Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these we devise an analytically solvable model of Susceptible-Infected (SI) dynamics infinite systems for arbitrary inter-event time distributions whole range. Our stationary from beginning, role lower bound times explicitly considered. The exact solution shows that early intermediate burstiness accelerates as...

We consider a dynamical model of distress propagation on complex networks, which we apply to the study financial contagion in networks banks connected each other by direct exposures. The that is an extension DebtRank algorithm, recently introduced literature. mechanics very simple: When bank suffers loss, propagates its creditors, who turn suffer losses, and so on. original assumes losses are propagated linearly between banks. Here relax this assumption introduce one-parameter family...

Inhomogeneous temporal processes in natural and social phenomena have been described by bursts that are rapidly occurring events within short time periods alternating with long of low activity. In addition to the analysis heavy-tailed inter-event distributions, higher-order correlations between times, called correlated bursts, studied only recently. As possible mechanisms underlying such far from being fully understood, we devise a simple model for using self-exciting point process variable...

The inference of rankings plays a central role in the theory social choice, which seeks to establish preferences from collectively generated data, such as pairwise comparisons. Examples include political elections, ranking athletes based on competition results, ordering web pages search engines using hyperlink networks, and generating recommendations online stores user behavior. Various methods have been developed infer incomplete or conflicting data. One method, HodgeRank, introduced by...

Although most networks in nature exhibit complex topologies, the origins of such complexity remain unclear. We propose a general evolutionary mechanism based on global stability. This is incorporated into model growing network interacting agents which each new agent's membership determined by effect network's It shown that out this stability constraint topological properties emerge self-organized manner, offering an explanation for their observed ubiquity biological networks.

Hierarchical organization is an important, prevalent characteristic of complex systems; to understand their organization, the study underlying (generally complex) networks that describe interactions between constituents plays a central role. Numerous previous works have shown many real-world in social, biologic, and technical systems present hierarchical often form hierarchy community structures. Many artificial benchmark graphs been proposed test different detection methods, but no has...

The study of network robustness focuses on the way overall functionality a is affected as some its constituent parts fail. Failures can occur at random or be part an intentional attack and, in general, networks behave differently against different removal strategies. Although much effort has been put this topic, there no unified framework to problem. While failures have mostly studied under percolation theory, targeted attacks recently restated terms dismantling. In work, we link these two...

The quest for a quantitative characterization of community and modular structure complex networks produced variety methods algorithms to classify different networks. However, it is not clear if such provide consistent, robust meaningful results when considering hierarchies as whole. Part the problem lack similarity measure comparison hierarchical structures. In this work we give contribution by introducing {\it mutual information}, which generalization traditional information, allows compare...

Evidence of critical dynamics has been found recently in both experiments and models large-scale brain dynamics. The understanding the nature features such a regime is hampered by relatively small size available connectome, which prevents, among other things, determination its associated universality class. To circumvent that, here we study neural model defined on class small-world networks that share some topological with human connectome. We find varying parameters can give rise to...

To understand the origin of bursty dynamics in natural and social processes we provide a general analysis framework, which temporal process is decomposed into sub-processes then bursts sub-processes, called contextual bursts, are combined to collective original process. For combination it required consider distribution different contexts over Based on minimal assumptions for inter-event time statistics, present theoretical relationship between distributions. Our framework helps exploit...

What makes soccer so unpredictable with respect to other sports? The authors suggest that, contrary basketball or baseball, an important part of the game dynamics is developed far from ball, making data analysis more involved. They try address this by analyzing a novel dataset and proposing new theoretical framework that able reproduce statistics ball possession intervals.

In this work we study the problem of targeting signals in networks using entropy information measurements to quantify cost targeting. We introduce a penalization rule that imposes restriction on long paths and therefore focuses signal target. By scheme go continuously from fully random walkers biased found optimal degree is mainly determined by topology network. analyzing several examples, have small amount reduces considerably typical walk length, conclude network can be efficiently...

Complexity develops via the incorporation of innovative properties. Chess is one most complex strategy games, where expert contenders exercise decision making by imitating old games or introducing innovations. In this work, we study innovation in chess analyzing how different move sequences are played at population level. It found that probability exploring a new decreases as power law with frequency preceding sequence. players also exploit already known according to their frequencies,...

In this paper, we study collective interaction dynamics emerging in the game of football (soccer). To do so, surveyed a database containing body-sensor traces measured during three professional matches, where observed statistical patterns that used to propose stochastic model for players' motion field. The model, which is based on linear interactions, captures good approximation spatiotemporal team. Our theoretical framework, therefore, can be an effective analytical tool uncover underlying...

Interactions in time-varying complex systems are often very heterogeneous at the topological level (who interacts with whom) and temporal (when interactions occur how often). While it is known that heterogeneities have strong effects on dynamical processes, e.g. burstiness of contact sequences associated slower spreading dynamics, picture far from complete. In this paper, we show result sparsity} time scale average inter-event times, sparsity determines amount slowdown Susceptible-Infectious...

Abstract Chess is an emblematic sport that stands out because of its age, popularity and complexity. It has served to study human behavior from the perspective a wide number disciplines, cognitive skills such as memory learning, aspects like innovation decision-making. Given extensive documentation chess games played throughout history available, it possible perform detailed statistically significant studies about this sport. Here we use one most databases in world construct two networks...

A series of recent works studying a database chronologically sorted chess games–containing 1.4 million games played by humans between 1998 and 2007– have shown that the popularity distribution game-lines follows Zipf’s law, time inferred from sequences those exhibit long-range memory effects. The presence law together with effects was observed in several systems, however, simultaneous emergence these two phenomena were always studied separately up to now. In this work, making use variant...

Complex systems often exhibit multiple levels of organization covering a wide range physical scales, so the study hierarchical decomposition their structure and function is frequently convenient. To better understand this phenomenon, we introduce generalization information theory that works with partitions. We begin revisiting recently introduced mutual (HMI), show it can be written as level by summation classical conditional terms. Then, prove HMI bounded from above corresponding joint...

In this work we introduce a variant of the Yule-Simon model for preferential growth by incorporating finite kernel to effects bounded memory. We characterize properties combining analytical arguments with extensive numerical simulations. particular, analyze lifetime and popularity distributions mapping dynamics corresponding Markov chains branching processes, respectively. These follow power-laws well defined exponents that are within range empirical data reported in ecologies....

The inference of rankings plays a central role in the theory social choice, which seeks to establish preferences from collectively generated data, such as pairwise comparisons. Examples include political elections, ranking athletes based on competition results, ordering web pages search engines using hyperlink networks, and generating recommendations online stores user behavior. Various methods have been developed infer incomplete or conflicting data. One method, HodgeRank, introduced by...