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Networks have been studied mainly using statistical methods. Here I collect some dynamical systems tools which are useful to study both the dynamics on networks and their evolution. They include decomposition of differential dynamics,…
Bone adapts in response to its mechanical environment. This evolution of bone density is one of the most important mechanisms for developing fracture resistance. A finite element framework for simulating bone adaptation, commonly called…
We study networks of coupled bistable elastic elements, recently proposed as a model for crumpled thin sheets. The networks are poised on the verge of a localized instability, and the model allows unique access to both local and global…
Missing data is pervasive in econometric applications, and rarely is it plausible that the data are missing (completely) at random. This paper proposes a methodology for studying the robustness of results drawn from incomplete datasets.…
We present an ab initio study of the electronic stopping power of protons in copper over a wide range of proton velocities $v = 0.02-10~\mathrm{a.u.}$ where we take into account non-linear effects. Time-dependent density functional theory…
This paper examines the impact of static sparsity on the robustness of a trained network to weight perturbations, data corruption, and adversarial examples. We show that, up to a certain sparsity achieved by increasing network width and…
Underpinning the past decades of work on the design, initialization, and optimization of neural networks is a seemingly innocuous assumption: that the network is trained on a \textit{stationary} data distribution. In settings where this…
As a surrogate for computationally intensive meso-scale simulation of woven composites, this article presents Recurrent Neural Network (RNN) models. Leveraging the power of transfer learning, the initialization challenges and sparse data…
Many social, technological and biological interactions involve network relationships whose outcome intimately depends on the structure of the network and on the strengths of the connections. Yet, although much information is now available…
The existence of considerable amount of redundancy in the Internet traffic at the packet level has stimulated the deployment of packet-level redundancy elimination techniques within the network by enabling network nodes to memorize data…
Several experiments have demonstrated the existence of an electro-mechanical effect in many biological tissues and hydrogels, and its actual influence on growth, migration, and pattern formation. Here, to model these interactions and…
A high dimensional artificial neural network interatomic potential for Mo is developed. To train and validate the potential density functional theory calculations on structures and properties that correlate to fracture, such as elastic…
Most empirical studies of networks assume that the network data we are given represent a complete and accurate picture of the nodes and edges in the system of interest, but in real-world situations this is rarely the case. More often the…
The most profound effect of disorder on the elastic response of solids is the nonaffinity of local displacements whereby the atoms (particles, network junctions) do not simply follow the macroscopic strain, as they do in perfect crystals,…
We present a new, novel approach to obtaining a network's connectivity. More specifically, we show that there exists a relationship between a network's graph isoperimetric properties and its conditional connectivity. A network's…
Cutting mechanics in soft solids have been a subject of study for several decades, an interest fuelled by the multitude of its applications, including material testing, manufacturing, and biomedical technology. Wire cutting is the simplest…
This paper focuses on network resilience to perturbation of edge weight. Other than connectivity, many network applications nowadays rely upon some measure of network distance between a pair of connected nodes. In these systems, a metric…
We review selected results related to robustness of networked systems in finite and asymptotically large size regimes, under static and dynamical settings. In the static setting, within the framework of flow over finite networks, we discuss…
Complex systems are large collections of entities that organize themselves into non-trivial structures that can be represented by networks. A key emergent property of such systems is robustness against random failures or targeted attacks…
The rigidity of a network of elastic beams crucially depends on the specific details of its structure. We show both numerically and theoretically that there is a class of isotropic networks which are stiffer than any other isotropic network…