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We introduce a classification scheme for parton distribution models and we model generalized parton distributions (GPDs), their form factors, and parton distribution functions (PDFs), integrated and unintegrated ones, in terms of…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
In this paper, we consider objective Bayesian inference of the generalized exponential distribution using the independence Jeffreys prior and validate the propriety of the posterior distribution under a family of structured priors. We…
This paper is devoted to study the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the…
In this talk an introduction to generalized parton distributions is given. Recent developments are shortly reviewed, including non-perturbative calculations, phenomenological aspects and evaluation of higher order perturbative and power…
A general construction of transmutation operators is developed for selfadjoint operators in Gelfand triples. Theorems regarding analyticity of generalized eigenfunctions and Paley-Wiener properties are proved.
Let $ k >0 $ be an integer and $ Y $ a standard Gamma$(k)$ distributed random variable. Let $ X $ be an independent positive random variable with a density that is hyperbolically monotone (HM) of order $ k.$ Then $Y\cdot X$ and $Y/X $ both…
Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of…
We develop a systematic approach for resolving the analytic wave front set for a class of integral geometry transforms appearing in various tomography problems. Combined with microlocal analytic continuation, this leads to uniqueness and…
Let Y be a hypersurface in projective space having only ordinary double points as singularities. We prove a variant of a conjecture of L. Wotzlaw on an algebraic description of the graded quotients of the Hodge filtration on the top…
We geometrically study the Legendre duality relation that plays an important role in statistical physics with the standard or generalized entropies. For this purpose, we introduce dualistic structure defined by information geometry, and…
Generative diffusion models showed high success in many fields with a powerful theoretical background. They convert the data distribution to noise and remove the noise back to obtain a similar distribution. Many existing reviews focused on…
We consider a generalised diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyse the probability distribution functions and we derive the mean squared displacement in $x$ and $y$ directions.…
Model-based clustering imposes a finite mixture modelling structure on data for clustering. Finite mixture models assume that the population is a convex combination of a finite number of densities, the distribution within each population is…
The generalized parton distributions are non-perturbative objects, which encode information on long distance dynamics in a number of exclusive processes. They are hybrids of conventional parton densities, distribution amplitudes and hadron…
This work describes a novel image analysis approach to characterize the uniformity of objects in agglomerates by using the propagation of normal wavefronts. The problem of width uniformity is discussed and its importance for the…
The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the…
We are able to rederive in a very simple way the standard generalized Wick's theorem for overlaps of mean field wave functions by using the extension of the statistical Wick's theorem (Gaudin's theorem) in the appropriate limits.
We review the basic theoretical underpinnings of the Grover algorithm, providing a rigorous and well motivated derivation. We then present a generalization of Grover's algorithm that searches an arbitrary subspace of the multi-dimensional…
Generalised parton distributions are instrumental to study both the three-dimensional structure and the energy-momentum tensor of the nucleon, and motivate numerous experimental programmes involving hard exclusive measurements. Based on a…