Related papers: The Minimal and Maximal Sensitivity of the Simplif…
The main object of this paper is to find closed form expressions for finite and infinite sums that are weighted by $\omega(n)$, where $\omega(n)$ is the number of distinct prime factors of $n$. We then derive general convergence criteria…
We define a measure for the complexity of Boolean functions related to their implementation in neural networks, and in particular close related to the generalization ability that could be obtained through the learning process. The measure…
For high volume data streams and large data warehouses, sampling is used for efficient approximate answers to aggregate queries over selected subsets. Mathematically, we are dealing with a set of weighted items and want to support queries…
The sensitivity parameter is widely used for quantifying fine tuning. However, examples show it fails to give correct results under certain circumstances. We argue that the problems of the sensitivity parameter are almost identical to the…
We study minimization of a structured objective function, being the sum of a smooth function and a composition of a weakly convex function with a linear operator. Applications include image reconstruction problems with regularizers that…
A weak measurement on a system is made by coupling a pointer weakly to the system and then measuring the position of the pointer. If the initial wavefunction for the pointer is real, the mean displacement of the pointer is proportional to…
We propose a framework for sensitivity analysis of linear programs (LPs) in minimization form, allowing for simultaneous perturbations in the objective coefficients and right-hand sides, where the perturbations are modeled in a compact,…
The paper deals with studying a connection of the Littlewood--Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions. It is shown that the values at zero of the concentration…
In this note we give a sharp weighted estimate for square function from $L^2(w)$ to $L^2(w)$, $w\in A_2$. This has been known. But we also give a sharpening of this weighted estimate in the spirit of $T1$-type testing conditions. Finally we…
We obtain asymptotic formulas for the $2k$th moments of partially smoothed divisor sums of the M\"obius function. When $2k$ is small compared with $A$, the level of smoothing, then the main contribution to the moments come from integers…
This paper introduces tools for assessing the sensitivity, to unobserved confounding, of a common estimator of the causal effect of a treatment on an outcome that employs weights: the weighted linear regression of the outcome on the…
For a matrix $W \in \mathbb{Z}^{m \times n}$, $m \leq n$, and a convex function $g: \mathbb{R}^m \rightarrow \mathbb{R}$, we are interested in minimizing $f(x) = g(Wx)$ over the set $\{0,1\}^n$. We will study separable convex functions and…
Let $X, X_1, X_2,...$ be a sequence of non-degenerate i.i.d. random variables with mean zero. The best possible weighted approximations are investigated in $D[0, 1]$ for the partial sum processes $\{S_{[nt]}, 0\le t\le 1\}$, where…
The Sensitivity Conjecture is a long-standing problem in theoretical computer science that seeks to fit the sensitivity of a Boolean function into a unified framework formed by the other complexity measures of Boolean functions, such as…
Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of…
We propose a flexible approach for computing the resolvent of the sum of weakly monotone operators in real Hilbert spaces. This relies on splitting methods where strong convergence is guaranteed. We also prove linear convergence under…
$\newcommand{\EC}{\mathsf{EC}}\newcommand{\KW}{\mathsf{KW}}\newcommand{\DT}{\mathsf{DT}}\newcommand{\psens}{\mathsf{psens}} \newcommand{\calB}{{\cal B}} $ For a Boolean function $f:\{0,1\}^n \to \{0,1\}$ computed by a circuit $C$ over a…
A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…
This paper is concerned with relationships of weakly mixing, topologically weakly mixing, and sensitivity for non-autonomous discrete systems. It is shown that weakly mixing implies topologically weakly mixing and sensitivity for measurable…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…