Cores and Other Dense Structures in Complex Networks

Complex networks are a powerful paradigm to model complex systems. Specific network models, e.g., multilayer networks, temporal networks, and signed networks, enrich the standard network representation with additional information to better capture real-world phenomena. Despite the keen interest in a variety of problems, algorithms, and analysis methods for these types of network, the problem of extracting cores and dense structures still has unexplored facets. In this work, we present advancements to the state of the art by the introduction of novel definitions and algorithms for the extraction of dense structures from complex networks, mainly cores. At first, we define core decomposition in multilayer networks together with a series of applications built on top of it, i.e., the extraction of maximal multilayer cores only, densest subgraph in multilayer networks, the speed-up of the extraction of frequent cross-graph quasi-cliques, and the generalization of community search to the multilayer setting. Then, we introduce the concept of core decomposition in temporal networks; also in this case, we are interested in the extraction of maximal temporal cores only. Finally, in the context of discovering polarization in large-scale online data, we study the problem of identifying polarized communities in signed networks. The proposed methodologies are evaluated on a large variety of real-world networks against na\"{\i}ve approaches, non-trivial baselines, and competing methods. In all cases, they show effectiveness, efficiency, and scalability. Moreover, we showcase the usefulness of our definitions in concrete applications and case studies, i.e., the temporal analysis of contact networks, and the identification of polarization in debate networks.Comment: arXiv admin note: text overlap with arXiv:1812.0871

Methods for protein complex prediction and their contributions towards understanding the organization, function and dynamics of complexes

Complexes of physically interacting proteins constitute fundamental functional units responsible for driving biological processes within cells. A faithful reconstruction of the entire set of complexes is therefore essential to understand the functional organization of cells. In this review, we discuss the key contributions of computational methods developed till date (approximately between 2003 and 2015) for identifying complexes from the network of interacting proteins (PPI network). We evaluate in depth the performance of these methods on PPI datasets from yeast, and highlight challenges faced by these methods, in particular detection of sparse and small or sub- complexes and discerning of overlapping complexes. We describe methods for integrating diverse information including expression profiles and 3D structures of proteins with PPI networks to understand the dynamics of complex formation, for instance, of time-based assembly of complex subunits and formation of fuzzy complexes from intrinsically disordered proteins. Finally, we discuss methods for identifying dysfunctional complexes in human diseases, an application that is proving invaluable to understand disease mechanisms and to discover novel therapeutic targets. We hope this review aptly commemorates a decade of research on computational prediction of complexes and constitutes a valuable reference for further advancements in this exciting area.Comment: 1 Tabl

Neural Distributed Autoassociative Memories: A Survey

Introduction. Neural network models of autoassociative, distributed memory allow storage and retrieval of many items (vectors) where the number of stored items can exceed the vector dimension (the number of neurons in the network). This opens the possibility of a sublinear time search (in the number of stored items) for approximate nearest neighbors among vectors of high dimension. The purpose of this paper is to review models of autoassociative, distributed memory that can be naturally implemented by neural networks (mainly with local learning rules and iterative dynamics based on information locally available to neurons). Scope. The survey is focused mainly on the networks of Hopfield, Willshaw and Potts, that have connections between pairs of neurons and operate on sparse binary vectors. We discuss not only autoassociative memory, but also the generalization properties of these networks. We also consider neural networks with higher-order connections and networks with a bipartite graph structure for non-binary data with linear constraints. Conclusions. In conclusion we discuss the relations to similarity search, advantages and drawbacks of these techniques, and topics for further research. An interesting and still not completely resolved question is whether neural autoassociative memories can search for approximate nearest neighbors faster than other index structures for similarity search, in particular for the case of very high dimensional vectors.Comment: 31 page

Fibers in the NGC1333 proto-cluster

Are the initial conditions for clustered star formation the same as for non-clustered star formation? To investigate the initial gas properties in young proto-clusters we carried out a comprehensive and high-sensitivity study of the internal structure, density, temperature, and kinematics of the dense gas content of the NGC1333 region in Perseus, one of the nearest and best studied embedded clusters. The analysis of the gas velocities in the Position-Position-Velocity space reveals an intricate underlying gas organization both in space and velocity. We identified a total of 14 velocity-coherent, (tran-)sonic structures within NGC1333, with similar physical and kinematic properties than those quiescent, star-forming (aka fertile) fibers previously identified in low-mass star-forming clouds. These fibers are arranged in a complex spatial network, build-up the observed total column density, and contain the dense cores and protostars in this cloud. Our results demonstrate that the presence of fibers is not restricted to low-mass clouds but can be extended to regions of increasing mass and complexity. We propose that the observational dichotomy between clustered and non-clustered star-forming regions might be naturally explained by the distinct spatial density of fertile fibers in these environments.Comment: 25 pages, 17 figures; Accepted for publication in A&

Distance-generalized Core Decomposition

The $k$-core of a graph is defined as the maximal subgraph in which every vertex is connected to at least $k$ other vertices within that subgraph. In this work we introduce a distance-based generalization of the notion of $k$-core, which we refer to as the $(k,h)$-core, i.e., the maximal subgraph in which every vertex has at least $k$ other vertices at distance $\leq h$ within that subgraph. We study the properties of the $(k,h)$-core showing that it preserves many of the nice features of the classic core decomposition (e.g., its connection with the notion of distance-generalized chromatic number) and it preserves its usefulness to speed-up or approximate distance-generalized notions of dense structures, such as $h$-club. Computing the distance-generalized core decomposition over large networks is intrinsically complex. However, by exploiting clever upper and lower bounds we can partition the computation in a set of totally independent subcomputations, opening the door to top-down exploration and to multithreading, and thus achieving an efficient algorithm

The warm and dense Galaxy - tracing the formation of dense cloud structures out to the Galactic Center

The past two decades have seen extensive surveys of the far-infrared to submillimeter continuum emission in the plane of our Galaxy. We line out prospects for the coming decade for corresponding molecular and atomic line surveys which are needed to fully understand the formation of the dense structures that give birth to clusters and stars out of the diffuse interstellar medium. We propose to work towards Galaxy wide surveys in mid-J CO lines to trace shocks from colliding clouds, Galaxy-wide surveys for atomic Carbon lines in order to get a detailed understanding of the relation of atomic and molecular gas in clouds, and to perform extensive surveys of the structure of the dense parts of molecular clouds to understand the importance of filaments/fibers over the full range of Galactic environments and to study how dense cloud cores are formed from the filaments. This work will require a large (50m) Single Dish submillimeter telescope equipped with massively multipixel spectrometer arrays, such as envisaged by the AtLAST project.Comment: Science white paper submitted to the Astro2020 Decadal Surve