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We describe an extension to the density matrix renormalization group method incorporating real time evolution into the algorithm. Its application to transport problems in systems out of equilibrium and frequency dependent correlation…
We present a numerically efficient method to reconstruct a disordered network of thin biopolymers, such as collagen gels, from three-dimensional (3D) image stacks recorded with a confocal microscope. Our method is based on a template…
Using an asymmetric associative network with synchronous updating, it is possible to recall a sequence of patterns. To obtain a stable sequence generation with a large storage capacity, we introduce a threshold that eliminates the…
Scale-free and non-computable characteristics of natural networks are found to result from the least-time dispersal of energy. To consider a network as a thermodynamic system is motivated since ultimately everything that exists can be…
The large-scale shape and function of metabolic networks are intriguing topics of systems biology. Such networks are on one hand commonly regarded as modular (i.e. built by a number of relatively independent subsystems), but on the other…
Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…
A novel information-theoretic method for reconstruction of interaction networks is introduced. We prove that the method is exact for some class of networks. Performance tests on large synthetic transcriptional regulatory networks produce…
In this paper we derive an updating scheme for calculating some important network statistics such as degree, clustering coefficient, etc., aiming at reduce the amount of computation needed to track the evolving behavior of large networks;…
Galled networks, directed acyclic graphs that model evolutionary histories with reticulation cycles containing only tree nodes, have become very popular due to both their biological significance and the existence of polynomial time…
The problem of reconstructing and identifying intracellular protein signaling and biochemical networks is of critical importance in biology today. We sought to develop a mathematical approach to this problem using, as a test case, one of…
Recent advancements of complex network representation among several disciplines motivated the investigation of exoplanetary dynamics by means of recurrence networks. We are able to recover different dynamical regimes by means of various…
Irreversibility, in which a transient perturbation leaves a system in a new state, is an emergent property in systems of interacting entities. This property has well-established implications in statistical physics but remains underexplored…
Memorization of training data is an active research area, yet our understanding of the inner workings of neural networks is still in its infancy. Recently, Haim et al. (2022) proposed a scheme to reconstruct training samples from multilayer…
We develop a model-independent reduction method of chemical reaction systems based on the stoichiometry, which determines their network topology. A subnetwork can be eliminated systematically to give a reduced system with fewer degrees of…
Rooted phylogenetic networks provide a way to describe species' relationships when evolution departs from the simple model of a tree. However, networks inferred from genomic data can be highly tangled, making it difficult to discern the…
Multicellular self-organization drives development in biological organisms, yet a comprehensive theory is lacking as basic properties of cells can complicate common approaches. Framing such properties by dynamic graphs led to new…
Topological features of gene regulatory networks can be successfully reproduced by a model population evolving under selection for short dynamical attractors. The evolved population of networks exhibit motif statistics, summarized by…
Chemical reaction networks underpin biological and physical phenomena across scales, from microbial interactions to planetary atmosphere dynamics. Bacterial communities exhibit complex competitive interactions for resources, human organs…
We propose a statistical model of a large random network with high connectivity in order to describe the behavior of {\it E.\,coli} cells after exposure to acute stress. The building blocks of this network are feedback cycles typical of the…
Network reconstruction lies at the heart of phylogenetic research. Two well studied classes of phylogenetic networks include tree-child networks and level-$k$ networks. In a tree-child network, every non-leaf node has a child that is a tree…