Determining the quality of mathematical software using reference data sets

This paper describes a methodology for evaluating the numerical accuracy of software that performs mathematical calculations. The authors explain how this methodology extends the concept of metrological traceability, which is fundamental to measurement, to include software quality. Overviews of two European Union-funded projects are also presented. The first project developed an infrastructure to allow software to be verified by testing, via the internet, using reference data sets. The primary focus of the project was software used within systems that make physical measurements. The second project, currently underway, explores using this infrastructure to verify mathematical software used within general scientific and engineering disciplines. Publications on using reference data sets for the verification of mathematical software are usually intended for a readership specialising in measurement science or mathematics. This paper is aimed at a more general readership, in particular software quality specialists and computer scientists. Further engagement with experts in these disciplines will be helpful to the continued development of this application of software quality

Sex differences in Cognitive Abilities Test scores: a UK national picture

Background and aims. There is uncertainty about the extent or even existence of sex differences in the mean and variability of reasoning test scores ( Jensen, 1998; Lynn, 1994, ; Mackintosh, 1996). This paper analyses the Cognitive Abilities Test (CAT) scores of a large and representative sample of UK pupils to determine the extent of any sex differences. Sample. A nationally representative UK sample of over 320,000 school pupils aged 11-12 years was assessed on the CAT (third edition) between September 2001 and August 2003. The CAT includes separate nationally standardized tests for verbal, quantitative, and non-verbal reasoning. The size and recency of the sample is unprecedented in research on this issue. Methods. The sheer size of the sample ensures that any sex difference will achieve statistical significance. Therefore, effect sizes (d) and variance ratios (VR) are employed to evaluate the magnitude of sex differences in mean scores and in score variability, respectively. Results. The mean verbal reasoning score for girls was 2.2 standard score points higher than the mean for boys, but only 0.3 standard points in favour of girls for non-verbal reasoning (NVR), and 0.7 points in favour of boys for quantitative reasoning (QR). However, for all three tests there were substantial sex differences in the standard deviation of scores, with greater variance among boys. Boys were over represented relative to girls at both the top and the bottom extremes for all tests, with the exception of the top 10% in verbal reasoning. Conclusions. Given the small differences in means, explanations for sex differences in wider domains such examination attainment at age 16 need to look beyond conceptions of `ability'. Boys tend to be both the lowest and the highest performers in terms of their reasoning abilities, which warns against the danger of stereotyping boys as low achievers

Shocks, cooling and the origin of star formation rates in spiral galaxies

Understanding star formation is problematic as it originates in the large scale dynamics of a galaxy but occurs on the small scale of an individual star forming event. This paper presents the first numerical simulations to resolve the star formation process on sub-parsec scales, whilst also following the dynamics of the interstellar medium (ISM) on galactic scales. In these models, the warm low density ISM gas flows into the spiral arms where orbit crowding produces the shock formation of dense clouds, held together temporarily by their external pressure. Cooling allows the gas to be compressed to sufficiently high densities that local regions collapse under their own gravity and form stars. The star formation rates follow a Schmidt-Kennicutt \Sigma_{SFR} ~ \Sigma_{gas}^{1.4} type relation with the local surface density of gas while following a linear relation with the cold and dense gas. Cooling is the primary driver of star formation and the star formation rates as it determines the amount of cold gas available for gravitational collapse. The star formation rates found in the simulations are offset to higher values relative to the extragalactic values, implying a constant reduction, such as from feedback or magnetic fields, is likely to be required. Intriguingly, it appears that a spiral or other convergent shock and the accompanying thermal instability can explain how star formation is triggered, generate the physical conditions of molecular clouds and explain why star formation rates are tightly correlated to the gas properties of galaxies.Comment: 13 pages, 12 figures. MNRAS in pres

Some kinetic and equilibrium studies of the reactions of carbonyl compounds with amines and/or sulfite

Studies have been made of the reaction of several carbonyl compounds with sulfite in aqueous solution. (^1)H NMR results indicate the formation of hydroxyalkanesulfonates, HXS, of general structure, RR'C(0H)(S0(_3)Na). Equilibrium and kinetic studies of the decomposition reactions have been made making use of the rapid reaction of iodine with liberated sulfite. The decomposition shows an acidity dependence; above pH 3 reaction mainly involves the dianion, RR'C(0’)(S0(_3)"), while below pH 3 the monoanion, RR'(OH)(S0(_3)’) is involved. In the case of adducts from propanal values obtained for the rate constants for decomposition were 370 s(^-1) and 3.9x10(^-6) s(^-1) for the dianion and monoanion respectively. pK(_a) values for acid dissociation of several HXS compounds were measured and found to be in the range 9-12. The reactions of hydroxypropanesulfonate, HPS, with aniline and aniline derivatives have been studied. (^1)H NMR spectra accord with formation of anilinopropanesulfonates, APS, kinetic and equilibrium measurements were made spectrophotometrically in the presence of added sulfite ions. The overall equilibrium constant for the reaction with aniline was found to be 84 dm(^3) moI(^1) The mechanism of the reaction is thought to involve decomposition of HPS to yield propanal which reacts with the amine to yield a carbinolamine intermediate. This subsequently dehydrates giving an imine which reacts rapidly with free sulfite to give the product, APS. The results suggest a change in rate limiting step from the^reaction of aniline with propanal at low pH to carbinolamine dehydration at high pH, the change occurring at pH 6 -7, the effects of ring substituents in the aniline on reactivity have been examined. Reaction of propanal with aniline in acetonitrile yields the imine. Kinetic studies of its decomposition back to reactants in the presence of aqueous sulfite solutions confirm the conclusion reached from measurements on the forward reaction. Reactions of hydroxymethanesulfonate, HMS, with benzylamine and some derivatives were observed by (^1) H NMR spectroscopy. Equilibrium constants for the formation of 1:1 and 1:2 adducts were measured and the variations of values with pH were examined. Trimerisations of the imines formed from formaldehyde and benzylamine and its derivatives were successfully achieved

A comparison of surface sensible and latent heat fluxes from aircraft and surface measurements in FIFE 1987

Surface fluxes of sensible and latent heat over a tall-grass prairie in central Kansas, as measured by 22 surface stations during FIFE 1987, are compared with values gained indirectly by linear extrapolation of aircraft-measured flux profiles to the surface. The results of 33 such comparisons covering the period 26 June to 13 October 1987 indicate that the sensible heat flux profiles were generally more linear with less scatter in the measurements at each level than were the latent heat flux profiles, the profile extrapolations of sensible heat flux in general underestimate the surface averages by about 30 percent, with slightly better agreement during periods of small flux, and the profile extrapolations of latent heat flux in general underestimate the surface averages by about 15 percent, with overestimates during periods of small fluxes (dry conditions) and overestimates during periods of large fluxes (moist conditions). Possible origins of the differences between the two sets of measurements are discussed, as directions for further research

Exploring inner worlds: where cognitive psychology may take us

Tim Smith researches visual cognition through a variety of techniques that capture what subjects do when they watch naturalistic visual scenes. Although much research into scene perception uses static visual scenes, he is interested in how we process dynamic visual scenes, including feature films. Using techniques such as tracking the eye movements of viewers watching film sequences in combination with behavioural probes during and after viewing, he investigates the cognitive processes occurring during film viewing. His research has contributed to a computational model of fixation durations in scene viewing (Nuthmann, Smith, Engbert, & Henderson, 2010), and he has proposed an Attentional Theory of Cinematic Continuity (Smith, 2012), which has attracted the interest of ‘cognitivist’ film scholars, leading to his involvement in a number of presentations and projects that use empirical testing and modelling to explain what happens when we watch film sequences. I too am interested in the long history of attempts to understand the perceptual and cognitive processes involved in film viewing, which stretch from pioneering work by Munsterberg and Rank in the 1910s, through the renewed interest of Russian psychologists in the 1920s, following Pavlov’s classic studies in conditioning, and later of the Gestalt school, up to present-day work such as that of James Cutting (starting from the ‘psychophysics’ tradition) and Uri Hasson (‘neurocinematics’). In this exchange, written as a dialogue over several months, I invite Tim Smith to summarise some of his own work and to speculate on what value it may have for non-scientists interested in understanding how and why we perceive film as we do – and how this may be changin

Real-world Quantum Sensors: Evaluating Resources for Precision Measurement

Quantum physics holds the promise of enabling certain tasks with better performance than possible when only classical resources are employed. The quantum phenomena present in many experiments signify nonclassical behavior, but do not always imply superior performance. Quantifying the enhancement achieved from quantum behavior requires careful analysis of the resources involved. We analyze the specific case of parameter estimation using an optical interferometer, where increased precision can be achieved using quantum probe states. Common performance measures are examined and it is shown that some overestimate the improvement. For the simplest experimental case we compare the different measures and show this overestimate explicitly. We give the preferred analysis of real-world experiments and calculate benchmark values for experimental parameters necessary to realize a precision enhancement.Comment: 8 pages, 3 figure

Continuous phase stabilization and active interferometer control using two modes

We present a computer-based active interferometer stabilization method that can be set to an arbitrary phase difference and does not rely on modulation of the interfering beams. The scheme utilizes two orthogonal modes propagating through the interferometer with a constant phase difference between them to extract a common phase and generate a linear feedback signal. Switching times of 50ms over a range of 0 to 6 pi radians at 632.8nm are experimentally demonstrated. The phase can be stabilized up to several days to within 3 degrees.Comment: 3 pages, 2 figure

Tuning biexciton binding and anti-binding in core/shell quantum dots

We use a path integral quantum Monte Carlo method to simulate excitons and biexcitons in core shell nanocrystals with Type-I, II and quasi-Type II band alignments. Quantum Monte Carlo techniques allow for all quantum correlations to be included when determining the thermal ground state, thus producing accurate predictions of biexciton binding. These subtle quantum correlations are found to cause the biexciton to be binding with Type-I carrier localization and strongly anti-binding with Type-II carrier localization, in agreement with experiment for both core shell nanocrystals and dot in rod nanocrystal structures. Simple treatments based on perturbative approaches are shown to miss this important transition in the biexciton binding. Understanding these correlations offers prospects to engineer strong biexciton anti-binding which is crucial to the design of nanocrystals for single exciton lasing applications.Comment: 10 pages, 11 figure

Testing use of mitochondrial COI sequences for the identification and phylogenetic analysis of New Zealand caddisflies (Trichoptera)

We tested the hypothesis that cytochrome c oxidase subunit 1 (COI) sequences would successfully discriminate recognised species of New Zealand caddisflies. We further examined whether phylogenetic analyses, based on the COI locus, could recover currently recognised superfamilies and suborders. COI sequences were obtained from 105 individuals representing 61 species and all 16 families of Trichoptera known from New Zealand. No sequence sharing was observed between members of different species, and congeneric species showed from 2.3 to 19.5% divergence. Sequence divergence among members of a species was typically low (mean = 0.7%; range 0.0–8.5%), but two species showed intraspecific divergences in excess of 2%. Phylogenetic reconstructions based on COI were largely congruent with previous conclusions based on morphology, although the sequence data did not support placement of the purse-cased caddisflies (Hydroptilidae) within the uncased caddisflies, and, in particular, the Rhyacophiloidea. We conclude that sequence variation in the COI gene locus is an effective tool for the identification of New Zealand caddisfly species, and can provide preliminary phylogenetic inferences. Further research is needed to ascertain the significance of the few instances of high intra-specific divergence and to determine if any instances of sequence sharing will be detected with larger sample sizes