Using Automatic Differentiation for Adjoint CFD Code Development

This paper addresses the concerns of CFD code developers who are facing the task of creating a discrete adjoint CFD code for design optimisation. It discusses how the development of such a code can be greatly eased through the selective use of Automatic Differentiation, and how the software development can be subjected to a sequence of checks to ensure the correctness of the final software

Accretion column eclipses in the X-ray pulsars GX 1+4 and RX J0812.4-3114

Sharp dips observed in the pulse profiles of three X-ray pulsars (GX 1+4, RX J0812.4-3114 and A 0535+26) have previously been suggested to arise from partial eclipses of the emission region by the accretion column occurring once each rotation period. We present pulse-phase spectroscopy from Rossi X-ray Timing Explorer satellite observations of GX 1+4 and RX J0812.4-3114 which for the first time confirms this interpretation. The dip phase corresponds to the closest approach of the column axis to the line of sight, and the additional optical depth for photons escaping from the column in this direction gives rise to both the decrease in flux and increase in the fitted optical depth measured at this phase. Analysis of the arrival time of individual dips in GX~1+4 provides the first measurement of azimuthal wandering of a neutron star accretion column. The column longitude varies stochastically with standard deviation 2-6 degrees depending on the source luminosity. Measurements of the phase width of the dip both from mean pulse profiles and individual eclipses demonstrates that the dip width is proportional to the flux. The variation is consistent with that expected if the azimuthal extent of the accretion column depends only upon the Keplerian velocity at the inner disc radius, which varies as a consequence of the accretion rate Mdot.Comment: 7 pages, 5 figures, accepted by MNRAS. Included reference

Spectral variation in the X-ray pulsar GX 1+4 during a low-flux episode

The X-ray pulsar GX 1+4 was observed with the RXTE satellite for a total of 51ks between 1996 July 19 - 21. During this period the flux decreased smoothly from an initial mean level of ~ 6 X 10^36 erg/s to a minimum of ~ 4 X 10^35 erg/s (2-60 keV, assuming a source distance of 10 kpc) before partially recovering towards the initial level at the end of the observation. BATSE pulse timing measurements indicate that a torque reversal took place approximately 10 d after this observation. Both the mean pulse profile and the photon spectrum varied significantly. The observed variation in the source may provide important clues as to the mechanism of torque reversals. The single best-fitting spectral model was based on a component originating from thermal photons with kT ~ 1 keV Comptonised by a plasma of temperature kT \~ 7 keV. Both the flux modulation with phase during the brightest interval and the evolution of the mean spectra over the course of the observation are consistent with variations in this model component; with, in addition, a doubling of the column density nH contributing to the mean spectral change. A strong flare of duration 50 s was observed during the interval of minimum flux, with the peak flux ~ 20 times the mean level. Although beaming effects are likely to mask the true variation in Mdot thought to give rise to the flare, the timing of a modest increase in flux prior to the flare is consistent with dual episodes of accretion resulting from successive orbits of a locally dense patch of matter in the accretion disc.Comment: 8 pages, 3 figures, submitted to MNRA

Conditional sampling for barrier option pricing under the LT method

We develop a conditional sampling scheme for pricing knock-out barrier options under the Linear Transformations (LT) algorithm from Imai and Tan (2006). We compare our new method to an existing conditional Monte Carlo scheme from Glasserman and Staum (2001), and show that a substantial variance reduction is achieved. We extend the method to allow pricing knock-in barrier options and introduce a root-finding method to obtain a further variance reduction. The effectiveness of the new method is supported by numerical results

Mechanism of Reconnection on Kinetic Scales Based on Magnetospheric Multiscale Mission Observations

We examine the role that ions and electrons play in reconnection using observations from the Magnetospheric Multiscale (MMS) mission on kinetic ion and electron scales, which are much shorter than magnetohydrodynamic scales. This study reports observations with unprecedented high resolution that MMS provides for magnetic eld (7.8 ms) and plasma (30 ms for electrons and 150 ms for ions). We analyze and compare approaches to the magnetopause in 2016 November, to the electron diffusion region in the magnetotail in 2017 July followed by a current sheet crossing in 2018 July. Besides magnetic eld reversals, changes in the direction of the ow velocity, and ion and electron heating, MMS observed large uctuations in the electron ow speeds in the magnetotail. As expected from numerical simulations, we have veried that when the eld lines and plasma become decoupled a large reconnecting electric eld related to the Hall current (110 mV/m) is responsible for fast reconnection in the ion diffusion region. Although inertial accelerating forces remain moderate (12 mV/m), the electric elds resulting from the divergence of the full electron pressure tensor provide the main contribution to the generalized Ohms law at the neutral sheet (as large as 200 mV/m). In our view, this illustrates that when ions decouple electron physics dominates. The results obtained on kinetic scales may be useful for better understanding the physical mechanisms governing reconnection processes in various magnetized laboratory and space plasmas

Predicting gene ontology from a global meta-analysis of 1-color microarray experiments

<p>Abstract</p> <p>Background</p> <p>Global meta-analysis (GMA) of microarray data to identify genes with highly similar co-expression profiles is emerging as an accurate method to predict gene function and phenotype, even in the absence of published data on the gene(s) being analyzed. With a third of human genes still uncharacterized, this approach is a promising way to direct experiments and rapidly understand the biological roles of genes. To predict function for genes of interest, GMA relies on a guilt-by-association approach to identify sets of genes with known functions that are consistently co-expressed with it across different experimental conditions, suggesting coordinated regulation for a specific biological purpose. Our goal here is to define how sample, dataset size and ranking parameters affect prediction performance.</p> <p>Results</p> <p>13,000 human 1-color microarrays were downloaded from GEO for GMA analysis. Prediction performance was benchmarked by calculating the distance within the Gene Ontology (GO) tree between predicted function and annotated function for sets of 100 randomly selected genes. We find the number of new predicted functions rises as more datasets are added, but begins to saturate at a sample size of approximately 2,000 experiments. For the gene set used to predict function, we find precision to be higher with smaller set sizes, yet with correspondingly poor recall and, as set size is increased, recall and F-measure also tend to increase but at the cost of precision.</p> <p>Conclusions</p> <p>Of the 20,813 genes expressed in 50 or more experiments, at least one predicted GO category was found for 72.5% of them. Of the 5,720 genes without GO annotation, 4,189 had at least one predicted ontology using top 40 co-expressed genes for prediction analysis. For the remaining 1,531 genes without GO predictions or annotations, ~17% (257 genes) had sufficient co-expression data yet no statistically significantly overrepresented ontologies, suggesting their regulation may be more complex.</p

String Bit Models for Superstring

We extend the model of string as a polymer of string bits to the case of superstring. We mainly concentrate on type II-B superstring, with some discussion of the obstacles presented by not II-B superstring, together with possible strategies for surmounting them. As with previous work on bosonic string we work within the light-cone gauge. The bit model possesses a good deal less symmetry than the continuous string theory. For one thing, the bit model is formulated as a Galilei invariant theory in $(D-2)+1$ dimensional space-time. This means that Poincar\'e invariance is reduced to the Galilei subgroup in $D-2$ space dimensions. Naturally the supersymmetry present in the bit model is likewise dramatically reduced. Continuous string can arise in the bit models with the formation of infinitely long polymers of string bits. Under the right circumstances (at the critical dimension) these polymers can behave as string moving in $D$ dimensional space-time enjoying the full $N=2$ Poincar\'e supersymmetric dynamics of type II-B superstring.Comment: 43 pages, phyzzx require