Related papers: A note on correlation and local dimensions
The Local Moran's I statistic is a valuable tool for identifying localized patterns of spatial autocorrelation. Understanding these patterns is crucial in spatial analysis, but interpreting the statistic can be difficult. To simplify this…
Pearson's correlation is an important summary measure of the amount of dependence between two variables. It is natural to want to generalise the concept of correlation as a single number that measures the inter-relatedness of three or more…
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…
This article is devoted to sets having the Moran structure. The main attention is given to topological, metric, and fractal properties of certain sets whose elements have restrictions on using digits or combinations of digits in own…
We construct finite sets of real numbers that have a small difference set and strong local properties. In particular, we construct a set $A$ of $n$ real numbers such that $|A-A|=n^{\log_2 3}$ and that every subset $A'\subseteq A$ of size…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
The area-perimeter scaling can be employed to evaluate the fractal dimension of urban boundaries. However, the formula in common use seems to be not correct. By means of mathematical method, a new formula of calculating the boundary…
Covariance is used as an inner product on a formal vector space built on n random variables to define measures of correlation Md across a set of vectors in a d-dimensional space. For d = 1, one has the diameter; for d = 2, one has an area.…
The structure of a local hidden variable model for experiments involving sequences of measurements rigorously is analyzed. Constraints imposed by local realism on the conditional probabilities of the outcomes of such measurement schemes are…
While entanglement plays an important role in characterizing quantum many-body systems, it is hardly possible to directly access many-body entanglement in real experiments. In this paper, we study how bipartite entanglement of many-body…
In analogy with the lower Assouad dimensions of a set, we study the lower Assouad dimensions of a measure. As with the upper Assouad dimensions, the lower Assouad dimensions of a measure provide information about the extreme local behaviour…
We introduce a local multifractal formalism adapted to functions, measures or distributions which display multifractal characteristics that can change with time, or location. We develop this formalism in a general framework and we work out…
We present a method to estimate entanglement measures in experiments. We show how a lower bound on a generic entanglement measure can be derived from the measured expectation values of any finite collection of entanglement witnesses. Hence…
City is proved to be a scale-free phenomenon, and spatial autocorrelation is often employed to analyze spatial redundancy of cities. Unfortunately, spatial analysis results deviated practical requirement in many cases due to fractal nature…
If nonlocality is to be inferred from a violation of Bell's inequality, an important assumption is that the measurement settings are freely chosen by the observers, or alternatively, that they are random and uncorrelated with the…
We use certain Morse functions to construct conformal metrics with negative sectional curvature on locally conformally flat manifolds with boundary. Moreover, without conformally flatness assumption, we also construct conformal metric of…
We study conformal properties of local terms such as contact terms and semi-local terms in correlation functions of a conformal field theory. Not all of them are universal observables but they do appear in physically important correlation…
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 this paper certain $n$-dimensional inequalities are shown to be equivalent to the inequalities in the one-dimensional setting. By this means, embeddings between weighted local Morrey-type spaces are characterized for some ranges of…
As a rule statistical measures are often vulnerable to the presence of outliers and spatial correlation coefficients, critical in the assessment of spatial data, remain susceptible to this inherent flaw. In contexts where data originates…