161 research outputs found

    On a new generalization of Huff curves

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    Recently two kinds of Huff curves were introduced as elliptic curves models and their arithmetic was studied. It was also shown that they are suitable for cryptographic use such as Montgomery curves or Koblitz curves (in Weierstrass form) and Edwards curves. In this work, we introduce the new generalized Huff curves ax(y2−c)=by(x2−d)ax(y^{2} -c) = by(x^{2}-d) with abcd(a2c−b2d)≠0abcd(a^{2}c-b^{2}d)\neq 0, which contains the generalized Huff\u27s model ax(y2−d)=by(x2−d)ax(y^{2}- d) = by(x^{2}-d) with abd(a2−b2)≠0abd(a^{2}-b^{2})\neq 0 of Joye-Tibouchi-Vergnaud and the generalized Huff curves x(ay2−1)=y(bx2−1)x(ay^{2} -1) =y(bx^{2}-1) with ab(a−b)≠0ab(a-b)\neq 0 of Wu-Feng as a special case. The addition law in projective coordinates is as fast as in the previous particular cases. More generally all good properties of the previous particular Huff curves, including completeness and independence of two of the four curve parameters, extend to the new generalized Huff curves. We verified that the method of Joye-Tibouchi-Vergnaud for computing of pairings can be generalized over the new curve

    Migration and Elastic Labour in Economic Development: Southeast Asia before World War II

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    Between 1880 and 1939, Burma, Malaya and Thailand received inflows of migrants from India and China comparable in size to European immigration in the New World. This article examines the forces that lay behind this migration to Southeast Asia and asks if experience there bears out Lewis' unlimited labor supply hypothesis. We find that it does and, furthermore, that immigration created a highly integrated labor market stretching from South India to Southeastern China. Emigration from India and China and elastic labor supply are identified as important components of Asian globalization before the Second World War.

    Analogue of Vélu\u27s Formulas for Computing Isogenies over Hessian Model of Elliptic Curves

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    Vélu\u27s formulas for computing isogenies over Weierstrass model of elliptic curves has been extended to other models of elliptic curves such as the Huff model, the Edwards model and the Jacobi model of elliptic curves. This work continues this line of research by providing efficient formulas for computing isogenies over elliptic curves of Hessian form. We provide explicit formulas for computing isogenies of degree 3 and isogenies of degree l not divisible by 3. The theoretical cost of computing these maps in this case is slightly faster than the case with other curves. We also extend the formulas to obtain isogenies over twisted and generalized Hessian forms of elliptic curves. The formulas in this work have been verified with the Sage software and are faster than previous results on the same curve

    Elliptic Curve Arithmetic for Cryptography

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    The advantages of using public key cryptography over secret key cryptography include the convenience of better key management and increased security. However, due to the complexity of the underlying number theoretic algorithms, public key cryptography is slower than conventional secret key cryptography, thus motivating the need to speed up public key cryptosystems. A mathematical object called an elliptic curve can be used in the construction of public key cryptosystems. This thesis focuses on speeding up elliptic curve cryptography which is an attractive alternative to traditional public key cryptosystems such as RSA. Speeding up elliptic curve cryptography can be done by speeding up point arithmetic algorithms and by improving scalar multiplication algorithms. This thesis provides a speed up of some point arithmetic algorithms. The study of addition chains has been shown to be useful in improving scalar multiplication algorithms, when the scalar is fixed. A special form of an addition chain called a Lucas chain or a differential addition chain is useful to compute scalar multiplication on some elliptic curves, such as Montgomery curves for which differential addition formulae are available. While single scalar multiplication may suffice in some systems, there are others where a double or a triple scalar multiplication algorithm may be desired. This thesis provides triple scalar multiplication algorithms in the context of differential addition chains. Precomputations are useful in speeding up scalar multiplication algorithms, when the elliptic curve point is fixed. This thesis focuses on both speeding up point arithmetic and improving scalar multiplication in the context of precomputations toward double scalar multiplication. Further, this thesis revisits pairing computations which use elliptic curve groups to compute pairings such as the Tate pairing. More specifically, the thesis looks at Stange's algorithm to compute pairings and also pairings on Selmer curves. The thesis also looks at some aspects of the underlying finite field arithmetic

    Chaos synchronization in generalized Lorenz systems and an application to image encryption

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    Examples of synchronization, pervasive throughout the natural world, are often awe-inspiring because they tend to transcend our intuition. Synchronization in chaotic dynamical systems, of which the Lorenz system is a quintessential example, is even more surprising because the very defining features of chaos include sensitive dependence on initial conditions. It is worth pursuing, then, the question of whether high-dimensional extensions of such a system also exhibit synchronization. This study investigates synchronization in a set of high-dimensional generalizations of the Lorenz system obtained from the inclusion of additional Fourier modes. Numerical evidence supports that these systems exhibit self-synchronization. An example application of this phenomenon to image encryption is also provided. Numerical experiments also suggest that there is much more to synchronization in these generalized Lorenz systems than self-synchronization; while setting the dimension of the driver system higher than that of the receiver system does not result in perfect synchrony, the smaller the dimensional difference between the two, the more closely the receiver system tends to follow the driver, leading to self-synchronization when their dimensions are equal. © 2021 The Author

    Range, Endurance, and Optimal Speed Estimates for Multicopters

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    Multicopters are among the most versatile mobile robots. Their applications range from inspection and mapping tasks to providing vital reconnaissance in disaster zones and to package delivery. The range, endurance, and speed a multirotor vehicle can achieve while performing its task is a decisive factor not only for vehicle design and mission planning, but also for policy makers deciding on the rules and regulations for aerial robots. To the best of the authors’ knowledge, this work proposes the first approach to estimate the range, endurance, and optimal flight speed for a wide variety of multicopters. This advance is made possible by combining a state-of-the-art first-principles aerodynamic multicopter model based on blade-element-momentum theory with an electric-motor model and a graybox battery model. This model predicts the cell voltage with only 1.3% relative error ( 43.1mV ), even if the battery is subjected to non-constant discharge rates. Our approach is validated with real-world experiments on a test bench as well as with flights at speeds up to 65km/h in one of the world’s largest motion-capture systems. We also present an accurate pen-and-paper algorithm to estimate the range, endurance and optimal speed of multicopters to help future researchers build drones with maximal range and endurance, ensuring that future multirotor vehicles are even more versatile

    Angular Power Spectra with Finite Counts

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    Angular anisotropy techniques for cosmic diffuse radiation maps are powerful probes, even for quite small data sets. A popular observable is the angular power spectrum; we present a detailed study applicable to any unbinned source skymap S(n) from which N random, independent events are observed. Its exact variance, which is due to the finite statistics, depends only on S(n) and N; we also derive an unbiased estimator of the variance from the data. First-order effects agree with previous analytic estimates. Importantly, heretofore unidentified higher-order effects are found to contribute to the variance and may cause the uncertainty to be significantly larger than previous analytic estimates---potentially orders of magnitude larger. Neglect of these higher-order terms, when significant, may result in a spurious detection of the power spectrum. On the other hand, this would indicate the presence of higher-order spatial correlations, such as a large bispectrum, providing new clues about the sources. Numerical simulations are shown to support these conclusions. Applying the formalism to an ensemble of Gaussian-distributed skymaps, the noise-dominated part of the power spectrum uncertainty is significantly increased at high multipoles by the new, higher-order effects. This work is important for harmonic analyses of the distributions of diffuse high-energy gamma-rays, neutrinos, and charged cosmic rays, as well as for populations of sparse point sources such as active galactic nuclei.Comment: 27 pages, 8 figure

    Impact of Point Spread Function Higher Moments Error on Weak Gravitational Lensing II: A Comprehensive Study

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    Weak gravitational lensing, or weak lensing, is one of the most powerful probes for dark matter and dark energy science, although it faces increasing challenges in controlling systematic uncertainties as \edit{the statistical errors become smaller}. The Point Spread Function (PSF) needs to be precisely modeled to avoid systematic error on the weak lensing measurements. The weak lensing biases induced by errors in the PSF model second moments, i.e., its size and shape, are well-studied. However, Zhang et al. (2021) showed that errors in the higher moments of the PSF may also be a significant source of systematics for upcoming weak lensing surveys. Therefore, the goal of this work is to comprehensively investigate the modeling quality of PSF moments from the 3rd3^{\text{rd}} to 6th6^{\text{th}} order, and estimate their impact on cosmological parameter inference. We propagate the \textsc{PSFEx} higher moments modeling error in the HSC survey dataset to the weak lensing \edit{shear-shear correlation functions} and their cosmological analyses. We find that the overall multiplicative shear bias associated with errors in PSF higher moments can cause a ∼0.1σ\sim 0.1 \sigma shift on the cosmological parameters for LSST Y10. PSF higher moment errors also cause additive biases in the weak lensing shear, which, if not accounted for in the cosmological parameter analysis, can induce cosmological parameter biases comparable to their 1σ1\sigma uncertainties for LSST Y10. We compare the \textsc{PSFEx} model with PSF in Full FOV (\textsc{Piff}), and find similar performance in modeling the PSF higher moments. We conclude that PSF higher moment errors of the future PSF models should be reduced from those in current methods to avoid a need to explicitly model these effects in the weak lensing analysis.Comment: 24 pages, 17 figures, 3 tables; Submitted to MNRAS; Comments welcome

    Anthropogenic fire patterns affect niche breadth and niche overlap in sympatric songbird species

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    The severity of wildfires increases globally, and return intervals decrease. Fires can benefit biodiversity, as post-burn early successional stages provide diverse habitats and niches for many species. How fire disturbance affects niche use and niche overlap of species is poorly understood so far. We studied the effect of anthropogenic fire on breeding habitat use, niche breadth and niche overlap of five sympatric bunting species breeding in wetlands of the Amur River floodplain (Russian Far East). Fire frequency, measured as the time an area burnt in the period 2000 to 2017, was mapped from Landsat imagery and related to the presence or absence of the species. Niche breadth and niche overlap were calculated separately for occurrences in burned (within the study year) and unburned patches. Fire frequency characterized differences in niche use among the species, but the probability of presence was not affected by recent fire in four of five species. Niche breadth was significantly lower in recently burned patches, but we found no increase in niche overlap between species after fire. Instead, the studied species seemed to occupy similar patches before and after fire, possibly because of a high site fidelity. Our results clearly show that fire frequency is a major determinant for the niche separation in the five studied species, while recent fire does not affect niche overlap.</p
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