Related papers: Proof of admissible weights
Our aim in this paper is to investigate the first Hochschild cohomology of {\em admissible algebras} which can be seen as a generalization of basic algebras. For this purpose, we study differential operators on an admissible algebra.…
We study polynomial functors in the incompressible category $\text{Ver}_4^+$, which can be viewed as super polynomial functors in characteristic 2. Concretely, we classify additive, exact and simple polynomial functors, and describe how…
We consider the problem of recovering an unknown vector from noisy data with the help of projection estimates. The goal is to find a convex combination of these estimates with the minimal risk. We study an aggregation method based on the…
We consider the problem of evaluating certain exponential sums. These sums take the form $\sum_{x_1,...,x_n \in Z_N} e^{f(x_1,...,x_n) {2 \pi i / N}} $, where each x_i is summed over a ring Z_N, and f(x_1,...,x_n) is a multivariate…
We give a simple proof of the Sawyer type characterization of the two weigh estimate for positive dyadic operators (also known as the bilinear embedding theorem).
We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions…
In this article we initiate a systematic study of irreducible weight modules over direct limits of reductive Lie algebras, and in particular over the simple Lie algebras $A(\infty)$, $B(\infty)$, $C(\infty)$ and $D(\infty)$. Our main tool…
Importance weighting is a fundamental procedure in statistics and machine learning that weights the objective function or probability distribution based on the importance of the instance in some sense. The simplicity and usefulness of the…
We revisit and generalize the concept of composite likelihood as a method to make a probabilistic inference by aggregation of multiple Bayesian agents, thereby defining a class of predictive models which we call composite Bayesian. This…
Let $G$ be a simple algebraic group in defining characteristic $p>0$, and let $V$ be an irreducible $G$-module which is the tensor product of exactly two non-trivial modules. We obtain a criterion for $V$ to have the zero weight. In…
The paper is about an arithmetic problem in $\F_2[x]$. We give \emph{admissible} (necessary) conditions satisfied by a set of odd prime divisors of perfect polynomials over $\F_2$. This allows us to prove a new characterization of…
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
Let $u(x)$ be a subpolynomial function in a Hardy field. We establish necessary and sufficient conditions for the weighted uniform distribution of the sequences $(u(n))_{n\in\mathbb{N}}$ and $(u(p_n))_{n\in\mathbb{N}}$, where $p_n$ denotes…
In this note, we consider the problem of aggregation of estimators in order to denoise a signal. The main contribution is a short proof of the fact that the exponentially weighted aggregate satisfies a sharp oracle inequality. While this…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
In this note we give an explicit description of the irreducible components of the reduced point varieties of quantum polynomial algebras.
Given a quasi-Hermitian semisimple Lie algebra, we describe possible spectra of the sum of two admissible elements from its dual vector space.
We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.
We define a statistic called the weight of oscillating tableaux. Oscillating tableaux, a generalization of standard Young tableaux, are certain walks in Young's lattice of partitions. The weight of an oscillating tableau is the sum of the…
We present elementary proofs of weighted embedding theorems for radial potential spaces and some generalizations of Ni's and Strauss' inequalities in this setting.