Hermite and Gegenbauer polynomials in superspace using Clifford analysis

The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way. This means that one does not a priori need an integration theory in superspace. Furthermore a lot of basic properties, such as orthogonality relations, differential equations and recursion formulae are proven. Finally, an interesting physical application of the super Clifford-Hermite polynomials is discussed, thus giving an interpretation to the super-dimension.Comment: 18 pages, accepted for publication in J. Phys.

Quadratic Lagrangians and Topology in Gauge Theory Gravity

We consider topological contributions to the action integral in a gauge theory formulation of gravity. Two topological invariants are found and are shown to arise from the scalar and pseudoscalar parts of a single integral. Neither of these action integrals contribute to the classical field equations. An identity is found for the invariants that is valid for non-symmetric Riemann tensors, generalizing the usual GR expression for the topological invariants. The link with Yang-Mills instantons in Euclidean gravity is also explored. Ten independent quadratic terms are constructed from the Riemann tensor, and the topological invariants reduce these to eight possible independent terms for a quadratic Lagrangian. The resulting field equations for the parity non-violating terms are presented. Our derivations of these results are considerably simpler that those found in the literature

Introductory clifford analysis

In this chapter an introduction is given to Clifford analysis and the underlying Clifford algebras. The functions under consideration are defined on Euclidean space and take values in the universal real or complex Clifford algebra, the structure and properties of which are also recalled in detail. The function theory is centered around the notion of a monogenic function, which is a null solution of a generalized Cauchy–Riemann operator, which is rotation invariant and factorizes the Laplace operator. In this way, Clifford analysis may be considered as both a generalization to higher dimension of the theory of holomorphic functions in the complex plane and a refinement of classical harmonic analysis. A notion of monogenicity may also be associated with the vectorial part of the Cauchy–Riemann operator, which is called the Dirac operator; some attention is paid to the intimate relation between both notions. Since a product of monogenic functions is, in general, no longer monogenic, it is crucial to possess some tools for generating monogenic functions: such tools are provided by Fueter’s theorem on one hand and the Cauchy–Kovalevskaya extension theorem on the other hand. A corner stone in this function theory is the Cauchy integral formula for representation of a monogenic function in the interior of its domain of monogenicity. Starting from this representation formula and related integral formulae, it is possible to consider integral transforms such as Cauchy, Hilbert, and Radon transforms, which are important both within the theoretical framework and in view of possible applications

Deep learning-based recognition of key anatomical structures during robot-assisted minimally invasive esophagectomy

Objective: To develop a deep learning algorithm for anatomy recognition in thoracoscopic video frames from robot-assisted minimally invasive esophagectomy (RAMIE) procedures using deep learning. Background: RAMIE is a complex operation with substantial perioperative morbidity and a considerable learning curve. Automatic anatomy recognition may improve surgical orientation and recognition of anatomical structures and might contribute to reducing morbidity or learning curves. Studies regarding anatomy recognition in complex surgical procedures are currently lacking. Methods: Eighty-three videos of consecutive RAMIE procedures between 2018 and 2022 were retrospectively collected at University Medical Center Utrecht. A surgical PhD candidate and an expert surgeon annotated the azygos vein and vena cava, aorta, and right lung on 1050 thoracoscopic frames. 850 frames were used for training of a convolutional neural network (CNN) to segment the anatomical structures. The remaining 200 frames of the dataset were used for testing the CNN. The Dice and 95% Hausdorff distance (95HD) were calculated to assess algorithm accuracy. Results: The median Dice of the algorithm was 0.79 (IQR = 0.20) for segmentation of the azygos vein and/or vena cava. A median Dice coefficient of 0.74 (IQR = 0.86) and 0.89 (IQR = 0.30) were obtained for segmentation of the aorta and lung, respectively. Inference time was 0.026 s (39 Hz). The prediction of the deep learning algorithm was compared with the expert surgeon annotations, showing an accuracy measured in median Dice of 0.70 (IQR = 0.19), 0.88 (IQR = 0.07), and 0.90 (0.10) for the vena cava and/or azygos vein, aorta, and lung, respectively. Conclusion: This study shows that deep learning-based semantic segmentation has potential for anatomy recognition in RAMIE video frames. The inference time of the algorithm facilitated real-time anatomy recognition. Clinical applicability should be assessed in prospective clinical studies.</p

Hilbert transforms in Clifford analysis

The Hilbert transform on the real line has applications in many fields. In particular in one–dimensional signal processing, the Hilbert operator is used to extract global as well as instantaneous characteristics, such as frequency, amplitude and phase, from real signals. The multidimensional approach to the Hilbert transform usually is a tensorial one, considering the so-called Riesz transforms in each of the cartesian variables separately. In this paper we give an overview of generalized Hilbert transforms in Euclidean space, developed within the framework of Clifford analysis. Roughly speaking, this is a function theory of higher dimensional holomorphic functions, which is particularly suited for a treatment of multidimensional phenomena since all dimensions are encompassed at once as an intrinsic feature

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

Early esophageal adenocarcinoma detection using deep learning methods

Purpose This study aims to adapt and evaluate the performance of different state-of-the-art deep learning object detection methods to automatically identify esophageal adenocarcinoma (EAC) regions from high-definition white light endoscopy (HD-WLE) images. Method Several state-of-the-art object detection methods using Convolutional Neural Networks (CNNs) were adapted to automatically detect abnormal regions in the esophagus HD-WLE images, utilizing VGG’16 as the backbone architecture for feature extraction. Those methods are Regional-based Convolutional Neural Network (R-CNN), Fast R-CNN, Faster R-CNN and Single-Shot Multibox Detector (SSD). For the evaluation of the different methods, 100 images from 39 patients that have been manually annotated by five experienced clinicians as ground truth have been tested. Results Experimental results illustrate that the SSD and Faster R-CNN networks show promising results, and the SSD outperforms other methods achieving a sensitivity of 0.96, specificity of 0.92 and F-measure of 0.94. Additionally, the Average Recall Rate of the Faster R-CNN in locating the EAC region accurately is 0.83. Conclusion In this paper, recent deep learning object detection methods are adapted to detect esophageal abnormalities automatically. The evaluation of the methods proved its ability to locate abnormal regions in the esophagus from endoscopic images. The automatic detection is a crucial step that may help early detection and treatment of EAC and also can improve automatic tumor segmentation to monitor its growth and treatment outcome

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