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Selling reduction versus Niggli reduction for crystallographic lattices.

ABSTRACT: The unit-cell reduction described by Selling and used by Delone (whose early publications were under the spelling Delaunay) is explained in a simple form. The transformations needed to implement the reduction are listed. The simplicity of this reduction contrasts with the complexity of Niggli reduction.

SUBMITTER: Andrews LC

PROVIDER: S-EPMC6302928 | biostudies-literature | 2019 Jan

REPOSITORIES: biostudies-literature

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Selling reduction versus Niggli reduction for crystallographic lattices.

Andrews Lawrence C LC Bernstein Herbert J HJ Sauter Nicholas K NK

Acta crystallographica. Section A, Foundations and advances 20190101 Pt 1

The unit-cell reduction described by Selling and used by Delone (whose early publications were under the spelling Delaunay) is explained in a simple form. The transformations needed to implement the reduction are listed. The simplicity of this reduction contrasts with the complexity of Niggli reduction. ...[more]

PMID: 30575589

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Project description:ObjectiveTo evaluate the potential impact of two alcohol control policies under consideration in England: banning below cost selling of alcohol and minimum unit pricing.DesignModelling study using the Sheffield Alcohol Policy Model version 2.5.SettingEngland 2014-15.PopulationAdults and young people aged 16 or more, including subgroups of moderate, hazardous, and harmful drinkers.InterventionsPolicy to ban below cost selling, which means that the selling price to consumers could not be lower than tax payable on the product, compared with policies of minimum unit pricing at £0.40 (€0.57; $0.75), 45 p, and 50 p per unit (7.9 g/10 mL) of pure alcohol.Main outcome measuresChanges in mean consumption in terms of units of alcohol, drinkers' expenditure, and reductions in deaths, illnesses, admissions to hospital, and quality adjusted life years.ResultsThe proportion of the market affected is a key driver of impact, with just 0.7% of all units estimated to be sold below the duty plus value added tax threshold implied by a ban on below cost selling, compared with 23.2% of units for a 45 p minimum unit price. Below cost selling is estimated to reduce harmful drinkers' mean annual consumption by just 0.08%, around 3 units per year, compared with 3.7% or 137 units per year for a 45 p minimum unit price (an approximately 45 times greater effect). The ban on below cost selling has a small effect on population health-saving an estimated 14 deaths and 500 admissions to hospital per annum. In contrast, a 45 p minimum unit price is estimated to save 624 deaths and 23,700 hospital admissions. Most of the harm reductions (for example, 89% of estimated deaths saved per annum) are estimated to occur in the 5.3% of people who are harmful drinkers.ConclusionsThe ban on below cost selling, implemented in the England in May 2014, is estimated to have small effects on consumption and health harm. The previously announced policy of a minimum unit price, if set at expected levels between 40 p and 50 p per unit, is estimated to have an approximately 40-50 times greater effect.

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Selling reduction versus Niggli reduction for crystallographic lattices.

Publications

Selling reduction versus Niggli reduction for crystallographic lattices.

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