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Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex…

Composite materials with different microstructural material symmetries are common in engineering applications where grain structure, alloying and particle/fiber packing are optimized via controlled manufacturing. In fact these…

Neural networks achieve remarkable performance through superposition: encoding multiple features as overlapping directions in activation space rather than dedicating individual neurons to each feature. This challenges interpretability, yet…

The study of dynamical systems defined on complex networks provides a natural framework with which to investigate myriad features of neural dynamics, and has been widely undertaken. Typically, however, networks employed in theoretical…

The structure and dynamics of a typical biological system are complex due to strong and inhomogeneous interactions between its constituents. The investigation of such systems with classical mathematical tools, such as differential equations…

Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal…

Discrete gene regulatory networks (GRNs) play a vital role in the study of robustness and modularity. A common method of evaluating the robustness of GRNs is to measure their ability to regulate a set of perturbed gene activation patterns…

Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…

A key task in the study of networked systems is to derive local and global properties that impact connectivity, synchronizability, and robustness; computing shortest paths or geodesics yields measures of network connectivity that can…

We propose a new family of neural networks to predict the behaviors of physical systems by learning their underpinning constraints. A neural projection operator lies at the heart of our approach, composed of a lightweight network with an…

We propose a statistical model for graphs with a core-periphery structure. To do this we define a precise notion of what it means for a graph to have this structure, based on the sparsity properties of the subgraphs of core and periphery…

Due to its non-crystalline nature, the glassy state has remained one the most exciting scientific challenges. To study such materials, Molecular Dynamics (MD) simulations have been extensively used because they provide a direct view into…

Network control refers to a very large and diverse set of problems including controllability of linear time-invariant dynamical systems, where the objective is to select an appropriate input to steer the network to a desired state. There…

This study addresses the challenge of predicting network dynamics, such as forecasting disease spread in social networks or estimating species populations in predator-prey networks. Accurate predictions in large networks are difficult due…

We characterize the large-sample properties of network modularity in the presence of covariates, under a natural and flexible nonparametric null model. This provides for the first time an objective measure of whether or not a particular…

Microstructural evolution in structural materials is known to occur in response to mechanical loading and can often accommodate substantial plastic deformation through the coupled motion of grain boundaries (GBs). This can produce desirable…

Networks capture pairwise interactions between entities and are frequently used in applications such as social networks, food networks, and protein interaction networks, to name a few. Communities, cohesive groups of nodes, often form in…

Resonator networks are ubiquitous in natural and engineered systems, such as solid-state materials, neural tissue, and electrical circuits. To understand and manipulate these networks, it is essential to characterize their building blocks,…

The network embedding problem aims to map nodes that are similar to each other to vectors in a Euclidean space that are close to each other. Like centrality analysis (ranking) and community detection, network embedding is in general…

Monolithic neural networks that make use of a single set of weights to learn useful representations for downstream tasks explicitly dismiss the compositional nature of data generation processes. This characteristic exists in data where…