Related papers: On the validity of linear response theory in high-…

Reliable prediction of large chaotic sytems in the short to middle time range is of interest in a number of fields, including climate, ecology, seismology, and economics. In this paper, results from chaos theory, and statistical theory are…

High-dimensional systems that have a low-dimensional dominant behavior allow for model reduction and simplified analysis. We use differential analysis to formalize this important concept in a nonlinear setting. We show that dominance can be…

Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…

The Multiscale Law of Requisite Variety is a scientific law relating, at each scale, the variation in an environment to the variation in internal state that is necessary for effective response by a system. While this law has been used to…

Linear dynamical systems are the foundational statistical model upon which control theory is built. Both the celebrated Kalman filter and the linear quadratic regulator require knowledge of the system dynamics to provide analytic…

In this work, the problem of designing observers for estimating a single nonlinear functional of the state is formulated for general nonlinear systems. Notions of functional observer linearization are also formulated, in terms achieving…

We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…

This paper shows how the theory of nonlinear adaptive observers can be effectively used in the design of internal models for nonlinear output regulation. The theory substantially enhances the existing results in the context of {\em…

We consider an extension of linear-time temporal logic (LTL) with both local and remote data constraints interpreted over a concrete domain. This extension is a natural extension of constraint LTL and the Temporal Logic of Repeating Values,…

The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates. The assumption that the response variables are…

This paper presents a computationally efficient robust model predictive control law for discrete linear time invariant systems subject to additive disturbances that may depend on the state and/or input norms. Despite the dependency being…

Open effective field theories provide a systematic framework for describing physical systems interacting with an environment whose microscopic details are unknown, unobservable, or uncalculable. A basic step in constructing any effective…

Feedback is a most important concept in control systems, its main purpose is to deal with internal and/or external uncertainties in dynamical systems, by using the on-line observed information. Thus, a fundamental problem in control theory…

A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…

We consider the dynamic linear regression problem, where the predictor vector may vary with time. This problem can be modeled as a linear dynamical system, with non-constant observation operator, where the parameters that need to be learned…

Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…

Data-driven control offers a powerful alternative to traditional model-based methods, particularly when accurate system models are unavailable or prohibitively complex. While existing data-driven control methods primarily aim to construct…

In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type…

A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…

This paper concerns the development of an inferential framework for high-dimensional linear mixed effect models. These are suitable models, for instance, when we have $n$ repeated measurements for $M$ subjects. We consider a scenario where…