Related papers: Taut and Tense Networks
Signed networks provide a principled framework for representing systems in which interactions are not merely present or absent but qualitatively distinct: friendly or antagonistic, supportive or conflicting, excitatory or inhibitory. This…
We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with $Z_2$ topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules.…
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…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
Mathematical theories are classified in two distinct classes : {\it rigid}, and on the other hand, {\it non-rigid} ones. Rigid theories, like group theory, topology, category theory, etc., have a basic concept - given for instance by a set…
Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that…
We look for a connection between string theories and Grand Unified Theories (GUTs), with the aim to look for new insights in the existing four dimensional string-GUT problems. We argue that the construction of consistent string-GUT models…
Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks. Our main results characterize networks…
Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and…
A spin network is a cubic ribbon graph labeled by representations of $\mathrm{SU}(2)$. Spin networks are important in various areas of Mathematics (3-dimensional Quantum Topology), Physics (Angular Momentum, Classical and Quantum Gravity)…
A network is a typical expressive form of representing complex systems in terms of vertices and links, in which the pattern of interactions amongst components of the network is intricate. The network can be static that does not change over…
High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
The roles that spin networks play in gauge theories, quantum gravity and topological quantum field theory are briefly described, with an emphasis on the question of the relationships among them. It is argued that spin networks and their…
The robustness of deep neural networks is crucial to modern AI-enabled systems and should be formally verified. Sigmoid-like neural networks have been adopted in a wide range of applications. Due to their non-linearity, Sigmoid-like…
Tensor network states are capable of describing many-body systems with complex quantum entanglement, including systems with non-trivial topological order. In this paper, we study methods to calculate the topological properties of a tensor…
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…
Convolutional neural networks typically consist of many convolutional layers followed by one or more fully connected layers. While convolutional layers map between high-order activation tensors, the fully connected layers operate on…
Network structures, consisting of nodes and edges, have applications in almost all subjects. A set of nodes is called a community if the nodes have strong interrelations. Industries (including cell phone carriers and online social media…
A string figure is topologically a trivial knot lying on an imaginary plane orthogonal to the fingers with some crossings. The fingers prevent cancellation of these crossings. As a mathematical model of string figure we consider a knot…