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Transport in crowded, complex environments occurs across many spatial scales. Geometric restrictions can hinder the motion of individuals and, combined with crowding between individuals, can have drastic effects on global transport…

We give a combinatorial characterization of generic frameworks that are minimally rigid under the additional constraint of maintaining symmetry with respect to a finite order rotation or a reflection. To establish these results we develop a…

Interactions between genes and gene products give rise to complex circuits that enable cells to process information and respond to external signals. Theoretical studies often describe these interactions using continuous, stochastic, or…

Network representation learning has exploded recently. However, existing studies usually reconstruct networks as sequences or matrices, which may cause information bias or sparsity problem during model training. Inspired by a cognitive…

Crack-templated networks, metallic frameworks fabricated from crack patterns in sacrificial thin films, can exhibit high optical transmittance, high electric conductivity, and a host of other properties attractive for applications. Despite…

Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…

Matrix-vector multiplications are a fundamental building block of artificial intelligence; this essential role has motivated their implementation in a variety of physical substrates, from memristor crossbar arrays to photonic integrated…

We show that the community structure of a network can be used as a coarse version of its embedding in a hidden space with hyperbolic geometry. The finding emerges from a systematic analysis of several real-world and synthetic networks. We…

Recent advances in spatial and temporal networks have enabled researchers to more-accurately describe many real-world systems such as urban transport networks. In this paper, we study the response of real-world spatio-temporal networks to…

Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose…

Network embedding is a fervid topic in current networks science and observes that most real complex systems can be embedded in hidden metrics space and emerge as the geometrical property, where the geometric distance between nodes…

The network paradigm is increasingly used to describe the topology and dynamics of complex systems. Here we review the results of the topological analysis of protein structures as molecular networks describing their small-world character,…

Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…

Complex networks are ubiquitous: a cell, the human brain, a group of people and the Internet are all examples of interconnected many-body systems characterized by macroscopic properties that cannot be trivially deduced from those of their…

Recent experiments have shown that training trajectories of multiple deep neural networks with different architectures, optimization algorithms, hyper-parameter settings, and regularization methods evolve on a remarkably low-dimensional…

Modularity is a quantity which has been introduced in the context of complex networks in order to quantify how close a network is to an ideal modular network in which the nodes form small interconnected communities that are joined together…

We consider a fully-connected network of leaky integrate-and-fire neurons with spike-timing-dependent plasticity. The plasticity is controlled by a parameter representing the expected weight of a synapse between neurons that are firing…

Controlling complex networks is of paramount importance in science and engineering. Despite the recent development of structural-controllability theory, we continue to lack a framework to control undirected complex networks, especially…

In this paper we provide an overview of a new framework for robot perception, real-world modelling, and navigation that uses a stochastic tesselated representation of spatial information called the Occupancy Grid. The Occupancy Grid is a…

Dynamic processes on networks, be it information transfer in the Internet, contagious spreading in a social network, or neural signaling, take place along shortest or nearly shortest paths. Unfortunately, our maps of most large networks are…