A novel radix-3/9 algorithm for type-III generalized discrete Hartley transform

A novel radix-3/9 algorithm for type-III generalized discrete Hartley transform (GDHT) is proposed, which applies to length-3(P) sequences. This algorithm is especially efficient in the case that multiplication is much more time-consuming than addition. A comparison analysis shows that the proposed algorithm outperforms a known algorithm when one multiplication is more time-consuming than five additions. When combined with any known radix-2 type-III GDHT algorithm, the new algorithm also applies to length-2(q)3(P) sequences.

Neural network enhanced generalised minimum variance self-tuning controller for nonlinear discrete-time systems

A neural network enhanced self-tuning controller is presented, which combines the attributes of neural network mapping with a generalised minimum variance self-tuning control (STC) strategy. In this way the controller can deal with nonlinear plants, which exhibit features such as uncertainties, nonminimum phase behaviour, coupling effects and may have unmodelled dynamics, and whose nonlinearities are assumed to be globally bounded. The unknown nonlinear plants to be controlled are approximated by an equivalent model composed of a simple linear submodel plus a nonlinear submodel. A generalised recursive least squares algorithm is used to identify the linear submodel and a layered neural network is used to detect the unknown nonlinear submodel in which the weights are updated based on the error between the plant output and the output from the linear submodel. The procedure for controller design is based on the equivalent model therefore the nonlinear submodel is naturally accommodated within the control law. Two simulation studies are provided to demonstrate the effectiveness of the control algorithm.

Use of the statistical properties of the wavelet-transform coefficients for optimization of integration time in Fourier transform spectrometry

We show that an analysis of the mean and variance of discrete wavelet coefficients of coaveraged time-domain interferograms can be used as a specification for determining when to stop coaveraging. We also show that, if a prediction model built in the wavelet domain is used to determine the composition of unknown samples, a stopping criterion for the coaveraging process can be developed with respect to the uncertainty tolerated in the prediction.

Comparing a discrete and continuum model of the intestinal crypt

The integration of processes at different scales is a key problem in the modelling of cell populations. Owing to increased computational resources and the accumulation of data at the cellular and subcellular scales, the use of discrete, cell-level models, which are typically solved using numerical simulations, has become prominent. One of the merits of this approach is that important biological factors, such as cell heterogeneity and noise, can be easily incorporated. However, it can be difficult to efficiently draw generalizations from the simulation results, as, often, many simulation runs are required to investigate model behaviour in typically large parameter spaces. In some cases, discrete cell-level models can be coarse-grained, yielding continuum models whose analysis can lead to the development of insight into the underlying simulations. In this paper we apply such an approach to the case of a discrete model of cell dynamics in the intestinal crypt. An analysis of the resulting continuum model demonstrates that there is a limited region of parameter space within which steady-state (and hence biologically realistic) solutions exist. Continuum model predictions show good agreement with corresponding results from the underlying simulations and experimental data taken from murine intestinal crypts.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

Endothelin-1 and fibroblast growth factors stimulate the mitogen-activated protein kinase signaling cascade in cardiac myocytes. The potential role of the cascade in the integration of two signaling pathways leading to myocyte hypertrophy.

Maximally effective concentrations of endothelin-1 (ET-1), acidic FGF (aFGF), or 12-O-tetradecanoylphorbol-13-acetate (TPA) activated mitogen-activated protein kinase (MAPK) by 3-4-fold in crude extracts of myocytes cultured from neonatal rat heart ventricles. Maximal activation was achieved after 5 min. Thereafter, MAPK activity stimulated by ET-1 or aFGF declined to control values within 1-2 h, whereas activation by TPA was more sustained. Two peaks of MAPK activity (a 42- and a 44-kDa MAPK) were resolved in cells exposed to ET-1 or aFGF by fast protein liquid chromatography on a Mono Q column. One major and one minor peak of MAPK kinase (MAPKK) was stimulated by ET-1 or aFGF. Cardiac myocytes expressed protein kinase C (PKC)-alpha, -delta, -epsilon and -zeta as shown immunoblotting. Exposure to 1 microM TPA for 24 h down-regulated PKC-alpha, -delta, and -epsilon, but not PKC-zeta. This maneuver wholly abolished the activation of MAPK on re-exposure to TPA but did not affect the response to aFGF. The effect of ET-1 was partially down-regulated. ET-1 stimulated phospho[3H]inositide hydrolysis 18-fold, whereas aFGF stimulated by only 30%. Agonists which initially utilize dissimilar signaling pathways may therefore converge at the level of MAPKK/MAPK and this may be relevant to the hypertrophic response of the heart.

Integration of steroid hormone initiated membrane action to genomic function in the brain

Estrogen is a ligand for the estrogen receptor (ER), which on binding 17beta-estradiol, functions as a ligand-activated transcription factor and regulates the transcription of target genes. This is the slow genomic mode of action. However, rapid non-genomic actions of estrogen also exist at the cell membrane. Using a novel two-pulse paradigm in which the first pulse rapidly initiates non-genomic actions using a membrane-limited estrogen conjugate (E-BSA), while the second pulse promotes genomic transcription from a consensus estrogen response element (ERE), we have demonstrated that rapid actions of estrogen potentiate the slower transcriptional response from an ERE-reporter in neuroblastoma cells. Since rapid actions of estrogen activate kinases, we used selective inhibitors in the two-pulse paradigm to determine the intracellular signaling cascades important in such potentiation. Inhibition of protein kinase A (PKA), PKC, mitogen activated protein kinase (MAPK) or phosphatidylinositol 3-OH kinase (PI-3K) in the first pulse decreases potentiation of transcription. Also, our data with both dominant negative and constitutive mutants of Galpha subunits show that Galpha(q) initiates the rapid signaling cascade at the membrane in SK-N-BE(2)C neuroblastoma cells. We discuss two models of multiple kinase activation at the membrane Pulses of estrogen induce lordosis behavior in female rats. Infusion of E-BSA into the ventromedial hypothalamus followed by 17beta-estradiol in the second pulse could induce lordosis behavior, demonstrating the applicability of this paradigm in vivo. A model where non-genomic actions of estrogen couple to genomic actions unites both aspects of hormone action.