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A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear equation. An err ...
It is shown that, in the framework of Scale Relativity Theory, correlations of type informational entropy/cross entropy - probability density, in the description of the dynamics of any complex system, can be perceived as interactions. Explaining these inte ...
The present invention describes an imaging system that allows visualization of a wide range of samples both in terms of morphology and in terms of material (e.g. density distribution, varying chemical composition, or anything that induces a change of optic ...
To assess the number of life-bearing worlds in astrophysical environments, it is necessary to take the intertwined processes of abiogenesis (birth), extinction (death), and transfer of life (migration) into account. We construct a mathematical model that i ...
Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requiremen ...
Probability distributions are key components of many learning from demonstration (LfD) approaches, with the spaces chosen to represent tasks playing a central role. Although the robot configuration is defined by its joint angles, end-effector poses are oft ...
We present a framework for performing regression when both covariate and response are probability distributions on a compact interval. Our regression model is based on the theory of optimal transportation, and links the conditional Frechet mean of the resp ...
We consider a system of d non-linear stochastic fractional heat equations in spatial dimension 1 driven by multiplicative d-dimensional space-time white noise. We establish a sharp Gaussian-type upper bound on the two-point probability density function of ...
Adaptability and ease of programming are key features necessary for a wider spread of robotics in factories and everyday assistance. Learning from demonstration (LfD) is an approach to address this problem. It aims to develop algorithms and interfaces such ...
A detailed theoretical and experimental study on the effect of the superposition of uncorrelated speckle patterns with polarization diversity on the spatial statistics of the superposed speckle pattern is presented. It is shown that depending on the mutual ...
