Related papers: AutoKnots: Adaptive Knot Allocation for Spline Int…
Higher order cumulants of point processes, such as skew and kurtosis, require significant computational effort to calculate. The traditional counts-in-cells method implicitly requires a large amount of computation since, for each sampling…
In this paper, we propose a stratified sampling algorithm in which the random drawings made in the strata to compute the expectation of interest are also used to adaptively modify the proportion of further drawings in each stratum. These…
Physics-informed neural networks (PINNs) have gained significant attention for solving forward and inverse problems related to partial differential equations (PDEs). While advancements in loss functions and network architectures have…
This paper constructs adaptive sparse grid collocation method onto arbitrary order piecewise polynomial space. The sparse grid method is a popular technique for high dimensional problems, and the associated collocation method has been well…
We outline here a simple yet efficient method for finding optimized configurations of the elements of radio-astronomical interferometers with fixed pad locations. The method can be successfully applied, as we demonstrate, to define new…
Adaptive rational interpolation has been designed in the context of image processing as a new nonlinear technique that avoids the Gibbs phenomenon when we approximate a discontinuous function. In this work, we present a generalization to…
Analytic methods are emerging in solid and configuration modeling, while providing new insights into a variety of shape and motion related problems by exploiting tools from group morphology, convolution algebras, and harmonic analysis.…
In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported…
AlphaFold, a groundbreaking protein prediction model, has revolutionized protein structure prediction, populating the AlphaFold Protein Database (AFDB) with millions of predicted structures. However, AlphaFold's accuracy in predicting…
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
Deep learning in k-space has demonstrated great potential for image reconstruction from undersampled k-space data in fast magnetic resonance imaging (MRI). However, existing deep learning-based image reconstruction methods typically apply…
We describe a novel approach to accelerating Monte Carlo Markov Chains. Our focus is cosmological parameter estimation, but the algorithm is applicable to any problem for which the likelihood surface is a smooth function of the free…
Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy --- simply increase the order $N$ of the Lagrange interpolating polynomial and the mathematics of convergence automates the distribution of the grid points.…
Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may…
The established redundancy in visual tokens within large vision-language models allows pruning to effectively reduce their substantial computational demands. Previous methods typically employ heuristic layer-specific pruning strategies…
Context: The huge and still rapidly growing amount of galaxies in modern sky surveys raises the need of an automated and objective classification method. Unsupervised learning algorithms are of particular interest, since they discover…
The problem of fixed knot approximation is convex and there are several efficient approaches to solve this problem, yet, when the knots joining the affine parts are also variable, finding conditions for a best Chebyshev approximation…
Physical knot classification is a challenging fine-grained recognition task in which the intended discriminative cue is rope crossing structure; however, high closed-set accuracy may still arise from low-level appearance shortcuts rather…
In current textbooks the use of Chebyshev nodes with Newton interpolation is advocated as the most efficient numerical interpolation method in terms of approximation accuracy and computational effort. However, we show numerically that the…
Accurate calibration of gravity adaptation zones is of great significance in fields such as underwater navigation, geophysical exploration, and marine engineering. With the increasing application of gravity field data in these areas,…