Global Saturation of Regularization Methods for Inverse Ill-Posed Problems

In this article the concept of saturation of an arbitrary regularization method is formalized based upon the original idea of saturation for spectral regularization methods introduced by A. Neubauer in 1994. Necessary and sufficient conditions for a regularization method to have global saturation are provided. It is shown that for a method to have global saturation the total error must be optimal in two senses, namely as optimal order of convergence over a certain set which at the same time, must be optimal (in a very precise sense) with respect to the error. Finally, two converse results are proved and the theory is applied to find sufficient conditions which ensure the existence of global saturation for spectral methods with classical qualification of finite positive order and for methods with maximal qualification. Finally, several examples of regularization methods possessing global saturation are shown.Comment: 29 page

Generalized Qualification and Qualification Levels for Spectral Regularization Methods

The concept of qualification for spectral regularization methods for inverse ill-posed problems is strongly associated to the optimal order of convergence of the regularization error. In this article, the definition of qualification is extended and three different levels are introduced: weak, strong and optimal. It is shown that the weak qualification extends the definition introduced by Mathe and Pereverzev in 2003, mainly in the sense that the functions associated to orders of convergence and source sets need not be the same. It is shown that certain methods possessing infinite classical qualification, e.g. truncated singular value decomposition (TSVD), Landweber's method and Showalter's method, also have generalized qualification leading to an optimal order of convergence of the regularization error. Sufficient conditions for a SRM to have weak qualification are provided and necessary and sufficient conditions for a given order of convergence to be strong or optimal qualification are found. Examples of all three qualification levels are provided and the relationships between them as well as with the classical concept of qualification and the qualification introduced by Mathe and Perevezev are shown. In particular, spectral regularization methods having extended qualification in each one of the three levels and having zero or infinite classical qualification are presented. Finally several implications of this theory in the context of orders of convergence, converse results and maximal source sets for inverse ill-posed problems, are shown.Comment: 20 pages, 1 figur

Parallel block structured adaptive mesh refinement on graphics processing units.

Block-structured adaptive mesh refinement is a technique that can be used when solving partial differential equations to reduce the number of zones necessary to achieve the required accuracy in areas of interest. These areas (shock fronts, material interfaces, etc.) are recursively covered with finer mesh patches that are grouped into a hierarchy of refinement levels. Despite the potential for large savings in computational requirements and memory usage without a corresponding reduction in accuracy, AMR adds overhead in managing the mesh hierarchy, adding complex communication and data movement requirements to a simulation. In this paper, we describe the design and implementation of a native GPU-based AMR library, including: the classes used to manage data on a mesh patch, the routines used for transferring data between GPUs on different nodes, and the data-parallel operators developed to coarsen and refine mesh data. We validate the performance and accuracy of our implementation using three test problems and two architectures: an eight-node cluster, and over four thousand nodes of Oak Ridge National Laboratory’s Titan supercomputer. Our GPU-based AMR hydrodynamics code performs up to 4.87x faster than the CPU-based implementation, and has been scaled to over four thousand GPUs using a combination of MPI and CUDA

Tailoring of the Tell-us Card communication tool for nurses to increase patient participation using Intervention Mapping

Aims and objectives: To describe the tailoring of the Tell-us Card intervention for enhanced patient participation to the Dutch hospital setting using Intervention Mapping as a systematic approach. Background: Even though patient participation is essential in any patient-to-nurse encounter, care plans often fail to take patients' preferences into account. The Tell-us Card intervention seems promising, but needs to be tailored and tested before implementation in a different setting or on large scale. Design: Description of the Intervention Mapping framework to systematically tailor the Tell-us Card intervention to the Dutch hospital setting. Methods: Intervention Mapping consists of: (i) identification of the problem through needs assessment and determination of fit, based on patients and nurses interviews and focus group interviews; (ii) developing a logic model of change and matrices, based on literature and interviews; (iii) selection of theory-based methods and practical applications; (iv) producing programme components and piloting; (v) planning for adoption, implementation and sustainability; and (vi) preparing for programme evaluation. Results: Knowledge, attitude, outcome expectations, self-efficacy and skills were identified as the main determinants influencing the use of the Tell-us Card. Linking identified determinants and performance objectives with behaviour change techniques from the literature resulted in a well-defined and tailored intervention and evaluation plan. Conclusions: The Tell-us Card intervention was adapted to fit the Dutch hospital setting and prepared for evaluation. The Medical Research Council framework was followed, and the Intervention Mapping approach was used to prepare a pilot study to confirm feasibility and relevant outcomes. Relevance to clinical practice: This article shows how Intervention Mapping is applied within the Medical Research Council framework to adapt the Tell-us Card intervention, which could serve as a guide for the tailoring of similar interventions

A randomised feasibility study of serial magnetic resonance imaging to reduce treatment times in Charcot neuroarthropathy in people with diabetes (CADOM): A protocol

Background Charcot neuroarthropathy is a complication of peripheral neuropathy associated with diabetes which most frequently affects the lower limb. It can cause fractures and dislocations within the foot, which may progress to deformity and ulceration. Recommended treatment is immobilisation and offloading, with a below knee non-removable cast or boot. Duration of treatment varies from six months to more than one year. Small observational studies suggest that repeated assessment with Magnetic Resonance Imaging improves decision making about when to stop treatment, but this has not been tested in clinical trials. This study aims to explore the feasibility of using serial Magnetic Resonance Imaging without contrast in the monitoring of Charcot neuroarthropathy to reduce duration of immobilisation of the foot. A nested qualitative study aims to explore participants’ lived experience of Charcot neuroarthropathy and of taking part in the feasibility study. Methods We will undertake a two arm, open study, and randomise 60 people with a suspected or confirmed diagnosis of Charcot neuroarthropathy from five NHS, secondary care multidisciplinary Diabetic Foot Clinics across England. Participants will be randomised 1:1 to receive Magnetic Resonance Imaging at baseline and remission up to 12 months, with repeated foot temperature measurements and x-rays (standard care plus), or standard care plus with additional three-monthly Magnetic Resonance Imaging until remission up to 12 months (intervention). Time to confirmed remission of Charcot neuroarthropathy with off-loading treatment (days) and its variance will be used to inform sample size in a full-scale trial. We will look for opportunities to improve the protocols for monitoring techniques and the clinical, patient centred, and health economic measures used in a future study. For the nested qualitative study, we will invite a purposive sample of 10-14 people able to offer maximally varying experiences from the feasibility study to take part in semi-structured interviews to be analysed using thematic analysis. Discussion The study will inform the decision whether to proceed to a full-scale trial. It will also allow deeper understanding of the lived experience of Charcot neuroarthropathy, and factors that contribute to engagement in management and contribute to the development of more effective patient centred strategies. Trial registration ISRCTN, ISRCTN, 74101606. Registered on 6 November 2017, http://www.isrctn.com/ISRCTN74101606?q=CADom&filters=&sort=&offset=1&totalResults=1&page=1&pageSize=10&searchType=basic-searc

(CNRS URA 2172),

Genotyping of axenic and non-axenic isolates of the genus Prochlorococcus and the OMF-‘Synechococcus ’ clade by size, sequence analysis or RFLP of the Internal Transcribed Spacer of the ribosomal opero

Vestibular Rehabilitation for Peripheral Vestibular Hypofunction: An Evidence-Based Clinical Practice Guideline: From the American Physical Therapy Association Neurology Section

Background: Uncompensated vestibular hypofunction results in postural instability, visual blurring with head movement, and subjective complaints of dizziness and/or imbalance. We sought to answer the question, \ Is vestibular exercise effective at enhancing recovery of function in people with peripheral (unilateral or bilateral) vestibular hypofunction?\ Methods: A systematic review of the literature was performed in 5 databases published after 1985 and 5 additional sources for relevant publications were searched. Article types included meta-analyses, systematic reviews, randomized controlled trials, cohort studies, case control series, and case series for human subjects, published in English. One hundred thirty-five articles were identified as relevant to this clinical practice guideline. Results/Discussion: Based on strong evidence and a preponderance of benefit over harm, clinicians should offer vestibular rehabilitation to persons with unilateral and bilateral vestibular hypofunction with impairments and functional limitations related to the vestibular deficit. Based on strong evidence and a preponderance of harm over benefit, clinicians should not include voluntary saccadic or smooth-pursuit eye movements in isolation (ie, without head movement) as specific exercises for gaze stability. Based on moderate evidence, clinicians may offer specific exercise techniques to target identified impairments or functional limitations. Based on moderate evidence and in consideration of patient preference, clinicians may provide supervised vestibular rehabilitation. Based on expert opinion extrapolated from the evidence, clinicians may prescribe a minimum of 3 times per day for the performance of gaze stability exercises as 1 component of a home exercise program. Based on expert opinion extrapolated from the evidence (range of supervised visits: 2-38 weeks, mean = 10 weeks), clinicians may consider providing adequate supervised vestibular rehabilitation sessions for the patient to understand the goals of the program and how to manage and progress themselves independently. As a general guide, persons without significant comorbidities that affect mobility and with acute or subacute unilateral vestibular hypofunction may need once a week supervised sessions for 2 to 3 weeks; persons with chronic unilateral vestibular hypofunction may need once a week sessions for 4 to 6 weeks; and persons with bilateral vestibular hypofunction may need once a week sessions for 8 to 12 weeks. In addition to supervised sessions, patients are provided a daily home exercise program. Disclaimer: These recommendations are intended as a guide for physical therapists and clinicians to optimize rehabilitation outcomes for persons with peripheral vestibular hypofunction undergoing vestibular rehabilitation

Introducing the composite time trade-off: a test of feasibility and face validity

__Abstract__ __Introduction__ This study was designed to test the feasibility and face validity of the composite time trade-off (composite TTO), a new approach to TTO allowing for a more consistent elicitation of negative health state values. __Methods__ The new instrument combines a conventional TTO to elicit values for states regarded better than dead and a lead-time TTO for states worse than dead. __Results__ A total of 121 participants completed the composite TTO for ten EQ-5D-5L health states. Mean values ranged from −0.104 for health state 53555 to 0.946 for 21111. The instructions were clear to 98 % of the respondents, and 95 % found the task easy to understand, indicating feasibility. Further, the average number of steps taken in the iteration procedure to achieve the point of indifference in the TTO and the average duration of each task were indicative of a deliberate cognitive process. __Conclusion__ Face validity was confirmed by the high mean values for the mild health states (>0.90) and low mean values for the severe states (<0.42). In conclusion, this study demonstrates the feasibility and face validity of the composite TTO in a face-to-face standardized computer-assisted interview setting

Telephone conversation impairs sustained visual attention via a central bottleneck

Recent research has shown that holding telephone conversations disrupts one's driving ability. We asked whether this effect could be attributed to a visual attention impairment. In Experiment 1, participants conversed on a telephone or listened to a narrative while engaged in multiple object tracking (MOT), a task requiring sustained visual attention. We found that MOT was disrupted in the telephone conversation condition, relative to single-task MOT performance, but that listening to a narrative had no effect. In Experiment 2, we asked which component of conversation might be interfering with MOT performance. We replicated the conversation and single-task conditions of Experiment 1 and added two conditions in which participants heard a sequence of words over a telephone. In the shadowing condition, participants simply repeated each word in the sequence. In the generation condition, participants were asked to generate a new word based on each word in the sequence. Word generation interfered with MOT performance, but shadowing did not. The data indicate that telephone conversation disrupts attention at a central stage, the act of generating verbal stimuli, rather than at a peripheral stage, such as listening or speaking