Related papers: Understanding Classical Decomposability of Inequal…

For classical discrete systems under constant composition, canonical average provides equilibrium configuration from a set of many-body interactions, which typically acts as nonlinear map. The nonlinearity has recently been investigated in…

The non-classical features of quantum mechanics are reproduced using models constructed with a classical theory - general relativity. The inability to define complete initial data consistently and independently of future measurements,…

The partial information decomposition (PID) framework is concerned with decomposing the information that a set of (two or more) random variables (the sources) has about another variable (the target) into three types of information: unique,…

Urban inequality, as reflected by uneven spatial allocations of resources, services, and opportunities, has arisen as a major topic for quantitative research and policy intervention. Geographic Information Systems (GIS) provide a solid…

Grouped data in form of income shares have been conventionally used to estimate income inequality due to the lack of availability of individual records. Most prior research on economic inequality relies on lower bounds of inequality…

This work will incorporate a few related tools for addressing the conceptual difficulties arising from sewing together classical and quantum mechanics: deterministic operators, weak measurements and post-selection. Weak Measurement, based…

To gain insights into the problem of regional inequality, we proposed new regional asset exchange models based on existing kinetic income-exchange models in economic physics. We did this by setting the spatial exchange range and adding bias…

Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…

We study idempotent measures and the structure of the convolution semigroups of measures over definable groups. We isolate the property of generic transitivity and demonstrate that it is sufficient (and necessary) to develop stable group…

Partial information decomposition (PID) of the multivariate mutual information describes the distinct ways in which a set of source variables contains information about a target variable. The groundbreaking work of Williams and Beer has…

In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…

In this note we continue giving the characterisation of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the…

Classical learning theory suggests that the optimal generalization performance of a machine learning model should occur at an intermediate model complexity, with simpler models exhibiting high bias and more complex models exhibiting high…

We establish a quantitative isoperimetric inequality for weighted Riemannian manifolds with $\mathrm{Ric}_{\infty} \ge 1$. Precisely, we give an upper bound of the volume of the symmetric difference between a Borel set and a sub-level (or…

In this paper, we use analysis on graphs to study quantitative measures of segregation. We focus on a classical statistic from the geography and urban sociology literature known as Moran's I, which in our language is a score associated to a…

This paper promotes the application of a path-independent decomposition scheme. Besides presenting some theoretical arguments supporting this decomposition scheme, this study also illustrates the difference between the path-independent…

We introduce the notion of decomposition space as a general framework for incidence algebras and M\"obius inversion: it is a simplicial infinity-groupoid satisfying an exactness condition weaker than the Segal condition, which expresses…

Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…

A generalization of the notion of a (pseudo-) Riemannian space is proposed in a framework of noncommutative geometry. In particular, there are parametrized families of generalized Riemannian spaces which are deformations of classical…

Exploring and detecting community structures hold significant importance in genetics, social sciences, neuroscience, and finance. Especially in graphical models, community detection can encourage the exploration of sets of variables with…