Sliced Optimal Transport on the Sphere

Sliced optimal transport reduces optimal transport on multi-dimensional domains to transport on the line. More precisely, sliced optimal transport is the concatenation of the well-known Radon transform and the cumulative density transform, which analytically yields the solutions of the reduced transport problems. Inspired by this concept, we propose two adaptions for optimal transport on the 2-sphere. Firstly, as counterpart to the Radon transform, we introduce the vertical slice transform, which integrates along all circles orthogonal to a given direction. Secondly, we introduce the weighted semicircle transform, which integrates along all half great circles. Both transforms are generalized to arbitrary measures on the sphere. While the vertical slice transform can be combined with optimal transport on the interval and leads to a sliced Wasserstein distance restricted to even probability measures, the semicircle transform is related to optimal transport on the circle and results in a different sliced Wasserstein distance for arbitrary probability measures. The applicability of both novel sliced optimal transport concepts on the sphere is demonstrated by proof-of-concept examples dealing with the interpolation and classification of spherical probability measures. The numerical implementation relies on the singular value decompositions of both transforms and fast Fourier techniques. For the inversion with respect to probability measures, we propose the minimization of an entropy-regularized Kullback--Leibler divergence, which can be numerically realized using a primal-dual proximal splitting algorithm.Comment: 38 pages, 6 figure

The Pipeline for the Continuous Development of Artificial Intelligence Models -- Current State of Research and Practice

Companies struggle to continuously develop and deploy AI models to complex production systems due to AI characteristics while assuring quality. To ease the development process, continuous pipelines for AI have become an active research area where consolidated and in-depth analysis regarding the terminology, triggers, tasks, and challenges is required. This paper includes a Multivocal Literature Review where we consolidated 151 relevant formal and informal sources. In addition, nine-semi structured interviews with participants from academia and industry verified and extended the obtained information. Based on these sources, this paper provides and compares terminologies for DevOps and CI/CD for AI, MLOps, (end-to-end) lifecycle management, and CD4ML. Furthermore, the paper provides an aggregated list of potential triggers for reiterating the pipeline, such as alert systems or schedules. In addition, this work uses a taxonomy creation strategy to present a consolidated pipeline comprising tasks regarding the continuous development of AI. This pipeline consists of four stages: Data Handling, Model Learning, Software Development and System Operations. Moreover, we map challenges regarding pipeline implementation, adaption, and usage for the continuous development of AI to these four stages.Comment: accepted in the Journal Systems and Softwar

Motion Detection in Diffraction Tomography by Common Circle Methods

The method of common lines is a well-established reconstruction technique in cryogenic electron microscopy (cryo-EM), which can be used to extract the relative orientations of an object in tomographic projection images from different directions. In this paper, we deal with an analogous problem in optical diffraction tomography. Based on the Fourier diffraction theorem, we show that rigid motions, i.e., a map composed of rotations and translations, can be determined by detecting common circles in the Fourier-transformed data. We introduce two methods based on the idea of identifying common circles to reconstruct the object motion: While the first one is motivated by the common line approach for projection images and detects the relative orientation by the shape of the common circles in the two images, the second one assumes a smooth motion over time and calculates the angular velocity of the rotational motion from an infinitesimal version of the common circle method. Interestingly, using the stereographic projection, both methods can be reformulated as common line methods, but these lines are, in contrast to those used in cryo-EM, not confined to pass through the origin and allow for a full reconstruction of the relative orientation. Numerical proof-of-the-concept examples demonstrate the performance of our reconstruction methods.Comment: 35 pages, 13 figure

Effect of two cleaning processes for bone allografts on gentamicin impregnation and in vitro antibiotic release.

Bone allografts are a useful and sometimes indispensable tool for the surgeon to repair bone defects. Microbial contamination is a major reason for discarding allografts from bone banks. To improve the number of safe allografts, we suggest chemical cleaning of the grafts followed by antibiotic impregnation. Comparison of two chemical cleaning processes for bone allografts aiming for antibiotic impregnation and consequently delivery rates in vitro. Bone chips of 5–10 mm were prepared from human femoral heads. Two cleaning methods (cleaning A and cleaning B) based on solutions containing hydrogen peroxide, paracetic acid, ethanol and biological detergent were carried out and compared. After the cleaning processes, the bone chips were impregnated with gentamicin. Bacillus subtilis bioassay was used to determine the gentamicin release after intervals of 1–7 days. Differences were compared with non-parametric Mann–Whitney U tests. The zones of inhibition obtained from the bone grafts cleaned with both cleaning processes were similar between the groups. The concentration of the released antibiotic was decreasing gradually over time, following a similar pattern for both groups. The cleaning procedure A as well as the cleaning procedure B for bone allografts allowed the impregnation with gentamicin powder in the same concentrations in both groups. The delivery of gentamicin was similar for both groups. Both cleaning procedures were easy to be carried out, making them suitable for routine use at the bone banks

Biological Maturity Status, Anthropometric Percentiles, and Core Flexion to Extension Strength Ratio as Possible Traumatic and Overuse Injury Risk Factors in Youth Alpine Ski Racers: A Four-Year Prospective Study

The aim of the present study was to investigate prospectively the role of biological maturity status, anthropometric percentiles, and core flexion to extension strength ratios in the context of traumatic and overuse injury risk identification in youth ski racing. In this study, 72 elite youth ski racers (45 males, 27 females) were prospectively observed from the age of 10 to 14 years. Anthropometric parameters, biological maturity status, and core flexion to extension strength ratios were assessed twice per year. Type and severity of traumatic and overuse injuries were prospectively recorded during the 4 years. Generalized estimating equations were used to model the binary outcome (0: no injury; 1: ≥1 injury). Factors tested on association with injury risk were sex, relative age quarter, age, maturity group, puberty status, core flexion to extension strength ratio, height percentile group, and weight percentile group. In total, 104 traumatic injuries and 39 overuse injuries were recorded. Age (odds ratio (OR) = 3.36) and weight percentile group (OR = 0.38) were significant risk factors for traumatic injuries (tendency: pubertal status). No significant risk factor for overuse injuries was identified (tendency: maturity group, puberty status, height percentile group). Future studies should focus on identifying risk factors for overuse injuries; growth rates might be of importance