Related papers: Statistical Consistency of Set-Membership Estimato…
This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the…
Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…
Bose-condensed systems with broken global gauge symmetry are considered. The description of these systems, as has been shown by Hohenberg and Martin, possesses an internal inconsistency, resulting in either nonconserving theories or…
We discuss the problem how to determine the quality of a nonlinear system with respect to a measurement task. Due to amplification, filtering, quantization and internal noise sources physical measurement equipment in general exhibits a…
The paper introduces robust independence tests with non-asymptotically guaranteed significance levels for stochastic linear time-invariant systems, assuming that the observed outputs are synchronous, which means that the systems are driven…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. However, the theoretical aspects, e.g., identifiability and asymptotic properties of statistical estimation are still obscure. This paper…
Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent, but numerically…
We discuss a model of repeated measurements of position in a quantum system which is monitored for a finite amount of time with a finite instrumental error. In this framework we recover the optimum monitoring of a harmonic oscillator…
Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
This paper focuses on the stabilization and regulation of linear systems affected by quantization in state-transition data and actuated input. The observed data are composed of tuples of current state, input, and the next state's interval…
We introduce a stability criterion for quantum statistical ensembles describing macroscopic systems. An ensemble is called "stable" when a small number of local measurements cannot significantly modify the probability distribution of the…
Symmetry breaking--the phenomenon in which the symmetry of a system is not inherited by its stable states--underlies pattern formation, superconductivity, and numerous other effects. Recent theoretical work has established the possibility…
Recent work has shown that models trained to the same objective, and which achieve similar measures of accuracy on consistent test data, may nonetheless behave very differently on individual predictions. This inconsistency is undesirable in…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…
The state estimation of continuous-time nonlinear systems in which a subset of sensor outputs can be maliciously controlled through injecting a potentially unbounded additive signal is considered in this paper. Analogous to our earlier work…
In this paper, we investigate the verification of dissipativity properties for polynomial systems without an explicitly identified model but directly from noise-corrupted measurements. Contrary to most data-driven approaches for nonlinear…
In answer set programming, inconsistencies arise when the constraints placed on a program become unsatisfiable. In this paper, we introduce a technique for dynamic consistency checking for our goal-directed method for computing answer sets,…
Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs,…