On the Consistency of Prony's Method and Related Algorithms

Abstract

Modifications of Prony's classical technique for estimating rate constants in exponential fitting problems have many contemporary applications. In this article the consistency of Prony's method and of related algorithms based on maximum likelihood is discussed as the number of observations n → ∞ by considering the simplest possible models for fitting sums of exponentials to observed data. Two sampling regimes are relevant, corresponding to transient problems and problems of frequency estimation, each of which is associated with rather different kinds of behavior. The general pattern is that the stronger results are obtained for the frequency estimation problem. However, the algorithms considered are all scaling dependent and consistency is not automatic. A new feature that emerges is the importance of an appropriate choice of scale in order to ensure consistency of the estimates in certain cases. The tentative conclusion is that algorithms referred to as Objective function Reweighting Algorithms (ORA's) are superior to their exact maximum likelihood counterparts, referred to as Gradient condition Reweighting Algorithms (GRA's), especially in the frequency estimation problem. This conclusion does not extend to fitting other families of functions such as rational functions.     

Unimodularity of zeros of self-inversive polynomials

We generalise a necessary and sufficient condition given by Cohn for all the zeros of a self-inversive polynomial to be on the unit circle. Our theorem implies some sufficient conditions found by Lakatos, Losonczi and Schinzel. We apply our result to the study of a polynomial family closely related to Ramanujan polynomials, recently introduced by Gun, Murty and Rath, and studied by Murty, Smyth and Wang as well as by Lalín and Rogers. We prove that all polynomials in this family have their zeros on the unit circle, a result conjectured by Lalín and Rogers on computational evidence.     

Near infrared spectroscopy as a rapid tool to measure volatile aroma compounds in Riesling wine: possibilities and limits

Volatile chemical compounds responsible for the aroma of wine are derived from a number of different biochemical and chemical pathways. These chemical compounds are formed during grape berry metabolism, crushing of the berries, fermentation processes (i.e. yeast and malolactic bacteria) and also from the ageing and storage of wine. Not surprisingly, there are a large number of chemical classes of compounds found in wine which are present at varying concentrations (ng L⁻¹ to mg L⁻¹), exhibit differing potencies, and have a broad range of volatilities and boiling points. The aim of this work was to investigate the potential use of near infrared (NIR) spectroscopy combined with chemometrics as a rapid and low-cost technique to measure volatile compounds in Riesling wines. Samples of commercial Riesling wine were analyzed using an NIR instrument and volatile compounds by gas chromatography (GC) coupled with selected ion monitoring mass spectrometry. Correlation between the NIR and GC data were developed using partial least-squares (PLS) regression with full cross validation (leave one out). Coefficients of determination in cross validation (R ²) and the standard error in cross validation (SECV) were 0.74 (SECV: 313.6 μg L⁻¹) for esters, 0.90 (SECV: 20.9 μg L⁻¹) for monoterpenes and 0.80 (SECV: 1658 μg L⁻¹) for short-chain fatty acids. This study has shown that volatile chemical compounds present in wine can be measured by NIR spectroscopy. Further development with larger data sets will be required to test the predictive ability of the NIR calibration models developed.     

Lempel–Ziv Factorization Using Less Time & Space

For 30 years the Lempel–Ziv factorization LZ _x of a string x = x[1..n] has been a fundamental data structure of string processing, especially valuable for string compression and for computing all the repetitions (runs) in x. Traditionally the standard method for computing LZ _x was based on Θ(n)-time (or, depending on the measure used, O(n log n)-time) processing of the suffix tree ST _x of x. Recently Abouelhoda et al. proposed an efficient Lempel–Ziv factorization algorithm based on an “enhanced” suffix array – that is, a suffix array SA _x together with supporting data structures, principally an “interval tree”. In this paper we introduce a collection of fast space-efficient algorithms for LZ factorization, also based on suffix arrays, that in theory as well as in many practical circumstances are superior to those previously proposed; one family out of this collection achieves true Θ(n)-time alphabet-independent processing in the worst case by avoiding tree structures altogether. The work of the first and third authors was supported in part by grants from the Natural Sciences & Engineering Research Council of Canada.     

Fast pattern-matching on indeterminate strings

In a string x on an alphabet Σ, a position i is said to be indeterminate iff x[i] may be any one of a specified subset {λ₁,λ₂,…,λ_j} of Σ, 2j|Σ|. A string x containing indeterminate positions is therefore also said to be indeterminate. Indeterminate strings can arise in DNA and amino acid sequences as well as in cryptological applications and the analysis of musical texts. In this paper we describe fast algorithms for finding all occurrences of a pattern p=p[1..m] in a given text x=x[1..n], where either or both of p and x can be indeterminate. Our algorithms are based on the Sunday variant of the Boyer–Moore pattern-matching algorithm, one of the fastest exact pattern-matching algorithms known. The methodology we describe applies more generally to all variants of Boyer–Moore (such as Horspool's, for example) that depend only on calculation of the δ (“rightmost shift”) array: our method therefore assumes that Σ is indexed (essentially, an integer alphabet), a requirement normally satisfied in practice.     

Analysis of chemical shift changes reveals the binding modes of isoindolinone inhibitors of the MDM2-p53 interaction

In this study we present a method for defining the binding modes of a set of structurally related isoindolinone inhibitors of the MDM2-p53 interaction. This approach derives the location and orientation of isoindolinone binding, based on an analysis of the patterns of magnitude and direction of chemical shift perturbations for a series of inhibitors of the MDM2-p53 interaction. The MDM2-p53 complex is an attractive target for therapeutic intervention in cancer cells with intact tumor suppressor p53, as it offers the possibility of releasing p53 by blocking the MDM2-p53 binding site with a small molecule antagonist to promote apoptosis. Isoindolinones are a novel class of MDM2-antagonists of moderate affinity, which still require the development of more potent candidates for clinical applications. As the applicability of conventional structural methods to this system is limited by a number of fundamental factors, the exploitation of the information contained in chemical shift perturbations has offered a useful route to obtaining structural information to guide the development of more potent compounds. For a set of 12 structurally related isoindolinones, the data suggests 4 different orientations of binding, caused by subtle changes in the chemical structure of the inhibitors.     

An aqueous ammonia sensor based on an inkjet-printed polyaniline nanoparticle-modified electrode

A sensor for the amperometric detection of aqueous ammonia was fabricated using the inkjet printing of dodecylbenzene sulfonate (DBSA)-doped polyaniline nanoparticles (nanoPANI) onto a screen-printed carbon paste electrode. The combination of the environmentally inert, aqueous nanoparticle dispersion with the inkjet printing technique allowed the rapid fabrication of sensors based on polyaniline that was not easily achievable in the past due to the lack of processability of bulk forms of the conducting polymer. The resulting modified electrode was characterised with respect to its operating pH and number of print layers and was found to perform optimally at near neutral pH with four nanoPANI inkjet-printed layers. The sensor was tested in a flow injection system for its response to aqueous ammonia using amperometric detection at -0.3 V vs. Ag/AgCl pseudo-reference and was found to have reproducibility to injections of ammonia of below 5% RSD and good sensitivity with an experimental detection limit of 20 microM and a theoretical detection limit of 3.17 microM (0.54 ppm). The sensor was also tested for its day-to-day stability and its response towards a range of interferents common to refrigerant waste waters. This system allows the rapid production of an ultra-low-cost, solid state, polyaniline-based aqueous ammonia sensor.     

Recent studies of the electrospray ionisation behaviour of selected drugs and their application in capillary electrophoresis-mass spectrometry and liquid chromatography-mass spectrometry

This review is concerned with recent studies of electrospray ionisation-mass spectrometry (ESI-MS) of selected small molecular mass drugs and their application in qualitative and quantitative analytical methods using the techniques liquid chromatography mass spectrometry (LC-ESI-MS) and capillary electrophoresis mass spectrometry (CE-ESI-MS). The publications reviewed are taken from the Web of Knowledge database for the year 2006. The drugs have molecular mass less than 1000 Da and are chosen according to selected drug classifications in which they give ESI signals primarily as [M+H]+ ions. The drug classifications are antibiotics/antibacterials, steroids, anti-tumour drugs, erectile dysfunction agents, anti-epileptic drugs, antiasthmatic drugs, psychoactive drugs and miscellaneous drugs. Details are given on the fragmentations, where available, that these ionic species exhibit in-source and in ion trap, triple quadrupole and time-of-flight mass spectrometers. Analytical methods for the detection and determination of these small molecular mass drug molecules are also discussed, where appropriate, under the particular drug classifications. Analytical information on, for example, sample concentration techniques, separation conditions, recoveries from biological media and limits of detection/quantitation (LODs and LOQs) are provided.     

Development of an electrochemical flow injection immunoassay (FIIA) for the real-time monitoring of biospecific interactions

Not only are sensors a revolution in analysis; they themselves are also experiencing a revolution brought about by parallel developments in sensor fabrication techniques and materials, polymer chemistry, signal processing methodologies, the increased use of biomolecular processes as a means of analyte detection, and the coupling of sensors to other techniques such as flow injection analysis. Many of these developments have been incorporated into the present study, which we are undertaking in the development of our immunosensor technology. The system described here utilises screen-printed electrodes which are low-cost, disposable devices that are simple to fabricate. Incorporated into our sensor is the electroactive polymer, polyaniline, which brings about mediatorless redox coupling between the electrode and biomolecular components attached to the polymer surface. This system also utilises enzyme-labelled antibodies as the biomolecular recognition component for the analysis of the test analyte, biotin. The system has also been integrated into a flow injection system. This has led to the monitoring of real-time antibody-antigen interactions using electrochemical methods and foreshadows the development of single-step immunosensors.     

Optimisation and characterisation of biosensors based on polyaniline

With lower limits of detection and increased stability constantly being demanded of biosensor devices, characterisation of the constituent layers that make up the sensor has become unavoidable, since this is inextricably linked with its performance. This work describe the optimisation and characterisation of two aspects of sensor performance: a conductive polymer layer (polyaniline) and the immobilised protein layer. The influence of the thickness of polyaniline films deposited electrochemically onto screen-printed electrode surfaces is described in this work in terms of its influence on a variety of amperometric sensor performance characteristics: time to reach steady state, charging current, catalytic current, background current and signal/background ratios. The influence of polymer film thickness on the conductivity and morphology of finished films is also presented.

An electrostatic method of protein immobilisation is used in this work and scanning electron microscopy in conjunction with gold-labelled antibodies and back-scattered electron detection has enabled the direct visualisation of individual groups of proteins on the sensor surface. Such information can provide an insight into the performance of sensors under influence of increasing protein concentrations.