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We propose the concepts of distributed robustness and r-robustness, well adapted to functional genetics. Then we discuss the robustness of the relaxation time using a chemical reaction description of genetic and signalling networks. First,…

The past decade has witnessed the development and success of coarse-grained network models of proteins for predicting many equilibrium properties related to collective modes of motion. Curiously, the results are usually robust towards the…

Representation of cities as organisms with metabolic processes is a useful analogy for urban design, development and sustainability. Urban metabolism can be modeled by representing urban systems as networks. The various networks included in…

We propose a robust elastic net (REN) model for high-dimensional sparse regression and give its performance guarantees (both the statistical error bound and the optimization bound). A simple idea of trimming the inner product is applied to…

The use of deep neural network (DNN) models as surrogates for linear and nonlinear structural dynamical systems is explored. The goal is to develop DNN based surrogates to predict structural response, i.e., displacements and accelerations,…

This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…

The rapid advancement of technology underscores the critical importance of robustness in complex network systems. This paper presents a framework for investigating the structural robustness of interconnected network models. This paper…

We present a model for disordered 3D fiber networks to study their linear and nonlinear elasticity over a wide range of network densities and fiber lengths. In contrast to previous 2D models, these 3D networks with binary cross-links are…

The modeling of the elastic properties of granular or nanoscale systems requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which a…

A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear…

Elastomers that can sustain large reversible strain are essential components for stretchable electronics. The stretchability and mechanical robustness of unfilled elastomers can be enhanced by introducing easier-to-break cross-links, e.g.…

In this paper we study the optimal reinforcement of an elastic membrane, fixed at its boundary, by means of a network (connected onedimensional structure), that has to be found in a suitable admissible class. We show the existence of an…

The response function of a network of springs and masses, an elastodynamic network, is the matrix valued function $W(\omega)$, depending on the frequency $\omega$, mapping the displacements of some accessible or terminal nodes to the net…

Disordered elastic networks are a model material system in which it is possible to achieve tunable and trainable functions. This work investigates the modification of local mechanical properties in disordered networks inspired by allosteric…

Machine learning-based methods have achieved successful applications in machinery fault diagnosis. However, the main limitation that exists for these methods is that they operate as a black box and are generally not interpretable. This…

We review the physical properties of macromolecular networks, consisting of semiflexible polymers such as actin. We start by giving a theoretical analysis of the conformational statistics and mechanical response of single filaments.…

We propose models in nonlinear elasticity for nonsimple materials that include surface energy terms. Additionally, we also discuss living surface loads on the boundary. We establish corresponding linearized models and show their…

The problem of characterizing the structure of an elastic network constrained to lie on a frozen curved surface appears in many areas of science and has been addressed by many different approaches, most notably, extending linear elasticity…

The performance of recurrence networks and symbolic networks to detect weak nonlinearities in time series is compared to the nonlinear prediction error. For the synthetic data of the Lorenz system, the network measures show a comparable…

Elastomers are used in a wide range of applications because of their large strain to failure, low density, and tailorable stiffness and toughness. The mechanical behavior of elastomers derives mainly from the entropic elasticity of the…