Estimation in the continuous time mover‐stayer model with an application to bond ratings migration

The usual tool for modelling bond ratings migration is a discrete, time‐homogeneous Markov chain. Such model assumes that all bonds are homogeneous with respect to their movement behaviour among rating categories and that the movement behaviour does not change over time. However, among recognized sources of heterogeneity in ratings migration is age of a bond (time elapsed since issuance). It has been observed that young bonds have a lower propensity to change ratings, and thus to default, than more seasoned bonds. The aim of this paper is to introduce a continuous, time‐non‐homogeneous model for bond ratings migration, which also incorporates a simple form of population heterogeneity. The specific form of heterogeneity postulated by the proposed model appears to be suitable for modelling the effect of age of a bond on its propensity to change ratings. This model, called a mover–stayer model, is an extension of a Markov chain. This paper derives the maximum likelihood estimators for the parameters of a continuous time mover–stayer model based on a sample of independent continuously monitored histories of the process, and develops the likelihood ratio statistic for discriminating between the Markov chain and the mover–stayer model. The methods are illustrated using a sample of rating histories of young corporate issuers. For these issuers the default probabilities predicted by the Markov chain and mover–stayer models are different. In particular for 1–4 years old bonds the mover–stayer model estimates substantially lower default probabilities from rating C than a Markov chain. Copyright © 2004 John Wiley & Sons, Ltd.     

Determination of Taxotere in human plasma by a semi-automated high-performance liquid chromatographic method.

A rapid, selective and reproducible high-performance liquid chromatographic (HPLC) method with ultraviolet detection was developed for the determination of the anti-cancer agent Taxotere in biological fluids. The method involves a solid-phase extraction step (C2 ethyl microcolumns) using a Varian Advanced Automated Sample Processor (AASP) followed by reversed-phase HPLC. The validated quantitation range of the method is 10-2500 ng/ml in plasma with coefficients of variation < or = 11%. The method is also suitable for the determination of Taxotere in urine samples under the same conditions. The method was applied in a phase I tolerance study of Taxotere in cancer patients, allowing the pharmacokinetic profile of Taxotere to be established.     

An Accelerated Coordinate Gradient Descent Algorithm for Non-separable Composite Optimization

Journal of Optimization Theory and Applications - Coordinate descent algorithms are popular in machine learning and large-scale data analysis problems due to their low computational cost iterative...     

Solid state separated-local-field NMR spectroscopy on half-integer quadrupolar nuclei: principles and applications to borane analysis

New multidimensional NMR methods correlating the quadrupolar and heteronuclear dipolar interactions affecting a half-integer quadrupolar spin in the solid state are introduced and exemplified. The methods extend separated-local-field magic-angle spinning (SLF MAS) NMR techniques that have been used successfully in spin-(1)/(2) spectroscopy to the study of S >/= (3)/(2) nuclei. In our implementation, these techniques avoid homonuclear proton decoupling requirements by relying on moderately fast MAS rates (6-15 kHz) and use rotor-synchronized constant-time pulse sequences to achieve nearly arbitrary amplifications of the apparent dipolar coupling strengths. The result is a suite of simple 2D NMR experiments, whose line shapes carry valuable information about the structure and dynamics of solids containing quadrupolar and proton nuclei. The potential of these sequences was exploited to gather new insight into the structure and dynamics of a variety of boron-containing samples. These experimental SLF schemes were also extended to 3D NMR experiments that incorporate multiple-quantum MAS, thus enabling the resolution needed to study multiple chemical sites in a solid and providing a useful tool for the assignment of inequivalent sites.     

Longitudinal Relaxation Enhancement in 1H NMR Spectroscopy of Tissue Metabolites via Spectrally Selective Excitation

Nuclear magnetic resonance spectroscopy is governed by longitudinal (T₁) relaxation. For protein and nucleic acid experiments in solutions, it is well established that apparent T₁ values can be enhanced by selective excitation of targeted resonances. The present study explores such longitudinal relaxation enhancement (LRE) effects for molecules residing in biological tissues. The longitudinal relaxation recovery of tissue resonances positioned both down‐ and upfield of the water peak were measured by spectrally selective excitation/refocusing pulses, and compared with conventional water‐suppressed, broadband‐excited counterparts at 9.4 T. Marked LRE effects with up to threefold reductions in apparent T₁ values were observed as expected for resonances in the 6–9 ppm region; remarkably, statistically significant LRE effects were also found for several non‐exchanging metabolite resonances in the 1–4 ppm region, encompassing 30–50 % decreases in apparent T₁ values. These LRE effects suggest a novel means of increasing the sensitivity of tissue‐oriented experiments, and open new vistas to investigate the nature of interactions among metabolites, water and macromolecules at a molecular level.     

Heteronuclear Cross‐Relaxation Effects in the NMR Spectroscopy of Hyperpolarized Targets

Dissolution dynamic nuclear polarization (DNP) enables high‐sensitivity solution‐phase NMR experiments on long‐lived nuclear spin species such as ¹⁵N and ¹³C. This report explores certain features arising in solution‐state ¹H NMR upon polarizing low‐γ nuclear species. Following solid‐state hyperpolarization of both ¹³C and ¹H, solution‐phase ¹H NMR experiments on dissolved samples revealed transient effects, whereby peaks arising from protons bonded to the naturally occurring ¹³C nuclei appeared larger than the typically dominant ¹²C‐bonded ¹H resonances. This enhancement of the satellite peaks was examined in detail with respect to a variety of mechanisms that could potentially explain this observation. Both two‐ and three‐spin phenomena active in the solid state could lead to this kind of effect; still, experimental observations revealed that the enhancement originates from ¹³C→¹H polarization‐transfer processes active in the liquid state. Kinetic equations based on modified heteronuclear cross‐relaxation models were examined, and found to well describe the distinct patterns of growth and decay shown by the ¹³C‐bound ¹H NMR satellite resonances. The dynamics of these novel cross‐relaxation phenomena were determined, and their potential usefulness as tools for investigating hyperpolarized ensembles and for obtaining enhanced‐sensitivity ¹H NMR traces was explored.     

Interlaced Fourier transformation of ultrafast 2D NMR data

A new protocol for processing the data arising in ultrafast 2D NMR is discussed and exemplified, based on the interlaced Fourier transformation. This approach is capable of dealing in a single, combined fashion, with the two mirror-imaged interferograms arising in this kind of experiment as a result of the acquisition of a train of magnetic field gradient echoes. By combining all the acquired data points into a common Fourier processing procedure the spectral width along the direct-acquisition domain becomes effectively doubled, giving the opportunity of employing acquisition gradients that are approximately half as strong as hitherto required. This in turn should lead to an overall enhancement in the signal-to-noise ratio of the experiment of ca. 2, as well as to improvements in the achievable digital resolution. These expectations were tested by carrying out a series of homo- and heteronuclear ultrafast 2D NMR acquisitions, and found systematically fulfilled. The robustness and conditions that allow the interlaced numerical procedure to be implemented in routine analytical applications were explored and are briefly discussed.     

Real-time 2D NMR identification of analytes undergoing continuous chromatographic separation

We have recently proposed and demonstrated an approach that enables the acquisition of multidimensional nuclear magnetic resonance (NMR) spectra within a single scan. A promising application opened up by this new accelerated form of data acquisition concerns the possibility of monitoring in real time the chemical nature of analytes subject to a continuous flow. The present paper illustrates such potential, with the real-time acquisition of a series of 2D 1H NMR spectra arising from a mixture of compounds subject to a continuous liquid chromatography (LC) separation. This real-time 2D NMR identification of chemicals eluted minutes apart under usual LC-NMR conditions differs from the way in which LC-2D NMR has hitherto been carried out, which relies on stopped-flow modes of operations whereby fractions are first collected and then subject to individual, aliquot-by-aliquot analyses. The real-time LC-2D NMR experiment hereby introduced can be implemented in a straightforward manner using modern commercial LC-NMR hardware, thus opening up immediate possibilities in high-throughput characterizations of complex molecules.     

An improvement on the complexity of factoring read-once Boolean functions

Read-once functions have gained recent, renewed interest in the fields of theory and algorithms of Boolean functions, computational learning theory and logic design and verification. In an earlier paper [M.C. Golumbic, A. Mintz, U. Rotics, Factoring and recognition of read-once functions using cographs and normality, and the readability of functions associated with partial k-trees, Discrete Appl. Math. 154 (2006) 1465-1677], we presented the first polynomial-time algorithm for recognizing and factoring read-once functions, based on a classical characterization theorem of Gurvich which states that a positive Boolean function is read-once if and only if it is normal and its co-occurrence graph is P₄-free.In this note, we improve the complexity bound by showing that the method can be modified slightly, with two crucial observations, to obtain an O(n|f|) implementation, where |f| denotes the length of the DNF expression of a positive Boolean function f, and n is the number of variables in f. The previously stated bound was O(n²k), where k is the number of prime implicants of the function. In both cases, f is assumed to be given as a DNF formula consisting entirely of the prime implicants of the function.