Related papers: Ensemble computation approach to the Hough transfo…
In the present time we observe a growing number of publications where the, so-called, flow equations are successfully used to diagonalize Hamiltonians by means of an appropriate unitary transformation. Here we discuss and compare the flow…
Many bone shapes in the human skeleton are characterized by profiles that can be associated to equations of algebraic curves. Fixing the parameters in the curve equation, by means of a classical pattern recognition procedure like the Hough…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
Over a decade ago, it was demonstrated that quantum computing has the potential to revolutionize numerical linear algebra by enabling algorithms with complexity superior to what is classically achievable, e.g., the seminal HHL algorithm for…
In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…
We show that the discrete complex, and numerous hypercomplex, Fourier transforms defined and used so far by a number of researchers can be unified into a single framework based on a matrix exponential version of Euler's formula…
Classical shadow tomography is a sample-efficient technique for characterizing quantum systems and predicting many of their properties. Circuit cutting is a technique for dividing large quantum circuits into smaller fragments that can be…
Ensembles improve prediction performance and allow uncertainty quantification by aggregating predictions from multiple models. In deep ensembling, the individual models are usually black box neural networks, or recently, partially…
This paper advocates the use of complex variables to represent votes in the Hough transform for circle detection. Replacing the positive numbers classically used in the parameter space of the Hough transforms by complex numbers allows…
Error correction will add so much overhead to large quantum computations that we suspect the most efficient algorithms will use a classical co-processor to do as much work as possible. We present a method to offload portions of a quantum…
A generalized Hubbard-Stratonovitch transformation relating an integral over random unitary N times N matrices to an integral over Efetov's unitary sigma model manifold, is introduced. This transformation adapts the supersymmetry method to…
This tutorial introduces quantum computing with a focus on the applicability of formal methods in this relatively new domain. We describe quantum circuits and convey an understanding of their inherent combinatorial nature and the…
We revisit the interest of classical statistical techniques for sales forecasting like exponential smoothing and extensions thereof (as Holt's linear trend method). We do so by considering ensemble forecasts, given by several instances of…
Without unrealistic continuity and smoothness assumptions on a distributional density of one dimensional dataset, constructing an authentic possibly-gapped histogram becomes rather complex. The candidate ensemble is described via a…
In many applications one wants to identify identical subtrees of a program syntax tree. This identification should ideally be robust to alpha-renaming of the program, but no existing technique has been shown to achieve this with good…
A graph-theoretic parameter, in a form of a function, called the extra-factorial sum is discussed. The main results are presented in ref. [1] (Nastou et al., Optim Lett, 10, 1203-1220, 2016) and the reader is strongly advised to study the…
A general conversion strategy by involving a shifted parameter $\theta$ is proposed to construct high-order accuracy difference formulas for fractional calculus operators. By converting the second-order backward difference formula with such…
This paper considers the problem of signal decomposition and data visualization. For this purpose, we introduce a new multiscale transform, termed `ensemble patch transformation' that enhances identification of local characteristics…
We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this…
A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the…