Related papers: Dimension reduction of noisy interacting systems
We consider change-point estimation in a sequence of high-dimensional signals given noisy observations. Classical approaches to this problem such as the filtered derivative method are useful for sequences of scalar-valued signals, but they…
We present a measurement noise reduction scheme based on information flow of a chaotic system. This scheme operates on conditions of chaoticity and well-defined noise level, not depending on other detailed characteristics of noise. Starting…
Multivariate signal processing is often based on dimensionality reduction techniques. We propose a new method, Dynamical Component Analysis (DyCA), leading to a classification of the underlying dynamics and - for a certain type of dynamics…
The paper studies identification of linear systems with multiplicative noise from multiple-trajectory data. An algorithm based on the least-squares method and multiple-trajectory data is proposed for joint estimation of the nominal system…
Intracellular protein patterns regulate many vital cellular functions, such as the processing of spatiotemporal information or the control of shape deformations. To do so, pattern-forming systems can be sensitive to the cell geometry by…
We present a data-driven nonintrusive model order reduction method for dynamical systems with moving boundaries. The proposed method draws on the proper orthogonal decomposition, Gaussian process regression, and moving least squares…
In the thermodynamic limit, the time evolution of isolated long-range interacting systems is properly described by the Vlasov equation. This equation admits non-equilibrium dynamically stable stationary solutions characterized by a zero…
We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to…
The phenomenon of Stochastic Resonance (SR) is reported in a completely noise-free situation, with the role of thermal noise being taken by low-dimensional chaos. A one-dimensional, piecewise linear map and a pair of coupled…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
Dynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of \red{identifying a dynamic network with known topology, on the basis of…
By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order…
The evolution of high-dimensional phenotypes is investigated using a statistical physics model consists of interacting spins, in which genotypes, phenotypes, and environments are represented by spin configurations, interaction matrices, and…
Low-order thermoacoustic models are qualitatively correct, but they are typically quantitatively inaccurate. We propose a time-domain bias-aware method to make qualitatively low--order models quantitatively (more) accurate. First, we…
Given a set of response observations for a parametrized dynamical system, we seek a parametrized dynamical model that will yield uniformly small response error over a range of parameter values yet has low order. Frequently, access to…
We use particle dynamics simulations to probe the correlations between noise and dynamics in a variety of disordered systems, including superconducting vortices, 2D electron liquid crystals, colloids, domain walls, and granular media. The…
Dimension reduction lies at the heart of many statistical methods. In regression, dimension reduction has been linked to the notion of sufficiency whereby the relation of the response to a set of predictors is explained by a lower…
In this paper, we focus on learning a linear time-invariant (LTI) model with low-dimensional latent variables but high-dimensional observations. We provide an algorithm that recovers the high-dimensional features, i.e. column space of the…
Large scale neural recordings have established that the transformation of sensory stimuli into motor outputs relies on low-dimensional dynamics at the population level, while individual neurons exhibit complex selectivity. Understanding how…
In this Letter, we consider a model of dynamical agents coupled through a random connectivity matrix, as introduced in [Sompolinsky et. al, 1988] in the context of random neural networks. It is known that increasing the disorder parameter…