Related papers: Ridge Network in Crumpled Paper
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…
Great part of the interest in complex networks has been motivated by the presence of structured, frequently non-uniform, connectivity. Because diverse connectivity patterns tend to result in distinct network dynamics, and also because they…
One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of…
A model based on self-organizing nature of the surfaces is represented to capture the evolution of friction networks. Also, the curvatures of displacement fields are determined and critical curvature profiles are connected through links to…
We analyse the large-scale structure of the journal citation network built from information contained in the Thomson-Reuters Journal Citation Reports. To this end, we take advantage of the network science paraphernalia and explore network…
Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order…
Leaves, i.e., vertices of degree one, can play a significant role in graph structure, especially in sparsely connected settings in which leaves often constitute the largest fraction of vertices. We consider a leaf-based counterpart of the…
We study graphs that are formed by independently-positioned needles (i.e., line segments) in the unit square. To mathematically characterize the graph structure, we derive the probability that two line segments intersect and determine…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Minimizing the elastic free energy of a thin sheet of nematic polymer network among smooth isometric immersions is the strategy purported by the mainstream theory. In this paper, we broaden the class of admissible spontaneous deformations:…
Phylogenetic networks are used to study evolutionary relationships between species in biology. Such networks are often categorized into classes by their topological features, which stem from both biological and computational motivations. We…
The loss surface of deep neural networks has recently attracted interest in the optimization and machine learning communities as a prime example of high-dimensional non-convex problem. Some insights were recently gained using spin glass…
first-principles numerical simulation model for crumpling of a stiff tethered membrane is introduced. In our model membranes, wrinkles, ridge formation, ridge collapse, as well as the initiation of stiffness divergence, are observed. The…
Hand crumpled paper balls involve intricate structure with a network of creases and vertices, yet show simple scaling properties, which suggests self-similarity of the structure. We investigate the internal structure of crumpled papers by…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
Power law distribution is common in real-world networks including online social networks. Many studies on complex networks focus on the characteristics of vertices, which are always proved to follow the power law. However, few researches…
Confining an answer to the question whether and how the coherent operation of network elements is determined by the the network structure is the topic of our work. We map the structure of signal flow in directed networks by analysing the…
Crumpled thin sheets are complex fractal structures whose physical properties are influenced by a hierarchy of ridges. In this Letter, we report experiments that measure the stress-strain relation and show the coexistence of phases in the…
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…