Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com

Mapping Chemical Selection Pathways for Designing Multicomponent Alloys: an informatics framework for materials design

A data driven methodology is developed for tracking the collective influence of the multiple attributes of alloying elements on both thermodynamic and mechanical properties of metal alloys. Cobalt-based superalloys are used as a template to demonstrate the approach. By mapping the high dimensional nature of the systematics of elemental data embedded in the periodic table into the form of a network graph, one can guide targeted first principles calculations that identify the influence of specific elements on phase stability, crystal structure and elastic properties. This provides a fundamentally new means to rapidly identify new stable alloy chemistries with enhanced high temperature properties. The resulting visualization scheme exhibits the grouping and proximity of elements based on their impact on the properties of intermetallic alloys. Unlike the periodic table however, the distance between neighboring elements uncovers relationships in a complex high dimensional information space that would not have been easily seen otherwise. The predictions of the methodology are found to be consistent with reported experimental and theoretical studies. The informatics based methodology presented in this study can be generalized to a framework for data analysis and knowledge discovery that can be applied to many material systems and recreated for different design objectives

Mining topological structure in graphs through forest representations

We consider the problem of inferring simplified topological substructures—which we term backbones—in metric and non-metric graphs. Intuitively, these are subgraphs with ‘few’ nodes, multifurcations, and cycles, that model the topology of the original graph well. We present a multistep procedure for inferring these backbones. First, we encode local (geometric) information of each vertex in the original graph by means of the boundary coefficient (BC) to identify ‘core’ nodes in the graph. Next, we construct a forest representation of the graph, termed an f-pine, that connects every node of the graph to a local ‘core’ node. The final backbone is then inferred from the f-pine through CLOF (Constrained Leaves Optimal subForest), a novel graph optimization problem we introduce in this paper. On a theoretical level, we show that CLOF is NP-hard for general graphs. However, we prove that CLOF can be efficiently solved for forest graphs, a surprising fact given that CLOF induces a nontrivial monotone submodular set function maximization problem on tree graphs. This result is the basis of our method for mining backbones in graphs through forest representation. We qualitatively and quantitatively confirm the applicability, effectiveness, and scalability of our method for discovering backbones in a variety of graph-structured data, such as social networks, earthquake locations scattered across the Earth, and high-dimensional cell trajectory dat

The Kuramoto model in complex networks

181 pages, 48 figures. In Press, Accepted Manuscript, Physics Reports 2015 Acknowledgments We are indebted with B. Sonnenschein, E. R. dos Santos, P. Schultz, C. Grabow, M. Ha and C. Choi for insightful and helpful discussions. T.P. acknowledges FAPESP (No. 2012/22160-7 and No. 2015/02486-3) and IRTG 1740. P.J. thanks founding from the China Scholarship Council (CSC). F.A.R. acknowledges CNPq (Grant No. 305940/2010-4) and FAPESP (Grants No. 2011/50761-2 and No. 2013/26416-9) for financial support. J.K. would like to acknowledge IRTG 1740 (DFG and FAPESP).Peer reviewedPreprin

Synchronization in dynamical networks:synchronizability, neural network models and EEG analysis

Complex dynamical networks are ubiquitous in many fields of science from engineering to biology, physics, and sociology. Collective behavior, and in particular synchronization,) is one of the most interesting consequences of interaction of dynamical systems over complex networks. In this thesis we study some aspects of synchronization in dynamical networks. The first section of the study discuses the problem of synchronizability in dynamical networks. Although synchronizability, i.e. the ease by which interacting dynamical systems can synchronize their activity, has been frequently used in research studies, there is no single interpretation for that. Here we give some possible interpretations of synchronizability and investigate to what extent they coincide. We show that in unweighted dynamical networks different interpretations of synchronizability do not lie in the same line, in general. However, in networks with high degrees of synchronization properties, the networks with properly assigned weights for the links or the ones with well-performed link rewirings, the different interpretations of synchronizability go hand in hand. We also show that networks with nonidentical diffusive connections whose weights are assigned using the connection-graph-stability method are better synchronizable compared to networks with identical diffusive couplings. Furthermore, we give an algorithm based on node and edge betweenness centrality measures to enhance the synchronizability of dynamical networks. The algorithm is tested on some artificially constructed dynamical networks as well as on some real-world networks from different disciplines. In the second section we study the synchronization phenomenon in networks of Hindmarsh-Rose neurons. First, the complete synchronization of Hindmarsh-Rose neurons over Newman-Watts networks is investigated. By numerically solving the differential equations of the dynamical network as well as using the master-stability-function method we determine the synchronizing coupling strength for diffusively coupled Hindmarsh-Rose neurons. We also consider clustered networks with dense intra-cluster connections and sparse inter-cluster links. In such networks, the synchronizability is more influenced by the inter-cluster links than intra-cluster connections. We also consider the case where the neurons are coupled through both electrical and chemical connections and obtain the synchronizing coupling strength using numerical calculations. We investigate the behavior of interacting locally synchronized gamma oscillations. We construct a network of minimal number of neurons producing synchronized gamma oscillations. By simulating giant networks of this minimal module we study the dependence of the spike synchrony on some parameters of the network such as the probability and strength of excitatory/inhibitory couplings, parameter mismatch, correlation of thalamic input and transmission time-delay. In the third section of the thesis we study the interdependencies within the time series obtained through electroencephalography (EEG) and give the EEG specific maps for patients suffering from schizophrenia or Alzheimer's disease. Capturing the collective coherent spatiotemporal activity of neuronal populations measured by high density EEG is addressed using measures estimating the synchronization within multivariate time series. Our EEG power analysis on schizophrenic patients, which is based on a new parametrization of the multichannel EEG, shows a relative increase of power in alpha rhythm over the anterior brain regions against its reduction over posterior regions. The correlations of these patterns with the clinical picture of schizophrenia as well as discriminating of the schizophrenia patients from normal control subjects supports the concept of hypofrontality in schizophrenia and renders the alpha rhythm as a sensitive marker of it. By applying a multivariate synchronization estimator, called S-estimator, we reveal the whole-head synchronization topography in schizophrenia. Our finding shows bilaterally increased synchronization over temporal brain regions and decreased synchronization over the postcentral/parietal brain regions. The topography is stable over the course of several months as well as over all conventional EEG frequency bands. Moreover, it correlates with the severity of the illness characterized by positive and negative syndrome scales. We also reveal the EEG features specific to early Alzheimer's disease by applying multivariate phase synchronization method. Our analyses result in a specific map characterized by a decrease in the values of phase synchronization over the fronto-temporal and an increase over temporo-parieto-occipital region predominantly of the left hemisphere. These abnormalities in the synchronization maps correlate with the clinical scores associated to the patients and are able to discriminate patients from normal control subjects with high precision

visone - Software for the Analysis and Visualization of Social Networks

We present the software tool visone which combines graph-theoretic methods for the analysis of social networks with tailored means of visualization. Our main contribution is the design of novel graph-layout algorithms which accurately reflect computed analyses results in well-arranged drawings of the networks under consideration. Besides this, we give a detailed description of the design of the software tool and the provided analysis methods

Action A3 : analysis of spatial connectivity and preparation of environmental impact assessment guidelines : prepared within A3 action of LIFE DINALP BEAR Project (LIFE13 NAT/SI/0005)

As for other large carnivores in Europe, the brown bear shows a trend of recovering under different management scenarios. However, this recovery comes with specific biological and conservation requirements at individual and population levels often followed by conflicts in a highly humanized continent. To foresee conflicts with humans and to facilitate decisionmaking, spatially-explicit research is required to identify potential habitats and the connectivity of fragmented bear populations. First, we conducted multiscale modeling based on scale-integrated resource selection functions (SRSFs) to identify drivers shaping the spaceuse of three bear populations/demographic units (Trentino-Swiss, pre-Alps, and Dinaric), and across 3 scales of space (population distribution, home range establishment, and use of individual home range). Secondly, we also conducted an analysis of the connectivity patterns of suitable habitat patches (nodes) to identify the potential importance of each node to contribute to individual mobility, survival, and population connectivity. Lastly, to support further environmental impact assessment analyses, we identified the most plausible least-cost paths connecting different areas of the same large patch with itself and surrounding patches. Using topographic, landcover, and anthropogenic predictors, our analytical approach transcended from scale dependence bias to produce a predictive map on habitat suitability while delivered information on habitat selection trends for each population. Bears mostly selected forest habitats in all the populationshowever, habitat selection differed for the other variables among populations and scales, especially in the Trentino area where the species selected the most intricate topography. Predictive maps revealed a broad range of suitable but fragmented patches of bear habitat. The largest and most important patches for connectivity occurred in the current distribution range of the species, with the most suitable habitat lying in the pre-Alpine and Dinaric populations. Connecting viable patches to host female homeranges is possible through stepping-stone patches of corridors reachable within the estimated dispersal distance of females. Unified transnational decision-making is required for the conservation of stepping-stone patches, facilitate bear mobility, and ultimately connect bear populations.Podobno kot pri drugih vrstah velikih zveri se tudi pri rjavemu medvedu njegovo območje razširjenosti in številčnost povečujeta v več delih Evrope, in to ob različnih upravljavskih pristopih. Vendar uspešno širjenje vrste vselej zahteva specifične biološke in varstvene pogoje na individualni in populacijski ravni. V gosto poseljeni Evropi širjenje medveda pogosto spremljajo tudi konflikti s človekom. Za pravočasno napovedovanje in racionalno preprečevanje konfliktnih situacij s človekom in s tem lajšanja procesa odločanja so ključne zanesljive prostorske raziskave. Te nam omogočajo prepoznavanje potencialnih habitatov za medveda in območij/koridorjev, ki so ključna za ohranjanje povezljivosti populacije. V prvi fazi pričujoče raziskave smo zato izvedli večstopenjsko hierarhično prostorsko eksplicitno napovedno modeliranje habitatne ustreznosti prostora (scale integrated RSF), s katerim smo lahko prepoznali glavne omejitvene dejavnike rabe prostora za tri obravnavane medvedje populacije oz demografske enote (Trentino-Švicarske, pred-Alpska in Dinarska) na treh prostorskih nivojih (populacijski nivo, nivo območja aktivnosti in nivo notranje rabe znotraj območij aktivnosti). Izvedli smo tudi analizo povezljivosti prostora med osnovnimi zaplatami habitata in opredelili prispevek vsake zaplate k %vitalnosti% celotne medvedje populacije v raziskovalnem območju. Končno smo z namenom lažjega prepoznavanja potreb po prihodnjih presojah vplivov posegov na okolje (PVO) opredelili še najbolj verjetne prehode med habitatnimi krpami (least-cost paths). Na osnovi napovednih spremenljivk, ki opisujejo rabo tal, reliefne značilnosti in prisotnost človeka (npr. ceste, naselja) smo pripravili modele habitatne ustreznosti prostora za medveda in prepoznali tudi razlike v habitatnem izboru med 3 obravnavanimi populacijami in prostorskimi merili. V vseh treh populacijah so medvedi primarno izbirali gozdnata območja, so pa med populacijami in prostorskimi merili opazne razlike v rabi/pomenu ostalih okoljskih spremenljivk. Zlasti odstopa skupina medvedov v Trentinu, za katere je značilna izbira bolj nedostopnih območij (težji, topografsko bolj razgiban teren). Naš prostorsko eksplicitni model kaže, da je v obravnavanem območju veliko habitata, ki je primeren za medveda, vendar pa je zanj značilna močna fragmentiranost. Največje in najbolj pomembne zaplate habitata za povezljivost populacije se nahajajo na območju trenutne razširjenosti vrste, z najbolj primernim habitatom na območju pred-Alpske in Dinarske populacije. Zadostno povezanost najprimernejših zaplat (ki so dovolj velike, da v njih lahko žive samice % medvedke), bi bilo mogoče vzdrževati preko ohranjanja dovolj povezanih habitatnih krp v koridorjih (step-stones). Za ohranjanje zadostne povezanosti prostora/habitatov, zagotavljanja povezav med deli populacij in populacijami medvedov ter za dolgoročno viabilnost medveda v območju Alp in Dinaridov je ključna poenotena % med državami usklajena - politika odločanja in rabe prostora