Control and Filtering for Discrete Linear Repetitive Processes with H infty and ell 2--ell infty Performance

Repetitive processes are characterized by a series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This can lead to oscillations which increase in amplitude in the pass to pass direction and cannot be controlled by standard control laws. Here we give new results on the design of physically based control laws for the sub-class of so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control. The main contribution is to show how control law design can be undertaken within the framework of a general robust filtering problem with guaranteed levels of performance. In particular, we develop algorithms for the design of an H? and $\ell_{2}–\ell_{\infty}$ dynamic output feedback controller and filter which guarantees that the resulting controlled (filtering error) process, respectively, is stable along the pass and has prescribed disturbance attenuation performance as measured by $H_{\infty}$ and $\ell_{2}$–$\ell_{\infty}$ norms

Direct measurement of penetration length in ultra-thin and/or mesoscopic superconducting structures

We describe a method for direct measurement of the magnetic penetration length in thin (10 - 100 nm) superconducting structures having overall dimensions in the range 1 to 100 micrometers. The method is applicable for broadband magnetic fields from dc to MHz frequencies.Comment: Accepted by Journal of Applied P:hysics (Jun 2006).5 pages, 5 figure

Gradient Echo Quantum Memory for Light using Two-level Atoms

We propose a quantum memory for light that is analogous to the NMR gradient echo. Our proposal is ideally perfectly efficient and provides simplifications to current 3-level quantum memory schemes based on controlled inhomogeneous broadening. Our scheme does not require auxiliary light fields. Instead the input optical pulse interacts only with two-level atoms that have linearly increasing Stark shifts. By simply reversing the sign of the atomic Stark shifts, the pulse is retrieved in the forward direction. We present analytical, numerical and experimental results of this scheme. We report experimental efficiencies of up to 15% and suggest simple realizable improvements to significantly increase the efficiency.Comment: 4 pages, 4 figure

Accumulator pricing

Accumulator is a highly path dependant derivative structure that has been introduced as a retail financial product in recent years and becomes very popular in some Asian cities with its speculative nature. Despite its popularity, its pricing formula is not well known especially when there is a barrier structure. When the barrier in an accumulator contract is applied continuously, this paper obtains exact analytic pricing formulae for immediate settlement and for delay settlement. For discrete barrier, we also obtain analytic formulae which can approximate the fair price of an accumulator under both settlement methods. Through Monte Carlo simulation, we show that the approximation is highly satisfactory. With price formulae in close forms, this paper further explains how to price the product fairly to fit into its zero-cost structure. The analytic formulae also help in computing the Greeks of an accumulator which are documented in this paper. An asymmetry can be observed here that when the buyer is suffering a loss, risk characteristics like delta and vega are substantially larger than when the buyer is enjoying a profit. This means that losing buyers will be more vulnerable to price changes and volatility changes than winning buyers. This is consistent with another observation in the paper that the value at risk for the buyer can be several times larger than that of the seller. © 2009 IEEE.published_or_final_versionThe IEEE Symposium on Computational Intelligence for Financial Engineering (CIFEr) 2009, Nashville, TN., 30 March-2 April 2009. In Proceedings of the CIFEr, 2009, p. 72-7

Isolating Geometry in Weak Lensing Measurements

Given a foreground galaxy-density field or shear field, its cross-correlation with the shear field from a background population of source galaxies scales with the source redshift in a way that is specific to lensing. Such a source-scaling can be exploited to effectively measure geometrical distances as a function of redshift and thereby constrain dark energy properties, free of any assumptions about the galaxy-mass/mass power spectrum (its shape, amplitude or growth). Such a geometrical method can yield a ~ 0.03 - 0.07 f_{sky}^{-1/2} measurement on the dark energy abundance and equation of state, for a photometric redshift accuracy of dz ~ 0.01 - 0.05 and a survey with median redshift of ~ 1. While these constraints are weaker than conventional weak lensing methods, they provide an important consistency check because the geometrical method carries less theoretical baggage: there is no need to assume any structure formation model (e.g. CDM). The geometrical method is at the most conservative end of a whole spectrum of methods which obtain smaller errorbars by making more restrictive assumptions -- we discuss some examples. Our geometrical approach differs from previous investigations along similar lines in three respects. First, the source-scaling we propose to use is less demanding on the photometric redshift accuracy. Second, the scaling works for both galaxy-shear and shear-shear correlations. Third, we find that previous studies underestimate the statistical errors associated with similar geometrical methods, the origin of which is discussed.Comment: 13 pages, 4 figures, submitted to Ap

Randomised controlled study of treatment for mild and moderate sleep apnoea

Health Services Research Fund & Health Care and Promotion Fund: Research Dissemination Reports (Series 6)published_or_final_versio

A one-sided Prime Ideal Principle for noncommutative rings

Completely prime right ideals are introduced as a one-sided generalization of the concept of a prime ideal in a commutative ring. Some of their basic properties are investigated, pointing out both similarities and differences between these right ideals and their commutative counterparts. We prove the Completely Prime Ideal Principle, a theorem stating that right ideals that are maximal in a specific sense must be completely prime. We offer a number of applications of the Completely Prime Ideal Principle arising from many diverse concepts in rings and modules. These applications show how completely prime right ideals control the one-sided structure of a ring, and they recover earlier theorems stating that certain noncommutative rings are domains (namely, proper right PCI rings and rings with the right restricted minimum condition that are not right artinian). In order to provide a deeper understanding of the set of completely prime right ideals in a general ring, we study the special subset of comonoform right ideals.Comment: 38 page

Activation Energy of Metastable Amorphous Ge2Sb2Te5 from Room Temperature to Melt

Resistivity of metastable amorphous Ge2Sb2Te5 (GST) measured at device level show an exponential decline with temperature matching with the steady-state thin-film resistivity measured at 858 K (melting temperature). This suggests that the free carrier activation mechanisms form a continuum in a large temperature scale (300 K - 858 K) and the metastable amorphous phase can be treated as a super-cooled liquid. The effective activation energy calculated using the resistivity versus temperature data follow a parabolic behavior, with a room temperature value of 333 meV, peaking to ~377 meV at ~465 K and reaching zero at ~930 K, using a reference activation energy of 111 meV (3kBT/2) at melt. Amorphous GST is expected to behave as a p-type semiconductor at Tmelt ~ 858 K and transitions from the semiconducting-liquid phase to the metallic-liquid phase at ~ 930 K at equilibrium. The simultaneous Seebeck (S) and resistivity versus temperature measurements of amorphous-fcc mixed-phase GST thin-films show linear S-T trends that meet S = 0 at 0 K, consistent with degenerate semiconductors, and the dS/dT and room temperature activation energy show a linear correlation. The single-crystal fcc is calculated to have dS/dT = 0.153 {\mu}V/K for an activation energy of zero and a Fermi level 0.16 eV below the valance band edge.Comment: 5 pages, 5 figure

Quantum Noise Locking

Quantum optical states which have no coherent amplitude, such as squeezed vacuum states, can not rely on standard readout techniques to generate error signals for control of the quadrature phase. Here we investigate the use of asymmetry in the quadrature variances to obtain a phase-sensitive readout and to lock the phase of a squeezed vacuum state, a technique which we call noise locking (NL). We carry out a theoretical derivation of the NL error signal and the associated stability of the squeezed and anti-squeezed lock points. Experimental data for the NL technique both in the presence and absence of coherent fields are shown, including a comparison with coherent locking techniques. Finally, we use NL to enable a stable readout of the squeezed vacuum state on a homodyne detector.Comment: Accepted for publication in Journal of Optics:B special issue on Quantum Contro

Distribution of cells responsive to 5-HT6 receptor antagonist-induced hypophagia

Open Access funded by Medical Research CouncilPeer reviewedPublisher PD