Correct biological timing in Arabidopsis requires multiple light-signaling pathways.

Circadian oscillators provide rhythmic temporal cues for a range of biological processes in plants and animals, enabling anticipation of the day/night cycle and enhancing fitness-associated traits. We have used engineering models to understand the control principles of a plant's response to seasonal variation. We show that the seasonal changes in the timing of circadian outputs require light regulation via feed-forward loops, combining rapid light-signaling pathways with entrained circadian oscillators. Linear time-invariant models of circadian rhythms were computed for 3,503 circadian-regulated genes and for the concentration of cytosolic-free calcium to quantify the magnitude and timing of regulation by circadian oscillators and light-signaling pathways. Bioinformatic and experimental analysis show that rapid light-induced regulation of circadian outputs is associated with seasonal rephasing of the output rhythm. We identify that external coincidence is required for rephasing of multiple output rhythms, and is therefore important in general phase control in addition to specific photoperiod-dependent processes such as flowering and hypocotyl elongation. Our findings uncover a fundamental design principle of circadian regulation, and identify the importance of rapid light-signaling pathways in temporal control.

Image deconvolution using a Gaussian scale mixtures model to approximate the wavelet sparseness constraint

This paper proposes to use an extended Gaussian Scale Mixtures (GSM) model instead of the conventional ℓ1 norm to approximate the sparseness constraint in the wavelet domain. We combine this new constraint with subband-dependent minimization to formulate an iterative algorithm on two shift-invariant wavelet transforms, the Shannon wavelet transform and dual-tree complex wavelet transform (DTCWT). This extented GSM model introduces spatially varying information into the deconvolution process and thus enables the algorithm to achieve better results with fewer iterations in our experiments. ©2009 IEEE.

Models for acoustic propagation through turbofan exhaust flows-lined ducts

Turbomachinery noise radiating into the rearward arc is an important problem. This noise is scattered by the trailing edges of the nacelle and the jet exhaust, and interacts with the shear layers between the external flow, bypass stream and jet, en route to the far field. In the past a range of relevant model problems involving semi-infinite cylinders have been solved. However, one limitation of these previous solutions is that they do not allow for the jet nozzle protruding a finite distance beyond the end of the nacelle (or in certain configurations being buried a finite distance upstream). With this in mind, we have used the matrix Wiener-Hopf technique to allow precisely this finite nacelle-jet nozzle separation to be included. We have previously reported results for the case of hard-walled ducts, which requires factorisation of a 2 × 2 matrix. In this paper we extend this work by allowing one of the duct walls, in this case the outer wall of the jet pipe, to be acoustically lined. This results in the need to factorise a 3 × 3 matrix, which is completed by use of a combination of pole-removal and Pad́e approximant techniques. Sample results are presented, investigating in particular the effects of exit plane stagger and liner impedance. Here we take the mean flow to be zero, but extension to nonzero Mach numbers in the core and bypass flow has also been completed. Copyright © 2009 by Nigel Peake & Ben Veitch.

Surface-waves, stability, and scattering for a lined duct with flow

We consider a straight cylindrical duct with a steady subsonic axial flow and a reacting boundary (e.g. an acoustic lining). The wave modes are separated into ordinary acoustic duct modes, and surface modes confined to a small neighbourhood of the boundary. Many researchers have used a mass-spring-damper boundary model, for which one surface mode has previously been identified as a convective instability; however, we show the stability analysis used in such cases to be questionable. We investigate instead the stability of the surface modes using the Briggs-Bers criterion for a Flügge thin-shell boundary model. For modest frequencies and wavenumbers the thin-shell has an impedance which is effectively that of a mass-spring-damper, although for the large wavenumbers needed for the stability analysis the thin-shell and mass-spring-damper impedances diverge, owing to the thin shell's bending stiffness. The thin shell model may therefore be viewed as a regularization of the mass-spring-damper model which accounts for nonlocally-reacting effects. We find all modes to be stable for realistic thin-shell parameters, while absolute instabilities are demonstrated for extremely thin boundary thicknesses. The limit of vanishing bending stiffness is found to be a singular limit, yielding absolute instabilities of arbitrarily large temporal growth rate. We propose that the problems with previous stability analyses are due to the neglect of something akin to bending stiffness in the boundary model. Our conclusion is that the surface mode previously identified as a convective instability may well be stable in reality. Finally, inspired by Rienstra's recent analysis, we investigate the scattering of an acoustic mode as it encounters a sudden change from a hard-wall to a thin-shell boundary, using a Wiener-Hopf technique. The thin-shell is considered to be clamped to the hard-wall. The acoustic mode is found to scatter into transmitted and reflected acoustic modes, and surface modes strongly linked to the solid waves in the boundary, although no longitudinal or transverse waves within the boundary are excited. Examples are provided that demonstrate total transmission, total reflection, and a combination of the two. This thin-shell scattering problem is preferable to the mass-spring-damper scattering problem presented by Rienstra, since the thin-shell problem is fully determined and does not need to appeal to a Kutta-like condition or the inclusion of an instability in order to avoid a surface-streamline cusp at the boundary change.

Multi-channel signal separation

The separation of independent sources from mixed observed data is a fundamental and challenging problem. In many practical situations, observations may be modelled as linear mixtures of a number of source signals, i.e. a linear multi-input multi-output system. A typical example is speech recordings made in an acoustic environment in the presence of background noise and/or competing speakers. Other examples include EEG signals, passive sonar applications and cross-talk in data communications. In this paper, we propose iterative algorithms to solve the n × n linear time invariant system under two different constraints. Some existing solutions for 2 × 2 systems are reviewed and compared.

Generation and scattering of sound in vortical flow

We present solutions to scattering problems for unsteady disturbances to a mean swirling flow in an annular duct with a rigid 'splitter'. This situation has application to rotor-stator interaction noise in aeroengines, where the flow downstream of the fan is swirling and bifurcates into the by-pass duct and the engine core. We also consider the trailing edge extension of this problem. Inviscid mean flow in a cylindrical annulus is considered, with both axial and swirling (azimuthal) velocity components. The presence of vorticity in the mean flow couples the acoustic and vorticity modes of irrotational flow. Instead we have one combined spectrum of acoustic-vorticity waves in which the 'sonic' and 'nearly-convected' modes are fully coupled. In addition to the aeroacoustics application the results offer insight into the behaviour of these acoustic-vorticity waves, and the precise nature of the coupling between the two types of mode. Two regimes are discussed in which progress has been made, one for a specialised mean flow, uniform axial flow and rigid body swirl, and a second regime in which the frequency is assumed large, valid for any axisymmetric mean flow. The Wiener-Hopf technique is used to solve the scattering problems mathematically, and we present numerical evaluations of these solutions. Several new effects are seen to arise due to the mean vorticity, in particular the generation of sound at a trailing edge due to the scattering of a nearly convected disturbance, in contrast to the way a convected gust silently passes a trailing edge in uniform mean flow.

Modal scattering at an impedance transition in a lined flow duct

An explicit Wiener-Hopf solution is derived to describe the scattering of duct modes at a hard-soft wall impedance transition in a circular duct with uniform mean flow. Specifically, we have a circular duct r = 1, - ∞ < x < ∞ with mean flow Mach number M > 0 and a hard wall along x < 0 and a wall of impedance Z along x > 0. A minimum edge condition at x = 0 requires a continuous wall streamline r = 1 + h(x, t), no more singular than h = Ο(x1/2) for x ↓ 0. A mode, incident from x < 0, scatters at x = 0 into a series of reflected modes and a series of transmitted modes. Of particular interest is the role of a possible instability along the lined wall in combination with the edge singularity. If one of the "upstream" running modes is to be interpreted as a downstream-running instability, we have an extra degree of freedom in the Wiener-Hopf analysis that can be resolved by application of some form of Kutta condition at x = 0, for example a more stringent edge condition where h = Ο(x3/2) at the downstream side. The question of the instability requires an investigation of the modes in the complex frequency plane and therefore depends on the chosen impedance model, since Z = Z (ω) is essentially frequency dependent. The usual causality condition by Briggs and Bers appears to be not applicable here because it requires a temporal growth rate bounded for all real axial wave numbers. The alternative Crighton-Leppington criterion, however, is applicable and confirms that the suspected mode is usually unstable. In general, the effect of this Kutta condition is significant, but it is particularly large for the plane wave at low frequencies and should therefore be easily measurable. For ω → 0, the modulus fends to |R001| → (1 + M)/(1 -M) without and to 1 with Kutta condition, while the end correction tends to ∞ without and to a finite value with Kutta condition. This is exactly the same behaviour as found for reflection at a pipe exit with flow, irrespective if this is uniform or jet flow.

Vision-based global localization using a visual vocabular

This paper presents a novel coarse-to-fine global localization approach that is inspired by object recognition and text retrieval techniques. Harris-Laplace interest points characterized by SIFT descriptors are used as natural land-marks. These descriptors are indexed into two databases: an inverted index and a location database. The inverted index is built based on a visual vocabulary learned from the feature descriptors. In the location database, each location is directly represented by a set of scale invariant descriptors. The localization process consists of two stages: coarse localization and fine localization. Coarse localization from the inverted index is fast but not accurate enough; whereas localization from the location database using voting algorithm is relatively slow but more accurate. The combination of coarse and fine stages makes fast and reliable localization possible. In addition, if necessary, the localization result can be verified by epipolar geometry between the representative view in database and the view to be localized. Experimental results show that our approach is efficient and reliable. ©2005 IEEE.

Quantifying the limits of HANPP and carbon emissions which prolong total species well-being

Anthropogenic climate and land-use change are leading to irreversible losses of global biodiversity, upon which ecosystem functioning depends. Since total species' well-being depends on ecosystem goods and services, man must determine how much net primary productivity (NPP) may be appropriated and carbon emitted so as to not adversely impact this and future generations. In 2005, man ought to have only appropriated 9.72 Pg C of NPP, representing a factor 2.50, or 59.93%, reduction in human-appropriated NPP in that year. Concurrently, the carbon cycle would have been balanced with a factor 1.26, or 20.84%, reduction from 7.60 Gt C/year to 5.70 Gt C/year, representing a return to the 1986 levels. This limit is in keeping with the category III stabilization scenario of the Intergovernmental Panel for Climate Change. Projecting population growth to 2030 and its associated basic food requirements, the maximum HANPP remains at 9.74 ± 0.02 Pg C/year. This time-invariant HANPP may only provide for the current global population of 6.51 billion equitably at the current average consumption of 1.49 t C per capita, calling into question the sustainability of developing countries striving for high-consuming country levels of 5.85 t C per capita and its impacts on equitable resource distribution. © Springer Science+Business Media B.V. 2009.

Development and validation of a new method for measuring friction between skin and nonwoven materials.

A new method for measuring the coefficient of friction between nonwoven materials and the curved surface of the volar forearm has been developed and validated. The method was used to measure the coefficient of static friction for three different nonwoven materials on the normal (dry) and over-hydrated volar forearms of five female volunteers (ages 18-44). The method proved simple to run and had good repeatability: the coefficient of variation (standard deviation expressed as a percentage of the mean) for triplets of repeat measurements was usually (80 per cent of the time) less than 10 per cent. Measurements involving the geometrically simpler configuration of pulling a weighted fabric sample horizontally across a quasi-planar area of volar forearm skin proved experimentally more difficult and had poorer repeatability. However, correlations between values of coefficient of static friction derived using the two methods were good (R = 0.81 for normal (dry) skin, and 0.91 for over-hydrated skin). Measurements of the coefficient of static friction for the three nonwovens for normal (dry) and for over-hydrated skin varied in the ranges of about 0.3-0.5 and 0.9-1.3, respectively. In agreement with Amontons' law, coefficients of friction were invariant with normal pressure over the entire experimental range (0.1-8.2 kPa).

Multimode radiation from an unflanged, semi-infinite circular duct with uniform flow.

Multimode sound radiation from an unflanged, semi-infinite, rigid-walled circular duct with uniform subsonic mean flow everywhere is investigated theoretically. The multimode directivity depends on the amplitude and directivity function of each individual cut-on mode. The amplitude of each mode is expressed as a function of cut-on ratio for a uniform distribution of incoherent monopoles, a uniform distribution of incoherent axial dipoles, and for equal power per mode. The directivity function of each mode is obtained by applying a Lorentz transformation to the zero-flow directivity function, which is given by a Wiener-Hopf solution. This exact numerical result is compared to an analytic solution, valid in the high-frequency limit, for multimode directivity with uniform flow. The high-frequency asymptotic solution is derived assuming total transmission of power at the open end of the duct, and gives the multimode directivity function with flow in the forward arc for a general family of mode amplitude distribution functions. At high frequencies the agreement between the exact and asymptotic solutions is shown to be excellent.

Optimal H2 order-one reduction by solving eigenproblems for polynomial equations

A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based search, and hence avoids the usual problems of local minima. We examine mostly the case when the model order is reduced by one, and when the original system has distinct poles. This case exhibits special structure which allows us to provide a complete solution. The problem is converted into linear algebra by exhibiting a finite-dimensional basis for a certain space, and can then be solved by eigenvalue calculations, following the methods developed by Stetter and Moeller. The use of Buchberger's algorithm is avoided by writing the first-order optimality conditions in a special form, from which a Groebner basis is immediately available. Compared with our previous work the method presented here has much smaller time and memory requirements, and can therefore be applied to systems of significantly higher McMillan degree. In addition, some hypotheses which were required in the previous work have been removed. Some examples are included.

Designing MPC controllers by reverse-engineering existing LTI controllers

This technical report presents a method for designing a constrained output-feedback model predictive controller (MPC) that behaves in the same way as an existing baseline stabilising linear time invariant output-feedback controller when constraints are inactive. The baseline controller is cast into an observer-compensator form and an inverse-optimal cost function is used as the basis of the MPC controller. The available degrees of design freedom are explored, and some guidelines provided for the selection of an appropriate observer-compensator realisation that will best allow exploitation of the constraint-handling and redundancy management capabilities of MPC. Consideration is given to output setpoint tracking, and the method is demonstrated with three different multivariable plants of varying complexity.

Asymptotic Recovery for Discrete-Time Systems

An asymptotic recovery design procedure is proposed for square, discrete-time, linear, time-invariant multivariable systems, which allows a state-feedback design to be approximately recovered by a dynamic output feedback scheme. Both the case of negligible processing time (compared to the sampling interval) and of significant processing time are discussed. In the former case, it is possible to obtain perfect. © 1985 IEEE.

H∞ sampled-data synthesis and related numerical issues

In this paper we present a new, compact derivation of state-space formulae for the so-called discretisation-based solution of the H∞ sampled-data control problem. Our approach is based on the established technique of continuous time-lifting, which is used to isometrically map the continuous-time, linear, periodically time-varying, sampled-data problem to a discretetime, linear, time-invariant problem. State-space formulae are derived for the equivalent, discrete-time problem by solving a set of two-point, boundary-value problems. The formulae accommodate a direct feed-through term from the disturbance inputs to the controlled outputs of the original plant and are simple, requiring the computation of only a single matrix exponential. It is also shown that the resultant formulae can be easily re-structured to give a numerically robust algorithm for computing the state-space matrices. © 1997 Elsevier Science Ltd. All rights reserved.