相关论文: Distorted sums of models

When teaching and discussing statistical assumptions, our focus is oftentimes placed on how to test and address potential violations rather than the effects of violating assumptions on the estimates produced by our statistical models. The…

Integration at a point is a new kind of integration derived from integration over an interval in infinitesimal and infinity domains which are spaces larger than the reals. Consider a continuous monotonic divergent function that is…

For a positive integer $m$ and a subgroup $\Lambda$ of the unit group $(\mathbb{Z}/m\mathbb{Z})^\times$, the corresponding generalized Kloosterman sum is the function $K(a,b,m,\Lambda) = \sum_{u \in \Lambda}e(\frac{au + bu^{-1}}{m})$.…

Let F be a quasi-linear map on a separable normed space X, and assume that F splits on an infinite-dimensional subspace of X. Then the twisted sum topology induced by F on the direct sum of X and the real line can be written as the supremum…

After the introduction of $\lambda$-symmetries by Muriel and Romero, several other types of so called "twisted symmetries" have been considered in the literature (their name refers to the fact they are defined through a deformation of the…

The average properties of the well-known Subset Sum Problem can be studied by the means of its randomised version, where we are given a target value $z$, random variables $X_1, \ldots, X_n$, and an error parameter $\varepsilon > 0$, and we…

A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual…

The Fourier coefficient of a second order Eisenstein series is described as a shifted convolution sum. This description is used to obtain the spectral decomposition of and estimates for the shifted convolution sum.

We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras…

We introduce a novel, training-free method for sampling differentiable representations (diffreps) using pretrained diffusion models. Rather than merely mode-seeking, our method achieves sampling by "pulling back" the dynamics of the…

This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…

We give an explicit version for van der Corput's $d$-th derivative estimate of exponential sums. $ \textbf{Theorem.}$ Let $X$, and $Y\in\mathbb{R}$ be such that $\lfloor Y\rfloor>d$ where $d\ge3$ is a natural number. Let…

We extend an implicit regularization scheme to be applicable in the $n$-dimensional space-time. Within this scheme divergences involving parity violating objects can be consistently treated without recoursing to dimensional continuation.…

Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…

The normal forms of different one- and two- parametric solutions of Thirring model are connected with each other by making use of generalized conformal shift transformations. A new alternative sources of superselection rules are shown and…

In this article, we characterize the distortion elements of the group of smooth diffeomorphisms of the circle and of the group of compactly supported smooth diffeomorphisms of the real line. More precisely, we prove that, in this context,…

We study the general theory of weighted Dirichlet series and associated summatory functions of their coefficients. We show that any non-real pole leads to oscillatory error terms. This applies even if there are infinitely many non-real…

The theory of q-analogs develops many combinatorial formulas for finite vector spaces over a finite field with q elements--all in analogy with formulas for finite sets (which are the special case of q=1). A direct-sum decomposition of a…

In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…

Rapid advancements in data science require us to have fundamentally new frameworks to tackle prevalent but highly non-trivial "irregular" inference problems, to which the large sample central limit theorem does not apply. Typical examples…