Sharing storage using dirty vectors

Consider a computation F with n inputs (independent variables) and m outputs (dependent variables) and suppose that we wish to evaluate the Jacobian of F. Automatic differentiation commonly performs this evaluation by associating vector storage either with the program variables (in the case of forward-mode automatic differentiation) or with the adjoint variables (in the case of reverse). Each vector component contains a partial derivative with respect to an independent variable, or a partial derivative of a dependent variable, respectively. The vectors may be full vectors, or they may be dynamically managed sparse data structures. In either case, many of these vectors will be scalar multiples of one another. For example, any intermediate variable produced by a unary operation in the forward mode will have a derivative vector that is a multiple of the derivative for the argument. Any computational graph node that is read just once during its lifetime will have an adjoint vector that is a multiple of the adjoint of the node that reads it. It is frequently wasteful to perform component multiplications explicitly. A scalar multiple of another vector can be replaced by a single multiplicative "scale factor" together with a pointer to the other vector. Automated use of this "dirty vector" technique can save considerable memory management overhead and dramatically reduce the number of floating-point operations required. In particular, dirty vectors often allow shared threads of computation to be reverse-accumulated cheaply. The mechanism permits a number of generalizations, some of which give efficient techniques for preaccumulation

Coating thickness and elastic modulus measurement using ultrasonic bulk wave resonance

Measurement of the resonant through thickness ultrasonic modes of a homogeneous plate using a fast Fourier transform of the temporal data can be used to calculate plate thickness very accurately. We describe an extension of this principle to two-layer systems, examining a thin coating on a substrate of known properties. The resonant behavior of these systems is predicted and we explain how this approach is used to measure coating thickness and elastic modulus. Noncontact electromagnetic acoustic transducers are used for ultrasonic measurement, as they do not significantly affect the resonant response of the system, unlike alternative contact transducers

Non-linear enhancement of laser generated ultrasonic Rayleigh waves by cracks

Laser generated ultrasound has been widely used for detecting cracks, surface and sub-surface defects in many different materials. It provides a non-contact wideband excitation source which can be focused into different geometries. Previous workers have reported enhancement of the laser generated Rayleigh wave when a crack is illuminated by pulsed laser beam irradiation. We demonstrate that the enhancement observed is due to a combination of source truncation, the free boundary condition at the edge of the crack and interference effects. Generating a Rayleigh wave over a crack can lead to enhancement of the amplitude of the Rayleigh wave signal, a shift in the dominant frequency of the wideband Rayleigh wave and strong enhancement of the high frequency components of the Rayleigh wave

Canadian national sport organisations’ use of the web for relationship marketing in promoting sport participation

Sport participation development requires a systematic process which involves knowledge creation, dissemination and interactions between National Sport Organisations, participants, clubs and associations as well as other agencies. Using a relationship marketing approach (Grönroos, 1997, Gummesson, 2002, Olkkonen, 1999), this paper addressed the question ‘How do Canadian NSOs use the Web, in terms of functionality and services offered, to create and maintain relationships with sport participants and their sport delivery partners?’ Ten Canadian NSOs’ websites were examined: functionality was analysed using Burgess and Cooper’s (2000) eMICA model, while NSOs’ utilisation of the Internet to establish and maintain relationships with sport participants was analysed using Wang, Head and Archer’s (2000) relationship-building process model for the Web. It was found that Canadian NSOs were receptive to the use of the Web, but their information-gathering and dissemination activities, which make-up the relationship-building process, appear sparse, and in some cases are lagging behind the voluntary sector in the country

High-precision radiocarbon dating of the construction phase of Oakbank Crannog, Loch Tay, Perthshire

Many of the Loch Tay crannogs were built in the Early Iron Age and so calibration of the radiocarbon ages produces very broad calendar age ranges due to the well-documented Hallstatt plateau in the calibration curve. However, the large oak timbers that were used in the construction of some of the crannogs potentially provide a means of improving the precision of the dating through subdividing them into decadal or subdecadal increments, dating them to high precision and wiggle-matching the resulting data to the master <sup>14</sup>C calibration curve. We obtained a sample from 1 oak timber from Oakbank Crannog comprising 70 rings (Sample OB06 WMS 1, T103) including sapwood that was complete to the bark edge. The timber is situated on the northeast edge of the main living area of the crannog and as a large and strong oak pile would have been a useful support in more than 1 phase of occupation and may be related to the earliest construction phase of the site. This was sectioned into 5-yr increments and dated to a precision of approximately ±8–16 <sup>14</sup>C yr (1 σ). The wiggle-match predicts that the last ring dated was formed around 500 BC (maximum range of 520–465 BC) and should be taken as indicative of the likely time of construction of Oakbank Crannog. This is a considerable improvement on the estimates based on single <sup>14</sup>C ages made on oak samples, which typically encompassed the period from around 800–400 BC

Prevalence of vertebral fractures on chest radiographs of elderly African American and Caucasian women.

The prevalence of vertebral fractures on routine chest radiographs of elderly Caucasian women was only 1.3 times higher than in African American (AA) women, a difference considerably smaller than reported in population studies. AAs with medical problems may have higher risk of vertebral fractures than previously suspected.IntroductionEarlier studies noted a 1.9- to 3.7-fold higher prevalence of vertebral fractures in Caucasian (CA) compared to African American (AA) women. These studies, however, may have suffered from selection bias. We reported that among women referred for bone density testing, the prevalence of vertebral fractures in AA was the same as in CA women. Suspecting that the latter might have been due to a referral bias, we examined the racial difference in the prevalence of vertebra fractures on chest radiographs of patients seeking general medical care, not selected for osteoporosis.MethodsConsecutive chest radiographs (N = 1,200) of women over age 60 were evaluated using Genant's semi-quantitative method. Patients' race and the presence of diseases or medications associated with increased fracture risk were ascertained from the electronic medical records.ResultsAmong 1,011 women (76% AA) with usable radiographs, 11% had moderate or severe vertebral fractures. The prevalence of vertebral fractures was 10.3% in 773 AA and 13% in 238 CA women (p = 0.248 for difference between races). The lack of difference persisted after controlling for age, smoking, use of glucocorticoids, or presence of cancer, rheumatoid arthritis, organ transplantation, and end-stage renal disease. Among all subjects, CA women were more likely to be diagnosed and treated for osteoporosis (p <0.001).ConclusionAmong subjects seeking medical care, the difference in the prevalence of vertebral fractures between AA and CA women is smaller than previously suspected. Greater attention to the detection of vertebral fractures and the management of osteoporosis is warranted in AA women with medical problems

Speckle-visibility spectroscopy: A tool to study time-varying dynamics

We describe a multispeckle dynamic light scattering technique capable of resolving the motion of scattering sites in cases that this motion changes systematically with time. The method is based on the visibility of the speckle pattern formed by the scattered light as detected by a single exposure of a digital camera. Whereas previous multispeckle methods rely on correlations between images, here the connection with scattering site dynamics is made more simply in terms of the variance of intensity among the pixels of the camera for the specified exposure duration. The essence is that the speckle pattern is more visible, i.e. the variance of detected intensity levels is greater, when the dynamics of the scattering site motion is slow compared to the exposure time of the camera. The theory for analyzing the moments of the spatial intensity distribution in terms of the electric field autocorrelation is presented. It is demonstrated for two well-understood samples, a colloidal suspension of Brownian particles and a coarsening foam, where the dynamics can be treated as stationary. However, the method is particularly appropriate for samples in which the dynamics vary with time, either slowly or rapidly, limited only by the exposure time fidelity of the camera. Potential applications range from soft-glassy materials, to granular avalanches, to flowmetry of living tissue.Comment: review - theory and experimen

Obesity management: Update on orlistat

Over the past 20 years obesity has become a worldwide concern of frightening proportion. The World Health Organization estimates that there are over 400 million obese and over 1.6 billion overweight adults, a figure which is projected to almost double by 2015. This is not a disease restricted to adults – at least 20 million children under the age of 5 years were overweight in 2005 (WHO 2006). Overweight and obesity lead to serious health consequences including coronary artery disease, stroke, type-2 diabetes, heart failure, dyslipidemia, hypertension, reproductive and gastrointestinal cancers, gallstones, fatty liver disease, osteoarthritis and sleep apnea (Padwal et al 2003)

The GHZ/W-calculus contains rational arithmetic

Graphical calculi for representing interacting quantum systems serve a number of purposes: compositionally, intuitive graphical reasoning, and a logical underpinning for automation. The power of these calculi stems from the fact that they embody generalized symmetries of the structure of quantum operations, which, for example, stretch well beyond the Choi-Jamiolkowski isomorphism. One such calculus takes the GHZ and W states as its basic generators. Here we show that this language allows one to encode standard rational calculus, with the GHZ state as multiplication, the W state as addition, the Pauli X gate as multiplicative inversion, and the Pauli Z gate as additive inversion.Comment: In Proceedings HPC 2010, arXiv:1103.226