Related papers: On the basis-set extrapolation
This paper presents a method to interpolate a periodic band-limited signal from its samples lying at nonuniform positions in a regular grid, which is based on the FFT and has the same complexity order as this last algorithm. This kind of…
This paper investigates two important analytical properties of hyperbolic-polynomial penalized splines, HP-splines for short. HP-splines, obtained by combining a special type of difference penalty with hyperbolic-polynomial B-splines…
Nonlinear partial differential equations appear in many domains of physics, and we study here a typical equation which one finds in effective field theories (EFT) originated from cosmological studies. In particular, we are interested in the…
We calculate energy spectra of a two-dimensional electron system in a perpendicular magnetic field and periodic potentials of short periods. The Coulomb interaction is included within a screened Hartree-Fock approximation. The electrostatic…
Scaling has been a major driver of recent advancements in deep learning. Numerous empirical studies have found that scaling laws often follow the power-law and proposed several variants of power-law functions to predict the scaling behavior…
We present results of numerical simulations to estimate scaling exponents associated with driven surface growth in two spatial dimensions. We have simulated the restricted solid--on--solid growth model and used the time and system size…
A popular robust alternative of the classic principal component analysis (PCA) is the $\ell_1$-norm PCA (L1-PCA), which aims to find a subspace that captures the most variation in a dataset as measured by the $\ell_1$-norm. L1-PCA has shown…
We give the first nonconstant lower bounds for the approximability of the Independent Set Problem on the Power Law Graphs. These bounds are of the form $n^{\epsilon}$ in the case when the power law exponent satisfies $\beta <1$. In the case…
Recently there has been growing interest in modeling sets with exchangeability such as point clouds. A shortcoming of current approaches is that they restrict the cardinality of the sets considered or can only express limited forms of…
We introduce the Binary Matrix Guessing Problem and provide two algorithms to solve this problem. The first algorithm we introduce is Elementwise Probing Algorithm (EPA) which is very fast under a score which utilizes Frobenius Distance.…
In finite element methods (FEMs), the accuracy of the solution cannot increase indefinitely because the round-off error increases when the number of degrees of freedom (DoFs) is large enough. This means that the accuracy that can be reached…
Neural networks are very effective when trained on large datasets for a large number of iterations. However, when they are trained on non-stationary streams of data and in an online fashion, their performance is reduced (1) by the online…
We introduce constellation ensembles, in which charged particles on a line (or circle) are linked with charged particles on parallel lines (or concentric circles). We present formulas for the partition functions of these ensembles in terms…
In this paper we study the set of digit frequencies that are realised by elements of the set of $\beta$-expansions. The main result of this paper demonstrates that as $\beta$ approaches $1,$ the set of digit frequencies that occur amongst…
Sparsity, defined as the presence of missing or zero values in a dataset, often poses a major challenge while operating on real-life datasets. Sparsity in features or target data of the training dataset can be handled using various…
We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal expansion of the kernel. Uniform error estimates are proved for kernel…
We present an efficient algorithm for determining the Hilbert series of an effective theory and provide a companion code called ECO (Efficient Counting of Operators) in FORM. For example, the Hilbert series for the dimension 15 operators in…
Calculating free energy differences is a topic of substantial interest and has many applications including molecular docking and hydration, solvation, and binding free energies which is used in computational drug discovery. However, in…
The energy variance extrapolation method consists in relating the approximate energies in many-body calculations to the corresponding energy variances and inferring eigenvalues by extrapolating to zero variance. The method needs a fast…
We present a combination of the incremental expansion of potential energy surfaces (PESs), known as n-mode expansion, with the incremental evaluation of the electronic energy in a many-body approach. The application of semi-local…