Brief note on the variation of constants formula for fuzzy differential equations

This note gives a theory of state transition matrices for linear systems of fuzzy differential equations. This is used to give a fuzzy version of the classical variation of constants formula. A simple example of a time-independent control system is used to illustrate the methods. While similar problems to the crisp case arise for time-dependent systems, in time-independent cases the calculations are elementary solutions of eigenvalue-eigenvector problems. In particular, for nonnegative or nonpositive matrices, the problems at each level set, can easily be solved in MATLAB to give the level sets of the fuzzy solution. (C) 2002 Elsevier Science B.V. All rights reserved.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Maximum Likelihood Estimation of Mixture Densities for Binned and Truncated Multivariate Data

Binning and truncation of data are common in data analysis and machine learning. This paper addresses the problem of fitting mixture densities to multivariate binned and truncated data. The EM approach proposed by McLachlan and Jones (Biometrics, 44: 2, 571-578, 1988) for the univariate case is generalized to multivariate measurements. The multivariate solution requires the evaluation of multidimensional integrals over each bin at each iteration of the EM procedure. Naive implementation of the procedure can lead to computationally inefficient results. To reduce the computational cost a number of straightforward numerical techniques are proposed. Results on simulated data indicate that the proposed methods can achieve significant computational gains with no loss in the accuracy of the final parameter estimates. Furthermore, experimental results suggest that with a sufficient number of bins and data points it is possible to estimate the true underlying density almost as well as if the data were not binned. The paper concludes with a brief description of an application of this approach to diagnosis of iron deficiency anemia, in the context of binned and truncated bivariate measurements of volume and hemoglobin concentration from an individual's red blood cells.

Efficient simulation of a Tandem Jackson Network

The two-node tandem Jackson network serves as a convenient reference model for the analysis and testing of different methodologies and techniques in rare event simulation. In this paper we consider a new approach to efficiently estimate the probability that the content of the second buffer exceeds some high level L before it becomes empty, starting from a given state. The approach is based on a Markov additive process representation of the buffer processes, leading to an exponential change of measure to be used in an importance sampling procedure. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer. We prove that when the first buffer is finite, this method yields asymptotically efficient simulation for any set of arrival and service rates. In fact, the relative error is bounded independent of the level L; a new result which is not established for any other known method. When the first buffer is infinite, we propose a natural extension of the exponential change of measure for the finite buffer case. In this case, the relative error is shown to be bounded (independent of L) only when the second server is the bottleneck; a result which is known to hold for some other methods derived through large deviations analysis. When the first server is the bottleneck, experimental results using our method seem to suggest that the relative error is bounded linearly in L.

Field quantization, photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.

Development of a mungbean (Vigna radiata) RFLP linkage map and its comparison with lablab (Lablab purpureus) revelas a high level of colinearity between the two genomes

A genetic linkage map of mungbean (Vigna radiata, 2n = 2x = 22) consisting of 255 RFLP loci was developed using a recombinant inbred population of 80 individuals. The population was derived from an intersubspecific cross between the cultivated mungbean variety 'Berken' and a wild mungbean genotype 'ACC 41' (V radiata subsp. sublobata). The total length of the map, which comprised 13 linkage groups, spanned 737.9 cM with an average distance between markers of 3.0 cM and a maximum distance between linked markers of 15.4 cM. The mungbean map was compared to a previously published map of lablab (Lablab purpureus, 2n = 2x = 24) using a common set of 65 RFLP probes. In contrast to some other comparative mapping studies among members of the Fabaceae, where a high level of chromosomal rearrangement has been observed, marker order between mungbean and lablab was found to be highly conserved. However, the two genomes have apparently accumulated a large number of duplications/deletions after they diverged.

Interlabial contact pressures exhibited in dysarthria following traumatic brain injury during speech and nonspeech tasks

A miniature pressure transducer was used to assess the interlabial contact pressures produced by a group of 19 adults (mean age 30.6 years) with dysarthria following severe traumatic brain injury (TBI) during a set of speech and nonspeech tasks. Ten parameters relating to lip strength, endurance, rate of movement and lip pressure accuracy and stability were measured from the nonspeech tasks. The results attained by the TBI group were compared against a group of 19 age- and sex-matched control subjects. Significant differences between the groups were found for maximum interlabial contact pressure, maximum rate of repetition of maximum pressure, and lip pressure accuracy at 50 and 10% levels of maximum pressure. In regards to speech, the interlabial contact pressures generated by the TBI group and control group did not differ significantly. When expressed as percentages of maximum pressure, however, the TBI group's interlabial pressures appeared to have been generated with greater physiological effort. Copyright (C) 2002 S. Karger AG, Basel.

RNA trafficking and stabilization elements associate with multiple brain proteins

Two of the best understood somatic cell mRNA cytoplasmic trafficking elements are those governing localization of beta-actin and myelin basic protein mRNAs. These cis-acting elements bind the trans-acting factors fibroblast ZBP-1 and hnRNP A2, respectively. It is not known whether these elements fulfil other roles in mRNA metabolism. To address this question we have used Edman sequencing and western blotting to identify six rat brain proteins that bind the beta-actin element (zipcode). All are known RNA-binding proteins and differ from ZBP-1. Comparison with proteins that bind the hnRNP A2 and AU-rich response elements, A2RE/A2RE11 and AURE, showed that AURE and zipcode bind a similar set of proteins that does not overlap with those that bind A2RE11. The zipcode-binding protein, KSRP, and hnRNP A2 were selected for further study and were shown by confocal immunolluorescence microscopy to have similar distributions in the central nervous system, but they were found in largely separate locations in cell nuclei. In the cytoplasm of cultured oligodendrocytes they were segregated into separate populations of cytoplasmic granules. We conclude that not only may there be families of trans-acting factors for the same cis-acting element, which are presumably required at different stages of mRNA processing and metabolism, but independent factors may also target different and multiple RNAs in the same cell.

Viscoelasticity of radiation-formed PVA/PVP hydrogel

The dynamic theological behaviour of gamma-irradiated 12.8 wt% poly(vinyl alcohol) (PVA), 12.8 wt% poly(vinyl pyrrolidone) (PVP), and a blend of 8 wt% PVA and 4.8 wt% PVP aqueous solutions have been studied pre- and post-gelation. The non-irradiated solutions displayed theological behaviour typical of dilute to semi-dilute polymer solutions, with the complex viscosity being independent of the frequency and shear rate (i.e. Newtonian behaviour) over the range of frequencies tested and the loss modulus G(omega) and storage modulus G(omega) being nearly proportional to omega and omega(2) respectively. After a set of doses of gamma-radiation, the magnitudes of the dynamic moduli G'(omega) and G(omega) increased as the absorbed dose increased, with notable differences between the two homopolymers and the blend. The stages of gelation were effectively monitored by means of dynamic theological measurements, allowing the possible mechanisms of network formation to be elucidated. The doses required for gelation of the PVA, PVP, and blend samples, determined on the basis of the Winter and Chambon criteria for gelation, were found to be 12 kGy for the 12.8 wt% PVA, 4 kGy for the 12.8 wt% PVP, and 5 kGy for the 8 wt% PVA/4.8 wt% PVP solutions. The unexpected lower gelation dose demonstrated by the blend sample, compared with predictions based on the blend composition, and the associated gelation mechanism are also discussed.

Crystallization of the FAD-independent acetolactate synthase of Klebsiella pneumoniae

Leucine and valine are formed in a common pathway from pyruvate in which the first intermediate is 2-acetolactate. In some bacteria, this compound also has a catabolic fate as the starting point for the butanediol fermentation. The enzyme (EC 4.1.3.18) that forms 2-acetolactate is known as either acetohydroxyacid synthase (AHAS) or acetolactate synthase (ALS), with the latter name preferred for the catabolic enzyme. A significant difference between AHAS and ALS is that the former requires FAD for catalytic activity, although the reason for this requirement is not well understood. Both enzymes require the cofactor thiamine diphosphate. Here, the crystallization and preliminary X-ray diffraction analysis of the Klebsiella pneumoniae ALS is reported. Data to 2.6 Angstrom resolution have been collected at 100 K using a rotating-anode generator and an R-AXIS IV++ detector. Crystals have unit-cell parameters a = 137.4, b = 143.9, c = 134.4 Angstrom, alpha = 90, beta = 108.4, gamma = 90degrees and belong to space group C2. Preliminary analysis indicates that there are four monomers located in each asymmetric unit.

The first non-turnover voltammetric response from a molybdenum enzyme: direct electroscopy of dimethylsulfoxide reductase from Rhodobacter capsulatus

The first direct voltammetric response from a molybdenum enzyme under non-turnover conditions is reported. Cyclic voltammetry of dimethylsulfoxide reductase from Rhodobacter capsulatus reveals a reversible Mo-VI/V response at + 161 mV followed by a reversible Mo-V/IV response at -102 mV versus NHE at pH 8. The higher potential couple exhibits a pH dependence consistent with protonation upon reduction to the Mo-V state and we have determined the pK(a) for this semi-reduced species to be 9.0. The lower potential couple is pH independent within the range 5 < pH < 10. The optical spectrum of the Mo chromophore has been investigated with spectroelectrochemistry. At high potential, in its resting state, the enzyme exhibits a spectrum characteristic of the Mo-VI form. This changes significantly following bulk electrolysis (-400 mV versus NHE) at an optically transparent, indium-doped tin oxide working electrode, where a single visible electronic maximum at 632 nm is observed, which is comparable with spectra reported previously for the dithionite-reduced enzyme. This two-electron process is chemically reversible by reoxidizing the enzyme at the electrode in the absence of mediators or promoters. The activity of the enzyme has been established by observation of a catalytic current in the presence of DMSO at pH 8, where a sigmoidal (steady state) voltammogram is seen. Electronic supplementary material to this paper (Fig. S 1) can be obtained by using the Springer Link server located at http://dx.doi.org/10.1007/s00775-002-0374-y.

Efficient time-independent wave packet scattering calculations within a Lanczos subspace: H+O-2 (J=0) state-to-state reaction probabilities

An efficient Lanczos subspace method has been devised for calculating state-to-state reaction probabilities. The method recasts the time-independent wave packet Lippmann-Schwinger equation [Kouri , Chem. Phys. Lett. 203, 166 (1993)] inside a tridiagonal (Lanczos) representation in which action of the causal Green's operator is affected easily with a QR algorithm. The method is designed to yield all state-to-state reaction probabilities from a given reactant-channel wave packet using a single Lanczos subspace; the spectral properties of the tridiagonal Hamiltonian allow calculations to be undertaken at arbitrary energies within the spectral range of the initial wave packet. The method is applied to a H+O-2 system (J=0), and the results indicate the approach is accurate and stable. (C) 2002 American Institute of Physics.

Lanczos subspace time-independent wave packet calculations of S(D-1)+H-2 reactive scattering

In this paper. we present the results of quantum dynamical simulations of the S (D-1) + H-2 insertion reaction on a newly developed potential energy surface (J. Chem. Phys. 2001, 114, 320). State-to-state reaction probabilities. product state distributions, and initial-state resolved cumulative reaction probabilities from a given incoming reactant channel are obtained from a time-independent wave packet analysis, performed within a single Lanczos subspace. Integral reaction cross sections are then estimated by J-shifting method and compared with the results from molecular beam experiment and QCT calculations.

A comparison of peak power in the shoulder press and shoulder throw

The ability to generate peak power is central for performance in many sports. Currently two distinct resistance training methods are used to develop peak power, the heavy weight/slow velocity and light weight/fast velocity regimes. When using the light weight/fast velocity power training method it was proposed that peak power would be greater in a shoulder throw exercise compared with a normal shoulder press. Nine males performed three lifts in the shoulder press and shoulder throw at 30% and 40% of their one repetition maximum (1RM). These lifts were performed identically, except for the release of the bar in the throw condition. A potentiometer attached to the bar measured displacement and duration of the lifts. The time of bar release in the shoulder throw was determined with a pressure switch. ANOVA was used to examine statistically significant differences where the level of acceptance was set at p