相关论文: The NC-proximal average for multiple functions

This paper analyzes general spatially-coupled (SC) systems with multi-dimensional coupling. A continuum approximation is used to derive potential functions that characterize the performance of the SC systems. For any dimension of coupling,…

The first order loss function and its complementary function are extensively used in practical settings. When the random variable of interest is normally distributed, the first order loss function can be easily expressed in terms of the…

Approximating functions by a linear span of truncated basis sets is a standard procedure for the numerical solution of differential and integral equations. Commonly used concepts of approximation methods are well-posed and convergent, by…

In regression analysis, associations between continuous predictors and the outcome are often assumed to be linear. However, modeling the associations as non-linear can improve model fit. Many flexible modeling techniques, like (fractional)…

Functions with low differential uniformity have relevant applications in cryptography. Recently, functions with low $c$-differential uniformity attracted lots of attention. In particular, so-called APcN and PcN functions (generalization of…

In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…

We describe a procedure based on the iteration of an initial function by an appropriated operator, acting on continuous functions, in order to get a fixed point. This fixed point will be a calibrated subaction for the doubling map on the…

Truncating the Fourier transform averaged by means of a generalized Hausdorff operator, we approximate the adjoint to that Hausdorff operator of the given function. We find the formulas for the rate of approximation in various metrics in…

The optimization problem concerning the determination of the minimizer for the sum of convex functions holds significant importance in the realm of distributed and decentralized optimization. In scenarios where full knowledge of the…

A commonly used characteristic of statistical dependence of adjacency relations in real networks, the clustering coefficient, evaluates chances that two neighbours of a given vertex are adjacent. An extension is obtained by considering…

The main objective of this paper is to look from the unique point of view at some phenomena arising in different areas of probability theory and mathematical statistics. We will try to understand what is common between classical…

An elementary general result is proved that allows for simple characterizations of well-known location/consensus functions (median, mean and center) on the n-cube. In addition, alternate new characterizations are given for the median and…

This paper presents a novel approach to measuring statistical dependence between two random processes (r.p.) using a positive-definite function called the Normalized Cross Density (NCD). NCD is derived directly from the probability density…

For various Hilbert spaces of analytic functions on the unit disk, we characterize when a function $f$ has optimal polynomial approximants given by truncations of a single power series. We also introduce a generalized notion of optimal…

Precise estimation of cross-correlation or similarity between two random variables lies at the heart of signal detection, hyperdimensional computing, associative memories, and neural networks. Although a vast literature exists on different…

This paper studies the design and analysis of approximation algorithms for aggregating preferences over combinatorial domains, represented using Conditional Preference Networks (CP-nets). Its focus is on aggregating preferences over…

We find all subsets of $\mathbb{N}$ which occur as the set of possible cardinalities of preimages of a continuous function. We also study and answer this question for various subclasses of continuous functions.

Compressed Counting (CC) was recently proposed for very efficiently computing the (approximate) $\alpha$th frequency moments of data streams, where $0<\alpha <= 2$. Several estimators were reported including the geometric mean estimator,…

For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper…

We propose a novel foundation for calculus that focuses on the notion of approximations while avoiding the use of limits altogether. Continuity is defined as approximation at a point, while differentiability is defined as approximation with…