Related papers: Extending the Support Theorem to Infinite Dimensio…
Large language models are capable of in-context learning, the ability to perform new tasks at test time using a handful of input-output examples, without parameter updates. We develop a universal approximation theory to elucidate how…
The paper explores the differential inclusion of a special form. It is supposed that the support function of the set in the right-hand side of an inclusion may contain the maximum of the finite number of continuously differentiable (in…
We study a new class of Radon transforms defined on circular cones called the conical Radon transform. In $\mathbb{R}^3$ it maps a function to its surface integrals over circular cones, and in $\mathbb{R}^2$ it maps a function to its…
In 1927 Philomena Mader derived elegant inversion formulas for the hyperplane Radon transform on $\bbr^n$. These formulas differ from the original ones by Radon and seem to be forgotten. We generalize Mader's formulas to totally geodesic…
One constructs new operations of pull-back and push-forward on valuations on manifolds with respect to submersions and immersions. A general Radon type transform on valuations is introduced using these operations and the product on…
In 1917 Johann Radon introduced the Radon transform which is used in 1963 by A. M. Cormack for application in the context of tomographic image reconstruction. He proposed to reconstruct the spatial variation of the material density of the…
The standard Radon transform of holomorphic functions is not always well defined, as the integration of such functions over planes may not converge. In this paper, we introduce new Radon-type transforms of co-(real)dimension $2$ for…
Connections between integration along hypersufaces, Radon transforms, and neural networks are exploited to highlight an integral geometric mathematical interpretation of neural networks. By analyzing the properties of neural networks as…
We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…
Datasets containing geo-spatial resources are increasingly being represented according to the Linked Data principles. Several time-efficient approaches for discovering links between RDF resources have been developed over the last years.…
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
In this paper we prove an optimal $L^2-L^{2d}$ decay estimate of the adjoint Radon transform of compactly supported data in $d$-dimensional space via a geometric method. A similar problem in dimension $3$ has be considered in the author's…
The purpose of this report is a study of the algebraic approach possibilities to reconstruct images. This approach is reduced to solution of the large system of linear algebraic equations. We also point out some possible further…
Statistical properties of classical random process are considered in tomographic representation. The Radon integral transform is used to construct the tomographic form of kinetic equations. Relation of probability density on phase space for…
A theory for boson-assisted tunneling via randomly distributed resonant states in a layered metals is developed. As particular examples, we consider the electron-phonon interaction and the interaction between localized and conduction…
We initiate an investigation of learning tasks in a setting where the learner is given access to two competing provers, only one of which is honest. Specifically, we consider the power of such learners in assessing purported properties of…
The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable…
We present and demonstrate a method for optical homodyne tomography based on the inverse Radon transform. Different from the usual filtered back-projection algorithm, this method uses an appropriate polynomial series to expand the Wigner…
A long-standing topic in artificial intelligence is the effective recognition of patterns from noisy images. In this regard, the recent data-driven paradigm considers 1) improving the representation robustness by adding noisy samples in…
The purpose of this paper is to prove the L^p boundedness of singular Radon transforms and their maximal analogues. These operators differ from the traditional singular integrals and maximal functions in that their definition at any point x…