In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types relationships, change time include complications. Such systems subsystems layers connectivity, it is important to take such 'multilayer' features into account try improve our understanding complex systems. Consequently, necessary generalize 'traditional' network theory by developing (and validating) framework associated tools study multilayer...

Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, information sciences. A prominent problem in network algorithmic detection of tightly-connected groups nodes known as communities. We developed a generalized framework quality functions that allowed us to study community structure arbitrary multislice networks, which are combinations individual networks coupled through links connect each node one slice itself other slices....

Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities drive desired behavior. These two attributes—flexibility selection—must operate over multiple temporal scales as performance of skill changes from being slow challenging fast automatic. Such selective adaptability naturally provided by modular structure, which plays critical role evolution, development, optimal network function. Using...

A network representation is useful for describing the structure of a large variety complex systems. However, most real and engineered systems have multiple subsystems layers connectivity, data produced by such very rich. Achieving deep understanding necessitates generalizing "traditional" theory, newfound deluge now makes it possible to test increasingly general frameworks study networks. In particular, although adjacency matrices are describe traditional single-layer networks, insufficient...

Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of that persist across multiple scales. It robust perturbations input data, independent dimensions and coordinates, provides compact representation the input. The computation PH an open area with numerous important fascinating challenges. field evolving rapidly, new algorithms software implementations are being updated released at rapid pace. purposes our article (1) introduce theory...

Most reported power laws lack statistical support and mechanistic backing.

We describe techniques for the robust detection of community structure in some classes time-dependent networks. Specifically, we consider use statistical null models facilitating principled identification structural modules semi-decomposable systems. Null play an important role both optimization quality functions such as modularity and subsequent assessment validity identified structure. examine sensitivity methods to model parameters show how comparisons can help identify system scales. By...

We study the structure of social networks students by examining graphs Facebook “friendships” at five U.S. universities a single point in time. investigate community each single-institution network and employ visual quantitative tools, including standardized pair-counting methods, to measure correlations between communities set self-identified user characteristics (residence, class year, major, high school). review basic properties statistics employed indices recall, simplified notation,...

As a person learns new skill, distinct synapses, brain regions, and circuits are engaged change over time. In this paper, we develop methods to examine patterns of correlated activity across large set regions. Our goal is identify properties that enable robust learning motor skill. We measure during sequencing characterize network based on coherent between Using recently developed algorithms detect time-evolving communities, find the complex reconfiguration brain's putative functional...

Intermediate-scale (or “meso-scale'') structures in networks have received considerable attention, as the algorithmic detection of such makes it possible to discover network features that are not apparent either at local scale nodes and edges or global summary statistics. Numerous types meso-scale can occur networks, but investigations focused predominantly on identification study community structure. In this paper, we develop a new method investigate feature known core-periphery structure,...

Random walks are ubiquitous in the sciences, and they interesting from both theoretical practical perspectives. They one of most fundamental types stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, opinions among humans animals; extract information about important entities or dense groups a network. have been studied for many decades on regular lattices (especially last couple decades) networks with variety structures. In present article, we...

Limit order books (LOBs) match buyers and sellers in more than half of the world's financial markets. This survey highlights insights that have emerged from wealth empirical theoretical studies LOBs. We examine findings reported by statistical analyses historical LOB data discuss how several models provide insight into certain aspects mechanism. also illustrate many such poorly resemble real LOBs well-established facts yet to be reproduced satisfactorily. Finally, we identify key unresolved...

We report the experimental observation of modulational instability and discrete breathers in a one-dimensional diatomic granular crystal composed compressed elastic beads that interact via Hertzian contact. first characterize their effective linear spectrum both theoretically experimentally. then illustrate numerically lower edge optical band. This leads to dynamical formation long-lived breather structures, whose families solutions we compute throughout spectral gap. Finally, experimentally...

Multilayer relationships among entities and information about must be accompanied by the means to analyse, visualize obtain insights from such data. We present open-source software (muxViz) that contains a collection of algorithms for analysis multilayer networks, which are an important way represent large variety complex systems throughout science engineering. demonstrate ability muxViz analyse interactively data using empirical genetic, neuronal transportation networks. Our is available at...

Networks are a convenient way to represent complex systems of interacting entities. Many networks contain “communities” nodes that more densely connected each other than in the rest network. In this paper, we investigate detection communities temporal represented as multilayer networks. As focal example, study time-dependent financial-asset correlation We first argue use “modularity” quality function---which is defined by comparing edge weights an observed network expected “null...

The arrangements of particles and forces in granular materials have a complex organization on multiple spatial scales that ranges from local structures to mesoscale system-wide ones. This multiscale can affect how material responds or reconfigures when exposed external perturbations loading. theoretical study particle-level, force-chain, domain, bulk properties requires the development application appropriate physical, mathematical, statistical, computational frameworks. Traditionally, been...

Network theory provides a powerful tool for the representation and analysis of complex systems interacting agents. Here, we investigate U.S. House Representatives network committees subcommittees, with connected according to "interlocks," or common membership. Analysis this reveals clearly strong links between different committees, as well intrinsic hierarchical structure within whole. We show that theory, combined roll-call votes using singular value decomposition, successfully uncovers...