Related papers: A note on correlation and local dimensions

We survey recent results in hermitian integral geometry, i.e. integral geometry on complex vector spaces and complex space forms. We study valuations and curvature measures on complex space forms and describe how the global and local…

We present a linear program that is capable of determining whether a set of correlations can be captured by a local realistic model. If the correlations can be described by such a model, the linear program outputs a joint probability…

The precision with which we can measure operators that do not commute with conserved quantities is limited by the need to preserve the associated global symmetries. We show how to construct a local hidden-variable model that violates Bell…

We define a general framework that includes objects such as tilings, Delone sets, functions and measures. We define local derivability and mutual local derivability (MLD) between any two of these objects in order to describe their…

We propose a method for constructing confidence intervals that account for many forms of spatial correlation. The interval has the familiar `estimator plus and minus a standard error times a critical value' form, but we propose new methods…

Correlation testing provides a quick method of discriminating amongst potential terms to include in a nuclear mass formula or functional and is a necessary tool for further nuclear mass models; however a firm mathematical foundation of the…

The correlation function of two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor representation are…

Quantum systems generally exhibit different kinds of correlations. In order to compare them on equal footing, one uses the so-called distance-based approach where different types of correlations are captured by the distance to different…

Logistic growth process with nonlocal interactions is considered in one dimension. Spontaneous breakdown of translational invariance is shown to take place at some parameter region, and the bifurcation regime is identified for short and…

Local data structures are systems of neighbourhoods within data sets. Specifications of neighbourhoods can arise in multiple ways, for example, from global geometric structure (stellar charts), combinatorial structure (weighted graphs),…

We consider the problem of correlation clustering on graphs with constraints on both the cluster sizes and the positive and negative weights of edges. Our contributions are twofold: First, we introduce the problem of correlation clustering…

Distance correlation is a recent extension of Pearson's correlation, that characterises general statistical independence between Euclidean-space-valued random variables, not only linear relations. This review delves into how and when…

Persistent homology allows us to create topological summaries of complex data. In order to analyse these statistically, we need to choose a topological summary and a relevant metric space in which this topological summary exists. While…

Proposed the computerized method for calculating the relative level of order composites. Correlation between a level of structure order and properties of solids is shown. Discussed the possibility of clarifying the terminology used in…

In this paper,we develop a local-to-global and measure-theoretical approach to understand datasets. The idea is to take network models with restricted domains as local charts of datasets. We develop the mathematical foundations for these…

We derive a simple analytical expression for the level correlation function of an integrable system. It accounts for both the lack of correlations at smaller energy scales and for global rigidity (level number conservation) at larger…

A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.

Complex systems have become a popular lens for analyzing cities and complexity theory has many implications for urban performance and resilience. This paper develops a typology of measures and indicators for assessing the physical…

We present an analysis of eight measures used for quantifying morphological complexity of natural languages. The measures we study are corpus-based measures of morphological complexity with varying requirements for corpus annotation. We…

We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that…