Numerical method for determination of the NMR frequency of the single-qubit operation in a silicon-based solid-state quantum computer

A numerical method is introduced to determine the nuclear magnetic resonance frequency of a donor (P-31) doped inside a silicon substrate under the influence of an applied electric field. This phosphorus donor has been suggested for operation as a qubit for the realization of a solid-state scalable quantum computer. The operation of the qubit is achieved by a combination of the rotation of the phosphorus nuclear spin through a globally applied magnetic field and the selection of the phosphorus nucleus through a locally applied electric field. To realize the selection function, it is required to know the relationship between the applied electric field and the change of the nuclear magnetic resonance frequency of phosphorus. In this study, based on the wave functions obtained by the effective-mass theory, we introduce an empirical correction factor to the wave functions at the donor nucleus. Using the corrected wave functions, we formulate a first-order perturbation theory for the perturbed system under the influence of an electric field. In order to calculate the potential distributions inside the silicon and the silicon dioxide layers due to the applied electric field, we use the multilayered Green's functions and solve an integral equation by the moment method. This enables us to consider more realistic, arbitrary shape, and three-dimensional qubit structures. With the calculation of the potential distributions, we have investigated the effects of the thicknesses of silicon and silicon dioxide layers, the relative position of the donor, and the applied electric field on the nuclear magnetic resonance frequency of the donor.

Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems

We consider a problem of robust performance analysis of linear discrete time varying systems on a bounded time interval. The system is represented in the state-space form. It is driven by a random input disturbance with imprecisely known probability distribution; this distributional uncertainty is described in terms of entropy. The worst-case performance of the system is quantified by its a-anisotropic norm. Computing the anisotropic norm is reduced to solving a set of difference Riccati and Lyapunov equations and a special form equation.

A numerical study of steady state evaporative conditions applied to mine tailings

The suction profile of a desiccating soil is dependent on the water table depth, the soil-water retention characteristics, and the climatic conditions. In this paper, an unsaturated flow model, which simulates both liquid and vapour flow, was used to investigate the effects of varying the water table depth and the evaporation rate on the evaporative fluxes from a desiccating tailings deposit under steady-state conditions. Results obtained showed that at a critical evaporation rate, beyond which evaporation is no longer dictated by climatic conditions, the matric suction profiles remain basically unchanged. The critical evaporation rate varies inversely with the water table depth. It is associated with the maximum evaporative flux that might be extracted from a soil at steady-state conditions. The time required to establish steady-state conditions is directly proportional to the water table depth, and it acquires a maximum value at the critical evaporation rate. A detailed investigation of the movement of the drying front demonstrated the significance of attaining a matric suction of about 3000 kPa on the contribution to flow in the vapour phase.

The C-terminus of Raf-1 acts as a 14-3-3-dependent activation switch

The Raf-1 protein kinase is a major activator of the ERK MAPK pathway, which links signaling by a variety of cell surface receptors to the regulation of cell proliferation, survival, differentiation and migration. Signaling by Raf-1 is regulated by a complex and poorly understood interplay between phosphorylation events and protein-protein interactions. One important mode of Raf-1 regulation involves the phosphorylation-dependent binding of 14-3-3 proteins. Here, we have examined the mechanism whereby the C-terminal 14-3-3 binding site of Raf-1, S621, controls the activation of MEK-ERK signaling. We show that phosphorylation of S621 turns over rapidly and is enriched in the activated pool of endogenous Raf-1. The phosphorylation on this site can be mediated by Raf-1 itself but also by other kinase(s). Mutations that prevent the binding of 14-3-3 proteins to S621 render Raf-1 inactive by specifically disrupting its capacity to bind to ATP, and not by gross conformational alteration as indicated by intact MEK binding. Phosphorylation of S621 correlates with the inhibition of Raf-1 catalytic activity in vitro, but 14-3-3 proteins can completely reverse this inhibition. Our findings suggest that 14-3-3 proteins function as critical cofactors in Raf-1 activation, which induce and maintain the protein in a state that is competent for both ATP binding and MEK phosphorylation.

Analysis of tissue transglutaminase function in the migration of Swiss 3T3 fibroblasts:the active-state conformation of the enzyme does not affect cell motility but is important for its secretion

Increasing evidence suggests that tissue transglutaminase (tTGase; type II) is externalized from cells, where it may play a key role in cell attachment and spreading and in the stabilization of the extracellular matrix (ECM) through protein cross-linking. However, the relationship between these different functions and the enzyme's mechanism of secretion is not fully understood. We have investigated the role of tTGase in cell migration using two stably transfected fibroblast cell lines in which expression of tTGase in its active and inactive (C277S mutant) states is inducible through the tetracycline-regulated system. Cells overexpressing both forms of tTGase showed increased cell attachment and decreased cell migration on fibronectin. Both forms of the enzyme could be detected on the cell surface, but only the clone overexpressing catalytically active tTGase deposited the enzyme into the ECM and cell growth medium. Cells overexpressing the inactive form of tTGase did not deposit the enzyme into the ECM or secrete it into the cell culture medium. Similar results were obtained when cells were transfected with tTGase mutated at Tyr(274) (Y274A), the proposed site for the cis,trans peptide bond, suggesting that tTGase activity and/or its tertiary conformation dependent on this bond may be essential for its externalization mechanism. These results indicate that tTGase regulates cell motility as a novel cell-surface adhesion protein rather than as a matrix-cross-linking enzyme. They also provide further important insights into the mechanism of externalization of the enzyme into the extracellular matrix.

A procedure for determining a spacewise dependent heat source and the initial temperature

The inverse problem of determining a spacewise dependent heat source, together with the initial temperature for the parabolic heat equation, using the usual conditions of the direct problem and information from two supplementary temperature measurements at different instants of time is studied. These spacewise dependent temperature measurements ensure that this inverse problem has a unique solution, despite the solution being unstable, hence the problem is ill-posed. We propose an iterative algorithm for the stable reconstruction of both the initial data and the source based on a sequence of well-posed direct problems for the parabolic heat equation, which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for a typical benchmark test example, which has the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure gives accurate numerical approximations in relatively few iterations.

A variational method for identifying a spacewise-dependent heat source

The inverse problem of determining a spacewise-dependent heat source for the parabolic heat equation using the usual conditions of the direct problem and information from one supplementary temperature measurement at a given instant of time is studied. This spacewise-dependent temperature measurement ensures that this inverse problem has a unique solution, but the solution is unstable and hence the problem is ill-posed. We propose a variational conjugate gradient-type iterative algorithm for the stable reconstruction of the heat source based on a sequence of well-posed direct problems for the parabolic heat equation which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterative procedure at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented which have the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure yields stable and accurate numerical approximations after only a few iterations.

Determination of a spacewise dependent heat source

This paper investigates the inverse problem of determining a spacewise dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from a supplementary temperature measurement at a given single instant of time. The spacewise dependent temperature measurement ensures that the inverse problem has a unique solution, but this solution is unstable, hence the problem is ill-posed. For this inverse problem, we propose an iterative algorithm based on a sequence of well-posed direct problems which are solved at each iteration step using the boundary element method (BEM). The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for various typical benchmark test examples which have the input measured data perturbed by increasing amounts of random noise.

Spin dependent photoconductivity in silicon-on-sapphire

Resonant and non resonant spin dependent photoconductivity is observed in(100) silicon films grown on sapphire by CVD and MBE techniques. The CVD films are either in their as-grown state or have undergone single or double solid phase epitaxial regrowth. For all samples, a resonant decrease in photoconductivity is observed at a field of about 0.34 T for a microwave frequency of about 9.7 GHz and at about 3.3 mT when the frequency is about 92 MHz. For all samples the maximum fractional change in photoconductivity is approximately 10-4 independent of magnetic field strength.

Fully probabilistic control for stochastic nonlinear control systems with input dependent noise

Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained.

A probabilistic indirect adaptive control for systems with input-dependent noise

A probabilistic indirect adaptive controller is proposed for the general nonlinear multivariate class of discrete time system. The proposed probabilistic framework incorporates input–dependent noise prediction parameters in the derivation of the optimal control law. Moreover, because noise can be nonstationary in practice, the proposed adaptive control algorithm provides an elegant method for estimating and tracking the noise. For illustration purposes, the developed method is applied to the affine class of nonlinear multivariate discrete time systems and the desired result is obtained: the optimal control law is determined by solving a cubic equation and the distribution of the tracking error is shown to be Gaussian with zero mean. The efficiency of the proposed scheme is demonstrated numerically through the simulation of an affine nonlinear system.

The development and growth of tissues derived from cranial neural crest and primitive mesoderm is dependent on the ligation status of retinoic acid receptor γ:evidence that retinoic acid receptor γ functions to maintain stem/progenitor cells in the absence of retinoic acid

Retinoic acid (RA) signaling is important to normal development. However, the function of the different RA receptors (RARs)-RARα, RARβ, and RARγ-is as yet unclear. We have used wild-type and transgenic zebrafish to examine the role of RARγ. Treatment of zebrafish embryos with an RARγ-specific agonist reduced somite formation and axial length, which was associated with a loss of hoxb13a expression and less-clear alterations in hoxc11a or myoD expression. Treatment with the RARγ agonist also disrupted formation of tissues arising from cranial neural crest, including cranial bones and anterior neural ganglia. There was a loss of Sox 9-immunopositive neural crest stem/progenitor cells in the same anterior regions. Pectoral fin outgrowth was blocked by RARγ agonist treatment. However, there was no loss of Tbx-5-immunopositive lateral plate mesodermal stem/progenitor cells and the block was reversed by agonist washout or by cotreatment with an RARγ antagonist. Regeneration of the caudal fin was also blocked by RARγ agonist treatment, which was associated with a loss of canonical Wnt signaling. This regenerative response was restored by agonist washout or cotreatment with the RARγ antagonist. These findings suggest that RARγ plays an essential role in maintaining stem/progenitor cells during embryonic development and tissue regeneration when the receptor is in its nonligated state.

Generalised Riccati solution and pinning control of complex stochastic networks

This paper considers the global synchronisation of a stochastic version of coupled map lattices networks through an innovative stochastic adaptive linear quadratic pinning control methodology. In a stochastic network, each state receives only noisy measurement of its neighbours' states. For such networks we derive a generalised Riccati solution that quantifies and incorporates uncertainty of the forward dynamics and inverse controller in the derivation of the stochastic optimal control law. The generalised Riccati solution is derived using the Lyapunov approach. A probabilistic approximation type algorithm is employed to estimate the conditional distributions of the state and inverse controller from historical data and quantifying model uncertainties. The theoretical derivation is complemented by its validation on a set of representative examples.

A Limit Theorem for Multi-Type Subcritical Age-Dependent Branching Processes with two Types of Immigration

Марусия Н. Славчова-Божкова - В настоящата работа се обобщава една гранична теорема за докритичен многомерен разклоняващ се процес, зависещ от възрастта на частиците с два типа имиграция. Целта е да се обобщи аналогичен резултат в едномерния случай като се прилагат “coupling” метода, теория на възстановяването и регенериращи процеси.

Comparison between Numerical and Simulation Methods for Age-dependent Branching Models with Immigration

2000 Mathematics Subject Classification: primary: 60J80, 60J85, secondary: 62M09, 92D40