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

Classical String in Curved Backgrounds

The Mathisson-Papapetrou method is originally used for derivation of the particle world line equation from the covariant conservation of its stress-energy tensor. We generalize this method to extended objects, such as a string. Without specifying the type of matter the string is made of, we obtain both the equations of motion and boundary conditions of the string. The world sheet equations turn out to be more general than the familiar minimal surface equations. In particular, they depend on the internal structure of the string. The relevant cases are classified by examining canonical forms of the effective 2-dimensional stress-energy tensor. The case of homogeneously distributed matter with the tension that equals its mass density is shown to define the familiar Nambu-Goto dynamics. The other three cases include physically relevant massive and massless strings, and unphysical tahyonic strings.Comment: 12 pages, REVTeX 4. Added a note and one referenc

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

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

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

Does Eating a Meal before Testing Alter the Percent Body Fat Measurement Determined by Bioelectrical Impedance Analysis?

Please view abstract in the attached PDF file

Flaw IdeNtification Through The Application Of Loading (FINAL)

The teardown and inspection of aircraft, which have completed a significant period of service, is a central requirement of many Aircraft Structural Integrity Management Plans (ASIMP). The reasons for this include a need to inspect for the potential onset of wide spread fatigue damage and to assess the impact of corrosion and in-service mechanical damage. Furthermore, service life data from fleet aircraft are required to confirm laboratory fatigue test results and substantiate the assumptions made during safe-life calculations or probabilistic risk and reliability studies. A teardown and inspection of the fracture critical F/A-18 wing attachment bulkheads (or centre barrel - CB) has been initiated to achieve these goals for the RAAF's F/A-18 fleet. Use is being made of ex-service CBs supplied from the Canadian Forces and U.S. Navy (USN) CB replacement programs. Investigations suggest that the largest 'likely' cracks in the critical bulkheads will be less than 1 mm deep at the time a CB is replaced. Since the detectable crack depth threshold for current NDI (using high frequency eddy current (HFEC) detection) is 1.0 mm or greater, these cracks may not be found. To significantly improve the probability of detecting cracks that are below the lower threshold of NDI, an increase in their size by accelerated fatigue testing of the CBs has been implemented. Cyclic loads (using the mini-FALSTAFF spectrum) are applied to the wing attachment lugs of ex-service CBs in a test rig to simulate in-flight wing loads. The loading is of sufficient magnitude and duration to ensure that any existing cracks will be grown to a size that ensures their detection under laboratory conditions. Quantitative fractography has been performed on observed cracking to obtain crack growth data and to determine the size, nature and cause of discontinuities that initiate fatigue cracking. This paper will provide a summary of the teardown philosophy, methodology and preliminary results

ANALYSIS OF BORROWER AND LENDER USE OF INTEREST ASSISTANCE ON FSA GUARANTEED FARM LOANS

The Farm Security and Rural Investment Act of 2002 made permanent the interest assistance program for the Farm Service Agency's guaranteed loans, authorized a significant increase in funding for the program, and targeted funding for beginning farmers and ranchers. The research presented here provides a basic descriptive analysis of past use. In particular, borrower data for Federal fiscal years 1985 through 2002 are examined in several dimensions. These dimensions include geographic, borrower type, lender type, interest rate differentials, percent guarantee, and the status of the loan as to whether a loss claim was paid or the loan remained active. Even though the program has been in existence for more than 15 years, little is known about its impact and utilization. This research is an initial step in documenting usage of the program.Agricultural and Food Policy, Agricultural Finance,

On Lorentz invariance and supersymmetry of four particle scattering amplitudes in SNR8S^N\R^8 orbifold sigma model

The $S^N\R^8$ supersymmetric orbifold sigma model is expected to describe the IR limit of the Matrix string theory. In the framework of the model the type IIA string interaction is governed by a vertex which was recently proposed by R.Dijkgraaf, E.Verlinde and H.Verlinde. By using this interaction vertex we derive all four particle scattering amplitudes directly from the orbifold model in the large $N$ limit.Comment: Latex, 23 page

Equational reasoning with context-free families of string diagrams

String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allows for mechanised equational reasoning by double-pushout rewriting. However, one often wishes to express not just single equations, but entire families of equations between diagrams of arbitrary size. To do this we define a class of context-free grammars, called B-ESG grammars, that are suitable for defining entire families of string graphs, and crucially, of string graph rewrite rules. We show that the language-membership and match-enumeration problems are decidable for these grammars, and hence that there is an algorithm for rewriting string graphs according to B-ESG rewrite patterns. We also show that it is possible to reason at the level of grammars by providing a simple method for transforming a grammar by string graph rewriting, and showing admissibility of the induced B-ESG rewrite pattern.Comment: International Conference on Graph Transformation, ICGT 2015. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-21145-9_