Related papers: A note on correlation and local dimensions
It is surprising that last two decades many works in time series data mining and clustering were concerned with measures of similarity of time series but not with measures of association that can be used for measuring possible direct and…
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric…
We give a sufficiently detailed account on the construction of marked Gibbs measures in the high temperature and low fugacity regime. This is proved for a wide class of underlying spaces and potentials such that stability and integrability…
Study of time series data often involves measuring the strength of temporal dependence, on which statistical properties like consistency and central limit theorem are built. Historically, various dependence measures have been proposed. In…
We present observable lower bounds for several bipartite entanglement measures including entanglement of formation, geometric measure of entanglement, concurrence, convex-roof extended negativity, and G-concurrence. The lower bounds…
We establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of…
An ensemble consisting on systems of two entangled spin 1/2 particles, all of them in the same global quantum state, are considered. The two spins are measured, each of them, on a fixed direction, at two randomly selected measurement times.…
Quantum metrology is studied in the presence of quantum correlation. The quantum correlation measure based on quantum Fisher information enables us to gain a deeper insight on how quantum correlations are instrumental in setting…
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…
This paper concerns the development of partial and semi-partial measures of spatial associations in the context of multivariate spatial lattice data which describe global or local associations among spatially aggregated measurements for…
The geometry of Arithmetic Random Waves has been extensively investigated in the last fifteen years, starting from the seminal papers [RW08, ORW08]. In this paper we study the correlation structure among different functionals such as nodal…
Intuitively, there is a relation between measures of spatial dependence and information theoretical measures of entropy. For instance, we can provide an intuition of why spatial data is special by stating that, on average, spatial data…
We show that any equicontractive, self-similar measure arising from the IFS of contractions $(S_{j})$, with self-similar set $[0,1]$, admits an isolated point in its set of local dimensions provided the images of $S_{j}(0,1)$ (suitably)…
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…
We introduce a concept of porosity for measures and study relations between dimensions and porosities for two classes of measures: measures on $R^n$ which satisfy the doubling condition and strongly porous measures on $R$.
Measuring comodules are defined and shown to provide a useful generalization of the set of maps between modules with a broad range of applications. Three applications are described. Connections on bundles are described in terms of measuring…
Comparing spatial data sets is a ubiquitous task in data analysis, however the presence of spatial autocorrelation means that standard estimates of variance will be wrong and tend to over-estimate the statistical significance of…
The information-theoretic definition of quantum correlation, e.g., quantum discord, is measurement dependent. By considering the more general quantum measurements, weak measurements, which include the projective measurement as a limiting…
Quantum correlations often defy an explanation in terms of fundamental notions of classical physics, such as causality, locality, and realism. While the mathematical theory underpinning quantum correlations between spacelike separated…
Electron correlation effects are essential for an accurate ab initio description of molecules. A quantitative a priori knowledge of the single- or multi-reference nature of electronic structures as well as of the dominant contributions to…