相关论文: The cosine measure relative to a subspace

Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical…

We introduce a procedure based on quantum expectation values of measurement observables to characterize quantum coherence. Our measure allows one to quantify coherence without having to perform tomography of the quantum state, and can be…

In this paper, we introduce for the first time the notions of neutrosophic measure and neutrosophic integral, and we develop the 1995 notion of neutrosophic probability. We present many practical examples. It is possible to define the…

Uniform measures are defined as the functionals on the space of bounded uniformly continuous functions that are continuous on bounded uniformly equicontinuous sets. If every cardinal has measure zero then every countably additive measure is…

Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. This is applied by Du (2010) [A note on cone…

This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…

Cosine similarity is an established similarity metric for computing associations on vectors, and it is commonly used to identify related samples from biological perturbational data. The distribution of cosine similarity changes with the…

Bound-to-Bound Data Collaboration (B2BDC) provides a natural framework for addressing both forward and inverse uncertainty quantification problems. In this approach, QOI (quantity of interest) models are constrained by related experimental…

We introduce the notion of coarse metric. Every coarse metric induces a coarse structure on the underlying set. Conversely, we observe that all coarse spaces come from a particular type of coarse metric in a unique way. In the case when the…

A causal set is a countably infinite poset in which every element is above finitely many others; causal sets are exactly the posets that have a linear extension with the order-type of the natural numbers -- we call such a linear extension a…

We investigate a measure of quantum coherence and its extension to quantify quantum macroscopicity. The coherence measure can also quantify the asymmetry of a quantum state with respect to a given group transformation. We then show that a…

Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…

The measurement process in quantum mechanics is usually described by the von Neumann projection postulate, which forms a basic constituent of the laws of quantum mechanics. Since this postulate requires the outside observer of the system,…

The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the…

This paper concerns the convergence of empirical measures in high dimensions. We propose a new class of probability metrics and show that under such metrics, the convergence is free of the curse of dimensionality (CoD). Such a feature is…

If a compact set K \subset R^2 contains a positive-dimensional family of line-segments in positively many directions, then K has positive measure.

We consider the question of characterising the incompatibility of sets of high-dimensional quantum measurements. We introduce the concept of measurement incompatibility in subspaces. That is, starting from a set of measurements that is…

The set of indices that correspond to the positive entries of a sequence of numbers is called its positivity set. In this paper, we study the density of the positivity set of a given linear recurrence sequence, that is the question of how…

In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define…

Motivated by Leinster-Cobbold measures of biodiversity, the notion of the spread of a finite metric space is introduced. This is related to Leinster's magnitude of a metric space. Spread is generalized to infinite metric spaces equipped…