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An Introduction to Affine Arithmetic
Trends in Computational and Applied Mathematics, 2003 Affine arithmetic (AA) is a model for self-validated computation which, like standard interval arithmetic (IA), produces guaranteed enclosures for computed quantities, taking into account any uncertainties in the input data as well as all internal ...
J. Stolfi, L.H. de Figueiredo
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Implementation and improvements of affine arithmetic
Nonlinear Theory and Its Applications IEICE, 2015 Affine arithmetic is a well-known tool to reduce the wrapping effect of ordinary interval arithmetic. We discuss several improvements both in theory and in terms of practical implementation. In particular details of INTLAB's affine arithmetic toolbox are presented. Computational examples demonstrate advantages and weaknesses of the approach.
Siegfried M Rump, Masahide Kashiwagi
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Energies, 2017 With consideration of the intermittency of renewable generation and uncertain load, a regional control strategy is presented to smooth the unscheduled power fluctuation in this letter.
Wei Gu, Lizi Luo
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Cryptographic protection of RGB images using SPN over Eisenstein integer ring modulo Eisenstein prime [PDF]
Scientific ReportsThis research introduces a fortified cryptographic paradigm for safeguarding RGB image data, founded upon a substitution–permutation network (SPN) architecture defined over the residue class rings of Eisenstein integers modulo a selected prime element ...
Muhammad Sajjad +4 more
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A novel color images security-based on SPN over the residue classes of quaternion integers $$\:\varvec{H}{\left(\mathbb{Z}\right)}_{\varvec{\pi\:}}$$ [PDF]
Scientific ReportsThe exponential growth of multimedia data transmission has intensified the demand for advanced image encryption systems capable of resisting contemporary cryptanalytic attacks while maintaining computational efficiency.
Muhammad Sajjad, Nawaf A. Alqwaifly
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Self-verified extension of affine arithmetic to arbitrary order
Le Matematiche, 2008 Affine Arithmetic (AA) is a self-verifying computational approach that keeps track of first-order correlation between uncertainties in the data and intermediate and final results.In this paper we propose a higher-order extension satisfying the requirements ...
Giuseppe Bilotta
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A dividing method utilizing the best multiplication in affine arithmetic
IEICE Electronics Express, 2004 Affine arithmetic (AA) is a variant of interval arithmetic. In AA, it is difficult to realize the efficient nonlinear binomial operations. The purpose of this paper is to propose a new dividing method which consists of a reciprocal and the best multiplication.
Masahide Kashiwagi
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Multiple color images security by SPN over the residue classes of Gaussian integer $$\:Z{\left[i\right]}_{h}$$ [PDF]
Scientific ReportsIn this paper, the authors present the design of a new pair of 8 × 8 S-boxes over the residue classes of Gaussian integers $$\:Z{\left[i\right]}_{h}$$ and their usage for the encryption of multiple RGB images using a three-stage Substitution-Permutation ...
Muhammad Sajjad +4 more
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Bi-level Multi-objective Joint Planning of Distribution Networks Considering Uncertainties
Journal of Modern Power Systems and Clean Energy, 2022 With the increasing penetration of photovoltaics in distribution networks, the adaptability of distribution network under uncertainties needs to be considered in the planning of distribution systems.
Shouxiang Wang +3 more
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Arpra: An Arbitrary Precision Range Analysis Library
Frontiers in Neuroinformatics, 2021 Motivated by the challenge of investigating the reproducibility of spiking neural network simulations, we have developed the Arpra library: an open source C library for arbitrary precision range analysis based on the mixed Interval Arithmetic (IA)/Affine
James Paul Turner, Thomas Nowotny
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