Building Support Vector Machines in the Context of Regularised Least Squares

This paper formulates a linear kernel support vector machine (SVM) as a regularized least-squares (RLS) problem. By defining a set of indicator variables of the errors, the solution to the RLS problem is represented as an equation that relates the error vector to the indicator variables. Through partitioning the training set, the SVM weights and bias are expressed analytically using the support vectors. It is also shown how this approach naturally extends to Sums with nonlinear kernels whilst avoiding the need to make use of Lagrange multipliers and duality theory. A fast iterative solution algorithm based on Cholesky decomposition with permutation of the support vectors is suggested as a solution method. The properties of our SVM formulation are analyzed and compared with standard SVMs using a simple example that can be illustrated graphically. The correctness and behavior of our solution (merely derived in the primal context of RLS) is demonstrated using a set of public benchmarking problems for both linear and nonlinear SVMs.

Model reduction for nonlinear aeroelasticity using the Discrete Empirical Interpolation Method

A novel surrogate model is proposed in lieu of computational fluid dynamic (CFD) code for fast nonlinear aerodynamic modeling. First, a nonlinear function is identified on selected interpolation points defined by discrete empirical interpolation method (DEIM). The flow field is then reconstructed by a least square approximation of flow modes extracted by proper orthogonal decomposition (POD). The proposed model is applied in the prediction of limit cycle oscillation for a plunge/pitch airfoil and a delta wing with linear structural model, results are validate against a time accurate CFD-FEM code. The results show the model is able to replicate the aerodynamic forces and flow fields with sufficient accuracy while requiring a fraction of CFD cost.

UK consensus project on quality in palliative day services: developing a quality indicator set using the RAND/UCLA appropriateness method

Introduction
Evaluating quality of palliative day services is essential for assessing care across diverse settings, and for monitoring quality improvement approaches.

Aim
To develop a set of quality indicators for assessment of all aspects (structure, process and outcome) of care in palliative day services.

Methods
Using a modified version of the RAND/UCLA appropriateness method (Fitch et al., 2001), a multidisciplinary panel of 16 experts independently completed a survey rating the appropriateness of 182 potential quality indicators previously identified during a systematic evidence review. Panel members then attended a one day, face-to-face meeting where indicators were discussed and subsequently re-rated. Panel members were also asked to rate the feasibility and necessity of measuring each indicator.

Results
71 indicators classified as inappropriate during the survey were removed based on median appropriateness ratings and level of agreement. Following the panel discussions, a further 60 were removed based on appropriateness and feasibility ratings, level of agreement and assessment of necessity. Themes identified during the panel discussion and findings of the evidence review were used to translate the remaining 51 indicators into a final set of 27.

Conclusion
The final indicator set included information on rationale and supporting evidence, methods of assessment, risk adjustment, and recommended performance levels. Further implementation work will test the suitability of this ‘toolkit’ for measurement and benchmarking. The final indicator set provides the basis for standardised assessment of quality across services, including care delivered in community and primary care settings.

Reference

• Fitch K, Bernstein SJ, Aguilar MD, et al. The RAND/UCLA Appropriateness Method User’s Manual. Santa Monica, CA: RAND Corporation; 2001. http://www.rand.org/pubs/monograph_reports/MR1269

Applying the expanding photosphere and standardized candle methods to Type II-Plateau supernovae at cosmologically significant redshifts . The distance to SN 2013eq

Based on optical imaging and spectroscopy of the Type II-Plateau SN 2013eq, we present a comparative study of commonly used distance determination methods based on Type II supernovae. The occurrence of SN 2013eq in the Hubble flow (z = 0.041 ± 0.001) prompted us to investigate the implications of the difference between "angular" and "luminosity" distances within the framework of the expanding photosphere method (EPM) that relies upon a relation between flux and angular size to yield a distance. Following a re-derivation of the basic equations of the EPM for SNe at non-negligible redshifts, we conclude that the EPM results in an angular distance. The observed flux should be converted into the SN rest frame and the angular size, θ, has to be corrected by a factor of (1 + z)2. Alternatively, the EPM angular distance can be converted to a luminosity distance by implementing a modification of the angular size. For SN 2013eq, we find EPM luminosity distances of DL = 151 ± 18 Mpc and DL = 164 ± 20 Mpc by making use of different sets of dilution factors taken from the literature. Application of the standardized candle method for Type II-P SNe results in an independent luminosity distance estimate (DL = 168 ± 16 Mpc) that is consistent with the EPM estimate. Spectra of SN 2013eq are available in the Weizmann Interactive Supernova data REPository (WISeREP): http://wiserep.weizmann.ac.il