相关论文: Reaction Network Motifs for Static and Dynamic Abs…

Recurrent Neural Cascades (RNCs) are the recurrent neural networks with no cyclic dependencies among recurrent neurons. This class of recurrent networks has received a lot of attention in practice. Besides training methods for a fixed…

We analyze a model of interacting agents (e.g. prebiotic chemical species) which are represended by nodes of a network, whereas their interactions are mapped onto directed links between these nodes. On a fast time scale, each agent follows…

The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…

We analyze a 1-d ring structure composed of many two-level systems, in the limit where only one excitation is present. The two-level systems are coupled to a common environment, where the excitation can be lost, which induces super and…

The Turing completeness of continuous chemical reaction networks (CRNs) states that any computable real function can be computed by a continuous CRN on a finite set of molecular species, possibly restricted to elementary reactions, i.e.…

A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the…

For a reaction network with species set $\mathscr{S}$, a log-parametrized (LP) set is a non-empty set of the form $E(P, x^*) = \{x \in \mathbb{R}^\mathscr{S}_> \mid \log x - \log x^* \in P^\perp\}$ where $P$ (called the LP set's flux…

Across many disciplines, chemical reaction networks (CRNs) are an established population model defined as a system of coupled nonlinear ordinary differential equations. In many applications, for example, in systems biology and epidemiology,…

We characterize the dynamics of all single-target networks under mass-action kinetics: either the system is (i) globally stable for all choice of rate constants (in fact, dynamically equivalent to a detailed-balanced system) or (ii) has no…

We study the set of output stable configurations of chemical reaction deciders (CRDs). It turns out that CRDs with only bimolecular reactions (which are almost equivalent to population protocols) have a special structure that allows for an…

Network robustness against attacks has been widely studied in fields as diverse as the Internet, power grids and human societies. Typically, in these studies, robustness is assessed only in terms of the connectivity of the nodes unaffected…

A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear…

Neural networks storing multiple discrete attractors are canonical models of biological memory. Previously, the dynamical stability of such networks could only be guaranteed under highly restrictive conditions. Here, we derive a theory of…

Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and when a network exhibits bistability is a hard and open…

A crisp survey is given of chemical reaction networks from the perspective of general nonlinear network dynamics, in particular of consensus dynamics. It is shown how by starting from the complex-balanced assumption the reaction dynamics…

The control of complex networks is of paramount importance in areas as diverse as ecosystem management, emergency response, and cell reprogramming. A fundamental property of networks is that perturbations to one node can affect other nodes,…

We study a family of networks of autocatalytic reactions, which we call hyperchains, that are a generalization of hypercycles. Hyperchains, and the associated dynamical system called replicator equations, are a possible mechanism for…

The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…

We investigate certain structural properties of random interdependent networks. We start by studying a property known as $r$-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and…

Random Threshold Networks (RTNs) are an idealized model of diluted, non symmetric spin glasses, neural networks or gene regulatory networks. RTNs also serve as an interesting general example of any coordinated causal system. Here we study…