Dual formulation of second order target problems

This paper provides a new formulation of second order stochastic target problems introduced in [SIAM J. Control Optim. 48 (2009) 2344-2365] by modifying the reference probability so as to allow for different scales. This new ingredient enables us to prove a dual formulation of the target problem as the supremum of the solutions of standard backward stochastic differential equations. In particular, in the Markov case, the dual problem is known to be connected to a fully nonlinear, parabolic partial differential equation and this connection can be viewed as a stochastic representation for all nonlinear, scalar, second order, parabolic equations with a convex Hessian dependence.Comment: Published in at http://dx.doi.org/10.1214/12-AAP844 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Revisiting the hydrogen storage behavior of the Na-O-H system

Solid-state reactions between sodium hydride and sodium hydroxide are unusual among hydride-hydroxide systems since hydrogen can be stored reversibly. In order to understand the relationship between hydrogen uptake/release properties and phase/structure evolution, the dehydrogenation and hydrogenation behavior of the Na-O-H system has been investigated in detail both ex- and in-situ. Simultaneous thermogravimetric-differential thermal analysis coupled to mass spectrometry (TG-DTA-MS) experiments of NaH-NaOH composites reveal two principal features: Firstly, an H2 desorption event occurring between 240 and 380 °C and secondly an additional endothermic process at around 170 °C with no associated weight change. In-situ high-resolution synchrotron powder X-ray diffraction showed that NaOH appears to form a solid solution with NaH yielding a new cubic complex hydride phase below 200 °C. The Na-H-OH phase persists up to the maximum temperature of the in-situ diffraction experiment shortly before dehydrogenation occurs. The present work suggests that not only is the inter-phase synergic interaction of protic hydrogen (in NaOH) and hydridic hydrogen (in NaH) important in the dehydrogenation mechanism, but that also an intra-phase Hδ+… Hδ– interaction may be a crucial step in the desorption process

Wellposedness of Second Order Backward SDEs

We provide an existence and uniqueness theory for an extension of backward SDEs to the second order. While standard Backward SDEs are naturally connected to semilinear PDEs, our second order extension is connected to fully nonlinear PDEs, as suggested by Cheridito et.al. In particular, we provide a fully nonlinear extension of the Feynman-Kac formula. Unlike the earlier papers, the alternative formulation of this paper insists that the equation must hold under a non-dominated family of mutually singular probability measures. The key argument is a stochastic representation, suggested by the optimal control interpretation, and analyzed in our accompanying paperComment: 36 page

"Dose of the day" based on cone beam computed tomography and deformable image registration for lung cancer radiotherapy.

PURPOSE:Adaptive radiotherapy (ART) has potential to reduce toxicity and facilitate safe dose escalation. Dose calculations with the planning CT deformed to cone beam CT (CBCT) have shown promise for estimating the "dose of the day". The purpose of this study is to investigate the "dose of the day" calculation accuracy based on CBCT and deformable image registration (DIR) for lung cancer radiotherapy. METHODS:A total of 12 lung cancer patients were identified, for which daily CBCT imaging was performed for treatment positioning. A re-planning CT (rCT) was acquired after 20 Gy for all patients. A virtual CT (vCT) was created by deforming initial planning CT (pCT) to the simulated CBCT that was generated from deforming CBCT to rCT acquired on the same day. Treatment beams from the initial plan were copied to the vCT and rCT for dose calculation. Dosimetric agreement between vCT-based and rCT-based accumulated doses was evaluated using the Bland-Altman analysis. RESULTS:Mean differences in dose-volume metrics between vCT and rCT were smaller than 1.5%, and most discrepancies fell within the range of ± 5% for the target volume, lung, esophagus, and heart. For spinal cord Dmax , a large mean difference of -5.55% was observed, which was largely attributed to very limited CBCT image quality (e.g., truncation artifacts). CONCLUSION:This study demonstrated a reasonable agreement in dose-volume metrics between dose accumulation based on vCT and rCT, with the exception for cases with poor CBCT image quality. These findings suggest potential utility of vCT for providing a reasonable estimate of the "dose of the day", and thus facilitating the process of ART for lung cancer

Wellposedness of second order backward SDEs

We provide an existence and uniqueness theory for an extension of backward SDEs to the second order. While standard Backward SDEs are naturally connected to semilinear PDEs, our second order extension is connected to fully nonlinear PDEs, as suggested in Cheridito etal. (Commun. Pure Appl. Math. 60(7):1081-1110, 2007). In particular, we provide a fully nonlinear extension of the Feynman-Kac formula. Unlike (Cheridito etal. in Commun. Pure Appl. Math. 60(7):1081-1110, 2007), the alternative formulation of this paper insists that the equation must hold under a non-dominated family of mutually singular probability measures. The key argument is a stochastic representation, suggested by the optimal control interpretation, and analyzed in the accompanying paper (Soner etal. in Dual Formulation of Second Order Target Problems. arXiv:1003.6050, 2009

Converting Treatment Plans From Helical Tomotherapy to L-Shape Linac: Clinical Workflow and Dosimetric Evaluation.

This work evaluated a commercial fallback planning workflow designed to provide cross-platform treatment planning and delivery. A total of 27 helical tomotherapy intensity-modulated radiotherapy plans covering 4 anatomical sites were selected, including 7 brain, 5 unilateral head and neck, 5 bilateral head and neck, 5 pelvis, and 5 prostate cases. All helical tomotherapy plans were converted to 7-field/9-field intensity-modulated radiotherapy and volumetric-modulated radiotherapy plans through fallback dose-mimicking algorithm using a 6-MV beam model. The planning target volume (PTV) coverage ( D1, D99, and homogeneity index) and organs at risk dose constraints were evaluated and compared. Overall, all 3 techniques resulted in relatively inferior target dose coverage compared to helical tomotherapy plans, with higher homogeneity index and maximum dose. The organs at risk dose ratio of fallback to helical tomotherapy plans covered a wide spectrum, from 0.87 to 1.11 on average for all sites, with fallback plans being superior for brain, pelvis, and prostate sites. The quality of fallback plans depends on the delivery technique, field numbers, and angles, as well as user selection of structures for organs at risk. In actual clinical scenario, fallback plans would typically be needed for 1 to 5 fractions of a treatment course in the event of machine breakdown. Our results suggested that <1% dose variance can be introduced in target coverage and/or organs at risk from fallback plans. The presented clinical workflow showed that the fallback plan generation typically takes 10 to 20 minutes per case. Fallback planning provides an expeditious and effective strategy for transferring patients cross platforms, and minimizing the untold risk of a patient missing treatment(s)