Related papers: Measurement incompatibility cannot be stochastical…
We study a system of stochastically forced infinite-dimensional coupled harmonic oscillators. Although this system formally conserves energy and is not explicitly dissipative, we show that it has a nontrivial invariant probability measure.…
Particle filters are a powerful and flexible tool for performing inference on state-space models. They involve a collection of samples evolving over time through a combination of sampling and re-sampling steps. The re-sampling step is…
We consider two nonlinear state estimation problems in a setting where an extended Kalman filter receives measurements from two sets of sensors via two channels (2C). In the stochastic-2C problem, the channels drop measurements…
In a seminal paper [8] it was shown that Heisenberg-limited measurements could be achieved without using entangled states by coupling the quantum resources to a common environment that could be measured, at least, in part. The authors also…
In this paper, we present an optimal filter for linear time-varying continuous-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense. We first show that the unknown inputs…
The fidelity between the state of a continuously observed quantum system and the state of its associated quantum filter, is shown to be always a submartingale. The observed system is assumed to be governed by a continuous-time Stochastic…
In this paper we first introduce the setting of filtering on Stiefel manifolds. Then, assuming the underlying system process is constant, the convergence of the extended Kalman filter with Stiefel manifold-valued observations is proved.…
We introduce the concept of assemblage moment matrices, i.e., a collection of matrices of expectation values, each associated with a conditional quantum state obtained in a steering experiment. We demonstrate how it can be used for quantum…
We study the kinetic Fokker-Planck equation perturbed by a stochastic Vlasov force term. When the noise intensity is not too large, we solve the Cauchy Problem in a class of well-localized (in velocity) functions. We also show that, when…
Aggregating preferences under incomplete or constrained feedback is a fundamental problem in social choice and related domains. While prior work has established strong impossibility results for pairwise comparisons, this paper extends the…
Incompatibility of certain measurements -- impossibility of obtaining deterministic outcomes simultaneously -- is a well known property of quantum mechanics. This feature can be utilized in many contexts, ranging from Bell inequalities to…
Instead of testing solely a precise hypothesis, it is often useful to enlarge it with alternatives that are deemed to differ from it negligibly. For instance, in a bioequivalence study one might consider the hypothesis that the…
Conformance is defined as a measure of distance between the behaviors of two dynamical systems. The notion of conformance can accelerate system design when models of varying fidelities are available on which analysis and control design can…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
Despite being a foundational concept of modern systems theory, there have been few studies on observability of non-linear stochastic systems under partial observations. In this paper, we introduce a definition of observability for…
In randomized experiments with noncompliance, tests may focus on compliers rather than on the overall sample. Rubin (1998) put forth such a method, and argued that testing for the complier average causal effect and averaging permutation…
This paper proves that, under a monotonicity condition, the invariant probability measure of a McKean--Vlasov process can be approximated by weighted empirical measures of some processes including itself. These processes are described by…
We introduce local filters as a means to detect the entanglement of bound entangled states which do not yield to detection by witnesses based on positive (P) maps which are not completely positive (CP). We demonstrate how such…
We analyze the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of dynamics governed by the two-dimension…
In sequential anytime-valid inference, any admissible procedure must be based on e-processes: generalizations of test martingales that quantify the accumulated evidence against a composite null hypothesis at any stopping time. This paper…