Related papers: Spectral Derivatives
In this paper, we introduce a new generalized derivative, which we term the specular derivative. We establish the Quasi-Rolles' Theorem, the Quasi-Mean Value Theorem, and the Fundamental Theorem of Calculus in light of the specular…
One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised…
Recent waves of technological transformation are reshaping work in uncertain and hard-to-predict ways. However, jobs at the forefront of the digitizing economy offer an early glimpse of these changes and leave rich activity traces. We…
The Additive Transform of an arithmetic function represents a novel approach to examining the interplay between multiplicative arithmetic function and additive functions. This transform concept introduces a method to systematically generate…
InferPy is a Python package for probabilistic modeling with deep neural networks. It defines a user-friendly API that trades-off model complexity with ease of use, unlike other libraries whose focus is on dealing with very general…
It is shown here that precision is gained by analyzing the interferometric spectra directly from the interferograms, with no previous Fourier transformation to put them in the standard frequency domain. The method is based on the…
Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by…
Fourier transforms are an often necessary component in many computational tasks, and can be computed efficiently through the fast Fourier transform (FFT) algorithm. However, many applications involve an underlying continuous signal, and a…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
The paper studies functions defined on continuous branching lines connected into a system. A notion of spectrum degeneracy for these functions is introduced. This degeneracy is based on the properties of the Fourier transforms for processes…
A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
We use Fourier analysis to access risk in financial products. With it we analyze price changes of e.g. stocks. Via Fourier analysis we scrutinize quantitatively whether the frequency of change is higher than a change in (conserved) company…
Gravitational-wave memory is characterized by a signal component that persists after a transient signal has decayed. Treating such signals in the frequency domain is non-trivial, since discrete Fourier transforms assume periodic signals on…
Computations in high-dimensional spaces can often be realized only approximately, using a certain number of projections onto lower dimensional subspaces or sampling from distributions. In this paper, we are interested in pairs of…
In this paper a set of analytic formulae are presented with which the partial derivatives of the flux obscuration function can be evaluated -- for planetary transits and eclipsing binaries -- under the assumption of quadratic limb…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
The focus of Part I of this monograph has been on both the fundamental properties, graph topologies, and spectral representations of graphs. Part II embarks on these concepts to address the algorithmic and practical issues centered round…
This paper introduces the theory and hardware implementation of two new algorithms for computing a single component of the discrete Fourier transform. In terms of multiplicative complexity, both algorithms are more efficient, in general,…