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The Erd\H{o}s discrepancy problem, now a theorem by T. Tao, asks whether every sequence with values plus or minus one has unbounded discrepancy along all homogeneous arithmetic progressions. We establish weighted variants of this problem,…
We present a parallelizable algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
In this paper, we establish the sharp boundedness of p-adic multilinear Hausdorff operators on the product of Lebesgue and central Morrey spaces associated with both power weights and Muckenhoupt weights. Moreover, the boundedness for the…
In this paper we describe some new algebraic features of the Gram matrices of complex Equiangular Tight Frames (ETF). This lead on the one hand to the nonexistence of several low dimensional complex ETFs; and on the other hand to the full…
The problem of estimating the frequencies of an exponential sum has been studied extensively over the last years. It can be understood as a sparse estimation problem, as it strives to identify the sparse representation of a signal using…
Kernel approximation with exponentials is useful in many problems with convolution quadrature and particle interactions such as integral-differential equations, molecular dynamics and machine learning. This paper proposes a weighted…
The design of numerical boundary conditions is a challenging problem that has been tackled in different ways depending on the nature of the problem and the numerical scheme used to solve it. In this paper we present a new weighted…
We discuss continuity of the twisted convolution on (weighted) Fourier modulation spaces. We use these results to establish continuity results for the twisted convolution on Lebesgue spaces. For example we prove that if $\omega$ is an…
We study how powerful algebraic discrete Morse theory is when applied to hull resolutions. The main result describes all cases when the hull resolution of the edge ideal of the complement of a triangle-free graph can be made minimal using…
The theories of hypergeometric functions and modular forms are highly intertwined. For example, particular values of truncated hypergeometric functions and hypergeometric character sums are often congruent or equal to Fourier coefficients…
We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Numerous distinct such expansions are possible for a complex number. They can be arrived at through various algorithms, as…
We consider elliptic transmission problems with complex coefficients across an interface. Under proper transmission conditions, that extend known conditions for well-posedness, and sub-ellipticity we derive microlocal and local Carleman…
Normally hyperbolic invariant manifolds theory provides an efficient tool for proving diffusion in dynamical systems. In this paper we develop a methodology for computer assisted proofs of diffusion in a-priori chaotic systems based on this…
The Bayesian evidence is a key tool in model selection, allowing a comparison of models with different numbers of parameters. Its use in analysis of cosmological models has been limited by difficulties in calculating it, with current…
In this paper we extend a Calderon-Zygmund commutator-type estimate. This estimate enables us to prove an embedding result concerning weighted function spaces.
We associate to each real algebraic variety a filtered chain complex, the weight complex, which is well-defined up to filtered quasi-isomorphism, and which induces on classical (compactly supported) homology with Z/2 coefficients an analog…
Recent years have seen a rise in the application of machine learning techniques to aid the simulation of hard-to-sample systems that cannot be studied using traditional methods. Despite the introduction of many different architectures and…
Iterated commutators of multilinear Calderon-Zygmund operators and pointwise multiplication with functions in $BMO$ are studied in products of Lebesgue spaces. Both strong type and weak end-point estimates are obtained, including weighted…
We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…