Related papers: Stochastic and deterministic dynamics in networks …
The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network…
A one dimensional stochastic exclusion process with two species of particles, $+$ and $-$, is studied where density of each species can fluctuate but the total particle density is conserved. From the exact stationary state weights we show…
We present a theory for the two kinds of dynamical quantum phase transitions, termed DPT-I and DPT-II, based on a minimal set of symmetry assumptions. In the special case of collective systems with infinite-range interactions, both are…
One of the main challenges in the study of time-varying networks is the interplay of memory effects with structural heterogeneity. In particular, different nodes and dyads can have very different statistical properties in terms of both link…
We consider a discrete-time voter model process on a set of nodes, each being in one of two states, either 0 or 1. In each time step, each node adopts the state of a randomly sampled neighbor according to sampling probabilities, referred to…
In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to…
Dynamic models of signaling networks allow the formulation of hypotheses on the topology and kinetic rate laws characterizing a given molecular network, in-depth exploration and confrontation with kinetic biological data. Despite its…
We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…
In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…
Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
This work proposes to model the space environment as a stochastic dynamic network where each node is a group of objects of a given class, or species, and their relationship is represented by stochastic links. A set of stochastic dynamic…
Conventional studies of network growth models mainly look at the steady state degree distribution of the graph. Often long time behavior is considered, hence the initial condition is ignored. In this contribution, the time evolution of the…
Much recent research has dealt with the identifiability of a dynamical network in which the node signals are connected by causal linear time-invariant transfer functions and are possibly excited by known external excitation signals and/or…
Spreading on networks is influenced by a number of factors including different parts of the inter-event time distribution (IETD), the topology of the network and non-stationarity. In order to understand the role of these factors we study…
In this paper, we study estimation of potentially unstable linear dynamical systems when the observations are distributed over a network. We are interested in scenarios when the information exchange among the agents is restricted. In…
First-passage times are often the most relevant aspect of a complex Markovian network, because they signify when information processing has resulted in a definite decision. Previous studies have shown that for kinetic proofreading networks…
We study the dynamics of a tree-level $\Lambda$-type atoms driven by a coherent train of short, non-overlapping laser pulses.We derive analytical non-perturbative expressions for density matrix by approximating pulses by delta-function.We…
Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it.…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…