Related papers: Weighted Bounded Variation Revisited
Many spatial processes exhibit nonstationary features. We estimate a variance function from a single process observation where the errors are nonstationary and correlated. We propose a difference-based approach for a one-dimensional…
Recently, the so-called Hermite-Hadamard inequality for (operator) convex functions with one variable has known extensive several developments by virtue of its nice properties and various applications. The fundamental target of this paper…
We prove several new results on the Hamming weight of bounded uniform and small-bias distributions. We exhibit bounded-uniform distributions whose weight is anti-concentrated, matching existing concentration inequalities. This construction…
In the present paper we shall study a variational problem relating the weighted Hardy inequalities with sharp missing terms. As weights we treat non-doubling functions of the distance to the boundary of bounded domain.
Based on the assumption that there exists a neural network that efficiently represents a set of Boolean functions between all binary inputs and outputs, we propose a process for developing and deploying neural networks whose weight…
We study Einstein gravity in a finite spatial region. By requiring a well-defined variational principle, we identify all local boundary conditions, derive surface observables, and compute their algebra. The observables arise as induced…
We investigate the initial-boundary value problem for the Stokes system in the half-space, within the framework of weighted Lebesgue spaces. Introducing a new weight function defined via a product of powers of distances from fixed points,…
We prove trace theorems for weighted mixed norm Sobolev spaces in the upper-half space where the weight is a power function of the vertical variable. The results show the differentiability order of the trace functions depends only on the…
In this paper we introduce the \textit{multivariate} Brownian semistationary (BSS) processes and study the joint asymptotic behaviour of its realised covariation using in-fill asymptotics. First, we present a central limit theorem for…
Consider a Bernoulli random field satisfying the Hannan's condition. Recently, invariance principles for partial sums of random fields over rectangular index sets are established. In this note we complement previous results by investigating…
In this paper, first we give a new generalization of the Bohr's inequality for the class of bounded analytic functions $\mathcal{B'}$ and for the class of sense-preserving $K$-quasiconformal harmonic mappings of the form $f=h+\overline{g},$…
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…
The main purpose of this survey is to gather results on the boundedness of the Bergman projection. First, we shall go over some equivalent norms on weighted Bergman spaces $A^p_\omega$ which are useful in the study of this question. In…
This is the first part of our research on certain sharp Hardy-Sobolev inequalities and the related elliptic equations. In this part we shall establish some sharp weighted Hardy-Sobolev inequalities whose weights are distance functions to…
We first extend Calder\'on's transfer principle to weighted spaces, and then we apply our results to obtain some new weighted inequalities in ergodic theory and ergodic $H^1$ spaces.
We introduce a new, efficient, principled and backpropagation-compatible algorithm for learning a probability distribution on the weights of a neural network, called Bayes by Backprop. It regularises the weights by minimising a compression…
Estimating causal effects from observational data is a central problem in many domains. A general approach is to balance covariates with weights such that the distribution of the data mimics randomization. We present generalized balancing…
In this paper we focus our attention on an embedding result for a weighted Sobolev space that involves as weight the distance function from the boundary taken with respect to a general smooth gauge function $F$. Starting from this type of…
We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then we discuss the existence of extremals and in some cases we compute the best…
In this work, we study the weighted empirical risk minimization (weighted ERM) schema, in which an additional data-dependent weight function is incorporated when the empirical risk function is being minimized. We show that under a general…