Rarita-Schwinger Type Operators on Spheres and Real Projective Space

In this paper we deal with Rarita-Schwinger type operators on spheres and real projective space. First we define the spherical Rarita-Schwinger type operators and construct their fundamental solutions. Then we establish that the projection operators appearing in the spherical Rarita-Schwinger type operators and the spherical Rarita-Schwinger type equations are conformally invariant under the Cayley transformation. Further, we obtain some basic integral formulas related to the spherical Rarita-Schwinger type operators. Second, we define the Rarita-Schwinger type operators on the real projective space and construct their kernels and Cauchy integral formulas.Comment: 21 pages. arXiv admin note: text overlap with arXiv:1106.358

Spherical harmonics and integration in superspace

In this paper the classical theory of spherical harmonics in R^m is extended to superspace using techniques from Clifford analysis. After defining a super-Laplace operator and studying some basic properties of polynomial null-solutions of this operator, a new type of integration over the supersphere is introduced by exploiting the formal equivalence with an old result of Pizzetti. This integral is then used to prove orthogonality of spherical harmonics of different degree, Green-like theorems and also an extension of the important Funk-Hecke theorem to superspace. Finally, this integration over the supersphere is used to define an integral over the whole superspace and it is proven that this is equivalent with the Berezin integral, thus providing a more sound definition of the Berezin integral.Comment: 22 pages, accepted for publication in J. Phys.

Optical diagnosis of colorectal polyp images using a newly developed computer-aided diagnosis system (CADx) compared with intuitive optical diagnosis

Background Optical diagnosis of colorectal polyps remains challenging. Image-enhancement techniques such as narrow-band imaging and blue-light imaging (BLI) can improve optical diagnosis. We developed and prospectively validated a computer-aided diagnosis system (CADx) using high-definition white-light (HDWL) and BLI images, and compared the system with the optical diagnosis of expert and novice endoscopists.Methods CADx characterized colorectal polyps by exploiting artificial neural networks. Six experts and 13 novices optically diagnosed 60 colorectal polyps based on intuition. After 4 weeks, the same set of images was permuted and optically diagnosed using the BLI Adenoma Serrated International Classification (BASIC).Results CADx had a diagnostic accuracy of 88.3% using HDWL images and 86.7% using BLI images. The overall diagnostic accuracy combining HDWL and BLI (multimodal imaging) was 95.0%, which was significantly higher than that of experts (81.7%, P =0.03) and novices (66.7%, P <0.001). Sensitivity was also higher for CADx (95.6% vs. 61.1% and 55.4%), whereas specificity was higher for experts compared with CADx and novices (95.6% vs. 93.3% and 93.2%). For endoscopists, diagnostic accuracy did not increase when using BASIC, either for experts (intuition 79.5% vs. BASIC 81.7%, P =0.14) or for novices (intuition 66.7% vs. BASIC 66.5%, P =0.95).Conclusion CADx had a significantly higher diagnostic accuracy than experts and novices for the optical diagnosis of colorectal polyps. Multimodal imaging, incorporating both HDWL and BLI, improved the diagnostic accuracy of CADx. BASIC did not increase the diagnostic accuracy of endoscopists compared with intuitive optical diagnosis

Riemann-Hilbert problems for monogenic functions in axially symmetric domains

We consider Riemann-Hilbert boundary value problems (for short RHBVPs) with variable coefficients for axially symmetric monogenic functions defined in axial symmetric domains. This is done by constructing a method to reduce the RHBVPs for axially symmetric monogenic functions defined in four-dimensional axial symmetric domains into the RHBVPs for analytic functions defined over the complex plane. Then we derive solutions to the corresponding Schwarz problem. Finally, we generalize the results obtained to null-solutions of (D−α)ϕ=0, α∈R, where R denotes the field of real numbers

Chloroquine dosing recommendations for pediatric COVID-19 supported by modeling and simulation

As chloroquine (CHQ) is part of the Dutch Centre for Infectious Disease Control COVID-19 experimental treatment guideline, pediatric dosing guidelines are needed. Recent pediatric data suggest that existing WHO dosing guidelines for children with malaria are suboptimal. The aim of our study was to establish best-evidence to inform pediatric CHQ doses for children infected with COVID-19. A previously developed physiologically-based pharmacokinetic (PBPK) model for CHQ was used to simulate exposure in adults and children and verified against published pharmacokinetic data. The COVID-19 recommended adult dosage regimen of 44mg/kg total was tested in adults and children to evaluate the extent of variation in exposure. Based on differences in AUC0-70h the optimal CHQ dose was determined in children of different ages compared to adults. Revised doses were re-introduced into the model to verify that overall CHQ exposure in each age band was within 5% of the predicted adult value. Simulations showed differences in drug exposure in children of different ages and adults when the same body-weight based dose is given. As such, we propose the following total cumulative doses: 35 mg/kg (CHQ base) for children 0-1 month, 47 mg/kg for 1-6 months, 55 mg/kg for 6 months-12 years and 44 mg/kg for adolescents and adults, not to exceed 3300 mg in any patient. Our study supports age-adjusted CHQ dosing in children with COVID-19 in order to avoid suboptimal or toxic doses. The knowledge-driven, model-informed dose selection paradigm can serve as a science-

HIV in hiding: methods and data requirements for the estimation of the number of people living with undiagnosed HIV

Many people who are HIV positive are unaware of their infection status. Estimation of the number of people with undiagnosed HIV within a country or region is vital for understanding future need for treatment and for motivating testing programs. We review the available estimation approaches which are in current use. They can be broadly classified into those based on prevalence surveys and those based on reported HIV and AIDS cases. Estimation based on prevalence data requires data from regular prevalence surveys in different population groups together with estimates of the size of these groups. The recommended minimal case reporting data needed to estimate the number of patients with undiagnosed HIV are HIV diagnoses, including CD4 count at diagnosis and whether there has been an AIDS diagnosis in the 3 months before or after HIV diagnosis, and data on deaths in people with HIV. We would encourage all countries to implement several methods that will help develop our understanding of strengths and weaknesses of the various methods

Multi-state models and arthroplasty histories after unilateral total hip arthroplasties: Introducing the Summary Notation for Arthroplasty Histories

Background and purpose: An increasing number of patients have several joint replacement procedures during their lifetime. We investigated the use and suitability of multi-state model techniques in providing a more comprehensive analysis and description of complex arthroplasty histories held in arthroplasty registries than are allowed for with traditional survival methods. Patients and methods: We obtained data from the Australian Orthopaedic Association National Joint Replacement Registry on patients (n = 84,759) who had undergone a total hip arthroplasty for osteoarthritis in the period 2002–2008. We set up a multi-state model where patients were followed from their first recorded arthroplasty to several possible states: revision of first arthroplasty, either a hip or knee as second arthroplasty, revision of the second arthroplasty, and death. The Summary Notation for Arthroplasty Histories (SNAH) was developed in order to help to manage and analyze this type of data. Results: At the end of the study period, 12% of the 84,759 patients had received a second hip, 3 times as many as had received a knee. The estimated probabilities of having received a second arthroplasty decreased with age. Males had a lower transition rate for receiving a second arthroplasty, but a higher mortality rate. Interpretation: Multi-state models in combination with SNAH codes are well suited to the management and analysis of arthroplasty registry data on patients who experience multiple joint procedures over time. We found differences in the progression of joint replacement procedures after the initial total hip arthroplasty regarding type of joint, age, and sex.Marianne H Gillam, Philip Ryan, Amy Salter, Stephen E Grave

A deep learning system for detection of early Barrett's neoplasia:a model development and validation study

BACKGROUND: Computer-aided detection (CADe) systems could assist endoscopists in detecting early neoplasia in Barrett's oesophagus, which could be difficult to detect in endoscopic images. The aim of this study was to develop, test, and benchmark a CADe system for early neoplasia in Barrett's oesophagus.METHODS: The CADe system was first pretrained with ImageNet followed by domain-specific pretraining with GastroNet. We trained the CADe system on a dataset of 14 046 images (2506 patients) of confirmed Barrett's oesophagus neoplasia and non-dysplastic Barrett's oesophagus from 15 centres. Neoplasia was delineated by 14 Barrett's oesophagus experts for all datasets. We tested the performance of the CADe system on two independent test sets. The all-comers test set comprised 327 (73 patients) non-dysplastic Barrett's oesophagus images, 82 (46 patients) neoplastic images, 180 (66 of the same patients) non-dysplastic Barrett's oesophagus videos, and 71 (45 of the same patients) neoplastic videos. The benchmarking test set comprised 100 (50 patients) neoplastic images, 300 (125 patients) non-dysplastic images, 47 (47 of the same patients) neoplastic videos, and 141 (82 of the same patients) non-dysplastic videos, and was enriched with subtle neoplasia cases. The benchmarking test set was evaluated by 112 endoscopists from six countries (first without CADe and, after 6 weeks, with CADe) and by 28 external international Barrett's oesophagus experts. The primary outcome was the sensitivity of Barrett's neoplasia detection by general endoscopists without CADe assistance versus with CADe assistance on the benchmarking test set. We compared sensitivity using a mixed-effects logistic regression model with conditional odds ratios (ORs; likelihood profile 95% CIs).FINDINGS: Sensitivity for neoplasia detection among endoscopists increased from 74% to 88% with CADe assistance (OR 2·04; 95% CI 1·73-2·42; p&lt;0·0001 for images and from 67% to 79% [2·35; 1·90-2·94; p&lt;0·0001] for video) without compromising specificity (from 89% to 90% [1·07; 0·96-1·19; p=0·20] for images and from 96% to 94% [0·94; 0·79-1·11; ] for video; p=0·46). In the all-comers test set, CADe detected neoplastic lesions in 95% (88-98) of images and 97% (90-99) of videos. In the benchmarking test set, the CADe system was superior to endoscopists in detecting neoplasia (90% vs 74% [OR 3·75; 95% CI 1·93-8·05; p=0·0002] for images and 91% vs 67% [11·68; 3·85-47·53; p&lt;0·0001] for video) and non-inferior to Barrett's oesophagus experts (90% vs 87% [OR 1·74; 95% CI 0·83-3·65] for images and 91% vs 86% [2·94; 0·99-11·40] for video).INTERPRETATION: CADe outperformed endoscopists in detecting Barrett's oesophagus neoplasia and, when used as an assistive tool, it improved their detection rate. CADe detected virtually all neoplasia in a test set of consecutive cases.FUNDING: Olympus.</p