Search results for "Linear"
showing 10 items of 7165 documents
The Effective Sample Size
2013
Model selection procedures often depend explicitly on the sample size n of the experiment. One example is the Bayesian information criterion (BIC) criterion and another is the use of Zellner–Siow priors in Bayesian model selection. Sample size is well-defined if one has i.i.d real observations, but is not well-defined for vector observations or in non-i.i.d. settings; extensions of critera such as BIC to such settings thus requires a definition of effective sample size that applies also in such cases. A definition of effective sample size that applies to fairly general linear models is proposed and illustrated in a variety of situations. The definition is also used to propose a suitable ‘sc…
Agreement among 3 optical imaging methods for the assessment of optic disc topography.
2005
Purpose To assess the agreement of disc topography measurements between the Heidelberg Retina Tomograph (HRT II), Retinal Thickness Analyzer (RTA), and Optical Coherence Tomograph (StratusOCT). Design Observational cross-sectional study. Participants Forty-two randomly chosen eyes of 42 subjects. Methods Each subject underwent HRT II, RTA, and StratusOCT examination. Two experienced examiners drew the contour lines for the HRT II and RTA. Bland and Altman plots were used to evaluate agreement for each topographic parameter among the instruments. The Spearman coefficient of rank correlation was evaluated for each topographic parameter. Main Outcome Measures Agreement in the measurement of op…
3D and multispectral imaging for subcutaneous veins detection.
2009
The first and perhaps most important phase of a surgical procedure is the insertion of an intravenous (IV) catheter. Currently, this is performed manually by trained personnel. In some visions of future operating rooms, however, this process is to be replaced by an automated system. Experiments to determine the best NIR wavelengths to optimize vein contrast for physiological differences such as skin tone and/or the presence of hair on the arm or wrist surface are presented. For illumination our system is composed of a mercury arc lamp coupled to a 10nm band-pass spectrometer. A structured lighting system is also coupled to our multispectral system in order to provide 3D information of the p…
An Analysis of Earthquakes Clustering Based on a Second-Order Diagnostic Approach
2009
A diagnostic method for space–time point process is here introduced and applied to seismic data of a fixed area of Japan. Nonparametric methods are used to estimate the intensity function of a particular space–time point process and on the basis of the proposed diagnostic method, second-order features of data are analyzed: this approach seems to be useful to interpret space–time variations of the observed seismic activity and to focus on its clustering features.
Analytic gradients for the coupled-cluster singles, doubles, and triples (CCSDT) model
2002
The first implementation of analytic gradients for the coupled-cluster singles, doubles, triples (CCSDT) model is described. The relevant theoretical expressions are given in a diagrammatic form together with the corresponding algebraic formulas. The computational requirements of CCSDT gradient calculations are discussed and their applicability demonstrated by performing benchmark calculations for molecular geometries with large correlation-consistent basis sets. A statistical analysis of the data reveals that CCSDT and CCSD(T) in most cases perform equally well. The CCSDT calculations thus provide further evidence for the high accuracy of the CCSD(T) approach.
Atom- and Bond-Based 2D TOMOCOMD-CARDD Approach and Ligand-Based Virtual Screening for the Drug Discovery of New Tyrosinase Inhibitors
2008
Two-dimensional atom- and bond-based TOMOCOMD-CARDD descriptors and linear discriminant analysis (LDA) are used in this report to perform a quantitative structure-activity relationship (QSAR) study of tyrosinase-inhibitory activity. A database of inhibitors of the enzyme is collected for this study, within 246 highly dissimilar molecules presenting antityrosinase activity. In total, 7 discriminant functions are obtained by using the whole set of atom- and bond-based 2D indices. All the LDA-based QSAR models show accuracies above 90% in the training set and values of the Matthews correlation coefficient (C) varying from 0.85 to 0.90. The external validation set shows globally good classifica…
Positive solutions for a discrete two point nonlinear boundary value problem with p-Laplacian
2017
Abstract In the framework of variational methods, we use a two non-zero critical points theorem to obtain the existence of two positive solutions to Dirichlet boundary value problems for difference equations involving the discrete p -Laplacian operator.
Indefinite integrals involving Jacobi polynomials from integrating factors
2020
A method was presented recently for deriving integrals of special functions using two kinds of integrating factor for the homogeneous second-order linear differential equations which many special f...
Indefinite integrals of Lommel functions from an inhomogeneous Euler–Lagrange method
2015
ABSTRACTA method given recently for deriving indefinite integrals of special functions which satisfy homogeneous second-order linear differential equations has been extended to include functions which obey inhomogeneous equations. The extended method has been applied to derive indefinite integrals for the Lommel functions, which obey an inhomogeneous Bessel equation. The method allows integrals to be derived for the inhomogeneous equation in a manner which closely parallels the homogeneous case, and a number of new Lommel integrals are derived which have well-known Bessel analogues. Results will be presented separately for other special functions which obey inhomogeneous second-order linear…
A third integrating factor for indefinite integrals of special functions
2020
An integrating factor f ~ x is presented involving the terms in y ′ ′ x and q x y x of the general homogenous second-order linear ordinary differential equation. The new integrating factors obey se...