The accuracy of parameter estimation from noisy data, with application to resonance peak estimation in distributed Brillouin sensing

Distributed Brillouin sensing of strain and temperature works by making spatially resolved measurements of the position of the measurand-dependent extremum of the resonance curve associated with the scattering process in the weakly nonlinear regime. Typically, measurements of backscattered Stokes intensity (the dependent variable) are made at a number of predetermined fixed frequencies covering the design measurand range of the apparatus and combined to yield an estimate of the position of the extremum. The measurand can then be found because its relationship to the position of the extremum is assumed known. We present analytical expressions relating the relative error in the extremum position to experimental errors in the dependent variable. This is done for two cases: (i) a simple non-parametric estimate of the mean based on moments and (ii) the case in which a least squares technique is used to fit a Lorentzian to the data. The question of statistical bias in the estimates is discussed and in the second case we go further and present for the first time a general method by which the probability density function (PDF) of errors in the fitted parameters can be obtained in closed form in terms of the PDFs of the errors in the noisy data.

Toward the prediction of class I and II mouse major histocompatibility complex-peptide-binding affinity:in silico bioinformatic step-by-step guide using quantitative structure-activity relationships

Quantitative structure-activity relationship (QSAR) analysis is a cornerstone of modern informatics. Predictive computational models of peptide-major histocompatibility complex (MHC)-binding affinity based on QSAR technology have now become important components of modern computational immunovaccinology. Historically, such approaches have been built around semiqualitative, classification methods, but these are now giving way to quantitative regression methods. We review three methods--a 2D-QSAR additive-partial least squares (PLS) and a 3D-QSAR comparative molecular similarity index analysis (CoMSIA) method--which can identify the sequence dependence of peptide-binding specificity for various class I MHC alleles from the reported binding affinities (IC50) of peptide sets. The third method is an iterative self-consistent (ISC) PLS-based additive method, which is a recently developed extension to the additive method for the affinity prediction of class II peptides. The QSAR methods presented here have established themselves as immunoinformatic techniques complementary to existing methodology, useful in the quantitative prediction of binding affinity: current methods for the in silico identification of T-cell epitopes (which form the basis of many vaccines, diagnostics, and reagents) rely on the accurate computational prediction of peptide-MHC affinity. We have reviewed various human and mouse class I and class II allele models. Studied alleles comprise HLA-A*0101, HLA-A*0201, HLA-A*0202, HLA-A*0203, HLA-A*0206, HLA-A*0301, HLA-A*1101, HLA-A*3101, HLA-A*6801, HLA-A*6802, HLA-B*3501, H2-K(k), H2-K(b), H2-D(b) HLA-DRB1*0101, HLA-DRB1*0401, HLA-DRB1*0701, I-A(b), I-A(d), I-A(k), I-A(S), I-E(d), and I-E(k). In this chapter we show a step-by-step guide into predicting the reliability and the resulting models to represent an advance on existing methods. The peptides used in this study are available from the AntiJen database (http://www.jenner.ac.uk/AntiJen). The PLS method is available commercially in the SYBYL molecular modeling software package. The resulting models, which can be used for accurate T-cell epitope prediction, will be made are freely available online at the URL http://www.jenner.ac.uk/MHCPred.

Quantitative online prediction of peptide binding to the major histocompatibility complex

With its implications for vaccine discovery, the accurate prediction of T cell epitopes is one of the key aspirations of computational vaccinology. We have developed a robust multivariate statistical method, based on partial least squares, for the quantitative prediction of peptide binding to major histocompatibility complexes (MHC), the principal checkpoint on the antigen presentation pathway. As a service to the immunobiology community, we have made a Perl implementation of the method available via a World Wide Web server. We call this server MHCPred. Access to the server is freely available from the URL: http://www.jenner.ac.uk/MHCPred. We have exemplified our method with a model for peptides binding to the common human MHC molecule HLA-B*3501.

Inverse space-dependent force problems for the wave equation

The determination of the displacement and the space-dependent force acting on a vibrating structure from measured final or time-average displacement observation is thoroughly investigated. Several aspects related to the existence and uniqueness of a solution of the linear but ill-posed inverse force problems are highlighted. After that, in order to capture the solution a variational formulation is proposed and the gradient of the least-squares functional that is minimized is rigorously and explicitly derived. Numerical results obtained using the Landweber method and the conjugate gradient method are presented and discussed illustrating the convergence of the iterative procedures for exact input data. Furthermore, for noisy data the semi-convergence phenomenon appears, as expected, and stability is restored by stopping the iterations according to the discrepancy principle criterion once the residual becomes close to the amount of noise. The present investigation will be significant to researchers concerned with wave propagation and control of vibrating structures.