctuation And Noise Letters, vol. 3, pp. L127L136,
2003.
[ bib 
pdf ]
The control of the lowfrequency fluctuations exhibited by two mutually coupled semiconductor lasers is studied experimentally and numerically. We observe that coupling enhances the response of the system to a weak periodic modulation of the injection current of one of the lasers, leading to a highly efficient entrainment of the synchronized lowfrequency power dropouts to the external periodic driving. We compare the quality of the entrainment with the one obtained in a single semiconductor laser with optical feedback, showing the beneficial role of coupling in this pursuit. The experimental observations are satisfactorily reproduced by numerical simulations of a set of coupled delaydifferential rate equations.

[6] 
C. Mirasso, J. Buldu, D. Chialvo, M. Torrent, and J. GarciaOjalvo, “Ghost
resonance in a semiconductor laser operating in an excitable regime,”
Fluctuations And Noise In Photonics And Quantum Optics, vol. 5111,
pp. 118125, 2003.
[ bib 
pdf ]
We show both numerically and experimentally that a semiconductor laser prepared in an excitable state and driven by two weak periodic signals with different frequencies is able to resonate at a ghost frequency, i.e., a frequency that it is not present in the forcing signal. The small signal modulation together with the complex internal dynamics of the system produces this resonance. This is an eminently nonlinear effect that agrees with the recent theoretical predictions by Chialvo et al. [Phys. Rev. E 65, 650902(R), 2002].

[7] 
F. t. Arecchi, E. Allaria, and I. Leyva, “Propensity criterion for networking
in an array of coupled chaotic systems.,” Phys Rev Lett, vol. 91,
p. 234101, 2003.
[ bib 
pdf ]
We examine the mutual synchronization of a onedimensional chain of chaotic identical objects in the presence of a stimulus applied to the first site. We first describe the characteristics of the local elements, and then the process whereby a global nontrivial behavior emerges. A propensity criterion for networking is introduced, consisting in the coexistence within the attractor of a localized chaotic region, which displays high sensitivity to external stimuli, and an island of stability, which provides a reliable coupling signal to the neighbors in the chain. Based on this criterion, we compare homoclinic chaos, recently explored in lasers and conjectured to be typical of a single neuron, with Lorenz chaos.

[8] 
I. Leyva, E. Allaria, and R. Meucci, “Transient polarization dynamics in a co2
laser,” Optics Communications, vol. 217, pp. 335342, 2003.
[ bib 
pdf ]
We study experimentally and theoretically the polarization alternation during the switchon transient of a quasiisotropic CO2 laser emitting on the fundamental mode. The observed transient dynamics is well reproduced by means of a model which provides a quantitative discrimination between the intrinsic asymmetry due to the kinetic coupling of molecules with different angular momenta, and the extrinsic anisotropies, due to a tilted intracavity window. Furthermore, the experiment provides a numerical assignment for the decay rate of the coherence term for a CO2 laser. (C) 2003 Published by Elsevier Science B.V.

[9] 
I. Leyva, E. Allaria, and R. Meucci, “Polarization and spatial competition in
a transverse multimode co2 laser,” Physical Review A, vol. 68, 2003.
[ bib 
pdf ]
We experimentally study the polarization dynamics during the switchon transient of a quasiisotropic CO2 laser emitting on the TEM01* mode. We observe a complex dynamics in which a spatial mode and polarization competition are involved. The observed dynamics is well reproduced by means of a model that provides a quantitative discrimination between the intrinsic asymmetry due to the kinetic coupling of molecules with different angular momenta and the residual extrinsic anisotropies due to cavity misalignments.

[10] 
I. Leyva, E. Allaria, S. Boccaletti, and F. t. Arecchi, “Competition of
synchronization domains in arrays of chaotic homoclinic systems.,” Phys
Rev E Stat Nonlin Soft Matter Phys, vol. 68, p. 066209, 2003.
[ bib 
pdf ]
We investigate the response of an open chain of bidirectionally coupled chaotic homoclinic systems to external periodic stimuli. When one end of the chain is driven by a periodic signal, the system propagates a phase synchronization state in a certain range of coupling strengths and external frequencies. When two simultaneous forcings are applied at different points of the array, a rich phenomenology of stable competitive states is observed, including temporal alternation and spatial coexistence of synchronization domains.

[11] 
F. Arecchi, E. Allaria, I. Leyva, and S. Boccaletti, “Synchronization domains
in arrays of chaotic homoclinic systems,” 2003 International Conference
Physics And Control, Vols 14, Proceedings, pp. 539547, 2003.
[ bib 
pdf ]
With reference to experiments on a CO2 laser with feedback, we summarize the main features of chaotic orbits homoclinic to a saddle focus, and then face the problem of an array of coupled identical systems of this kind, We rst investigate the dynamics of a closed chain of unidirectionally coupled oscillators in a, regime of homoclinic chaos. The emerging synchronization regimes show analogies with the experimental behavior of a single chaotic laser self synchronized by a delayed feedback. Then we explore the response of an open chain of bidirectionally coupled chaotic homoclinic systems to external periodic stimuli. When one end of the chain is driven by a periodic signal, the system propagates a phase synchronization state in a certain range of coupling strengths and external frequencies. When two simultaneous forcings are applied at di erent points of the array, a rich phenomenology of stable competitive states is observed, including temporal alternation and spatial coexistence synchronization domains.

[1] 
J. Buldu, F. Rogister, J. Trull, C. Serrat, M. Torrent, C. Mirasso, and
J. GarciaOjalvo, “Dynamics of power distribution in multimode semiconductor
lasers with optical feedback,” Physics And Simulation Of Optoelectronic
Devices X, vol. 4646, pp. 411419, 2002.
[ bib 
pdf ]
Semiconductor lasers with optical feedback are prone to exhibit unstable behavior. When working near threshold with moderate to low optical feedback, intensity dropouts are observed. These intensity drops, also called lowfrequency fluctuations, occur both in singlemode and multimode semiconductor lasers. In this paper, the dynamics of the power distribution between the longitudinal modes of a multimode semiconductor laser is experimentally and numerically analyzed in the lowfrequency fluctuation regime. It is observed that power dropouts of the total intensity, corresponding to drops in the dominant modes of the laser, are invariably accompanied by sudden activations of several longitudinal side modes. These activations are seen not. to be simultaneous to the dropouts of the main modes, but to occur after them. The phenomenon is statistically analyzed in a systematic way, and the corresponding delay is estimated, leading to the conclusion that the side mode activation is a consequence of the dropouts of the dominant modes. A multimode extension of the LangKobayashi equations is used to model the experimental setup. Numerical simulations also exhibit a time delay between the sidemode activation and the power dropout of the total intensity.

[2] 
J. Buldu, F. Rogister, J. Trull, C. Serrat, M. Torrent, J. GarciaOjalvo, and
C. Mirasso, “Asymmetric and delayed activation of side modes in multimode
semiconductor lasers with optical feedback,” Journal Of Optics
BQuantum And Semiclassical Optics, vol. 4, pp. 415420, 2002.
[ bib 
pdf ]
We study the multimode dynamics of a semiconductor laser with optical feedback operating in the lowfrequency fluctuation regime. A multimode extension of the LangKobayashi (LK) model shows, in agreement with experimental observations, that the lowfrequency power dropouts exhibited by the main modes are accompanied by sudden, asymmetric, activations of dormant longitudinal side modes. Furthermore, these activations are delayed with respect to the dropouts of the active modes. In order to satisfactorily reproduce both the asymmetric activation of side modes and their delay with respect to the dropouts, the generalized LK model has to include a parabolic gain profile, together with a frequency shift of the gain curve with carrier population.

[3] 
J. m. Buldu, J. GarciaOjalvo, C. R. Mirasso, and M. c. Torrent, “Stochastic
entrainment of optical power dropouts.,” Phys Rev E Stat Nonlin Soft
Matter Phys, vol. 66, p. 021106, 2002.
[ bib 
pdf ]
We show that the natural pulsed behavior, in the form of sudden power dropouts, exhibited by semiconductor lasers subject to optical feedback can be entrained by the joint action of external noise and weak periodic driving. These power dropouts, which in the absence of forcing do not occur periodically, acquire the periodicity of the harmonic driving for an optimal amount of external noise, in what constitutes a form of stochastic resonance. This phenomenon is analyzed by means of a generalized LangKobayashi model with external nonwhite noise in the modulated pump current, in terms of both the temporal correlation and the amplitude of the noise.

[4] 
J. Buldu, R. Vicente, T. Perez, C. Mirasso, M. Torrent, and J. GarciaOjalvo,
“Periodic entrainment of power dropouts in mutually coupled semiconductor
lasers,” Applied Physics Letters, vol. 81, pp. 51055107, 2002.
[ bib 
pdf ]
We examine the effect of current modulation in the irregular dropout dynamics exhibited by two mutually coupled semiconductor lasers. Our experimental results show that a weak periodic modulation in the injection current of one of the lasers entrains the power dropouts in a very efficient way. It is also observed that the laser. with the highest frequency leads the dynamics independent, of which laser is modulated. As a result, the entrainment is anticipative when modulation is applied to the laser with lowest frequency. Numerical simulations of a model based on delaycoupled rate equations successfully reproduce the behavior observed. (C) 2002 American Institute of Physics. [DOI: 10.1063/1.1533837].

[5] 
J. Buldu, J. Trull, M. Torrent, J. GarciaOjalvo, and C. Mirasso, “Dynamics of
modal power distribution in a multimode semiconductor laser with optical
feedback,” Journal Of Optics BQuantum And Semiclassical Optics,
vol. 4, pp. L1L3, 2002.
[ bib 
pdf ]
The dynamics of power distribution between longitudinal modes of a multimode semiconductor laser subjected to external optical feedback is experimentally analysed in the lowfrequency fluctuation regime. Power dropouts in the totat light intensity are invariably accompanied by sudden activations of several longitudinal modes. These activations are seen not to be simultaneous to the dropouts, but to occur after them. The phenomenon is statistically analysed in a systematic way, and the corresponding delay is estimated.

[6] 
I. Leyva and J. Guerra, “Timeresolved pattern evolution in a largeaperture
class a laser,” Physical Review A, vol. 66, 2002.
[ bib 
pdf ]
Quasiinstantaneous transverse patterns have been measured in a broadaperture class A laser, using an ultrafast camera. The evolution from order to fully developed turbulence is observed as the Fresnel number increases up to 110. In the turbulent regime, two very different spatial scales coexist, one order of magnitude apart. The linear analysis allows us to interpret most of the features of the experiment.

[7] 
I. SendiñaNadal, M. de Castro, F. Sagues, and M. GomezGesteira,
“Unidirectional mechanism for reentrant activity generation in excitable
media,” Phys Rev E, vol. 66, p. 016215, 2002.
[ bib 
DOI 
pdf ]
A closed excitable pathway with one pointtopoint connection is used to generate a rotating wave both in experiments using the photosensitive BelousovZhabotinsky system and numerically with an Oregonator reactiondiffusion model. By varying the excitability and geometrical properties of the medium, propagation can be made unidirectional or bidirectional, giving rise, respectively, to the existence or not of sustained reentrant activity in a closed excitable track.

[1] 
J. m. Buldu, J. GarciaOjalvo, C. r. Mirasso, M. c. Torrent, and J. m. Sancho,
“Effect of external noise correlation in optical coherence resonance.,”
Phys Rev E Stat Nonlin Soft Matter Phys, vol. 64, p. 051109, 2001.
[ bib 
pdf ]
Coherence resonance occurring in semiconductor lasers with optical feedback is studied via the LangKobayashi model with external nonwhite noise in the pumping current. The temporal correlation and the amplitude of the noise have a highly relevant influence in the system, leading to an optimal coherent response for suitable values of both the noise amplitude and correlation time. This phenomenon is quantitatively characterized by means of several statistical measures.

[2] 
F. EncinasSanz, I. Leyva, and J. Guerra, “Time averaging of irregular
spatiotemporal patterns of a large aperture laser in transitory regime,”
International Journal Of Bifurcation And Chaos, vol. 11,
pp. 17711779, 2001.
[ bib 
pdf ]
By means of a new experimental technique, we measure quasiintantaneous transverse intensity patterns in the gainswitch peak of a transversely excited atmospheric CO2 laser with large aperture. The patterns recorded with a 2 ns resolution show a completely irregular spatiotemporal behavior, but when the exposure time of the measurements increases, boundarydetermined ordered structures can be observed. As a quantification of this averaging process, the contrast of the intensity distributions decreases as the time integration grows. The results are numerically reproduced by integration of the full MaxwellBloch equations.

[3] 
I. Leyva, E. Allaria, and R. Meucci, “Polarization competition in a
quasiisotropic co2 laser,” Optics Letters, vol. 26, pp. 605607,
2001.
[ bib 
pdf ]
We experimentally study the polarization dynamics of a singlemode CO2 laser during the switchon transient of the laser intensity. We find a strong competition between two linearly polarized fields, which finally collapse into a single field. As a result of this competition, the two coexisting fields oscillate out of phase by rr rad for time intervals much longer than that of the relaxation oscillation. One can control the oscillation frequency of the two polarized fields by varying the intracavity anisotropies. This phenomenon is interpreted in the framework of MaxwellBloch equations by addition of nonlinear terms to the polarization equations that allow the fields to compete while they interact with the same population inversion. (C) 2001 Optical Society of America.

[4] 
S. Alonso, I. SendiñaNadal, V. PerezMuñuzuri, J. m. Sancho, and
F. Sagues, “Regular wave propagation out of noise in chemical active
media,” Phys Rev Lett, vol. 87, p. 078302, 2001.
[ bib 
DOI 
pdf ]
A pacemaker, regularly emitting chemical waves, is created out of noise when an excitable photosensitive BelousovZhabotinsky medium, strictly unable to autonomously initiate autowaves, is forced with a spatiotemporal patterned random illumination. These experimental observations are also reproduced numerically by using a set of reactiondiffusion equations for an activatorinhibitor model, and further analytically interpreted in terms of genuine coupling effects arising from parametric fluctuations. Within the same framework we also address situations of noisesustained propagation in subexcitable media.

[5] 
I. SendiñaNadal, E. Mihaliuk, J. Wang, V. PerezMuñuzuri, and
K. Showalter, “Wave propagation in subexcitable media with periodically
modulated excitability,” Phys Rev Lett, vol. 86, pp. 16461649, 2001.
[ bib 
DOI 
pdf ]
Wave propagation in a photosensitive, subexcitable BelousovZhabotinsky medium is made possible by periodic modulation of a homogeneous illumination held. The propagation can be understood in terms of an interplay between the radial expansion of the wave and the motion of its free ends as the excitability varies periodically. This description leads to a simple kinematic analysis that provides insights into the initial conditions and forcing parameters giving rise to sustained wave propagation.

[6] 
I. SendiñaNadal and V. PerezMuñuzuri, “Noiseenhanced wave train
propagation in unexcitable media,” International Journal Of Bifurcation
And Chaos, vol. 11, pp. 28372843, 2001.
[ bib 
DOI 
pdf ]
The influence of spatiotemporal colored noise on wave train propagation in nonexcitable media is investigated. This study has been performed within the framework of the Oregonator model in terms of the characteristic noise parameters. Some features seen in single front propagation, like noise induced propagation facilitation for an optimal level of the noise intensity, are also found for periodic wave trains. The main new effect is, however, an enhancement of propagation for correlation times of the noise of the order of the period of the wave train.

[7] 
I. SendiñaNadal, V. PerezMuñuzuri, V. m. Eguiluz,
E. HernandezGarcia, and O. Piro, “Quasiperiodic patterns in
boundarymodulated excitable waves,” Phys Rev E, vol. 64, p. 046208,
2001.
[ bib 
DOI 
pdf ]
We investigate the impact of domain shape on wave propagation in excitable media. Channeled domains with sinusoidal boundaries are considered. Trains of fronts generated periodically at an extreme of the channel are found to adopt a quasiperiodic spatial configuration that repeats periodically in time. The phenomenon is numerically studied in a model for a photosensitive BelousovZabotinsky reaction. Spatial return maps for the height and position of the successive fronts are analytically obtained, and reveal the similarity between this spatial quasiperiodicity and the temporal quasiperiodicity appearing in forced oscillators.

[1] 
G. Burr and I. Leyva, “Multiplexed phaseconjugate holographic data storage
with a buffer hologram,” Optics Letters, vol. 25, pp. 499501, 2000.
[ bib 
pdf ]
We describe and demonstrate a volume holographic storage system in which a phaseconjugate object beam is reconstructed by the same reference beam that was used for recording. An intermediate hologram is used as a temporary buffer, recorded with its own reference beam and the databearing object beam. Reading this buffer hologram with the phase conjugate of its reference beam reconstructs the phase conjugate of the object beam, which can then be recorded into the desired volume hologram for longterm storage. This method combines the immunity to lens aberrations provided by phaseconjugate readout with the simplicity of using the same multiplexed reference beam for both recording and readout. Only a single pair of phaseconjugate reference beams is required. Experimental results are shown with a single LiNbO3:Fe crystal used as both buffer and storage holograms and a selfpumped phaseconjugate mirror in BaTiO3 that provides the pair of phaseconjugate reference beams. (C) 2000 Optical Society of America. OCIS codes: 210.2860, 070.5040.

[2] 
F. EncinasSanz, I. Leyva, and J. Guerra, “Timeresolved spatiotemporal
dynamics in a broadarea co2 laser,” Physical Review A, vol. 62, 2000.
[ bib 
pdf ]
We have measured quasiinstantaneous transverse patterns in a broad aperture laser. Nonordered patterns yielding boundarydetermined regular structures in progressive timeintegrated recording are observed. The linear analysis and numerical integration of the full MaxwellBloch equations allow us to interpret the features of the experiment. We show the limitations imposed by the boundary conditions to the theoretical predictions of the linear stability analysis.

[3] 
I. Leyva and J. Guerra, “The role of the molecular dynamics in the local
intensity instabilities of large aperture dye lasers,” Applied Physics
Letters, vol. 77, pp. 15991601, 2000.
[ bib 
pdf ]
We study experimentally the influence of the molecular dynamics in the local intensity fluctuations of large aperture dye lasers, and find dependencies on solvent viscosity and active molecular size. This is an example of the complexity of the still quite unknown nonlinear processes that underlie the pattern formation dynamics in large aperture optical systems, in which the diffraction has lost influence and the bulk dynamics dominate. (C) 2000 American Institute of Physics. [S00036951(00)048373].

[4] 
F. EncinasSanz, I. Leyva, and J. Guerra, “Time resolved pattern evolution in
a large aperture laser,” Physical Review Letters, vol. 84,
pp. 883886, 2000.
[ bib 
pdf ]
We have measured quasiinstantaneous transverse patterns in a broad aperture laser. Nonordered patterns yielding to boundary determined regular structures in progressive timeintegrated recording are observed. The linear analysis and numerical integration of the full MaxwellBloch equations allow us to interpret the features of the experiment. We show that this system being far from threshold cannot be fully understood with a perturbative model.

[5] 
I. SendiñaNadal, S. Alonso, V. PerezMuñuzuri, M. GomezGesteira,
V. PerezVillar, L. RamirezPiscina, J. Casademunt, J. Sancho, and F. Sagues,
“Brownian motion of spiral waves driven by spatiotemporal structured
noise,” Phys Rev Lett, vol. 84, pp. 27342737, 2000.
[ bib 
DOI 
pdf ]
Spiral chemical waves subjected to a spatiotemporal random excitability are experimentally and numerically investigated in relation to the lightsensitive BelousovZhabotinsky reaction. Brownian motion is identified and characterized by an effective diffusion coefficient which shows a rather complex dependence on the time and length scales of the noise relative to those of the spiral. A kinematically based model is proposed whose results are in good qualitative agreement with experiments and numerics.

[1] 
O. Calderon, I. Leyva, and J. Guerra, “Effect of the solvent viscosity on the
local irregular intensity fluctuations in high fresnel number dye lasers,”
Ieee Journal Of Quantum Electronics, vol. 35, pp. 16, 1999.
[ bib 
pdf ]
We study the influence of the solvent viscosity in the local irregular intensity fluctuations characteristic of high Fresnel number dye lasers, The relative amplitude of the fluctuations in a flashlamppumped dye laser is analyzed,We complete our previous work by using several solvents and different excitation energies above threshold. A decrease of the relative fluctuation amplitude is found as the solvent viscosity or the pumping energy increases, This effect is theoretically analyzed in the framework of the semiclassical MaxwellBloch equations, with a model based on the orientation of the dye molecules driven by the laser field in the solvent. These results point out the importance of the orientation of the dye molecules in the intensity fluctuation phenomenon.

[2] 
O. Calderon, I. Leyva, and J. Guerra, “The role of the solvent viscosity on
the spatiotemporal instabilities of large aperture dye lasers,” Applied
Physics Letters, vol. 73, pp. 557559, 1999.
[ bib 
pdf ]
Local intensity fluctuations in a large aperture dye laser have been measured for several solvent viscosities. A decrease on the relative fluctuations amplitude as the solvent viscosity increases is found. From a theoretical approach, we show that the intensity fluctuations follow the same behavior as the molecular polarization orientation driven by the laser field. (C) 1998 American Institute of Physics. [S00036951(98)001314].

[3] 
I. Leyva and J. Guerra, “A compacted ernstelectrodes profile for pulsed
highpressure lasers,” Measurement Science & Technology, vol. 10,
pp. N1N2, 1999.
[ bib 
pdf ]
A compacted form of the usual Ernst profile for highpressure gas lasers is derived, without reduction in the held uniformity for a given aspect ratio.

[4] 
I. SendiñaNadal, V. PerezMuñuzuri, M. GomezGesteira, A. Munuzuri,
V. PerezVillar, D. Vives, F. Sagues, J. Casademunt, J. Sancho, and
L. RamirezPiscina, “Effects of a quenched disorder on wave propagation in
excitable media,” International Journal Of Bifurcation And Chaos,
vol. 9, pp. 23532361, 1999.
[ bib 
DOI 
pdf ]
The behavior of autowaves under the effect of a quenched disorder is studied in the framework of the lightsensitive BelousovZhabotinsky reaction. This allows us to introduce spatial disorder on the excitability by projecting patterns of light transmittance. In particular, we have selected a dichotomic random distribution of levels of transmittance. If the two values of transmittance are equally probable and allows wave propagation without breaking the waves, we find an opposite effect on the wave front velocity and shape depending on the considered dimension. On the other hand, if one of the two values of the transmittance distribution is set on the nonexcitable region, percolation phenomena can arise by changing the number of excitable sites. The different addressed situations are analytically interpreted giving theoretical predictions for the experimental and numerical results.

[1] 
O. Calderon, I. Leyva, and J. Guerra, “The role of the solvent viscosity on
the spatiotemporal instabilities of large aperture dye lasers,” Applied
Physics Letters, vol. 73, pp. 557559, 1998.
[ bib 
pdf ]
Local intensity fluctuations in a large aperture dye laser have been measured for several solvent viscosities. A decrease on the relative fluctuations amplitude as the solvent viscosity increases is found. From a theoretical approach, we show that the intensity fluctuations follow the same behavior as the molecular polarization orientation driven by the laser field. (C) 1998 American Institute of Physics.

[2] 
J. Guerra, I. Leyva, and O. Calderon, “Local irregular intensity fluctuations
in high fresnel number dye lasers,” Solid State Lasers Vii, vol. 3265,
pp. 2936, 1998.
[ bib 
pdf ]
Local intensity fluctuations in a large aperture dye laser have been analyzed. We have studied the influence of solvent viscosity in the amplitude of these fluctuations. This experimental result provide a clear evidence of the role played by the molecular orientation in the spatiotemporal laser dynamics. The dependence of the average spectra of these fluctuations on the active laser mediun length has been studied. The mean frequency of the spectra change with the active laser medium length.

[3] 
I. SendiñaNadal, D. Roncaglia, D. Vives, V. PerezMuñuzuri,
M. GomezGesteira, V. PerezVillar, J. Echave, J. Casademunt,
L. RamirezPiscina, and F. Sagues, “Percolation thresholds in chemical
disordered excitable media,” Phys Rev E, vol. 58, pp. R1183R1186,
1998.
[ bib 
DOI 
pdf ]
The behavior of chemical waves advancing through a disordered excitable medium is investigated in terms of percolation theory and autowave properties in the framework of the lightsensitive BelousovZhabotinsky reaction. By controlling the number of sites with a given illumination, different percolation thresholds for propagation are observed; which depend on the relative wave transmittances of the twostate medium considered.

[4] 
I. SendiñaNadal, A. Muñuzuri, D. Vives, V. PerezMunuzuri,
J. Casademunt, L. RamirezPiscina, J. Sancho, and F. Sagues, “Wave
propagation in a medium with disordered excitability,” Phys Rev Lett,
vol. 80, pp. 54375440, 1998.
[ bib 
DOI 
pdf ]
The effect of quenched disorder on the propagation of autowaves in excitable media is studied both experimentally and numerically in relation to the lightsensitive BelousovZhabotinsky reaction. The spatial disorder is introduced through a random distribution with two different levels of transmittance. In one dimension the (timeaveraged) wave speed is smaller than the corresponding to a homogeneous medium with the mean excitability. Contrarily, in two dimensions the velocity increases due to the roughening of the front. Results are interpreted using kinematic and scaling arguments. In particular, for d = 2 we verify a theoretical prediction of a powerlaw dependence for the relative change of the propagation speed on the disorder amplitude.

[1] 
I. SendiñaNadal, M. GomezGesteira, V. PerezMuñuzuri,
V. PerezVillar, J. Armero, L. RamirezPiscina, J. Casademunt, F. Sagues, and
J. Sancho, “Wave competition in excitable modulated media,” Phys Rev
E, vol. 56, pp. 62986301), 1997.
[ bib 
DOI 
pdf ]
The propagation of an initially planar front is studied within the framework of the photosensitive BelousovZhabotinsky reaction modulated by a smooth spatial variation of the local front velocity in the direction perpendicular to front propagation. Under this modulation, the wave front develops several fingers corresponding to the local maxima of the modulation function. After a transient, the wave front achieves a stationary shape that does not necessarily coincide with the one externally imposed by the modulation. Theoretical predictions for the selection criteria of fingers and steadystate velocity are experimentally validated.

[1]  M. Zanin, J. M. Buldu, and P. Cano, “Preferential attachment, aging and weights in recommendation system,” in Proceedings of the Conference NetWorks 2007 (M. Zanin, J. M. Buldu, and P. Cano, eds.), (Aranjuez, Spain), pp. 135148, Sept. 1011 2007. [ bib  conference site ] 
[2]  A. Wagemakers, J. M. Buldu, and J. G.O. et Miguel A.F. Sanjuan, “Des circuits et des genes,” in CompteRendus de la 9eme Rencontre du NonLineaire 2006 (M. Lefranc, C. Lettelier, and L. Pastur, eds.), (Orsay, France), pp. 249254, NonLineaire Publications, 2006. [ bib ] 
[3]  F. Sagues, D. Vives, J. Sancho, J. Casademunt, L. RamirezPiscina, I. SendinaNadal, V. PerezMunuzuri, and M. GomezGesteira, “Wave propagation in media with nonuniform and disordered excitability,” vol. 218 of Abstracts Of Papers Of The American Chemical Society, pp. U277U277, 1999. [ bib ] 
[1]  J. M. Buldú, A. Wagemakers, M. Sanjuán, and A. C. y O. de Luís, “Redes genéticas sintéticas: de lo simple a lo complejo,” Revista Española de Física, pp. 1016, Nov. 2007. [ bib ] 
[1]  J. A. Almendral, Dynamics and Topology in Complex Networks. tesis, Universidad Rey Juan Carlos, 2006. [ bib  pdf ] 
[2]  J. Buldu, Entrainment of semiconductor lasers: Noise, modulation, and synchronization. tesis, Universidad Politecnica de Catalunya, 2003. ISBN 846888149X. [ bib  pdf ] 
[3]  I. Leyva, Formación y dinámica de patrones transversos en láseres de colorante y CO2. tesis, Universidad Complutense de Madrid, 2001. [ bib  pdf ] 
[4]  I. SendiñaNadal, Patterns on active media under the effect of periodical and fluctuating fields. tesis, Universidade de Santiago de Compostela, 2001. ISBN 8481219452. [ bib  pdf ] 