Use of lp norms in fitting curves and surfaces to data

Given a family of curves or surfaces in R s , an important problem is that of finding a member of the family which gives a "best" fit to m given data points. A criterion which is relevant to many application areas is orthogonal distance regression, where the sum of squares of the orthogonal distances from the data points to the surface is minimized. For example, this is important in metrology, where measured data from a manufactured part may have to be modelled. The least squares norm is not always suitable (for example, there may be wild points in the data, accept/reject decisions may be required, etc). So we use this to justify looking at the use of other l p norms. There are different ways to formulate the problem, and we examine methods which generalize in a natural way those available for least squares. The emphasis is on the efficient numerical treatment of the resulting problems

The role of metrology in axSpA : does it provide unique information in assessing patients and predicting outcome? Results from the BSRBR-AS registry

ACKNOWLEDGMENTS We thank the staff who contributed to running the BSRBR-AS register and we also thank the recruiting staff at the clinical centers, details of which are available at: www.abdn.ac.uk/bsrbr-as.Peer reviewedPostprin

Identifying Persons with Axial Spondyloarthritis At Risk of Poor Work Outcome : Results from the British Society for Rheumatology Biologics Register

MRC/Arthritis Research UK Centre for Musculoskeletal Health and Work (grant no: 20665 CI KW-B). The BSRBR-AS is funded by the British Society for Rheumatology who have received funding for this from Pfizer, AbbVie and UCB. These companies receive advance copies of manuscripts for comments. They have no input in determining the topics for analysis or work involved in undertaking it.Peer reviewedPostprin

Hybrid quantum-classical algorithms and quantum error mitigation

Quantum computers can exploit a Hilbert space whose dimension increases exponentially with the number of qubits. In experiment, quantum supremacy has recently been achieved by the Google team by using a noisy intermediate-scale quantum (NISQ) device with over 50 qubits. However, the question of what can be implemented on NISQ devices is still not fully explored, and discovering useful tasks for such devices is a topic of considerable interest. Hybrid quantum-classical algorithms are regarded as well-suited for execution on NISQ devices by combining quantum computers with classical computers, and are expected to be the first useful applications for quantum computing. Meanwhile, mitigation of errors on quantum processors is also crucial to obtain reliable results. In this article, we review the basic results for hybrid quantum-classical algorithms and quantum error mitigation techniques. Since quantum computing with NISQ devices is an actively developing field, we expect this review to be a useful basis for future studies

Topical Review: Extracting Molecular Frame Photoionization Dynamics from Experimental Data

Methods for experimental reconstruction of molecular frame (MF) photoionization dynamics, and related properties - specifically MF photoelectron angular distributions (PADs) and continuum density matrices - are outlined and discussed. General concepts are introduced for the non-expert reader, and experimental and theoretical techniques are further outlined in some depth. Particular focus is placed on a detailed example of numerical reconstruction techniques for matrix-element retrieval from time-domain experimental measurements making use of rotational-wavepackets (i.e. aligned frame measurements) - the ``bootstrapping to the MF" methodology - and a matrix-inversion technique for direct MF-PAD recovery. Ongoing resources for interested researchers are also introduced, including sample data, reconstruction codes (the \textit{Photoelectron Metrology Toolkit}, written in python, and associated \textit{Quantum Metrology with Photoelectrons} platform/ecosystem), and literature via online repositories; it is hoped these resources will be of ongoing use to the community.Comment: 65 pages, 17 figures. HTML version with interactive figures on Authorea: https://www.authorea.com/users/71114/articles/447808-extracting-molecular-frame-photoionization-dynamics-from-experimental-data Code and data archive on Figshare: http://dx.doi.org/10.6084/m9.figshare.2029378

Characterisation of computed tomography noise in projection space with applications to additive manufacturing

X-ray computed tomography can be used for defect detection in additive manufacturing. Typically, several x-ray projections of the product at hundreds of angles are used to reconstruct the object in 3D to look for any defects. The process can be time-consuming. This thesis aims to investigate if it is possible to conduct defect detection from a single projection to speed up the process. An additive manufacturing test sample was created with voids to see if they can be detected. The uncertainty of the projection was modelled using a compound Poisson distribution. This arises from x-ray photon arrivals being a Poisson process and each photon has random energy. This results in a linear relationship between the mean and variance of the grey values in the projection. Fitting of the compound Poisson distribution using the expectation maximisation algorithm was unsuccessful due to identifiability issues with the model. Instead, a gamma-distributed generalised linear model was fitted onto sample variance-mean data and used for variance prediction to quantify the uncertainty. Software, called aRTist, was used to simulate the projection and compared with the experimental projection in the face of uncertainty by treating each pixel as a hypothesis test. To overcome the imperfections of the simulation, the empirical null filter was used to cater for model misspecification so that sensible inference was achieved. This was done by locally normalising the test statistics using the mode. Voids with diameters in the order of millimetres were detectable. This thesis is a contribution to real-time quality control in additive manufacturing