Deconvolution of two-dimensional NMR spectra by fast maximum likelihood reconstruction: application to quantitative metabolomics

We have developed an algorithm called fast maximum likelihood reconstruction (FMLR) that performs spectral deconvolution of 1D-2D NMR spectra for the purpose of accurate signal quantification. FMLR constructs the simplest time-domain model (e.g., the model with the fewest number of signals and parameters) whose frequency spectrum matches the visible regions of the spectrum obtained from identical Fourier processing of the acquired data. We describe the application of FMLR to quantitative metabolomics and demonstrate the accuracy of the method by analysis of complex, synthetic mixtures of metabolites and liver extracts. The algorithm demonstrates greater accuracy (0.5-5.0% error) than peak height analysis and peak integral analysis with greatly reduced operator intervention. FMLR has been implemented in a Java-based framework that is available for download on multiple platforms and is interoperable with popular NMR display and processing software. Two-dimensional (1)H-(13)C spectra of mixtures can be acquired with acquisition times of 15 min and analyzed by FMLR in the range of 2-5 min per spectrum to identify and quantify constituents present at concentrations of 0.2 mM or greater.     

Linear matrix inequalities approach to reconstruction of biological networks

The general problem of reconstructing a biological interaction network from temporal evolution data is tackled via an approach based on dynamical linear systems identification theory. A novel algorithm, based on linear matrix inequalities, is devised to infer the interaction network. This approach allows to directly taking into account, within the optimisation procedure, the a priori available knowledge of the biological system. The effectiveness of the proposed algorithm is statistically validated, by means of numerical tests, demonstrating how the a priori knowledge positively affects the reconstruction performance. A further validation is performed through an in silico biological experiment, exploiting the well-assessed cell-cycle model of fission yeast developed by Novak and Tyson.     

Direction-of-arrival estimation in radar systems: moving window against approximate maximum likelihood estimator

In this study, we compare two radar target direction-of-arrival (DOA) estimation algorithms: the classical moving window (MW) estimator, implemented in many real radar systems and the approximate maximum likelihood (AML) estimator. The first technique exploits multiple detections in the same time-on-target and the second one exploits the fact that the radar antenna mechanical scanning impresses an amplitude modulation on the signals backscattered by the target. Performances of the two estimators are numerically investigated through Monte Carlo simulation and compared in terms of root-mean-square-error (RMSE), probability of detection and probability of target splitting, the latter being defined as the probability of detecting more than one target when instead only one is present in the cell under test. Numerical results show that the AML estimator generally outperforms the classical MW estimator, also in terms of robustness to target splitting.     

Computing the survival probability density function in jump-diffusion models: A new approach based on radial basis functions

We propose a numerical method to compute the survival (first-passage) probability density function in jump-diffusion models. This function is obtained by numerical approximation of the associated Fokker–Planck partial integro-differential equation, with suitable boundary conditions and delta initial condition. In order to obtain an accurate numerical solution, the singularity of the Dirac delta function is removed using a change of variables based on the fundamental solution of the pure diffusion model. This approach allows to transform the original problem to a regular problem, which is solved using a radial basis functions (RBFs) meshless collocation method. In particular the RBFs approximation is carried out in conjunction with a suitable change of variables, which allows to use radial basis functions with equally spaced centers and at the same time to obtain a sharp resolution of the gradients of the survival probability density function near the barrier. Numerical experiments are presented in which several different kinds of radial basis functions are employed. The results obtained reveal that the numerical method proposed is extremely accurate and fast, and performs significantly better than a conventional finite difference approach.     

A good property of the maximum likelihood estimator in a restricted normal model

Summary We consider a normal model with known diagonal covariance matrix and a vector of means constrained to belong to a polyhedral cone. The standard estimatorsX (unrestricted MLE) andX ^* (restricted MLE) are compared for estimation of several components of the parameter simultaneously. We show thatX ^* is preferred toX under several conditions.     

Variational density matrix approach to the temperature-dependent elementary excitation spectrum of two-dimensional liquid4He

Using the variational density matrix method, we obtain a temperature-dependent elementary excitation spectrum for two-dimensional liquid⁴He. For more precise results, we use a Jastrow-Feenberg-type trial wave function and include the contribution of elementary diagrams within the hypernetted chain approximation. The behavior of the excitation spectrum as a function of the temperature and density in two dimensions is similar to that of the bulk system, but has a smaller roton minimum. The roton minimum of the excitation spectrum decreases with increasing temperature and increases with increasing density at low densities but decreases at large densities. The results agree well with Monte Carlo calculations and are closer than pevious theories to experimental measurements of⁴He film adsorbed on substrates.     

Computational procedures for the maximum likelihood parameters of the gamma and beta distributions

A computational procedure is presented for calculating the maximum likelihood sampled parameters for the gamma and beta distributions. The procedure employed is both computationally efficient and easy to use. In order to facilitate immediate application, a self-contained FORTRAN IV computer code has been included to carry out the necessary operations.     

The method of maximum likelihood applied to the statistical analysis of fatigue data

The application of the principle of maximum likelihood to the analysis of fatigue test results, including run-outs, is described. The particular method used is that developed by Edwards, called ‘Support’. The paper describes the use of this method in determining means and standard deviations for test results, the determination of ‘best-fit’ S/N curves with their associated standard deviations and the determination of the significance of differences between groups of results, different S/N curves and the determination of ‘best’ common slopes and the intercepts of such curves. A computer program developed to perform the necessary calculations is outlined. Examples are given of the types of results produced by this analysis and of certain difficulties in the interpretation.     

“No-background” maximum likelihood analysis in HBT interferometry

We present a new “no-background” procedure, based on the maximum likelihood method, for fitting the space-time size parameters of the particle production region in ultra-relativistic heavy ion collisions. This procedure uses an approximation to avoid the necessity of constructing a mixed-event background before fitting the data.     

Coherent nonlinear optical studies of elementary processes in biological complexes: diagrammatic techniques based on the wave function versus the density matrix

Two types of diagrammatic approaches for the design and simulation of nonlinear optical experiments (closed-time path loops based on the wave function and double-sided Feynman diagrams for the density matrix) are presented and compared. We give guidelines for the assignment of relevant pathways and provide rules for the interpretation of existing nonlinear experiments in carotenoids.     

A comparison of maximum likelihood,exponential smoothing and Bayes forecasting procedures in inventory modelling

This paper compares four major schemes used for forecasting mean demand to be used as input into an inventory model so that ‘ optimum ’ stockage levels can be obtained. The inventory model is the classical order up to S, infinite horizon model with carry-over from period to period and complete back-ordering. Maximum likelihood, exponential smoothing, standard Bayes and adaptive Bayes schemes are used and results, via Monte Carlo simulation, are obtained on the average costs per period for (1) stationary demand, (2) long-term trend and (3) ‘ shock ’ changes in mean demand.     

Comparative study on basis functions for projection matrix of three-dimensional tomographic reconstruction for analysis of dropletbehavior from electrohydrodynamic jet

Three-dimensional optical tomography techniques were developed to reconstruct three-dimensional objects using a set of two-dimensional projection images. Five basis functions, such as cubic B-spline, o-Moms, keys, and cosine functions and Gaussian basis functions, were used to calculate the weighting coefficients for a projection matrix. Two different forms of a multiplicative algebraic reconstruction technique were also used to solve inverse problems. The reconstruction algorithm was examined by using several phantoms, which included droplet behaviors and random distributions of particles in a volume. The three-dimensional volume comprised of particles was reconstructed from four projection angles, which were positioned at an offset angle of 45° between each other. Then, three-dimensional velocity fields were obtained from the reconstructed particle volume by three-dimensional cross correlation. The velocity field of the synthetic vortex flow was reconstructed to analyze the three-dimensional tomography algorithm.     

An iterative method for maximum entropy regularization reconstruction in MRI

Many problems in physics involve imaging objects with high spatial frequency content in a limited amount of time. The limitation of available experimental data leads to the infamous problem of diffraction limited data, which manifests itself by causing ringing in the image. This ringing is due to interference phenomena in optics and is known as the Gibbs phenomenon in engineering. In this paper, an iterative maximum entropy regularization (IMER) algorithm for magnetic resonance imaging (MRI) is developed, which produces a super-resolution and optimal signal-to-noise solution to the problem of reconstructing a source from partial Fourier transform data. This method is capable, in principle, of unlimited resolution and is robust with respect to Gaussian white noise perturbation. Comparisons of the IMER method with the conventional Fourier transform method are carried out with the real magnetic resonance data to illustrate the performance of the proposed method. © 2000 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 10, 427–431, 1999     

A non-parametric monotone maximum likelihood estimator of time trend for repairable system data

The trend-renewal process (TRP) is defined to be a time-transformed renewal process, where the time transformation is given by a trend function λ(·) which is similar to the intensity of a non-homogeneous Poisson process (NHPP). A non-parametric maximum likelihood estimator of the trend function of a TRP is obtained under the often natural condition that λ(·) is monotone. An algorithm for computing the estimate is suggested and examined in detail in the case where the renewal distribution of the TRP is a Weibull distribution. The case where one has data from several systems is also briefly studied.     

The one-body density matrix in Helium droplets

The growth of the Bose condensate in Helium droplets is studied through variational Monte Carlo calculations of the one-body density matrix. Both the off-diagonal and the =0 component of the one-body density matrix show unmistakable finite range ordering within the core of the droplet.     

Selection of modulation code parameters for maximum lineal density

The relative performance capabilities for many known run-length-limited binary modulation codes useful in digital magnetic recording are placed in perspective. The criteria for grading is relative maximum achievable lineal recording density under conditions of quasi-optimal spectral shaping. The results are based upon a linear system analysis in which superposition is applicable in modeling saturation recording systems where the media is indeed fully saturated at the termination of each transition. The maximum relative achievable lineal density is shown in terms of code parameters for maximum theoretical information rate with run constraints. The results show which binary modulation code to select for maximal lineal density and how its performance compares with the maximum theoretically achievable for any binary modulation code.     

Measurement of absolute concentrations of individual compounds in metabolite mixtures by gradient-selective time-zero 1H-13C HSQC with two concentration references and fast maximum likelihood reconstruction analysis

Time-zero 2D (13)C HSQC (HSQC(0)) spectroscopy offers advantages over traditional 2D NMR for quantitative analysis of solutions containing a mixture of compounds because the signal intensities are directly proportional to the concentrations of the constituents. The HSQC(0) spectrum is derived from a series of spectra collected with increasing repetition times within the basic HSQC block by extrapolating the repetition time to zero. Here we present an alternative approach to data collection, gradient-selective time-zero (1)H-(13)C HSQC(0) in combination with fast maximum likelihood reconstruction (FMLR) data analysis and the use of two concentration references for absolute concentration determination. Gradient-selective data acquisition results in cleaner spectra, and NMR data can be acquired in both constant-time and non-constant-time mode. Semiautomatic data analysis is supported by the FMLR approach, which is used to deconvolute the spectra and extract peak volumes. The peak volumes obtained from this analysis are converted to absolute concentrations by reference to the peak volumes of two internal reference compounds of known concentration: DSS (4,4-dimethyl-4-silapentane-1-sulfonic acid) at the low concentration limit (which also serves as chemical shift reference) and MES (2-(N-morpholino)ethanesulfonic acid) at the high concentration limit. The linear relationship between peak volumes and concentration is better defined with two references than with one, and the measured absolute concentrations of individual compounds in the mixture are more accurate. We compare results from semiautomated gsHSQC(0) with those obtained by the original manual phase-cycled HSQC(0) approach. The new approach is suitable for automatic metabolite profiling by simultaneous quantification of multiple metabolites in a complex mixture.