Discrete commutative difference operator theory

The object of this thesis is to formulate a basic commutative difference operator theory for functions defined on a basic sequence, and a bibasic commutative difference operator theory for functions defined on a bibasic sequence of points, which can be applied to the solution of basic and bibasic difference equations. in this thesis a brief survey of the work done in this field in the classical case, as well as a review of the development of q~difference equations, q—analytic function theory, bibasic analytic function theory, bianalytic function theory, discrete pseudoanalytic function theory and finally a summary of results of this thesis

Studies in the geometry of the discrete plane

This thesis is an attempt to initiate the development of a discrete geometry of the discrete plane H = {(qmxo,qnyo); m,n e Z - the set of integers}, where q s (0,1) is fixed and (xO,yO) is a fixed point in the first quadrant of the complex plane, xo,y0 ¢ 0. The discrete plane was first considered by Harman in 1972, to evolve a discrete analytic function theory for geometric difference functions. We shall mention briefly, through various sections, the principle of discretization, an outline of discrete a alytic function theory, the concept of geometry of space and also summary of work done in this thesis

Analysis discrete function theory

There is a recent trend to describe physical phenomena without the use of infinitesimals or infinites. This has been accomplished replacing differential calculus by the finite difference theory. Discrete function theory was first introduced in l94l. This theory is concerned with a study of functions defined on a discrete set of points in the complex plane. The theory was extensively developed for functions defined on a Gaussian lattice. In 1972 a very suitable lattice H: {Ci qmxO,I qnyo), X0) 0, X3) 0, O < q < l, m, n 5 Z} was found and discrete analytic function theory was developed. Very recently some work has been done in discrete monodiffric function theory for functions defined on H. The theory of pseudoanalytic functions is a generalisation of the theory of analytic functions. When the generator becomes the identity, ie., (l, i) the theory of pseudoanalytic functions reduces to the theory of analytic functions. Theugh the theory of pseudoanalytic functions plays an important role in analysis, no discrete theory is available in literature. This thesis is an attempt in that direction. A discrete pseudoanalytic theory is derived for functions defined on H.

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.

Discrete retinal input to the parabrachial complex of a new-world primate, the common marmoset (Callithrix jacchus)

Traditional retinal projections target three functionally complementary systems it) the brain of mammals: the primary visual system, the visuomotor integration systems and the circadian timing system. In recent years, studies in several animals have been conducted to investigate the retinal projections to these three systems, despite some evidence of additional targets. The aim of this study was to disclose a previously unknown connection between the retina and the parabrachial complex of the common marmoset, by means of the intraocular injection of cholera toxin Subunit b. A few labeled retinal fibers/terminals that are detected in the medial parabrachial portion of the marmoset brain show clear varicosities, Suggesting terminal fields. Although the possible role of these projections remains unknown, they may provide a modulation of the cholinergic parabrachial neurons which project to the thalamic dorsal lateral geniculate nucleus. (c) 2008 Elsevier Ireland Ltd. All rights reserved.

A computational framework for uncertainty integration in stochastic unit commitment with intermittent renewable energy sources

The penetration of intermittent renewable energy sources (IRESs) into power grids has increased in the last decade. Integration of wind farms and solar systems as the major IRESs have significantly boosted the level of uncertainty in operation of power systems. This paper proposes a comprehensive computational framework for quantification and integration of uncertainties in distributed power systems (DPSs) with IRESs. Different sources of uncertainties in DPSs such as electrical load, wind and solar power forecasts and generator outages are covered by the proposed framework. Load forecast uncertainty is assumed to follow a normal distribution. Wind and solar forecast are implemented by a list of prediction intervals (PIs) ranging from 5% to 95%. Their uncertainties are further represented as scenarios using a scenario generation method. Generator outage uncertainty is modeled as discrete scenarios. The integrated uncertainties are further incorporated into a stochastic security-constrained unit commitment (SCUC) problem and a heuristic genetic algorithm is utilized to solve this stochastic SCUC problem. To demonstrate the effectiveness of the proposed method, five deterministic and four stochastic case studies are implemented. Generation costs as well as different reserve strategies are discussed from the perspectives of system economics and reliability. Comparative results indicate that the planned generation costs and reserves are different from the realized ones. The stochastic models show better robustness than deterministic ones. Power systems run a higher level of risk during peak load hours.

Dynamic Tracking with Zero Variation and Disturbance Rejection Applied to Discrete-Time Systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Naturally light invisible axion in models with large local discrete symmetries

We show that by introducing appropriate local Z(N)(Ngreater than or equal to13) symmetries in electroweak models it is possible to implement an automatic Peccei-Quinn symmetry, at the same time keeping the axion protected against gravitational effects. Although we consider here only an extension of the standard model and a particular 3-3-1 model, the strategy can be used in any kind of electroweak model. An interesting feature of this 3-3-1 model is that if we add (i) right-handed neutrinos, (ii) the conservation of the total lepton number, and (iii) a Z(2) symmetry, the Z(13) and the chiral Peccei-Quinn U(1)P-Q symmetries are both accidental symmetries in the sense that they are not imposed on the Lagrangian but are just a consequence of the particle content of the model, its gauge invariance, renormalizability, and Lorentz invariance. In addition, this model has no domain wall problem.

Equivalent representation of mutual coupling in transmission lines by discrete element

This paper describes a computational model based on lumped elements for the mutual coupling between phases in transmission lines without the explicit use of modal transformation matrices. The self and mutual parameters and the coupling between phases are modeled using modal transformation techniques. The modal representation is developed from the intrinsic consideration of the modal transformation matrix and the resulting system of time-domain differential equations is described as state equations. Thus, a detailed profile ofthe currents and the voltages through the line can be easily calculated using numerical or analytical integration methods. However, the original contribution of the article is the proposal of a time-domain model without the successive phase/mode transformations and a practical implementation based on conventional electrical circuits, without the use of electromagnetic theory to model the coupling between phases. © 2003-2012 IEEE.