Related papers: Correlation Angles and Inner Products: Application…
Measuring the correlation (association) between two random variables is one of the important goals in statistical applications. In the literature, the covariance between two random variables is a widely used criterion in measuring the…
In this manuscript we consider random objects being measured in multiple metric spaces, which may arise when those objects may be measured in multiple distinct ways. In this new multivariate setting, we define a Fr\'echet covariance and…
We examine the problem of covariance belief revision using a geometric approach. We exhibit an inner-product space where covariance matrices live naturally --- a space of random real symmetric matrices. The inner-product on this space…
We quantify the stationary correlations between the optical mode and the relative mechanical mode of a ring cavity composed of a fixed mirror and two movable ones in a triangular design. The bipartite covariance matrix, is used to evaluate…
We analyze correlation functions in a toy model of a random geometry interacting with matter. We show that in general the connected correlator will contain a long-range scaling part which is in some sense a remnant of the disconnected part.…
We present the results of a detailed study of energy correlations at steady state for a 1-D model of coupled energy and matter transport. Our aim is to discover -- via theoretical arguments, conjectures, and numerical simulations -- how…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…
Based on standardized vector and globally normalized weight matrix, Moran's index of spatial autocorrelation analysis has been expressed as a formula of quadratic form. Further, based on this formula, an inner product equation and outer…
In quantum theory, a measurement context is defined by an orthogonal basis in a Hilbert space, where each basis vector represents a specific measurement outcome. The precise quantitative relation between two different measurement contexts…
Data re-sampling methods such as the delete-one jackknife are a common tool for estimating the covariance of large scale structure probes. In this paper we investigate the concepts of internal covariance estimation in the context of cosmic…
The ability to measure characteristics of source shapes using non-identical particle correlations is discussed. Both strong-interaction induced and Coulomb induced correlations are shown to provide sensitivity to source shapes. By…
Spatial autocorrelation measures such as Moran's index can be expressed as a pair of equations based on a standardized size variable and a globally normalized weight matrix. One is based on inner product, and the other is based on outer…
When spatial correlations are short-range, the physics of strongly correlated systems is controlled by local quantum fluctuations. In those regimes, Dynamical Mean-Field Theory can be viewed as a `compass' which provides guidance on the…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…
Total correlation (`TC') and dual total correlation (`DTC') are two classical ways to quantify the correlation among an $n$-tuple of random variables. They both reduce to mutual information when $n=2$. The first part of this paper sets up…
The peculiar uncertainty or randomness of quantum measurements stems from coherence, whose information-theoretic characterization is currently under investigation. Under the resource theory of coherence, it is interesting to investigate…
After the recent ground-breaking advances in protein structure prediction, one of the remaining challenges in protein machine learning is to reliably predict distributions of structural states. Parametric models of fluctuations are…
Cosine similarity is a popular distance measure that measures the similarity between two vectors in the inner product space. It is widely used in many data classification algorithms like K-Nearest Neighbors, Clustering etc. This study…
We derive in this paper expressions for the covariance matrix of the cosmic shear two-point correlation functions which are readily applied to any survey geometry. Furthermore, we consider the more special case of a simple survey geometry…