Related papers: Stiffest Elastic Networks
In this paper we develop a new perspective on generalization of neural networks by proposing and investigating the concept of a neural network stiffness. We measure how stiff a network is by looking at how a small gradient step in the…
Mathematical models of stem cell differentiation are commonly based upon the concept of subsequent cell fate decisions, each controlled by a gene regulatory network. These networks exhibit a multistable behavior and cause the system to…
We present a theoretical framework for the linear and nonlinear visco-elastic properties of reversibly crosslinked networks of semiflexible polymers. In contrast to affine models where network strain couples to the polymer end-to-end…
Liquid-crystal networks consist of weakly crosslinked polymers that are coupled to liquid-crystal molecules. The resultant hybrid system has rich elastic properties. We develop a phase field model to describe mechanical properties of a…
This article describes a complex network model whose weights are proportional to the difference between uniformly distributed ``fitness'' values assigned to the nodes. It is shown both analytically and experimentally that the strength…
Many fibrous materials are modeled as elastic networks featuring a substantial separation between the stiffness scales that characterize different microscopic deformation modes of the network's constituents. This scale separation has been…
We consider a heavy, uniform, elastic beam rested on periodically distributed supports as a simplified model of a bridge. The supports are subjected to a partial destruction propagating as a failure wave along the beam. Three related models…
We suggest a new perspective of research towards understanding the relations between structure and dynamics of a complex network: Can we design a network, e.g. by modifying the features of units or interactions, such that it exhibits a…
In vitro collagen networks and in silico fiber network models are typically used to represent extracellular matrix in tissues. Such networks exhibit the phenomenon of strain-stiffening, or an increase in elastic modulus with increasing…
Elastic effects in a model of disordered nematic elastomers are numerically investigated in two dimensions. Networks crosslinked in the isotropic phase exhibit unusual soft mechanical response against stretching. It arises from gradual…
We study a material modeled as a network of nodes connected by edges. Using a discrete approach, we build a nonlinear algebraic system that connects applied forces to internal forces and node positions. The model can describe elasticity,…
An elastic graph is a graph with an elasticity associated to each edge. It may be viewed as a network made out of ideal rubber bands. If the rubber bands are stretched on a target space there is an elastic energy. We characterize when a…
Disordered athermal biopolymer materials, such as collagen networks that constitute a major component in extracellular matrices and various connective tissues, are initially soft and compliant but stiffen dramatically under strain. Such…
We investigate certain structural properties of random interdependent networks. We start by studying a property known as $r$-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and…
Biological networks are customarily described as structurally robust. This means that they often function extremely well under large forms of perturbations affecting both the concentrations and the kinetic parameters. In order to explain…
The recently introduced continuous Hopfield network (see Ramsauer et al.) exhibits large memorization capabilities, which manifest as attractive fixed points of its update rule -- a differentiable function consisting of two linear mappings…
Branched actin networks exert pushing forces in eukaryotic cells, and adapt their stiffness to their environment. The physical basis for their mechanics and adaptability is however not understood. Indeed, here we show that their high…
Many real networks feature the property of nestedness, i.e. the neighbours of nodes with a few connections are hierarchically nested within the neighbours of nodes with more connections. Despite the abstract simplicity of this notion,…
We characterize the force state of shear-loaded granular matter by relating the macroscopic stress to statistical properties of the force network. The purely repulsive nature of the interaction between grains naturally provides an upper…
The isotropic elastic moduli closest to a given anisotropic elasticity tensor are defined using three definitions of elastic distance, the standard Frobenius (Euclidean) norm, the Riemannian distance for tensors, and the log-Euclidean norm.…