相关论文: Robust motifs of threshold-linear networks

We have developed different network approaches to analyze complex patterns of frictional interfaces (contact area developments). Network theory is a fundamental tool for the modern understanding of complex systems in which, by a simple…

In weighted graphs the shortest path between two nodes is often reached through an indirect path, out of all possible connections, leading to structural redundancies which play key roles in the dynamics and evolution of complex networks. We…

Network motifs are small building blocks of complex networks. Statistically significant motifs often perform network-specific functions. However, the precise nature of the connection between motifs and the global structure and function of…

Network motifs are characteristic patterns which occur in the networks essentially more frequently than the other patterns. For five motifs found in S. Itzkovitz, U. Alon, Phys. Rev.~E, 2005, 71, 026117-1, hierarchical random graphs are…

We study learning of recurrent neural networks that produce temporal sequences consisting of the concatenation of re-usable "motifs". In the context of neuroscience or robotics, these motifs would be the motor primitives from which complex…

We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…

Threshold-linear networks consist of simple units interacting in the presence of a threshold nonlinearity. Competitive threshold-linear networks have long been known to exhibit multistability, where the activity of the network settles into…

Many real-world phenomena are best represented as interaction networks with dynamic structures (e.g., transaction networks, social networks, traffic networks). Interaction networks capture flow of data which is transferred between their…

This paper develops a structural theory of unique shortest paths in real-weighted graphs. Our main goal is to characterize exactly which sets of node sequences, which we call path systems, can be realized as unique shortest paths in a graph…

This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…

Topological network motifs represent functional relationships within and between regulatory and protein-protein interaction networks. Enriched motifs often aggregate into self-contained units forming functional modules. Theoretical models…

The relationship between the properties of a dynamical system and the structure of its defining equations has long been studied in many contexts. Here we study this problem for the class of conjunctive (resp. disjunctive) Boolean networks,…

Dynamic networks, a.k.a. graph streams, consist of a set of vertices and a collection of timestamped interaction events (i.e., temporal edges) between vertices. Temporal motifs are defined as classes of (small) isomorphic induced subgraphs…

Neural networks are powerful function estimators, leading to their status as a paradigm of choice for modeling structured data. However, unlike other structured representations that emphasize the modularity of the problem -- e.g., factor…

This paper studies the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix, and…

The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…

This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…

Dense regions in networks are an indicator of interesting and unusual information. However, most existing methods only consider simple, undirected, unweighted networks. Complex networks in the real-world often have rich information though:…

Link prediction plays an important role in network analysis and applications. Recently, approaches for link prediction have evolved from traditional similarity-based algorithms into embedding-based algorithms. However, most existing…

Highly connected and yet sparse graphs (such as expanders or graphs of high treewidth) are fundamental, widely applicable and extensively studied combinatorial objects. We initiate the study of such highly connected graphs that are, in…