Related papers: Image and Transfer Functions
We derive sharp, explicit constants in inverse trace inequalities for polynomial functions belonging to $\mathbb{P}_p(T)$ (polynomial space with total degree $p$) that are orthogonal to the lower-order subspace $\mathbb{P}_n(T)$, $n\leq p$,…
We consider functions of the type $f(z)=z+a_2z^2+a_3z^3+\cdots$ from a family of all analytic and univalent functions in the unit disk. Let $F$ be the inverse function of $f$, given by $F(z)=w+\sum_{n=2}^{\infty}A_nw^n$ defined on some…
The real projective plane has three well know isomorphic constructions: the extended euclidean plane, unit (hemi)sphere, and three dimensional vector space over the reals. In this paper we find the isomorphisms that map between these three…
Invertibility is an important concept in category theory. In higher category theory, it becomes less obvious what the correct notion of invertibility is, as extra coherence conditions can become necessary for invertible structures to have…
Some fixed point results are given for a class of functional contractions acting on (reflexive) triangular symmetric spaces. Technical connections with the corresponding theories over (standard) metric and partial metric spaces are also…
Task transfer learning is a popular technique in image processing applications that uses pre-trained models to reduce the supervision cost of related tasks. An important question is to determine task transferability, i.e. given a common…
A classification is provided of functors, in particular polynomial ones, from a category with a zero object in which every object is a finite sum of copies of a generating object, into an abelian category. This classification is extended to…
Several notions of "analytic" functor introduced recently in the literature fit into the graphic fourier transform context presented in [D].
The light field reconstruction from the focal stack can be mathematically formulated as an ill-posed integral equation inversion problem. Although the previous research about this problem has made progress both in practice and theory, its…
In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.
In valence approximation the fermion correlator is simply related to the light-front spectral function. Then the leading twist time-reversal even transverse momentum distributions can be explicitly obtained from the light-front wave…
Category theory has foundational importance because it provides conceptual lenses to characterize what is important in mathematics. Originally the main lenses were universal mapping properties and natural transformations. In recent decades,…
Let $(X,d)$ be a metric space and $X_0$ be an open and dense subset of $X$. We develop the Walters' theory and discuss the existence of conformal measures in terms of the Perron-Frobenius-Ruelle operator for a continuous map…
We give an abstract criterion for pasting pseudofunctors on two subcategories of a category into a pseudofunctor on the whole category. As an application we extend the variance theory of the twisted inverse image $(-)^!$ over schemes to…
We show how the categorial approach to inverse monoids can be described as a certain endofunctor (which we call the partialization functor) of some category. In this paper we show that this functor can be used to obtain several recently…
Transfer learning enables to re-use knowledge learned on a source task to help learning a target task. A simple form of transfer learning is common in current state-of-the-art computer vision models, i.e. pre-training a model for image…
The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this…
When labeled data is scarce for a specific target task, transfer learning often offers an effective solution by utilizing data from a related source task. However, when transferring knowledge from a less related source, it may inversely…
Relative theories(=closed subfunctors) are considered in exact, triangulated and extriangulated categories by Dr\"{a}xler-Reiten-Smal{\o}-Solberg-Keller, Beligiannis and Herschend-Liu-Nakaoka, respectively. We give a construction method of…
A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: 1) Property $C$ and applications, 2) Stable inversion of fixed-energy 3D scattering data and its error estimate, 3)…