Related papers: Basis-Spline Assisted Coded Computing: Strategies …
We consider a methodology based in B-splines scaling functions to numerically invert Fourier or Laplace transforms of functions in the space $L^2(\mathbb{R})$. The original function is approximated by a finite combination of $j^{th}$ order…
Adaptive approximation (or interpolation) takes into account local variations in the behavior of the given function, adjusts the approximant depending on it, and hence yields the smaller error of approximation. The question of constructing…
B-spline based orbital representations are widely used in Quantum Monte Carlo (QMC) simulations of solids, historically taking as much as 50% of the total run time. Random accesses to a large four-dimensional array make it challenging to…
Our main interest in this paper is to study some approximation problems for classes of functions with mixed smoothness. We use technique, based on a combination of results from hyperbolic cross approximation, which were obtained in 1980s --…
We propose novel methods for approximate sampling recovery and integration of functions in the Freud-weighted Sobolev space $W^r_{p,w}(\mathbb{R})$. The approximation error of sampling recovery is measured in the norm of the Freud-weighted…
There are many methods for image enhancement. Image inpainting is one of them which could be used in reconstruction and restoration of scratch images or editing images by adding or removing objects. According to its application, different…
Isogeometric Analysis generalizes classical finite element analysis and intends to integrate it with the field of Computer-Aided Design. A central problem in achieving this objective is the reconstruction of analysis-suitable models from…
We generalize the leverage score sampling sketch for $\ell_2$-subspace embeddings, to accommodate sampling subsets of the transformed data, so that the sketching approach is appropriate for distributed settings. This is then used to derive…
Gradient coding is a distributed computing technique aiming to provide robustness against slow or non-responsive computing nodes, known as stragglers, while balancing the computational load for responsive computing nodes. Among existing…
Today's massively-sized datasets have made it necessary to often perform computations on them in a distributed manner. In principle, a computational task is divided into subtasks which are distributed over a cluster operated by a…
Numerical preprocessing remains an important component of tabular deep learning, where the representation of continuous features can strongly affect downstream performance. Although its importance is well established for classical…
Approximating data points in three or higher dimension space based on cubic B-spline curve is presented. Representations for planar curves, are merged and extended to the higher dimension. The curve is fitted to the order of data points, or…
We show that polynomial codes (and some related codes) used for distributed matrix multiplication are interleaved Reed-Solomon codes and, hence, can be collaboratively decoded. We consider a fault tolerant setup where $t$ worker nodes…
We present new fault jump estimates to guide local refinement in surface approximation schemes with adaptive spline constructions. The proposed approach is based on the idea that, since discontinuities in the data should naturally…
This paper considers the problem of calculating the matrix multiplication of two massive matrices $\mathbf{A}$ and $\mathbf{B}$ distributedly. We provide a modulo technique that can be applied to coded distributed matrix multiplication…
In a distributed computing system for the master-worker framework, an erasure code can mitigate the effects of slow workers, also called stragglers. The distributed computing system combined with coding is referred to as coded computation.…
In many classification problems it is desirable to output well-calibrated probabilities on the different classes. We propose a robust, non-parametric method of calibrating probabilities called SplineCalib that utilizes smoothing splines to…
Coded distributed computing has been considered as a promising technique which makes large-scale systems robust to the "straggler" workers. Yet, practical system models for distributed computing have not been available that reflect the…
This work is concerned with phrasing the concepts of fault-tolerant quantum computation within the framework of disordered systems, Bernoulli site percolation in particular. We show how the so-called "threshold theorems" on the possibility…
In most work to date, graph signal sampling and reconstruction algorithms are intrinsically tied to graph properties, assuming bandlimitedness and optimal sampling set choices. However, practical scenarios often defy these assumptions,…