Talk Abstracts

We have generalized the q-voter model with independence (noise) p for duplex cliques. This kind of a network consists of two distinct levels (layers), each of which being represented by a complete graph (clique) of size N. Levels represent two different communities (e.g. Facebook and the school class), but composed of exactly the same people which means that each node possesses a counterpart node in the second level. Such an assumption reflects the fact that we consider fully overlapping levels, being an idealistic scenario. We also assume that each node possesses the same state on each level which means that the examined society consists only of non-hypocritical individuals.
We consider two criteria of level dependence -- first related to the peer pressure and the second to the status of independence. Regarding the criteria related to the peer pressure, we distinguish two rules: AND and OR. The AND dynamics is more restrictive and node changes its state only if  both levels suggest changes, in the OR version it one level is enough to change individual's state. We take into account also two rules related to the status of independence: GLOBAL when agent is independent on both levels, and LOCAL where the person might be independent in one clique and not in the other.In order to examine the influence of the presence of more than one level in the social network, we perform simulations on a particularly simple multiplex --  a duplex clique, which consists of two fully overlapped complete graphs (cliques). Solving numerically the rate equation and simultaneously conducting Monte Carlo simulations, we provide evidence that even a simple rearrangement into a duplex topology may lead to significant changes in the observed behavior. However, qualitative changes in the phase transitions can be observed for only one of the considered rules -- LOCAL&AND. For this rule the phase transition becomes discontinuous for q=5, whereas for a monoplex such a behavior is observed for q=6. The case of LOCAL independence is not only less trivial, but also the most interesting from the social point of view. It should be remembered that conformity (and simultaneously independence) is relative, i.e. individuals always conform in respect to the particular social group and there are many factors that influence the level of conformity. It means that the same individual may conform to one group and behave independently in respect to another. Therefore the idea of local independence is highly justified in modeling social systems. 

We take into consideration  two different mechanisms for spreading processes, named as simple and complex contagions and we couple them in a two layered system. Dynamics of one of the networks is governed by a threshold model (complex contagion), where individuals change internal states based on their neighbourhood. Second layer follows  SIS rules of contagion (simple contagion), where individuals states are a result of successive and independent contact with others. Threshold dynamics reveals discontinuous transition from endemic (fully infected state of the system) to healthy phase. In contrast, SIS model shows second order phase transition from healthy to endemic phase. We address the question of how these two types of behaviour  influence each other after coupling and what type of transition will characterize this kind of mixed dynamics.

We study two particularly interesting quantities, i.e.,  critical values of  parameters responsible for spreading: individuals thresholds $theta_c $ and infection probability $lambda_c$, correspond to transitions from endemic to healthy phase and healthy to endemic phase, respectively.  We measure how they depend on the coupling strength (number of links between layers, $M$) and average connectivity inside each layer, $left$ and $left$.  Numerical simulations show non-trivial effects in these observables. The critical threshold value $theta_c(M)$ increases with $M$. For SIS layer we can distinguish two critical points. First is observed for the lower value of infection probability in comparison to a single network case,$lambda_c^1(Mneq 0)< lambda_c^{single}$ and second one corresponds to critical value of threshold ($lambda_c^2=theta_c$) and causes rapid decrease of infected individuals. For weakly coupled network transition to healthy phase in threshold layer can prevent infection spreading in SIS layer (number of infected individuals goes to zero at $lambda^2_c$.  Between these two critical values and above $lambda^2_c$, SIS layer is in endemic phase. 

The structural properties of large-scale complex networks are often a result of unknown generative processes that cannot be directly observed, and need to be inferred only from their final outcome. Of particular importance are the so-called large or mesoscale structures, often represented by modules --- groups of nodes with similar topological patterns --- for which general formative mechanisms (or even unified descriptions) have not yet been fully identified. More recently, it has
been increasingly recognized that most network systems are in fact composed of different types of interactions (represented as layers or attributes on the edges) and change in time, and that these features
cannot be neglected when attempting to identify mechanisms of network formation. Since these elaborations increase the effective dimension of the network description, they are a double-edged sword: On one hand, the inclusion of layered or temporal structure can reveal important patterns that are otherwise obscured, while on the other hand the uncontrolled incorporation of many uncorrelated variables can in fact hide patterns which would otherwise be detected. In this work, we propose a robust and principled method to tackle this problem, by defining general generative models of modular network structure, incorporating layered, attributed and time-varying properties, together with alternative generative processes incorporating hierarchical structure, degree correction and overlapping groups, as well as a Bayesian methodology to infer the parameters from data and select between model variants. We show that the method is capable of revealing hidden structure in layered, edge-valued and time-varying networks, and that the most appropriate level of granularity with respect to the added dimensions can be reliably identified. We illustrate our approach on a variety of empirical
systems, including a social network of physicians, the voting
correlations of deputies in the Brazilian national congress, the global airport network, and a proximity network of high-school students.
References:
[1] Tiago P. Peixoto, "Inferring the mesoscale structure of layered, edge-valued and time-varying networks", in preparation (to appear in Arxiv in the following days)
[2] Tiago P. Peixoto, "Model selection and hypothesis testing for large-scale network models with overlapping groups", Phys. Rev. X 5, 011033 (2015)
[3] Tiago P. Peixoto, "Hierarchical block structures and high-resolution model selection in large networks", Phys. Rev. X 4, 011047 (2014)
[4] Tiago P. Peixoto, "Parsimonious Module Inference in Large Networks", Phys. Rev. Lett. 110 14 148701 (2013)

A network is a natural formalism for the contacts between farms that spread costly and upsetting contagious disease.  In Great Britain, as in much of Europe, we have a very large amount of information about these contacts: some are fenceline adjacencies, some are movements of animals, some are movements of trucks or personnel.  Some are social contacts that spread opinions and behaviours related to disease, rather than disease itself. Different diseases are able to travel in different ways over these different types of contacts.  

We propose that these contacts ought to be considered together as different layers of the same network, rather than as separate systems. We give a small example of the importance of the level of correlation between different layers to the spread of a simple contagion.   

Here, we discuss the multiplex network of people applying to study in Saratov State University. Variety of data accompanying the application enables us to build the multiplex network, where the applicants present themselves nodes, and links on diffent layers can be proposed as similarity between such characteristics as grades, the choice of department and exams. Besides, the discussed data was analyzed for different years of admission to the university, that gives us opportunity to study the real multiplex network in dynamics and investigate the evolution of its properties. This report contains the preliminary results of the study on the structural and spectral properties of this network.

Mutually intertwined supply chains in contemporary economy result in a complex
network of trade relationships with a highly non-trivial topology that varies with time. In order to understand the complex interrelationships among different countries and economic sectors, as well as their dynamics, a holistic view on the underlying structural properties of this network is necessary. This study employs multi-regional input-output data to decompose 186 national economies into 26 industry sectors and utilizes the approach of interdependent networks to analyze the substructure of the resulting international trade network for the years 1990-2011. The partition of the network into national economies is observed to be compatible with the notion of communities in the sense of complex network theory. By studying internal versus cross-subgraph contributions to established complex network metrics, new insights into the architecture of global trade are obtained, which allow to identify key elements of global economy. Specifically, financial services dominate domestic trade whereas electrical and machinery industries dominate foreign trade. In order to further specify each national sector’s role individually, (cross-)clustering coefficients and cross-betweenness are obtained for different pairs of subgraphs. The corresponding analysis reveals that specific industrial sectors tend to favor distinct directionality patterns and that the cross-clustering coefficient for geographically close country pairs is remarkably high, indicating that spatial factors are still of paramount importance for the organization of trade patterns in modern economy. Regarding the evolution of the trade network’s substructure, globalization is well-expressed by trends of several structural characteristics (e.g., link density and node strength) in the interacting network framework. Extreme events, such as the financial crisis 2008/2009, are manifested as anomalies superimposed to these trends. The marked reorganization of trade patterns, associated with this economic crisis in comparison to “normal” annual fluctuations in the network structure is traced and quantified by a new widely applicable generalization of the Hamming distance to weighted networks.

The brain is a prime example of a complex and interconnected system, with interactions occurring across multiple spatial and temporal scales.  Brain networks evolve over time, are measured using multiple modalities, are task and state dependent, and are often compared between individuals or groups.  While this makes a multilayer framework a natural choice to describe the evolution and interactions between network elements, the use of a multilayer formalism in network neuroscience is still in its infancy.  In this talk, I will explore the types of questions that neuroscientists can address using multilayer networks and present work detailing how multilayer modeling has been used to gain insight into the mechanisms of learning and to predict task performance.  Finally, I will close with a discussion of potential future applications of a multilayer approach and the mathematical advances required to address questions at the forefront of neuroscience research.

Genes of the major histocompatibility complex (MHC) encode proteins that recognize foreign antigens and are thus crucial for immune response. In a population of a single host species, parasite-mediated selection drives MHC allelic diversity. However, in a community-wide context, species interactions may modulate selection regimes because the prevalence of a given parasite in a given host may depend on its prevalence in other hosts, influencing MHC diversity, but this hypothesis was never studied. By combining ecological network analysis with immunogenetics for the first time, we quantified the association between the structure of a host-parasite network and the distribution of functional MHC alleles across hosts, represented as a host-allele network. In this ecological-immunogenetic multi-layer network system, we show that host species infected by similar parasites harbour similar MHC alleles with similar frequencies. We further show, using a Bayesian approach, that the probability of mutual occurrence of a functional allele and a parasite in a given host individual is non-random and depends on other host-parasite interactions. This drives co-evolution within subgroups of parasite species and functional alleles, as detected by analysis of network modularity. Therefore, indirect effects among hosts and parasites can shape host MHC diversity. Our results scale MHC theory from the population to the community level, opening new directions in the way we perceive the evolution of genes involved in ecological interactions.

Modularity is a key organization principle in many systems around us. Social, technological and biological systems are organized into cohesive groups of elements, called modules. The relatively sparse interactions between the modules are critical to the functionality of the system, and are often the first to fail, as for example the case in neuronal networks where aging and schizophrenia could result in a damage to the interconnected nodes. Here we quantify the implications of such failures to the resilience of multi-scale modular systems. We find, using percolation theory and simulations, a ”tipping point”, which distinct between two regimes. In one regime, the modules remain functional but become disconnected, while in the other regime the modules themselves are damaged causing the system to collapse. The first regime is characterized by abrupt percolation transition where modules break from the network while the in the second regime the transition is continuous. We show that scale-free networks mainly operate in the first regime, thus highly vulnerable to such attacks. Our model provides insights into the role modularity plays in real world systems, while considering advanced types of attacks that address the multilevel nature of the system.

In recent years extensive studies on the Earth's climate system have been
carried out by means of advanced complex network statistics. The great majority
of recent studies, however, have been focusing on investigating interaction
structures within single climatological fields directly on or parallel to the
Earth's surface. It is well-known, however, that many processes observed in the
Earth system can only be explained by analyzing interactions between different
climatological variables, especially those taken from the two major subsystems
atmosphere and ocean.

In this work we develop and apply a novel approach of node weighted interacting
network measures to study ocean-atmosphere coupling in the northern hemisphere
from mid to high latitudes.
Specifically, we construct 18 coupled climate networks based on monthly time
series from the ERA 40 reanalysis, each consisting of two subnetworks. In all
cases, one subnetwork represents sea-surface temperature (SST) anomalies while
the other is based on the geopotential height (HGT) of isobaric surfaces at
different pressure levels covering the troposphere as well as the lower
stratosphere. Nodes in the network are weighted according to the share on the
Earth's surface they represent so that biases in the network measures induced
by the inhomogeneous distribution of grid points in the input dataset are
minimized.

Our analysis reveals which isobaric layers show strong coupling with the
dynamics of the oceans and where. By an exploratory investigation of the
resulting interacting network's connectivity, we identify
well-known climatological phenomena such as eddy driven jet streams in the
northern Atlantic and signatures of the Hadley circulation, especially in the
northern Pacific. The analysis is performed separately for summer and winter
months to identify key differences in the atmospheric dynamics. A strong
coupling between the SST and HGT fields in the upper troposphere is detected
during winter months and the corresponding local network measures reveal its
spatial extent displaying well localized areas in the Atlantic and Pacific
Ocean where the interaction between the two subsystems is strongest. During summer
months the dynamical decoupling of the upper troposphere and lower stratosphere
is well observed and the eddy driven jets are proven to be weaker compared to
winter. Furthermore, our analysis reveals dynamic signatures which
can not be simply explained by the basic large-scale cellular structure of
atmospheric dynamics and need to be further disentangled in future work.

Our analysis complements results obtained from classical methods of statistical
climatology such as maximum covariance analysis and allows for a deeper
understanding of interaction structures between ocean and atmosphere revealing
dynamic signatures which have not been observed so far.

At this time, explosive synchronization (ES) of networked oscillators is thought of as being rooted in the setting of specific microscopic correlation features between the natural frequencies of the oscillators and their effective coupling strengths. We show that ES is, in fact, far more general and can occur in adaptive
and multilayer networks in the absence of such correlation properties. We first report evidence of ES for single-layer networks where a fraction f of the nodes have links adaptively controlled by a local order parameter, and we then extend the study to a variety of two-layer networks with a fraction f of their nodes
coupled with each other by means of dependency links. In the latter case, we give evidence of ES regardless of the differences in the frequency distribution, in the topology of connections between the layers, or both. Finally, we provide a rigorous, analytical treatment to properly ground all of the observed scenarios and to advance the understanding of the actual mechanisms at the basis of ES in real-world systems.