An algorithm for least-squares fitting of cubic spline surfaces to functions on a rectilinear mesh over a rectangle

AbstractIn this paper a method is presented for fitting, in the least-squares sense, a bivariate cubic spline function to values of a dependent variable, specified at points on a rectangular grid in the plane of the independent variables. Products of B-splines are used to represent the bicubic splines. The coefficients in this representation are determined by solving a set of one-dimensional least-squares problems

An algorithm for fitting data over a circle using tensor product splines

AbstractAn algorithm is described for surface fitting over a circle by using tensor product splines which satisfy certain boundary conditions. This algorithm is an extension of an existing one for fitting data over a rectangle. The knots of the splines are chosen automatically but a single parameter must be specified to control the tradeoff between closeness of fit and smoothness of fit. The algorithm can easily be generalized for fitting data over any domain that can be described in polar coordinates. Constraints at the boundaries of this approximation domain can be imposed

Additivity of the Renyi entropy of order 2 for positive-partial-transpose-inducing channels

We prove that the minimal Renyi entropy of order 2 (RE2) output of a positive-partial-transpose(PPT)-inducing channel joint to an arbitrary other channel is equal to the sum of the minimal RE2 output of the individual channels. PPT-inducing channels are channels with a Choi matrix which is bound entangled or separable. The techniques used can be easily recycled to prove additivity for some non-PPT-inducing channels such as the depolarizing and transpose depolarizing channels, though not all known additive channels. We explicitly make the calculations for generalized Werner-Holevo channels as an example of both the scope and limitations of our techniques.Comment: 4 page

One pot ‘click’ reactions: tandem enantioselective biocatalytic epoxide ring opening and [3+2] azide alkyne cycloaddition

Halohydrin dehalogenase (HheC) can perform enantioselective azidolysis of aromatic epoxides to 1,2-azido alcohols which are subsequently ligated to alkynes producing chiral hydroxy triazoles in a one-pot procedure with excellent enantiomeric excess.

Adaptive Path Planning for Depth Constrained Bathymetric Mapping with an Autonomous Surface Vessel

This paper describes the design, implementation and testing of a suite of algorithms to enable depth constrained autonomous bathymetric (underwater topography) mapping by an Autonomous Surface Vessel (ASV). Given a target depth and a bounding polygon, the ASV will find and follow the intersection of the bounding polygon and the depth contour as modeled online with a Gaussian Process (GP). This intersection, once mapped, will then be used as a boundary within which a path will be planned for coverage to build a map of the Bathymetry. Methods for sequential updates to GP's are described allowing online fitting, prediction and hyper-parameter optimisation on a small embedded PC. New algorithms are introduced for the partitioning of convex polygons to allow efficient path planning for coverage. These algorithms are tested both in simulation and in the field with a small twin hull differential thrust vessel built for the task.Comment: 21 pages, 9 Figures, 1 Table. Submitted to The Journal of Field Robotic

Drift of scrollwaves in a mathematical model of a heterogeneous human heart left ventricle

Rotating spiral waves of electrical excitation underlie many dangerous cardiac arrhythmias. The heterogeneity of myocardium is one of the factors that affects the dynamics of such waves. In this paper, we present results of our simulations for scroll wave dynamics in a heterogeneous model of the human left ventricle with analytical anatomically based representation of the geometry and anisotropy. We used a set of 18 coupled differential equations developed by ten Tusscher and Panfilov (TP06 model) which describes human ventricular cells based on their measured biophysical properties. We found that apicobasal heterogeneity dramatically changes the scroll wave dynamics. In the homogeneous model, the scroll wave annihilates at the base, but the moderate heterogeneity causes the wave to move to the apex and then continuously rotates around it. The rotation speed increased with the degree of the heterogeneity. However, for large heterogeneity, we observed formation of additional wavebreaks and the onset of complex spatio-temporal patterns. Transmural heterogeneity did not change the dynamics and decreased the lifetime of the scroll wave with an increase in heterogeneity. Results of our numerical experiments show that the apex may be a preferable location of the scroll wave, which may be important for development of clinical interventions. © 2020 by the authors.AAAA-A18-118020590031-8Russian Foundation for Basic Research, RFBR: 18-29-13008Russian Science Foundation, RSF: 14-35-00005Ural Federal University, UrFUP.K., S.P., O.S., and A.V.P. were funded by the Russian Science Foundation (project 14-35-00005). A.V.P., P.K., and O.S. were funded by the Russian Foundation for Basic Research (#18-29-13008). A.V.P. and O.S. were funded by RF Government Act #211 of 16 March 2013 (agreement 02. A03.21.0006). P.K. and O.S. work was carried out within the framework of the IIF UrB RAS theme No. AAAA-A18-118020590031-8. A.V.P. and H.D. were partially funded by BOF Ghent University. Simulations were performed at the supercomputer Uran of Institute of Mathematics and Mechanics (Ekaterinburg, Russia) and at the supercomputer of Ural Federal University (Ekaterinburg, Russia)

The integrated nuclear medicine and radiology residency program in the Netherlands:strengths and potential areas for improvement according to nuclear medicine physicians and radiologists

PURPOSE: To evaluate the Dutch integrated nuclear medicine and radiology residency program from the perspective of nuclear medicine physicians and radiologists. METHODS: A survey was distributed among nuclear medicine physicians and radiologists in hospitals that participate in the Dutch integrated nuclear medicine and radiology training program. RESULTS: A total of 139 completed questionnaires were included. Nuclear medicine physicians (n = 36) assigned a mean score of 5.7 ± 2.0, and radiologists (n = 103) assigned a mean score of 6.5 ± 2.8 (on a 1-10 scale) to the success of the integrated training program in their hospital. On multiple regression, female gender of the survey participant (B = 2.22, P = 0.034), musculoskeletal radiology as subspecialty of the survey participant (B = 3.36, P = 0.032), and the survey participant's expectancy of resident's ability to handle workload after completion of residency were significantly associated with perceived success of the integrated training program (B = 1.16, P = 0.023). Perceived strengths of the integrated training program included broadening of expertise, a better preparation of future imaging specialists for hybrid imaging, increased efficiency in training residents, and increased efficiency in multidisciplinary meetings. Perceived weaknesses of the integrated training program included reduced exposure to nuclear medicine, less time for research and innovation, and concerns about its international recognition. CONCLUSION: This study provided insights into the experiences of nuclear medicine physicians and radiologists with the Dutch integrated nuclear medicine and radiology residency program, which may be helpful to improve the program and similar residency programs in other countries

Time to Reconsider Routine Percutaneous Biopsy in Spondylodiscitis?

Percutaneous image-guided biopsy currently has a central role in the diagnostic work-up of patients with suspected spondylodiscitis. However, on the basis of recent evidence, the value of routine image-guided biopsy in this disease can be challenged. In this article, we discuss this recent evidence and also share a new diagnostic algorithm for spondylodiscitis that was recently introduced at our institution. Thus, we may move from a rather dogmatic approach in which routine image-guided biopsy is performed in any case to a more individualized use of this procedure. Percutaneous image-guided biopsy, while valuable, is an invasive procedure, and evidence has shown rather disappointing positive microbiologic culture yields of around 33%. Recent evidence also has shown that percutaneous image-guided biopsy rarely adds any new information when blood cultures have positive findings and that an effective empiric treatment can be started in most of cases even when the microbiologic culprit remains unknown. Finally, there is currently no evidence that percutaneous image-guided biopsy improves patient outcome

Validation of the AUDIT and AUDIT-C for hazardous drinking in community-dwelling older adults

Background: One of the best-known tools in screening for hazardous drinking is the Alcohol Use Disorders Identification Test (AUDIT) and its abbreviated form, the AUDIT-C. The aim of the present study is to determine the cut-offs of both instruments in identifying hazardous drinking in older adults. Method: A sample of 1577 older adults completed a questionnaire regarding alcohol behavior. Hazardous drinking was defined as drinking >10 units/week. Receiver operating characteristics (ROC) curves of AUDIT and AUDIT-C were calculated and cut-off scores were derived. Results: Respectively 27.3% and 12.3% of older men and women drank >10 units/week. For the AUDIT the best trade-off between sensitivity and specificity was using a cut-off of ≥5 for men and ≥4 for women, which yielded in men sensitivity and specificity values respectively of 80.7% and 81.3% and in women 100% and 71.7%, respectively. We found the AUDIT-C to perform well with an optimal cut-off of ≥5 for men and ≥4 for women, which generated in men sensitivity and specificity values respectively of 76.5% and 85.3% and in women 100% and 74.1%, respectively. Conclusion: The AUDIT-C is accurate and sufficient in screening for hazardous drinking in community-dwelling older adults if the cut-offs are tailored by gender