Related papers: Dynamic and static limitation in multiscale reacti…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
We present a selective review of statistical modeling of dynamic networks. We focus on models with latent variables, specifically, the latent space models and the latent class models (or stochastic blockmodels), which investigate both the…
Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations to component species' abundances without suffering adverse…
We describe the dynamics of a simple adaptive network. The network architecture evolves to a number of disconnected components on which the dynamics is characterized by the possibility of differently synchronized nodes within the same…
Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…
Networks of excitable nodes have recently attracted much attention particularly in regards to neuronal dynamics, where criticality has been argued to be a fundamental property. Refractory behavior, which limits the excitability of neurons…
We investigate the collective dynamics of excitatory-inhibitory excitable networks in response to external stimuli. How to enhance dynamic range, which represents the ability of networks to encode external stimuli, is crucial to many…
We introduce a simple model of static networks, where nodes are located on a ring structure, and two accompanying dynamic rules of repeated averaging on periodic node states. We assume nodes can interact with neighbors, and will add…
Self-stabilization is a versatile technique to withstand any transient fault in a distributed system. Mobile robots (or agents) are one of the emerging trends in distributed computing as they mimic autonomous biologic entities. The…
In this paper, we address the problem of dynamic network embedding, that is, representing the nodes of a dynamic network as evolving vectors within a low-dimensional space. While the field of static network embedding is wide and…
Complex systems are ubiquitous in nature and engineering, but their analysis and control are hampered by their high dimensionality and the influence of various factors on their dynamics. Dimensionality reduction aims to find a…
A recent article by Weidner et al. [2021] presents a method to extract graph properties that are predictive of the dynamical behavior of multivariate, discrete models of biochemical regulation. In other words, a method that uses only…
We examine the dynamical properties of a single-layer convolutional recurrent network with a smooth sigmoidal activation function, for small values of the inputs and when the convolution kernel is unitary, so all eigenvalues lie exactly at…
Recurrent neural network architectures can have useful computational properties, with complex temporal dynamics and input-sensitive attractor states. However, evaluation of recurrent dynamic architectures requires solution of systems of…
The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the…
The evolution of particulate and multiphase systems can transition from dynamic regimes, governed by classical transport equations with well-defined damping coefficients, to anomalously slow relaxation described by rate equations when the…
For spiking neural networks we consider the stability problem of global synchrony, arguably the simplest non-trivial collective dynamics in such networks. We find that even this simplest dynamical problem -- local stability of synchrony --…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
Dynamic logit models are popular tools in economics to measure state dependence. This paper introduces a new method to derive moment restrictions in a large class of such models with strictly exogenous regressors and fixed effects. We…
Habituation - a phenomenon in which a dynamical system exhibits a diminishing response to repeated stimulations that eventually recovers when the stimulus is withheld - is universally observed in living systems from animals to unicellular…