Related papers: Degenerate elastic networks
This paper is devoted to classical variational problems for planar elastic curves of clamped endpoints, so-called Euler's elastica problem. We investigate a straightening limit that means enlarging the distance of the endpoints, and obtain…
Two aspects of neural networks that have been extensively studied in the recent literature are their function approximation properties and their training by gradient descent methods. The approximation problem seeks accurate approximations…
Let $A$ be a gentle algebra. For every collection of string and band diagrammes, we consider the constructible subset of the variety of representations containing all modules with this underlying diagramme. We study degenerations of such…
Polymer network models construct the constitutive relationships of a broader polymer network from the behavior of a single polymer chain (e.g. viscoelastic response to applied forces, applied electromagnetic fields, etc.). Network models…
Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question…
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
We introduce a new class of deterministic networks by associating networks with Diophantine equations, thus relating network topology to algebraic properties. The network is formed by representing integers as vertices and by drawing cliques…
The analysis of complex networks has so far revolved mainly around the role of nodes and communities of nodes. However, the dynamics of interconnected systems is commonly focalised on edge processes, and a dual edge-centric perspective can…
Networks describe a range of social, biological and technical phenomena. An important property of a network is its degree correlation or assortativity, describing how nodes in the network associate based on their number of connections.…
A new family of graphs, {\it entangled networks}, with optimal properties in many respects, is introduced. By definition, their topology is such that optimizes synchronizability for many dynamical processes. These networks are shown to have…
We study models of weighted exponential random graphs in the large network limit. These models have recently been proposed to model weighted network data arising from a host of applications including socio-econometric data such as migration…
We study the question of reconstructing a weighted, directed network up to isomorphism from its motifs. In order to tackle this question we first relax the usual (strong) notion of graph isomorphism to obtain a relaxation that we call weak…
The evolutionary relationships among organisms have traditionally been represented using rooted phylogenetic trees. However, due to reticulate processes such as hybridization or lateral gene transfer, evolution cannot always be adequately…
Potential energy landscapes can be represented as a network of minima linked by transition states. The community structure of such networks has been obtained for a series of small Lennard-Jones clusters. This community structure is compared…
Much of social network analysis is - implicitly or explicitly - predicated on the assumption that individuals tend to be more similar to their friends than to strangers. Thus, an observed social network provides a noisy signal about the…
Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge of interest in network science to explore the relationship between the shape and connectivity of physical networks. We…
We consider atoms interacting each other through the topological structure of a complex network and investigate lattice vibrations of the system, the quanta of which we call {\em netons} for convenience. The density of neton levels,…
In this article, we explore the potential of artificial neural networks, which are trained using an exceptionally simplified catalog of ideal configurations encompassing both order and disorder. We explore the generalisation power of these…
We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative…
Almost all available results in elasticity on curved topographies are obtained within either a small curvature expansion or an empirical covariant generalization that accounts for screening between Gaussian curvature and disclinations. In…