Related papers: The Gaussian entropy map in valued fields
In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the…
An arrangement is a finite set of hyperplanes in a finite dimensional complex affine space. A complex rank one local system on the arrangement complement is determined by a set of complex weights for the hyperplanes. We study the…
For an ensemble of data points in a multi-parameter space, we present a visual analytics technique to select a representative distribution of parameter values, and analyse how representative this distribution is in all ensemble members. A…
Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…
Gamma distributions, which contain the exponential as a special case, have a distinguished place in the representation of near-Poisson randomness for statistical processes; typically, they represent distributions of spacings between events…
In this paper, we discuss vector-valued Gaussian processes for the approximation of divergence- or rotation-free functions. We establish the theory for such Gaussian processes, then link the theory to multivariate approximation theory, and…
We express the entropy of a scalar field phi directly in terms of its spacetime correlation function W(x,y) = <phi(x) phi(y)>, assuming that the higher correlators are of "Gaussian" form. The resulting formula associates an entropy S(R) to…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
Meta-elliptical copulas are often proposed to model dependence between the components of a random vector. They are specified by a correlation matrix and a map $g$, called density generator. While the latter correlation matrix can easily be…
We construct "stochastic mappings" between power law probability distributions (PD's) and Gaussian ones. To a given vector $N$, Gaussian distributed (respectively $Z$, exponentially distributed), one can associate a vector $X$, "power law…
We study the problem of estimating the mean of a random vector $X$ given a sample of $N$ independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that…
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…
The efficiency of graph-based semi-supervised algorithms depends on the graph of instances on which they are applied. The instances are often in a vectorial form before a graph linking them is built. The construction of the graph relies on…
A random vector whose norm and overlap (inner product with an independent copy) concentrates is shown to have random low-dimensional projections that are approximately random Gaussians. Conversely, asymptotically random Gaussian projections…
We describe the orbit space of the action of the group $\mathrm{Sp}(2)\mathrm{Sp}(1)$ on the real Grassmann manifolds $\mathrm{Gr}_k(\mathbb{H}^2)$ in terms of certain quaternionic matrices of Moore rank not larger than $2$. We then give a…
Random fields in nature often have, to a good approximation, Gaussian characteristics. For such fields, the relative densities of umbilical points -- topological defects which can be classified into three types -- have certain fixed values.…
We numerically study the two-dimensional, area preserving, web map. When the map is governed by ergodic behavior, it is, as expected, correctly described by Boltzmann-Gibbs statistics, based on the additive entropic functional $S_{BG}[p(x)]…
We use Lagrangian specialization to compute the degree of the Gauss map on Theta divisors with transversal $\mathrm{A}_1$ singularities. This computes the Gauss degree for a general abelian variety in the loci $\mathcal{A}^\delta_{t,g-t}$…
The contribution of the valence electrons to the Compton profiles of the alkali metals is calculated using density functional theory. We show that the Compton profiles can be modeled by a $q-$Gaussian distribution, which is characterized by…
The univariate generalized extreme value (GEV) distribution is the most commonly used tool for analyzing the properties of rare events. The ever greater utilization of Bayesian methods for extreme value analysis warrants detailed…