9,999 research outputs found

    Simple and Nearly Optimal Polynomial Root-finding by Means of Root Radii Approximation

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    We propose a new simple but nearly optimal algorithm for the approximation of all sufficiently well isolated complex roots and root clusters of a univariate polynomial. Quite typically the known root-finders at first compute some crude but reasonably good approximations to well-conditioned roots (that is, those isolated from the other roots) and then refine the approximations very fast, by using Boolean time which is nearly optimal, up to a polylogarithmic factor. By combining and extending some old root-finding techniques, the geometry of the complex plane, and randomized parametrization, we accelerate the initial stage of obtaining crude to all well-conditioned simple and multiple roots as well as isolated root clusters. Our algorithm performs this stage at a Boolean cost dominated by the nearly optimal cost of subsequent refinement of these approximations, which we can perform concurrently, with minimum processor communication and synchronization. Our techniques are quite simple and elementary; their power and application range may increase in their combination with the known efficient root-finding methods.Comment: 12 pages, 1 figur

    Real-time data coupling for hybrid testing in a geotechnical centrifuge

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    Geotechnical centrifuge models necessarily involve simplifications compared to the full-scale scenario under investigation. In particular, structural systems (e.g. buildings or foundations) generally can’t be replicated such that complex full-scale characteristics are obtained. Hybrid testing offers the ability to combine capabilities from physical and numerical modelling to overcome some of the experimental limitations. In this paper, the development of a coupled centrifuge-numerical model (CCNM) pseudo-dynamic hybrid test for the study of tunnel-building interaction is presented. The methodology takes advantage of the relative merits of centrifuge tests (modelling soil behaviour and soil-pile interactions) and numerical simulations (modelling building deformations and load redistribution), with pile load and displacement data being passed in real-time between the two model domains. To appropriately model the full-scale scenario, a challenging force-controlled system was developed (the first of its kind for hybrid testing in a geotechnical centrifuge). The CCNM application can accommodate simple structural frame analyses as well as more rigorous simulations conducted using the finite element analysis software ABAQUS, thereby extending the scope of application to non-linear structural behaviour. A novel data exchange method between ABAQUS and LabVIEW is presented which provides a significant enhancement compared to similar hybrid test developments. Data are provided from preliminary tests which highlight the capabilities of the system to accurately model the global tunnel-building interaction problem

    Size and shape constancy in consumer virtual reality

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    With the increase in popularity of consumer virtual reality headsets, for research and other applications, it is important to understand the accuracy of 3D perception in VR. We investigated the perceptual accuracy of near-field virtual distances using a size and shape constancy task, in two commercially available devices. Participants wore either the HTC Vive or the Oculus Rift and adjusted the size of a virtual stimulus to match the geometric qualities (size and depth) of a physical stimulus they were able to refer to haptically. The judgments participants made allowed for an indirect measure of their perception of the egocentric, virtual distance to the stimuli. The data show under-constancy and are consistent with research from carefully calibrated psychophysical techniques. There was no difference in the degree of constancy found in the two headsets. We conclude that consumer virtual reality headsets provide a sufficiently high degree of accuracy in distance perception, to allow them to be used confidently in future experimental vision science, and other research applications in psychology

    Mathematical Modelling of Optical Coherence Tomography

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    In this chapter a general mathematical model of Optical Coherence Tomography (OCT) is presented on the basis of the electromagnetic theory. OCT produces high resolution images of the inner structure of biological tissues. Images are obtained by measuring the time delay and the intensity of the backscattered light from the sample considering also the coherence properties of light. The scattering problem is considered for a weakly scattering medium located far enough from the detector. The inverse problem is to reconstruct the susceptibility of the medium given the measurements for different positions of the mirror. Different approaches are addressed depending on the different assumptions made about the optical properties of the sample. This procedure is applied to a full field OCT system and an extension to standard (time and frequency domain) OCT is briefly presented.Comment: 28 pages, 5 figures, book chapte

    The ALMaQUEST Survey - V. The non-universality of kpc-scale star formation relations and the factors that drive them

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    ABSTRACT Using a sample of ∼15 000 kpc-scale star-forming spaxels in 28 galaxies drawn from the ALMA-MaNGA QUEnching and STar formation (ALMaQUEST) survey, we investigate the galaxy-to-galaxy variation of the ‘resolved’ Schmidt–Kennicutt relation (rSK; ΣH2\Sigma _{\rm H_2}–ΣSFR), the ‘resolved’ star-forming main sequence (rSFMS; Σ⋆–ΣSFR), and the ‘resolved’ molecular gas main sequence (rMGMS; Σ⋆–ΣH2\Sigma _{\rm H_2}). The rSK relation, rSFMS, and rMGMS all show significant galaxy-to-galaxy variation in both shape and normalization, indicating that none of these relations is universal between galaxies. The rSFMS shows the largest galaxy-to-galaxy variation and the rMGMS the least. By defining an ‘offset’ from the average relations, we compute a ΔrSK, ΔrSFMS, ΔrMGMS for each galaxy, to investigate correlations with global properties. We find the following correlations with at least 2σ significance: The rSK is lower (i.e. lower star formation efficiency) in galaxies with higher M⋆, larger Sersic index, and lower specific SFR (sSFR); the rSFMS is lower (i.e. lower sSFR) in galaxies with higher M⋆ and larger Sersic index; and the rMGMS is lower (i.e. lower gas fraction) in galaxies with lower sSFR. In the ensemble of all 15 000 data points, the rSK relation and rMGMS show equally tight scatters and strong correlation coefficients, compared with a larger scatter and weaker correlation in the rSFMS. Moreover, whilst there is no correlation between ΔrSK and ΔrMGMS in the sample, the offset of a galaxy’s rSFMS does correlate with both of the other two offsets. Our results therefore indicate that the rSK and rMGMS are independent relations, whereas the rSFMS is a result of their combination.ERC STF

    An investigation of minimisation criteria

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    Minimisation can be used within treatment trials to ensure that prognostic factors are evenly distributed between treatment groups. The technique is relatively straightforward to apply but does require running tallies of patient recruitments to be made and some simple calculations to be performed prior to each allocation. As computing facilities have become more widely available, minimisation has become a more feasible option for many. Although the technique has increased in popularity, the mode of application is often poorly reported and the choice of input parameters not justified in any logical way

    Gauss-Bonnet Black Holes and Heavy Fermion Metals

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    We consider charged black holes in Einstein-Gauss-Bonnet Gravity with Lifshitz boundary conditions. We find that this class of models can reproduce the anomalous specific heat of condensed matter systems exhibiting non-Fermi-liquid behaviour at low temperatures. We find that the temperature dependence of the Sommerfeld ratio is sensitive to the choice of Gauss-Bonnet coupling parameter for a given value of the Lifshitz scaling parameter. We propose that this class of models is dual to a class of models of non-Fermi-liquid systems proposed by Castro-Neto et.al.Comment: 17 pages, 6 figures, pdfLatex; small corrections to figure 10 in this versio

    Bidirectional association between self-reported hypertension and gout: The Singapore Chinese health study

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    It has been hypothesized that the association between hypertension and gout is bidirectional, however, few studies have examined this in a prospective cohort.We analyzed data from the Singapore Chinese Health Study (SCHS) follow-up I (1999-2004) and II (2006-2010) interviews, when both physician-diagnosed hypertension and gout were self-reported. We included participants with data for both follow-up interviews and who were free of heart disease, stroke and cancer at follow-up I. The analysis of hypertension and risk of gout included 31,137 participants when prevalent gout cases were excluded, while the analysis of gout and risk of hypertension included 20,369 participants when prevalent hypertension cases were excluded. Cox proportional hazards models were used to estimate multivariable-adjusted hazard ratios (HRs) and 95% confidence intervals (CIs). The mean age at follow-up I was 60.1 (SD 7.3) years, and the average follow-up was 6.8 (SD 1.4) years. In the analysis of hypertension and risk of gout, 682 incident cases were identified. Compared to normotensive participants, hypertensive patients had an88% increased risk of developing gout (HR 1.88; 95% CI 1.61-2.21). In the parallel analysis, 5,450 participants reported to have newly diagnosed hypertension during followup. Compared to participants without gout, those with gout had an18% increased risk of developing hypertension (HR 1.18; 95% CI 1.02-1.37). The bidirectional association was stronger in normal weight adults compared to overweight/obese individuals (Pinteraction = 0.06 and 0.04, respectively). The hypertension to gout association was stronger in women compared to men (Pinteraction = 0.04), while the gout to hypertension association was evident in women but not in men (Pinteraction = 0.02). In conclusion, our results suggest that the hypertension-gout association is bidirectional in this cohort of Singapore Chinese adults. The potential interactions of the bidirectional association with obesity and sex deserve further investigations
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