相关论文: Support and Quantile Tubes

A new finite form of de Finetti's representation theorem is established using elementary information-theoretic tools. The distribution of the first $k$ random variables in an exchangeable vector of $n\geq k$ random variables is close to a…

This paper reviews some recent applications of the theory of the compensated convex transforms or of the proximity hull as developed by the authors to image processing and shape interrogation with special attention given to the Hausdorff…

Shannon's mathematical theory of communication defines fundamental limits on how much information can be transmitted between the different components of any man-made or biological system. This paper is an informal but rigorous introduction…

Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…

It is argued that there is a sensible way to define conditional probabilities in quantum mechanics, assuming only Bayes's theorem and standard quantum theory. These probabilities are equivalent to the ``weak measurement'' predictions due to…

The diffusion of particles in confining walls forming a tube is discussed. Such a transport phenomenon is observed in biological cells and porous media. We consider the case in which the tube is winding with curvature and torsion, and the…

Quantum information is about the entanglement of states. To this starting point we add parameters whereby a single state becomes a non-vanishing section of a bundle. We consider through examples the possible entanglement patterns of…

We discuss the construction of relational observables in time-reparametrization invariant quantum mechanics and we argue that their physical interpretation can be understood in terms of conditional probabilities, which are defined from the…

Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…

We explore some properties of the conditional distribution of an i.i.d. sample under large exceedances of its sum. Thresholds for the asymptotic independance of the summands are observed, in contrast with the classical case when the…

The entanglement-assisted classical capacity of a quantum channel is known to provide the formal quantum generalization of Shannon's classical channel capacity theorem, in the sense that it admits a single-letter characterization in terms…

In this paper, we prove the canonical bundle formula for Fano type fibrations and Shokurov's conjecture on boundedness of complements for Fano type threefold pairs $(X,B)$ with fibration structures in large characteristics. In particular,…

This paper develops estimation and inference methods for conditional quantile factor models. We first introduce a simple sieve estimation, and establish asymptotic properties of the estimators under large $N$. We then provide a bootstrap…

We propose a new measure of quantum entanglement. Our measure is defined in terms of conditional information transmission for a Quantum Bayesian Net. We show that our measure is identically equal to the Entanglement of Formation in the case…

The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…

Instrumental variables have proven useful, in particular within the social sciences and economics, for making inference about the causal effect of a random variable, B, on another random variable, C, in the presence of unobserved…

Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable…

Some bounds on the entropic informational quantities related to a quantum continual measurement are obtained and the time dependencies of these quantities are studied.

In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.

We revisit the quantum reverse Shannon theorem, a central result in quantum information theory that characterizes the resources needed to simulate quantum channels when entanglement is freely available. We derive a universal additive upper…