Related papers: Dynamical systems analysis of stack filters
This paper describes recursive algorithms for state estimation of linear dynamical systems when measurements are noisy with unknown bias and/or outliers. For situations with noisy and biased measurements, algorithms are proposed that…
Biological systems rely on robust internal information processing: Survival depends on highly reproducible dynamics of regulatory processes. Biological information processing elements, however, are intrinsically noisy (genetic switches,…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
Estimating the state of a dynamical system from a series of noise-corrupted observations is fundamental in many areas of science and engineering. The most well-known method, the Kalman smoother (and the related Kalman filter), relies on…
We examine stochastic dynamical systems where the transition matrix, $\Phi$, and the system noise, $\bf{\Gamma}\bf{Q}\bf{\Gamma}^T$, covariance are nearly block diagonal. When $\bf{H}^T \bf{R}^{-1} \bf{H}$ is also nearly block diagonal,…
A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…
This paper studies the distributed state estimation problem for a class of discrete-time stochastic systems with nonlinear uncertain dynamics over time-varying topologies of sensor networks. An extended state vector consisting of the…
In recent years, the discovery of complex dynamic systems in various fields through data-driven methods has attracted widespread attention. This method has played the role of data and has become an advantageous tool for us to study complex…
In most practical adaptive signal processing systems, e.g., active noise control, active vibration control, and acoustic echo cancellation, substantial nonlinearities that cannot be neglected exist. In this paper, we analyze the behaviors…
We develop a model in which interactions between nodes of a dynamic network are counted by non homogeneous Poisson processes. In a block modelling perspective, nodes belong to hidden clusters (whose number is unknown) and the intensity…
Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. The dynamic behavior of these networks depends on how these nodes are connected, which can…
Diverse biological networks exhibit universal features distinguished from those of random networks, calling much attention to their origins and implications. Here we propose a minimal evolution model of Boolean regulatory networks, which…
While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…
Conserved dynamical systems are generally considered to be critical. We study a class of critical routing models, equivalent to random maps, which can be solved rigorously in the thermodynamic limit. The information flow is conserved for…
In this work, we study dynamic programming (DP) algorithms for partially observable Markov decision processes with jointly continuous and discrete state-spaces. We consider a class of stochastic systems which have coupled discrete and…
This paper considers the problem of detecting topology variations in dynamical networks. We consider a network whose behavior can be represented via a linear dynamical system. The problem of interest is then that of finding conditions under…
Network filtering is an important form of dimension reduction to isolate the core constituents of large and interconnected complex systems. We introduce a new technique to filter large dimensional networks arising out of dynamical behavior…