Related papers: Data Interpolation: An Efficient Sampling Alternat…
For many use cases, combining information from different datasets can be of interest to improve a machine learning model's performance, especially when the number of samples from at least one of the datasets is small. However, a potential…
In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In…
We describe a spectrally-filtered discrete-in-time downscaling data assimilation algorithm and prove, in the context of the two-dimensional Navier--Stokes equations, that this algorithm works for a general class of interpolants, such as…
Very often for the same scientific question, there may exist different techniques or experiments that measure the same numerical quantity. Historically, various methods have been developed to exploit the information within each type of data…
Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by…
We address the problem of approximating an unknown function from its discrete samples given at arbitrarily scattered sites. This problem is essential in numerical sciences, where modern applications also highlight the need for a solution to…
We demonstrate the synthesis of sparse sampling and machine learning to characterize and model complex, nonlinear dynamical systems over a range of bifurcation parameters. First, we construct modal libraries using the classical proper…
For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…
We consider the problem of fusing measurements from multiple sensors, where the sensing regions overlap and data are non-negative---possibly resulting from a count of indistinguishable discrete entities. Because of overlaps, it is, in…
Big Data are huge amounts of digital information that are automatically accrued or merged from several sources and rarely result from properly planned surveys. A Big Dataset is herein conceived of as a collection of information concerning a…
To solve the problem of poor performance of deep neural network models due to insufficient data, a simple yet effective interpolation-based data augmentation method is proposed: MSMix (Manifold Swap Mixup). This method feeds two different…
In this paper we extend the Shepard-Bernoulli operators introduced in [6] to the bivariate case. These new interpolation operators are realized by using local support basis functions introduced in [23] instead of classical Shepard basis…
We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible…
This paper describes a recent mathematical method called conflation for consolidating data from independent experiments that are designed to measure the same quantity, such as Planck's constant or the mass of the top quark. Conflation is…
Given a straight-line program whose output is a polynomial function of the inputs, we present a new algorithm to compute a concise representation of that unknown function. Our algorithm can handle any case where the unknown function is a…
We solve an interpolation problem in $A^p_\alpha$ involving specifying a set of (possibly not distinct) $n$ points, where the $k^{\textrm{th}}$ derivative at the $k^{\textrm{th}}$ point is up to a constant as large as possible for functions…
An ever-increasing deluge of big data is becoming available to national statistical offices globally, but it is well documented that statistics produced by big data alone often suffer from selection bias and are not usually representative…
This paper introduces the concept of hyperpolation: a way of generalising from a limited set of data points that is a peer to the more familiar concepts of interpolation and extrapolation. Hyperpolation is the task of estimating the value…
Large-scale data collection by means of wireless sensor network and internet-of-things technology poses various challenges in view of the limitations in transmission, computation, and energy resources of the associated wireless devices.…
We propose a method called integrated diffusion for combining multimodal datasets, or data gathered via several different measurements on the same system, to create a joint data diffusion operator. As real world data suffers from both local…