Related papers: Optimal reinforcing networks for elastic membranes

It has been shown that the communities of complex networks often overlap with each other. However, there is no effective method to quantify the overlapping community structure. In this paper, we propose a metric to address this problem.…

Multilayer networks have been found to be prone to abrupt cascading failures under random and targeted attacks, but most of the targeting algorithms proposed so far have been mainly tested on uncorrelated systems. Here we show that the size…

We present an edge-based framework for the study of geometric elastic network models to model mechanical interactions in physical systems. We use a formulation in the edge space, instead of the usual node-centric approach, to characterise…

In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…

Multi-band transmission systems have emerged as a potential answer to the limited capacity of silica based optical fiber. It is based on utilizing the complete low-loss region of optical fibers. Additionally, elastic optical networks (EON)…

We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Every node is assigned an a-priori i.i.d. fitness with…

We consider the problem of an optimal distribution of soft and hard material for nonlinearly elastic planar beams. We prove that under gravitational force the optimal distribution involves no microstructure and is ordered, and we provide…

The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…

In this paper, we study robust distributed sub-optimal coordination of linear agents subject to input nonlinearities. Inspired by the robust agreement literature, we formulate a bounded distributed sub-optimal coordination problem, in which…

The network approach became a widely used tool to understand the behaviour of complex systems in the last decade. We start from a short description of structural rigidity theory. A detailed account on the combinatorial rigidity analysis of…

The structure of networks that provide optimal transport properties has been investigated in a variety of contexts. While many different formulations of this problem have been considered, it is recurrently found that optimal networks are…

Adhering cells actively probe the mechanical properties of their environment and use the resulting information to position and orient themselves. We show that a large body of experimental observations can be consistently explained from one…

The fluctuations of two-dimensional extended objects membranes is a rich and exciting field with many solid results and a wide range of open issues. We review the distinct universality classes of membranes, determined by the local order,…

We study numerically the cascading failure problem by using artificially created scale-free networks and the real network structure of the power grid. The capacity for a vertex is assigned as a monotonically increasing function of the load…

Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…

We study the maximal rank in affine subspaces of symmetric or alternating matrices, in terms of the matching numbers of certain associated graphs. Applications include simple proofs of upper bounds on the dimension of such subspaces in…

In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem.…

We consider the optimization of the vector of grasping forces that support a known generalized force acting on the grasped object---a rigid body or a mechanism. Working in the framework of finite-dimensional normed vector spaces and their…

Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…

Equivariant neural networks have been widely used in a variety of applications due to their ability to generalize well in tasks where the underlying data symmetries are known. Despite their successes, such networks can be difficult to…