Exploring the randomness of Directed Acyclic Networks

The feed-forward relationship naturally observed in time-dependent processes and in a diverse number of real systems -such as some food-webs and electronic and neural wiring- can be described in terms of so-called directed acyclic graphs (DAGs). An important ingredient of the analysis of such networks is a proper comparison of their observed architecture against an ensemble of randomized graphs, thereby quantifying the {\em randomness} of the real systems with respect to suitable null models. This approximation is particularly relevant when the finite size and/or large connectivity of real systems make inadequate a comparison with the predictions obtained from the so-called {\em configuration model}. In this paper we analyze four methods of DAG randomization as defined by the desired combination of topological invariants (directed and undirected degree sequence and component distributions) aimed to be preserved. A highly ordered DAG, called \textit{snake}-graph and a Erd\:os-R\'enyi DAG were used to validate the performance of the algorithms. Finally, three real case studies, namely, the \textit{C. elegans} cell lineage network, a PhD student-advisor network and the Milgram's citation network were analyzed using each randomization method. Results show how the interpretation of degree-degree relations in DAGs respect to their randomized ensembles depend on the topological invariants imposed. In general, real DAGs provide disordered values, lower than the expected by chance when the directedness of the links is not preserved in the randomization process. Conversely, if the direction of the links is conserved throughout the randomization process, disorder indicators are close to the obtained from the null-model ensemble, although some deviations are observed.Comment: 13 pages, 5 figures and 5 table

Markers of criticality in phase synchronization

The concept of the brain as a critical dynamical system is very attractive because systems close to criticality are thought to maximize their dynamic range of information processing and communication. To date, there have been two key experimental observations in support of this hypothesis: (i) neuronal avalanches with power law distribution of size and (ii) long-range temporal correlations (LRTCs) in the amplitude of neural oscillations. The case for how these maximize dynamic range of information processing and communication is still being made and because a significant substrate for information coding and transmission is neural synchrony it is of interest to link synchronization measures with those of criticality. We propose a framework for characterizing criticality in synchronization based on an analysis of the moment-to-moment fluctuations of phase synchrony in terms of the presence of LRTCs. This framework relies on an estimation of the rate of change of phase difference and a set of methods we have developed to detect LRTCs. We test this framework against two classical models of criticality (Ising and Kuramoto) and recently described variants of these models aimed to more closely represent human brain dynamics. From these simulations we determine the parameters at which these systems show evidence of LRTCs in phase synchronization. We demonstrate proof of principle by analysing pairs of human simultaneous EEG and EMG time series, suggesting that LRTCs of corticomuscular phase synchronization can be detected in the resting state and experimentally manipulated. The existence of LRTCs in fluctuations of phase synchronization suggests that these fluctuations are governed by non-local behavior, with all scales contributing to system behavior. This has important implications regarding the conditions under which one should expect to see LRTCs in phase synchronization. Specifically, brain resting states may exhibit LRTCs reflecting a state of readiness facilitating rapid task-dependent shifts toward and away from synchronous states that abolish LRTCs

A morphospace of functional configuration to assess configural breadth based on brain functional networks

The best approach to quantify human brain functional reconfigurations in response to varying cognitive demands remains an unresolved topic in network neuroscience. We propose that such functional reconfigurations may be categorized into three different types: i) Network Configural Breadth, ii) Task-to-Task transitional reconfiguration, and iii) Within-Task reconfiguration. In order to quantify these reconfigurations, we propose a mesoscopic framework focused on functional networks (FNs) or communities. To do so, we introduce a 2D network morphospace that relies on two novel mesoscopic metrics, Trapping Efficiency (TE) and Exit Entropy (EE), which capture topology and integration of information within and between a reference set of FNs. In this study, we use this framework to quantify the Network Configural Breadth across different tasks. We show that the metrics defining this morphospace can differentiate FNs, cognitive tasks and subjects. We also show that network configural breadth significantly predicts behavioral measures, such as episodic memory, verbal episodic memory, fluid intelligence and general intelligence. In essence, we put forth a framework to explore the cognitive space in a comprehensive manner, for each individual separately, and at different levels of granularity. This tool that can also quantify the FN reconfigurations that result from the brain switching between mental states.Comment: main article: 24 pages, 8 figures, 2 tables. supporting information: 11 pages, 5 figure

Threshold-limited spreading in social networks with multiple initiators

A classical model for social-influence-driven opinion change is the threshold model. Here we study cascades of opinion change driven by threshold model dynamics in the case where multiple {\it initiators} trigger the cascade, and where all nodes possess the same adoption threshold $\phi$. Specifically, using empirical and stylized models of social networks, we study cascade size as a function of the initiator fraction $p$. We find that even for arbitrarily high value of $\phi$, there exists a critical initiator fraction $p_c(\phi)$ beyond which the cascade becomes global. Network structure, in particular clustering, plays a significant role in this scenario. Similarly to the case of single-node or single-clique initiators studied previously, we observe that community structure within the network facilitates opinion spread to a larger extent than a homogeneous random network. Finally, we study the efficacy of different initiator selection strategies on the size of the cascade and the cascade window

Huddling For Anonymization Of Compacted And Disseminated Public Systems

Social network: a social structure consists of nodes and ties. Noes are the individual actors within the networks May be different kinds May have attributes, labels or classes Ties are the relationships between the actors May be different kinds Links may have attributes, directed or undirected Social networks have received dramatic interest in research and development. We developed heuristics to deal with the problem, In this paper, we survey the very recent research development on privacy-preserving publishing of graphs and social network data. Our metric for data quality is the number of rules that can still be mined and the number of rules that appear as a side effect We developed heuristic algorithms to minimize the new rules of the concept

The struggle for existence in the world market ecosystem

The global trade system can be viewed as a dynamic ecosystem in which exporters struggle for resources: the markets in which they export. We can think that the aim of an exporter is to gain the entirety of a market share (say, car imports from the United States). This is similar to the objective of an organism in its attempt to monopolize a given subset of resources in an ecosystem. In this paper, we adopt a multilayer network approach to describe this struggle. We use longitudinal, multiplex data on trade relations, spanning several decades. We connect two countries with a directed link if the source country's appearance in a market correlates with the target country's disappearing, where a market is defined as a country-product combination in a given decade. Each market is a layer in the network. We show that, by analyzing the countries' network roles in each layer, we are able to classify them as out-competing, transitioning or displaced. This classification is a meaningful one: when testing the future export patterns of these countries, we show that out-competing countries have distinctly stronger growth rates than the other two classes