Related papers: Coarse-Graining of Observables
Computer science theory provides many different measures of complexity of a system including Kolmogorov complexity, logical depth, computational depth, and Levin complexity. However, these measures are all defined only for deterministic…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
Every measurement determines a single value as its outcome, and yet quantum mechanics predicts it only probabilistically. The Kochen-Specker theorem and Bell's inequality are often considered to reject a realist view but favor a skeptical…
Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using…
With increasing use of digital control it is natural to view control inputs and outputs as stochastic processes assuming values over finite alphabets rather than in a Euclidean space. As control over networks becomes increasingly common,…
We show that a rank-1 quantum observable (POVM) M is jointly measurable with a quantum observable M' exactly when M' is a smearing of M. If M is extreme, rank-1 and discrete then M and M' are coexistent if and only if they are jointly…
We investigate four partial orderings on the space of quantum measurements (i.e on POVMs or positive operator valued measures), describing four notions of coarse/fine-ness of measurement. These are the partial orderings induced by: (1)…
Complex high-dimensional co-occurrence data are increasingly popular from a complex system of interacting physical, biological and social processes in discretely indexed modifiable areal units or continuously indexed locations of a study…
The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…
This article considers quantum systems described by a finite-dimensional complex Hilbert space $H$. We first define the concept of a finite observable on $H$. We then discuss ways of combining observables in terms of convex combinations,…
We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…
A coarse-grained simulation model eliminates microscopic degrees of freedom and represents a polymer by a simplified structure. A priori, two classes of coarse-grained models may be distinguished: those which are designed for a specific…
The goal of this paper is to understand the conditional law of a stochastic process once it has been observed over an interval. To make this precise, we introduce the notion of a continuous disintegration: a regular conditional probability…
In probabilistic modelling, joint distributions are often of more interest than their marginals, but the standard composition of stochastic channels is defined by marginalization. Last year at ACT, the notion of 'copy-composition' was…
While quantum metrology enables measurement precision beyond classical limits, its performance is often susceptible to experimental imperfections. Most prior studies have focused on imperfections in quantum states and operations. Here, we…
We discuss and experimentally demonstrate the role of quantum coherence in a sequence of two measurements collected at different times using weak measurements. For this purpose, we have realized a weak-sequential measurement protocol with…
Our basic concept is the set $\mathcal{E}(H)$ of effects on a finite dimensional complex Hilbert space $H$. If $a,b\in\mathcal{E}(H)$, we define the sequential product $a[\mathcal{I}]b$ of $a$ then $b$. The sequential product depends on the…
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
We present a new approach to study measures on ensembles of contours, polymers or other objects interacting by some sort of exclusion condition. For concreteness we develop it here for the case of Peierls contours. Unlike existing methods,…