Modified Newton-Raphson GRAPE methods for optimal control of spin systems.

Quadratic convergence throughout the active space is achieved for the gradient ascent pulse engineering (GRAPE) family of quantum optimal control algorithms. We demonstrate in this communication that the Hessian of the GRAPE fidelity functional is unusually cheap, having the same asymptotic complexity scaling as the functional itself. This leads to the possibility of using very efficient numerical optimization techniques. In particular, the Newton-Raphson method with a rational function optimization (RFO) regularized Hessian is shown in this work to require fewer system trajectory evaluations than any other algorithm in the GRAPE family. This communication describes algebraic and numerical implementation aspects (matrix exponential recycling, Hessian regularization, etc.) for the RFO Newton-Raphson version of GRAPE and reports benchmarks for common spin state control problems in magnetic resonance spectroscopy.

Auxiliary matrix formalism for interaction representation transformations, optimal control, and spin relaxation theories.

Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome, and hard to compute, theoretical methods: (1) average Hamiltonian theory following interaction representation transformations; (2) Bloch-Redfield-Wangsness theory of nuclear and electron relaxation; (3) gradient ascent pulse engineering version of quantum optimal control theory. In the context of spin dynamics, the auxiliary matrix exponential method is more efficient than methods based on matrix factorizations and also exhibits more favourable complexity scaling with the dimension of the Hamiltonian matrix.

The development of evidence-informed physical activity guidelines for adults with spinal cord injury.

OBJECTIVES: To systematically develop evidence-informed physical activity guidelines to improve physical fitness in people with spinal cord injury (SCI). SETTING: This study was conducted in Canada. METHODS: The Appraisal of Guidelines, Research and Evaluation II guideline development protocol was used to develop exercise guidelines to improve physical capacity and muscular strength. The evidence base for the guideline development process consisted of a systematic review and quality appraisal of research examining the effects of exercise on physical fitness among people with SCI. A multidisciplinary expert panel deliberated the evidence and generated the guidelines. Pilot testing led to refinement of the wording and presentation of the guidelines. RESULTS: The expert panel generated the following guidelines: for important fitness benefits, adults with a SCI should engage in (a) at least 20 min of moderate to vigorous intensity aerobic activity two times per week and (b) strength training exercises two times per week, consisting of three sets of 8-10 repetitions of each exercise for each major muscle group. CONCLUSION: People with SCI, clinicians, researchers and fitness programmers are encouraged to adopt these rigorously developed guidelines.

Clinical trials methods and the practice of medicine.

An important potential byproduct from clinical trials is validated clinical methods applicable to clinical practice. The potential for improved patient care is separate from the scientific and intellectual answers gained in such trials. The current mechanisms for the transfer of methodological information from clinical trials are inefficient and have identifiable barriers. Methods validated in clinical trials must be recognized and accentuated as a valuable resource. A central repository of clinical trials' methods and a retrieval system dedicated to this unique body of scientific literature is warranted. Reports of methodological advances from clinical trials should be published in the literature read by clinical practitioners. The effective transfer of methods information from clinical trials to the office of the clinical practitioner is possible but requires increased efforts on the part of clinical trials scientists.