A computer program for fuzzy reasoning

An interactive computer program is described which implements the procedure proposed in “A Formal System for Fuzzy Reasoning” [1]. The problem in question is that of deciding what conclusions may be drawn in the presence of (posibly conflicting) evidence provided, generally with associated partial degrees of belief, by several sources of differing reliability. In using the program, each piece of evidence is entered as a sentence (using the terms NOT, AND, OR, IMPLIES as necessary), with an associated ‘degree of belief’ and ‘weight’; followed by a tentative conclusion. The system returns the degree(s) of belief and weight(s) which may rationally be attached to the conclusion. Copies of the program, written in FORTRAN IV (870 lines) have been lodged with the program libraries CUBE, DECUS, and SHARE, or may be obtained by writing to the author.     

Pion production from deuterium bombarded with polarized protons of 277 and 500 MeV

Analyzing power measurements of the $\text{p}\text{→ tτ}{}^{\mathrm{+}}$ reaction are reported at incident proton energies of 277 and 500 MeV. The 277 MeV results span the angular range from 70° to 130° in the centre of mass while the two 500 MeV measurements at large angles were taken as a check of published results. With the angular distribution of the analyzing power at 277 MeV now known, it is possible to show that the energy dependence of the analyzing power exhibits characteristics closely resembling the shape and magnitude of the analyzing power distribution observed for 1p shell nuclei of similar excitation energies.     

Finite energy solutions of self‐adjoint elliptic mixed boundary value problems

This paper describes existence, uniqueness and special eigenfunction representations of H¹‐solutions of second order, self‐adjoint, elliptic equations with both interior and boundary source terms. The equations are posed on bounded regions with Dirichlet conditions on part of the boundary and Neumann conditions on the complement. The system is decomposed into separate problems defined on orthogonal subspaces of H¹(Ω). One problem involves the equation with the interior source term and the Neumann data. The other problem just involves the homogeneous equation with Dirichlet data. Spectral representations of the solution operators for each of these problems are found. The solutions are described using bases that are, respectively, eigenfunctions of the differential operator with mixed null boundary conditions, and certain mixed Steklov eigenfunctions. These series converge strongly in H¹(Ω). Necessary and sufficient conditions for the Dirichlet part of the boundary data to have a finite energy extension are described. The solutions for a problem that models a cylindrical capacitor is found explicitly. Copyright © 2009 John Wiley & Sons, Ltd.     

Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients

We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random coefficients. We focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter, and that only have limited spatial regularity. We extend the finite element error analysis for this type of equation, carried out in Charrier et al. (SIAM J Numer Anal, 2013), to more difficult problems, posed on non-smooth domains and with discontinuities in the coefficient. For this wider class of model problem, we prove convergence of the multilevel Monte Carlo algorithm for estimating any bounded, linear functional and any continuously Fréchet differentiable non-linear functional of the solution. We further improve the performance of the multilevel estimator by introducing level dependent truncations of the Karhunen–Loève expansion of the random coefficient. Numerical results complete the paper.     

Variational principles for variational inequalities

This paper describes, and analyzes, variational principles for the solutions of finite dimensional variational inequalities on closed convex sets. No symmetry conditions are required for the function. A saddle point characterization of the solutions is also described. The relevant functionals are explicitly described for some particular examples.     

Functional Generalized Additive Models

We introduce the functional generalized additive model (FGAM), a novel regression model for association studies between a scalar response and a functional predictor. We model the link-transformed mean response as the integral with respect to t of F{X(t), t} where F( ·, ·) is an unknown regression function and X(t) is a functional covariate. Rather than having an additive model in a finite number of principal components as by Müller and Yao (2008 Müller, H.G., and Yao, F. (2008), “Functional Additive Models,” Journal of the American Statistical Association, 103, 1534–1544.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), our model incorporates the functional predictor directly and thus our model can be viewed as the natural functional extension of generalized additive models. We estimate F( ·, ·) using tensor-product B-splines with roughness penalties. A pointwise quantile transformation of the functional predictor is also considered to ensure each tensor-product B-spline has observed data on its support. The methods are evaluated using simulated data and their predictive performance is compared with other competing scalar-on-function regression alternatives. We illustrate the usefulness of our approach through an application to brain tractography, where X(t) is a signal from diffusion tensor imaging at position, t, along a tract in the brain. In one example, the response is disease-status (case or control) and in a second example, it is the score on a cognitive test. The FGAM is implemented in R in the refund package. There are additional supplementary materials available online.     

Ion mobility augments the utility of mass spectrometry in the identification of human hemoglobin variants

The global dispersion of hemoglobin variants through population migration has precipitated a need for their identification. A particularly effective mass spectrometry (MS)-based procedure involves analysis of the intact globin chains in diluted blood to detect the variant through mass anomalies, followed by location of the variant amino acid residue by direct analysis of the enzymatically digested globins. Here we demonstrate the use of ion mobility separation in combination with this MS procedure to reduce mass spectral complexity. In one example, the doubly charged tryptic peptide from a low abundance variant (4%) occurred at the same m/z value as a singly and a doubly charged interfering ion. In another example, the singly charged tryptic peptide from an alpha-chain variant (26%) occurred at the same m/z value as a doubly charged interfering ion. Ion mobility was used to separate the variant ions from the interfering ions, thus allowing the variant peptides to be observed and sequenced by tandem mass spectrometry.     

Monitoring copopulated conformational states during protein folding events using electrospray ionization-ion mobility spectrometry-mass spectrometry

The precise mechanism of protein folding remains elusive and there is a deficiency of biophysical techniques that are capable of monitoring the individual behavior of copopulated protein conformers during the folding process. Herein, an ion mobility spectrometry (IMS) device integrated with electrospray ionization mass spectrometry (ESI-MS) has been used to successfully separate and analyze protein conformers differing in cross section and/or charge state. In an initial test, an ensemble of folded and partially folded conformers of the protein cytochrome c was separated. A detailed study undertaken on the amyloidogenic protein beta(2)-microglobulin (beta(2)m), which forms fibrils by protein unfolding followed by self-aggregation and is responsible for the disease dialysis-related amyloidosis, has generated important insights into its folding landscape. Initially, a systematic titration of beta(2)m over the pH range 2 to 7 using ESI-IMS-MS allowed individual conformers to be monitored and quantified throughout the acid denaturation process. Furthermore, a comparison of wild-type beta(2)m with single and double amino acid variants with a range of folding stabilities and propensities for amyloid fibril formation has provided illuminating evidence of the role of different conformers in protein stability and amyloidogenic aggregation. The ESI-IMS-MS data presented here not only demonstrate an important and informative further dimension to ESI-MS, but also illustrate the potential of the ESI-IMS-MS technique for unravelling protein folding enigmas in general and studying protein misfolding diseases in particular.