Related papers: Basis-Spline Assisted Coded Computing: Strategies …
In this work, we consider the problem of distributed computing of functions of structured sources, focusing on the classical setting of two correlated sources and one user that seeks the outcome of the function while benefiting from…
We consider the distributed computing problem of multiplying a set of vectors with a matrix. For this scenario, Li et al. recently presented a unified coding framework and showed a fundamental tradeoff between computational delay and…
The past decade has seen notable advances in our understanding of structured error-correcting codes, particularly binary Reed--Muller (RM) codes. While initial breakthroughs were for erasure channels based on symmetry, extending these…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
In this paper, we develop approximation error estimates as well as corresponding inverse inequalities for B-splines of maximum smoothness, where both the function to be approximated and the approximation error are measured in standard…
In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel interpolation with a properly defined rescaling operation, which…
In this paper we present a new class of cubature rules with the aim of accurately integrating weakly singular double integrals. In particular we focus on those integrals coming from the discretization of Boundary Integral Equations for 3D…
Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address…
We investigate error propagation in sliding window decoding of braided convolutional codes (BCCs). Previous studies of BCCs have focused on iterative decoding thresholds, minimum distance properties, and their bit error rate (BER)…
Particle tracing through numerical integration is a well-known approach to generating pathlines for visualization. However, for particle simulations, the computation of pathlines is expensive, since the interpolation method is complicated…
Continuous signal representations are naturally suited for inverse problems, such as magnetic resonance imaging (MRI) and computed tomography, because the measurements depend on an underlying physically continuous signal. While classical…
We consider the problem of coded computing, where a computational task is performed in a distributed fashion in the presence of adversarial workers. We propose techniques to break the adversarial toleration threshold barrier previously…
Matrix computations are a fundamental building-block of edge computing systems, with a major recent uptick in demand due to their use in AI/ML training and inference procedures. Existing approaches for distributing matrix computations…
Over the past two decades, we have seen an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient…
Coded distributed computing framework enables large-scale machine learning (ML) models to be trained efficiently in a distributed manner, while mitigating the straggler effect. In this work, we consider a multi-task assignment problem in a…
In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…
In distributed computing systems, it is well recognized that worker nodes that are slow (called stragglers) tend to dominate the overall job execution time. Coded computation utilizes concepts from erasure coding to mitigate the effect of…
In this paper we present a new algorithm for Polynomial Linear System Solving (via evaluation/interpolation) with errors. In this scenario, errors can occur in the black box evaluation step. We improve the bound on the number of errors that…
A scheme for concatenating the recently invented polar codes with non-binary MDS codes, as Reed-Solomon codes, is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation…
In this paper the numerical solution of potential problems defined on 3D unbounded domains is addressed with Boundary Element Methods (BEMs), since in this way the problem is studied only on the boundary, and thus any finite approximation…