相关论文: Dimension theory and parameterized normalization f…

The sum of all ladder and rainbow diagrams in $\phi^3$ theory near 6 dimensions leads to self-consistent higher order differential equations in coordinate space which are not particularly simple for arbitrary dimension D. We have now…

Domain adaptation seeks to leverage the abundant label information in a source domain to improve classification performance in a target domain with limited labels. While the field has seen extensive methodological development, its…

We show that in many parametrized families of self-similar measures, their projections, and their convolutions, the set of parameters for which the measure fails to be absolutely continuous is very small - of co-dimension at least one in…

We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…

The absence of the quadratic divergence in the Higgs sector of the Standard Model in the dimensional regularization is usually regarded to be an exceptional property of a specific regularization. To understand what is going on in the…

We introduce and study a dimensional-like characteristic of an uniformly almost periodic function, which we call the Diophantine dimension. By definition, it is the exponent in the asymptotic behavior of the inclusio length. Diophantine…

For first-order expansions of the field of real numbers, nondefinability of the set of natural numbers is equivalent to equality of topological and Assouad dimension on images of closed definable sets under definable continuous maps.

We propose semi-random features for nonlinear function approximation. The flexibility of semi-random feature lies between the fully adjustable units in deep learning and the random features used in kernel methods. For one hidden layer…

The seminormalization of an algebraic variety $X$ is the biggest variety linked to $X$ by a finite, birational and bijective morphism. In this paper we introduce a variant of the seminormalization, suited for real algebraic varieties,…

We say that a category $\mathscr{D}$ is dimension zero over a field $F$ provided that every finitely generated representation of $\mathscr{D}$ over $F$ is finite length. We show that $\textrm{Rel}(R)$, a category that arises naturally from…

We show that there is a very simple relationship between differential and dimensional renormalization of low-order Feynman graphs in renormalizable massless quantum field theories. The beauty of the differential approach is that it achieves…

A ten-dimensional supersymmetric gauge theory is written in terms of N=1, D=4 superfields. The theory is dimensionally reduced over six-dimensional coset spaces. We find that the resulting four-dimensional theory is either a softly broken…

We present part of our investigations on two dimensional N=1 and N=2 superconformal field theories. As a direct generalization we consider the SU(2) coset models, in particular their renormalization group properties. A search and possible…

Here we look at (collections of) semimetrics and seminorms, including their ultrametric versions. In particular, we are concerned with geometric properties related to connectedness and topological dimension 0.

We generalize the differential dimension polynomial from prime differential ideals to characterizable differential ideals. Its computation is algorithmic, its degree and leading coefficient remain differential birational invariants, and it…

The main goal of this project is to prove the equivalency of several characterizations of completeness of Archimedean ordered fields; some of which appear in most modern literature as theorems following from the Dedekind completeness of the…

Let K be an algebraically closed field endowed with a complete non-archimedean norm with valuation ring R. Let f:Y -> X be a map of K-affinoid varieties. In this paper we study the analytic structure of the image f(Y) in X; such an image is…

Recent studies have proven that DNNs, unlike human vision, tend to exploit texture information rather than shape. Such texture bias is one of the factors for the poor generalization performance of DNNs. We observe that the texture bias…

In this paper we introduce a model theoretic construction for the theories of uniform layered domains and semifields introduced in the paper of Izhakian, Knebusch and Rowen. We prove that, for a given layering semiring L, the theory of…

We present a new notion of decomposition of semialgebraic sets by introducing a mode of irreducibility based on arc-analytic functions. The result is a refinement of the decomposition of such sets with respect to the Zariski topology as…