Related papers: Stability of the Kauffman Model
We analyze the stability of the network's giant connected component under impact of adverse events, which we model through the link percolation. Specifically, we quantify the extent to which the largest connected component of a network…
Recent work has connected the type of fidelity decay in perturbed quantum models to the presence of chaos in the associated classical models. We demonstrate that a system's rate of fidelity decay under repeated perturbations may be measured…
Stabilizing large networks of nonlinear agents is challenging; decomposition and distributed analysis of these networks are crucial for computational tractability and information security. Vidyasagar's Network Dissipativity Theorem enables…
Neural mass models are ubiquitous in large scale brain modelling. At the node level they are written in terms of a set of ODEs with a nonlinearity that is typically a sigmoidal shape. Using structural data from brain atlases they may be…
Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…
Deterministic and stochastic Boolean network models are build for the dynamics of negative feedback loops of the p53 pathways. It is shown that the main function of the negative feedback in the p53 pathways is to keep p53 at a low steady…
Boolean networks have been successfully used in modelling gene regulatory networks. In this paper we propose a reduction method that reduces the complexity of a Boolean network but keeps dynamical properties and topological features and…
This paper introduces new model parameterizations for learning discrete-time dynamical systems from data via the Koopman operator and studies their properties. Whereas most existing works on Koopman learning do not take into account the…
One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb{R}^d$ and a random…
During neural network training, the sharpness of the Hessian matrix of the training loss rises until training is on the edge of stability. As a result, even nonstochastic gradient descent does not accurately model the underlying dynamical…
The relationship between the properties of a dynamical system and the structure of its defining equations has long been studied in many contexts. Here we study this problem for the class of conjunctive (resp. disjunctive) Boolean networks,…
We derive a simple and general relation between the fidelity of quantum motion, characterizing the stability of quantum dynamics with respect to arbitrary static perturbation of the unitary evolution propagator, and the integrated time…
In this paper, a distributed Kalman filtering (DKF) algorithm is proposed based on a diffusion strategy, which is used to track an unknown signal process in sensor networks cooperatively. Unlike the centralized algorithms, no fusion center…
The paper studies an implementation methodology for partial and disjunctive stable models where partiality and disjunctions are unfolded from a logic program so that an implementation of stable models for normal (disjunction-free) programs…
We study the stability of orbits in large Boolean networks with given complex topology. We impose no restrictions on the form of the update rules, which may be correlated with local topological properties of the network. While recent past…
We propose a noise-robust learning framework for the Koopman operator of nonlinear dynamical systems, with guaranteed long-term stability and improved model performance for better model-based predictive control tasks. Unlike some existing…
Although overparameterized models have achieved remarkable practical success, their theoretical properties, particularly their generalization behavior, remain incompletely understood. The well known double descents phenomenon suggests that…
This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…
To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…