Delay-dependent robust H-infinity control for uncertain systems with time-varying delay

This paper proposes a new approach for delay-dependent robust H-infinity stability analysis and control synthesis of uncertain systems with time-varying delay. The key features of the approach include the introduction of a new Lyapunov–Krasovskii functional, the construction of an augmented matrix with uncorrelated terms, and the employment of a tighter bounding technique. As a result, significant performance improvement is achieved in system analysis and synthesis without using either free weighting matrices or model transformation. Examples are given to demonstrate the effectiveness of the proposed approach.

Universal codes from switching strategies

We discuss algorithms for combining sequential prediction strategies, a task which can be viewed as a natural generalisation of the concept of universal coding. We describe a graphical language based on Hidden Markov Models for defining prediction strategies, and we provide both existing and new models as examples. The models include efficient, parameterless models for switching between the input strategies over time, including a model for the case where switches tend to occur in clusters, and finally a new model for the scenario where the prediction strategies have a known relationship, and where jumps are typically between strongly related ones. This last model is relevant for coding time series data where parameter drift is expected. As theoretical contributions we introduce an interpolation construction that is useful in the development and analysis of new algorithms, and we establish a new sophisticated lemma for analysing the individual sequence regret of parameterised models.

Leaf and inflorescence structure and phylogenetics of Tripogon and affiliated genera (Poaceae: Chloridoideae)

This thesis provides new knowledge on an understudied group of grasses, some of which are resurrection grasses (i.e. able to withstand extreme drought). The sole Australian species (Tripogon loliiformis) is morphologically diverse and could be more than one species. This study sought to determine how many species of Tripogon occur in Australia, their relationships to other species in the genus and to two other genera of resurrection grasses (Eragrostiella and Oropetium). Results of the research indicate there is not enough evidence, from DNA sequence data, to warrant splitting up T. loliiformis into multiple species. The extensive morphological diversity seems to be influenced by environmental conditions. The three genera are so closely related that they could be grouped into a single genus. This new knowledge opens up pathways for future investigations, including studying genes responsible for desiccation tolerance and the conservation of native grasses that occur in rocky habitats.

Independent distractor frequency and age-of-acquisition dffects in picture-word interference: FMRI evidence for post-lexical and lexical accounts according to distractor type

In two fMRI experiments, participants named pictures with superimposed distractors that were high or low in frequency or varied in terms of age of acquisition. Pictures superimposed with low-frequency words were named more slowly than those superimposed with high-frequency words, and late-acquired words interfered with picture naming to a greater extent than early-acquired words. The distractor frequency effect (Experiment 1) was associated with increased activity in left premotor and posterior superior temporal cortices, consistent with the operation of an articulatory response buffer and verbal selfmonitoring system. Conversely, the distractor age-of-acquisition effect (Experiment 2) was associated with increased activity in the left middle and posterior middle temporal cortex, consistent with the operation of lexical level processes such as lemma and phonological word form retrieval. The spatially dissociated patterns of activity across the two experiments indicate that distractor effects in picture-word interference may occur at lexical or postlexical levels of processing in speech production.

Trehalose Toxicity in Cuscuta refexal Correlation With low Trehalase Activity

A toxic effect of a,a-trehalose in an angiospermic plant, Cuscuta reflexa (dodder), Is described. This disaccharide and Its analogs, 2-aminotrehalose and 4-aminotbhakose, induced a raid blackening of the terminal region of the vine which is Involved in elongation growth. From the results of in vitro growth of several angkiopermic plants and determination of trehalase activity in them, it is concluded that the toxic effect of trehalose in Cucaa is because of the very low trehalas activity In the vine. As a result, trehalose accumulates In the vine and interferes with some process closely associated with growth. The growth potential of Lemma (a duckweed) in a medium containing trehalose as the carbon source was ihreversibly lost upon addition of trealosamine, an Inhibitor of trehalase activity. It is concluded that, if allowed to accumulate within the tissue, trehalose may be potentiaMly toxic or inhibitory to higher plants in generaL The presence of trhalase actvity in plants, where Its substrate has not been found to occur, is envisged to relieve the plant from the toxic effects of trehalose which it may encounter in soil or during association with fungi or insects.

A simplified approach to a three-part Wiener-Hopf problem arising in diffraction theory

A direct and simple approach, utilizing Watson's lemma, is presented for obtaining an approximate solution of a three-part Wiener-Hopf problem associated with the problem of diffraction of a plane wave by a soft strip.

A novel approach to 6-DOF adaptive trajectory tracking control of an AUV in the presence of parameter uncertainties

In this paper, the trajectory tracking control of an autonomous underwater vehicle (AUVs) in six-degrees-of-freedom (6-DOFs) is addressed. It is assumed that the system parameters are unknown and the vehicle is underactuated. An adaptive controller is proposed, based on Lyapunov׳s direct method and the back-stepping technique, which interestingly guarantees robustness against parameter uncertainties. The desired trajectory can be any sufficiently smooth bounded curve parameterized by time even if consist of straight line. In contrast with the majority of research in this field, the likelihood of actuators׳ saturation is considered and another adaptive controller is designed to overcome this problem, in which control signals are bounded using saturation functions. The nonlinear adaptive control scheme yields asymptotic convergence of the vehicle to the reference trajectory, in the presence of parametric uncertainties. The stability of the presented control laws is proved in the sense of Lyapunov theory and Barbalat׳s lemma. Efficiency of presented controller using saturation functions is verified through comparing numerical simulations of both controllers.

Analysis of the barley bract suppression gene Trd1

A typical barley (Hordeum vulgare) floret consists of reproductive organs three stamens and a pistil, and non-reproductive organs-lodicules and two floral bracts, abaxial called 'lemma' and adaxial 'palea'. The floret is subtended by two additional bracts called outer or empty glumes. Together these organs form the basic structural unit of the grass inflorescence, a spikelet. There are commonly three spikelets at each rachis (floral stem of the barley spike) node, one central and two lateral spikelets. Rare naturally occurring or induced phenotypic variants that contain a third bract subtending the central spikelets have been described in barley. The gene responsible for this phenotype was called the THIRD OUTER GLUME1 (Trd1). The Trd1 mutants fail to suppress bract growth and as a result produce leaf-like structures that subtend each rachis node in the basal portion of the spike. Also, floral development at the collar is not always suppressed. In rice and maize, recessive mutations in NECK LEAF1 (Nl1) and TASSEL SHEATH1 (Tsh1) genes, respectively, have been shown to be responsible for orthologous phenotypes. Fine mapping of the trd1 phenotype in an F-3 recombinant population enabled us to position on the long arm of chromosome 1H to a 10 cM region. We anchored this to a conserved syntenic region on rice chromosome Os05 and selected a set of candidate genes for validation by resequencing PCR amplicons from a series of independent mutant alleles. This analysis revealed that a GATA transcription factor, recently proposed to be Trd1, contained mutations in 10 out of 14 independent trd1 mutant alleles that would generate non-functional TRD1 proteins. Together with genetic linkage data, we confirm the identity of Trd1 as the GATA transcription factor ortholog of rice Nl1 and maize Tsh1 genes.

On the L2 stability of linear multidimensional time varying systems

This paper analyzes the L2 stability of solutions of systems with time-varying coefficients of the form [A + C(t)]x′ = [B + D(t)]x + u, where A, B, C, D are matrices. Following proof of a lemma, the main result is derived, according to which the system is L2 stable if the eigenvalues of the coefficient matrices are related in a simple way. A corollary of the theorem dealing with small periodic perturbations of constant coefficient systems is then proved. The paper concludes with two illustrative examples, both of which deal with the attitude dynamics of a rigid, axisymmetric, spinning satellite in an eccentric orbit, subject to gravity gradient torques.

Bounded-input/bounded-output stability of linear multidimensional time- varying systems

The present study of the stability of systems governed by a linear multidimensional time-varying equation, which are encountered in spacecraft dynamics, economics, demographics, and biological systems, gives attention the lemma dealing with L(inf) stability of an integral equation that results from the differential equation of the system under consideration. Using the proof of this lemma, the main result on L(inf) stability is derived according; a corollary of the theorem deals with constant coefficient systems perturbed by small periodic terms. (O.C.)

Capillary-gravity waves against a corrugated vertical cliff

An analysis involving a transformation of the velocity potential and a Fourier Sine Transform technique is described to study the effect of surface tension on incoming surface waves against a vertical cliff with a periodic wall perturbation. Known results are recovered as particular cases of the general problem considered. An analytical expression is derived for the surface elevation, at far distances from the shore-line, by using Watson's lemma and a representative table of numerical values of the coefficients of the resulting asymptotic expansion is also presented.

A maximal operator, Carleson's embedding, and tent spaces for vector-valued functions

This thesis is concerned with the area of vector-valued Harmonic Analysis, where the central theme is to determine how results from classical Harmonic Analysis generalize to functions with values in an infinite dimensional Banach space. The work consists of three articles and an introduction. The first article studies the Rademacher maximal function that was originally defined by T. Hytönen, A. McIntosh and P. Portal in 2008 in order to prove a vector-valued version of Carleson's embedding theorem. The boundedness of the corresponding maximal operator on Lebesgue-(Bochner) -spaces defines the RMF-property of the range space. It is shown that the RMF-property is equivalent to a weak type inequality, which does not depend for instance on the integrability exponent, hence providing more flexibility for the RMF-property. The second article, which is written in collaboration with T. Hytönen, studies a vector-valued Carleson's embedding theorem with respect to filtrations. An earlier proof of the dyadic version assumed that the range space satisfies a certain geometric type condition, which this article shows to be also necessary. The third article deals with a vector-valued generalizations of tent spaces, originally defined by R. R. Coifman, Y. Meyer and E. M. Stein in the 80's, and concerns especially the ones related to square functions. A natural assumption on the range space is then the UMD-property. The main result is an atomic decomposition for tent spaces with integrability exponent one. In order to suit the stochastic integrals appearing in the vector-valued formulation, the proof is based on a geometric lemma for cones and differs essentially from the classical proof. Vector-valued tent spaces have also found applications in functional calculi for bisectorial operators. In the introduction these three themes come together when studying paraproduct operators for vector-valued functions. The Rademacher maximal function and Carleson's embedding theorem were applied already by Hytönen, McIntosh and Portal in order to prove boundedness for the dyadic paraproduct operator on Lebesgue-Bochner -spaces assuming that the range space satisfies both UMD- and RMF-properties. Whether UMD implies RMF is thus an interesting question. Tent spaces, on the other hand, provide a method to study continuous time paraproduct operators, although the RMF-property is not yet understood in the framework of tent spaces.

A Circuit-Based Proof of Toda′s Theorem

We present a simple proof of Toda′s result (Toda (1989), in "Proceedings, 30th Annual IEEE Symposium on Foundations of Computer Science," pp. 514-519), which states that circled plus P is hard for the Polynomial Hierarchy under randomized reductions. Our approach is circuit-based in the sense that we start with uniform circuit definitions of the Polynomial Hierarchy and apply the Valiant-Vazirani lemma on these circuits (Valiant and Vazirani (1986), Thoeret. Comput. Sci.47, 85-93).

An interior penalty method for a sixth-order elliptic equation

We derive and study a C(0) interior penalty method for a sixth-order elliptic equation on polygonal domains. The method uses the cubic Lagrange finite-element space, which is simple to implement and is readily available in commercial software. After introducing some notation and preliminary results, we provide a detailed derivation of the method. We then prove the well-posedness of the method as well as derive quasi-optimal error estimates in the energy norm. The proof is based on replacing Galerkin orthogonality with a posteriori analysis techniques. Using this approach, we are able to obtain a Cea-like lemma with minimal regularity assumptions on the solution. Numerical experiments are presented that support the theoretical findings.

Information and Efficiency in the Nervous System-A Synthesis

In systems biology, questions concerning the molecular and cellular makeup of an organism are of utmost importance, especially when trying to understand how unreliable components-like genetic circuits, biochemical cascades, and ion channels, among others-enable reliable and adaptive behaviour. The repertoire and speed of biological computations are limited by thermodynamic or metabolic constraints: an example can be found in neurons, where fluctuations in biophysical states limit the information they can encode-with almost 20-60% of the total energy allocated for the brain used for signalling purposes, either via action potentials or by synaptic transmission. Here, we consider the imperatives for neurons to optimise computational and metabolic efficiency, wherein benefits and costs trade-off against each other in the context of self-organised and adaptive behaviour. In particular, we try to link information theoretic (variational) and thermodynamic (Helmholtz) free-energy formulations of neuronal processing and show how they are related in a fundamental way through a complexity minimisation lemma.