Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the-energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics; Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions.; In applying all the above models to. physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.

An improved novel method for solving nonlinear boundary value problems

A modified formula for the integral transform of a nonlinear function is proposed for a class of nonlinear boundary value problems. The technique presented in this paper results in analytical solutions. Iterations and initial guess, which are needed in other techniques, are not required in this novel technique. The analytical solutions are found to agree surprisingly well with the numerically exact solutions for two examples of power law reaction and Langmuir-Hinshelwood reaction in a catalyst pellet.

Improved methods for predicting individual leaf area and leaf senescence in maize (Zea mays)

The ability to predict leaf area and leaf area index is crucial in crop simulation models that predict crop growth and yield. Previous studies have shown existing methods of predicting leaf area to be inadequate when applied to a broad range of cultivars with different numbers of leaves. The objectives of the study were to (i) develop generalised methods of modelling individual and total plant leaf area, and leaf senescence, that do not require constants that are specific to environments and/or genotypes, (ii) re-examine the base, optimum, and maximum temperatures for calculation of thermal time for leaf senescence, and (iii) assess the method of calculation of individual leaf area from leaf length and leaf width in experimental work. Five cultivars of maize differing widely in maturity and adaptation were planted in October 1994 in south-eastern Queensland, and grown under non-limiting conditions of water and plant nutrient supplies. Additional data for maize plants with low total leaf number (12-17) grown at Katumani Research Centre, Kenya, were included to extend the range in the total leaf number per plant. The equation for the modified (slightly skewed) bell curve could be generalised for modelling individual leaf area, as all coefficients in it were related to total leaf number. Use of coefficients for individual genotypes can be avoided, and individual and total plant leaf area can be calculated from total leaf number. A single, logistic equation, relying on maximum plant leaf area and thermal time from emergence, was developed to predict leaf senescence. The base, optimum, and maximum temperatures for calculation of thermal time for leaf senescence were 8, 34, and 40 degrees C, and apply for the whole crop-cycle when used in modelling of leaf senescence. Thus, the modelling of leaf production and senescence is simplified, improved, and generalised. Consequently, the modelling of leaf area index (LAI) and variables that rely on LAI will be improved. For experimental purposes, we found that the calculation of leaf area from leaf length and leaf width remains appropriate, though the relationship differed slightly from previously published equations.

Improved one-step solid-phase extraction method for morphine, morphine-3-glucuronide, and morphine-6-glucuronide from plasma and quantitation using high-performance liquid chromatography with electrochemical detection

This communication describes an improved one-step solid-phase extraction method for the recovery of morphine (M), morphine-3-glucuronide (M3G), and morphine-6-glucuronide (M6G) from human plasma with reduced coextraction of endogenous plasma constituents, compared to that of the authors' previously reported method. The magnitude of the peak caused by endogenous plasma components in the chromatogram that eluted immediately before the retention time of M3G has been reduced (similar to 80%) significantly (p < 0.01) while achieving high extraction efficiencies for the compounds of interest, viz morphine, M6G, and M3G (93.8 +/- 2.5, 91.7 +/- 1.7, and 93.1 +/- 2.2%, respectively). Furthermore, when the improved solid-phase extraction method was used, the extraction cartridge-derived late-eluting peak (retention time 90 to 100 minutes) reported in our previous method, was no longer present in the plasma extracts. Therefore the combined effect of reducing the recovery of the endogenous components of plasma that chromatographed just before the retention time of M3G and the removal of the late-eluting, extraction cartridge-derived peak has resulted in a decrease in the chromatographic run-time to 20 minutes, thereby increasing the sample throughput by up to 100%.

Prediction of MHC class II-binding peptides using an evolutionary algorithm and artificial neural network

Motivation: Prediction methods for identifying binding peptides could minimize the number of peptides required to be synthesized and assayed, and thereby facilitate the identification of potential T-cell epitopes. We developed a bioinformatic method for the prediction of peptide binding to MHC class II molecules. Results: Experimental binding data and expert knowledge of anchor positions and binding motifs were combined with an evolutionary algorithm (EA) and an artificial neural network (ANN): binding data extraction --> peptide alignment --> ANN training and classification. This method, termed PERUN, was implemented for the prediction of peptides that bind to HLA-DR4(B1*0401). The respective positive predictive values of PERUN predictions of high-, moderate-, low- and zero-affinity binder-a were assessed as 0.8, 0.7, 0.5 and 0.8 by cross-validation, and 1.0, 0.8, 0.3 and 0.7 by experimental binding. This illustrates the synergy between experimentation and computer modeling, and its application to the identification of potential immunotheraaeutic peptides.

Improved beef production from supplementation of Hereford, Brahman and crossbred cattle grazing low and medium quality pastures in the subtropics of Australia

Subtropical grasslands are low in organic matter digestibility (OMD) (0.60) and nitrogen (N) (15 g/kg) for much of the year and this limits cattle production which is characterized by low calving rates and low weaning weights. Production has been based on Bos taurus British breeds of cattle but this is changing and now many breeding herds comprise B, indicus cows and their crosses. This change has increased some aspects of production, but low calving rates persist. A 4-year study was undertaken with a view to improve calving rates and weaner output by supplementing cows grazing either native or improved pastures with a high protein oilseed meal (cottonseed meal; CSM) on four sites. These sites were subdivided into a total of 36 paddocks to allow for two replications in a 3 breeds X 3 supplementation rates X 2 pastures factorial design. Selected cows (no. = 216) from Hereford (H), Brahman (B) and Brahman X Hereford (BH) breed types were set to graze either native pastures (0.45 to 0.62 OMD, 8 to 15 g N per kg; low quality) or improved pastures (0.47 to 0.67 OA ID, 10 to 22 g N per kg; medium quality). Cows were given either 0, 750 or 1500 g/day of CSM for 130 days from calving until 4 weeks into a 12- to 13-week mating period. The CSM was given as two meals per week. Live weight at mating of cows on the low quality pasture was increased (P < 0.01) over those not supplemented by feeding either 750 g CSM per day (H and B cows) or 1500 g CSM per day tall cows). There was no significant effect of supplementation on the mating weights of B cows grazing the medium quality sites. Calving rate of B cows was not increased by their supplementation on either low (4-year mean 58.3 %) or medium quality pastures (66.8%) but did tend to be higher in H cows when supplemented at 1500 g CSM per day on the low (66.7 v. 78.0 (s.e. 6.09) %; P < 0.1) and medium quality pastures (70.5 v. 93.5 (s.e. 4.72) %). An increased calving rate (65.8 (s.e. 6.6) % to 83.2 (s.e. 5.82) % in supplemented BH cows grazing low quality pastures approached significance (P < 0.1) when given CSM at 1500 g/day but there was no increased trend in calving rate when this breed type was supplemented on medium quality pastures. Weaning weights of calves from and B and BH cows were increased (P < 0.05) by supplementation of their darns at 750 g/day and for calves weaned from H cows supplemented at 1500 g/day of CSM. Supplementation at 1500 g/day on low quality pastures increased weaner output per cow mated by 120% for H, by 65% for BH cows and by 50% for B cows. Weaner output was increased by 34 and 40%, respectively, for B and H cows when supplemented at 750 g/day and grazing medium quality pastures but there teas no significant effect of supplementation on output from BH cows. Responses in many parameters differed between years. These results were interpreted as a response to the protein in the oilseed meal supplement by B, taurus and B. taurus X B. indicus cross cows grazing on the subtropical pastures. The study also highlighted that responses to the meal differed between breed types, between the quality of the grazed pasture and between the years of supplementation.

Improved high-performance liquid chromatography determination of methotrexate and its major metabolite in plasma using a poly(styrene-divinylbenzene) column

A sensitive high-performance liquid chromatographic assay has been developed for measuring plasma concentrations of methotrexate and its major metabolite, 7-hydroxymethotrexate. Methotrexate and metabolite were extracted from plasma using solid-phase extraction. An internal standard, aminopterin was used. Chromatographic separation was achieved using a 15-cm poly(styrene-divinylbenzene) (PRP-1(R)) column. This column is more robust than a silica-based stationary phase. Post column, the eluent was irradiated with UV light, producing fluorescent photolytic degradation products of methotrexate and the metabolite. The excitation and emission wavelengths of fluorescence detection were at 350 and 435 nm, respectively. The mobile phase consisted of 0.1 M phosphate buffer (pH 6.5), with 6% N,N-dimethylformamide and 0.2% of 30% hydrogen peroxide. The absolute recoveries for methotrexate and 7-hydroxymethotrexate were greater than 86%. Precision, expressed as a coefficient of variation (n=6), was

Exploring sequential data: Commentary on Bowers, Jentsch, Salas, and Braun (1998)

In an investigation intended to determine training needs of night crews, Bowers et al. (1998, this issue) report two studies showing that the patterning of communication is a better discriminator of good and poor crews than is the content of communication. Bowers et al. characterize their studies as intended to generate hypotheses for training needs and draw connections with Exploratory Sequential Data Analysis (ESDA). Although applauding the intentions of Bowers ct al., we point out some concerns with their characterization and implementation of ESDA. Our principal concern is that the Bowers et al. exploration of the data does not convincingly lead them back to a better fundamental understanding of the original phenomena they are investigating.

Algebraic Bethe ansatz for integrable Kondo impurities in the one-dimensional supersymmetric t-J model

An integrable Kondo problem in the one-dimensional supersymmetric t-J model is studied by means of the boundary supersymmetric quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras in a two-dimensional impurity Hilbert space. Further, the model is solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained. (C) 1999 Elsevier Science B.V.

A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements

To translate and transfer solution data between two totally different meshes (i.e. mesh 1 and mesh 2), a consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements is presented in this paper. The proposed algorithm has the following significant advantages: (1) The use of a point-searching strategy allows a point in one mesh to be accurately related to an element (containing this point) in another mesh. Thus, to translate/transfer the solution of any particular point from mesh 2 td mesh 1, only one element in mesh 2 needs to be inversely mapped. This certainly minimizes the number of elements, to which the inverse mapping is applied. In this regard, the present algorithm is very effective and efficient. (2) Analytical solutions to the local co ordinates of any point in a four-node quadrilateral element, which are derived in a rigorous mathematical manner in the context of this paper, make it possible to carry out an inverse mapping process very effectively and efficiently. (3) The use of consistent interpolation enables the interpolated solution to be compatible with an original solution and, therefore guarantees the interpolated solution of extremely high accuracy. After the mathematical formulations of the algorithm are presented, the algorithm is tested and validated through a challenging problem. The related results from the test problem have demonstrated the generality, accuracy, effectiveness, efficiency and robustness of the proposed consistent point-searching algorithm. Copyright (C) 1999 John Wiley & Sons, Ltd.

CXTANNEAL: an improved program for estimating solute transport parameters

CXTANNEAL is a program for analysing contaminant transport in soils. The code, written in Fortran 77, is a modified version of CXTFIT, a commonly used package for estimating solute transport parameters in soils. The improvement of the present code is that it includes simulated annealing as the optimization technique for curve fitting. Tests with hypothetical data show that CXTANNEAL performs better than the original code in searching for optimal parameter estimates. To reduce the computational time, a parallel version of CXTANNEAL (CXTANNEAL_P) was also developed. (C) 1999 Elsevier Science Ltd. All rights reserved.

Characterization of the sequential non-covalent and covalent interactions of the antitumour antibiotic hedamycin with double stranded DNA by NMR spectroscopy

Hedamycin, a member of the pluramycin class of antitumour antibiotics, consists of a planar anthrapyrantrione chromophore to which is attached two aminosugar rings at one end and a bisepoxide-containing sidechain at the other end, Binding to double-stranded DNA is known to involve both reversible and non-reversible modes of interaction. As a part of studies directed towards elucidating the structural basis for the observed 5'-pyGT-3' sequence selectivity of hedamycin, we conducted one-dimensional NMR titration experiments at low temperature using the hexadeoxyribonucleotide duplexes d(CACGTG)(2) and d(CGTACG)(2). Spectral changes which occurred during these titrations are consistent with hedamycin initially forming a reversible complex in slow exchange on the NMR timescale and binding through intercalation of the chromophore. Monitoring of this reversible complex over a period of hours revealed a second type of spectral change which corresponds with formation of a non-reversible complex. Copyright (C) 1999 John Wiley & Sons, Ltd.

Insect peptides with improved protease-resistance protect mice against bacterial infection

At a time of the emergence of drug-resistant bacterial strains, the development of antimicrobial compounds with novel mechanisms of action is of considerable interest. Perhaps the most promising among these is a family of antibacterial peptides originally isolated from insects. These were shown to act in a stereospecific manner on an as-yet unidentified target bacterial protein. One of these peptides, drosocin, is inactive in vivo due to the rapid decomposition in mammalian sera. However, another family member, pyrrhocoricin, is significantly more stable, has increased in vitro efficacy against Gram-negative bacterial strains, and if administered alone, as we show here, is devoid of in vitro or in vivo toxicity. At low doses, pyrrhocoricin protected mice against Escherichia call infection, but at a higher dose augmented the infection of compromised animals. Analogs of pyrrhocoricin were, therefore, synthesized to further improve protease resistance and reduce toxicity. A linear derivative containing unnatural amino acids at both termini showed high potency and lack of toxicity in vivo and an expanded cyclic analog displayed broad activity spectrum in vitro. The bioactive conformation of native pyrrhocoricin was determined by nuclear magnetic resonance spectroscopy, and similar to drosocin, reverse turns were identified as pharmacologically important elements at the termini, bridged by an extended peptide domain. Knowledge of the primary and secondary structural requirements for in vivo activity of these peptides allows the design of novel antibacterial drug leads.

Sequential increase in Egr-1 and AP-1 DNA binding activity in the dentate gyrus following the induction of long-term potentiation

Establishment of long-term potentiation (LTP) at perforant path synapses is highly correlated with increased expression of Egr and AP-1 transcription factors in rat dentate gyrus granule cells. We have investigated whether increased transcription factor levels are reflected in increased transcription factor activity by assessing Egr and AP-I DNA binding activity using gel shift assays. LTP produced an increase in binding to the Egr element, which was NMDA receptor-dependent and correlated closely with our previously reported increase in Egr-1 (zif/268) protein levels. Supershift analysis confirmed involvement of Egr-1, but not Egr-2 in the DNA binding activity. AP-1 DNA binding was also rapidly elevated in parallel with protein levels, however, the peak increase in activity was delayed until 4 h, a time point when we have previously shown that only jun-D protein was elevated. These data indicate that binding of Egr-1 and AP-1 to their response elements is increased in two phases. This may result in activation of distinct banks of target genes which contribute to the establishment of persistent LTP. (C) 2000 Elsevier Science B.V. All rights reserved.