Related papers: Directional distributions and the half-angle princ…
The radial distribution function is a characteristic geometric quantity of a point set in Euclidean space that reflects itself in the corresponding diffraction spectrum and related objects of physical interest. The underlying combinatorial…
The inverse approach is computationally efficient in aerodynamic design as the desired target performance distribution is prespecified. However, it has some significant limitations that prevent it from achieving full efficiency. First, the…
The inverse Radon transform allows to obtain partonic double distributions from (extended) generalized parton distributions. We express the extension of generalized parton distributions by their dual parts, generalized distribution…
The projected normal distribution, also known as the angular Gaussian distribution, is obtained by dividing a multivariate normal random variable $\mathbf{x}$ by its norm $\sqrt{\mathbf{x}^T \mathbf{x}}$. The resulting random variable…
The use of quantiles to obtain insights about multivariate data is addressed. It is argued that incisive insights can be obtained by considering directional quantiles, the quantiles of projections. Directional quantile envelopes are…
Hull form designing is an iterative process wherein the performance of the hull form needs to be checked via computational fluid dynamics calculations or model experiments. The stern shape has to undergo a process wherein the hull form…
The notion of pointwise differentials for distributions is a way to extract local information of distributions by rescaling the distribution at a point. In this paper, we study the pointwise differentials for distributions corresponding to…
The distribution of radiation is investigated for the modeless laser having a multilobe mirror with the lobes (planes) inclined by small angles to optical axis. It is shown that change of the direction resulting from many passages of a ray…
In this paper I present three new results of astronomical interest concerning the theory of Abel inversion. 1) I show that in the case of a spatial emissivity that is constant on toroidal surfaces and projected along the symmetry axis…
We consider the inverse problem of fitting atmospheric dispersion parameters based on time-resolved back-scattered differential absorption Lidar (DIAL) measurements. The obvious advantage of light-based remote sensing modalities is their…
In molecular physics, it is often necessary to average over the orientation of molecules when calculating observables, in particular when modelling experiments in the liquid or gas phase. Evaluated in terms of Euler angles, this is closely…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
When multiple forecasts are available for a probability distribution, forecast combining enables a pragmatic synthesis of the information to extract the wisdom of the crowd. The linear opinion pool has been widely used, whereby the…
The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…
Directional data consists of unit vectors in q-dimensions that can be described in polar or Cartesian coordinates. Axial data can be viewed as a pair of directions pointed in opposite directions or as a projection matrix of rank 1.…
We describe a new method for analyzing gravitational lens images, for the case where the source light distribution is pixelized. The method is suitable for high resolution, high S/N data of a multiply-imaged extended source. For a given…
A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…
Inspired by Gauss-Newton-like methods, we study the benefit of leveraging the structure of deep learning objectives, namely, the composition of a convex loss function and of a nonlinear network, in order to derive better direction oracles…
Astronomical source deblending is the process of separating the contribution of individual stars or galaxies (sources) to an image comprised of multiple, possibly overlapping sources. Astronomical sources display a wide range of sizes and…
Mutual space-frequency distribution is proposed and it is shown that Wigner and Weyl distribution functions are only particular cases of these distribution. Mutual distribution for Gaussian signal is analytically obtained. The simple…