L2-stability of nonstationary feedback systems: Frequency-domain criteria

A frequency-domain positivity condition is derived for linear time-varying operators in2and is used to develop2stability criteria for linear and nonlinear feedback systems. These criteria permit the use of a very general class of operators in2with nonstationary kernels, as multipliers. More specific results are obtained by using a first-order differential operator with a time-varying coefficient as multiplier. Finally, by employing periodic multipliers, improved stability criteria are derived for the nonlinear damped Mathieu equation with a forcing function.

Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.

Homoclinic Splitting without Trees

We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. When the coupling takes place through an even trigonometric polynomial in the angle variables, we extend analytically the solutions of the equations of motion, order by order in the perturbation parameter, to a large neighbourhood of the real line representing time. Subsequently, we devise an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing gravity, by a shift-of-countour argument. Hence, we infer a similar upper bound for the splitting itself. In particular, the derivation of the result does not call for a tree expansion with explicit cancellation mechanisms.

Topological stability through tame retractions

A smooth map is said to be stable if small perturbations of the map only differ from the original one by a smooth change of coordinates. Smoothly stable maps are generic among the proper maps between given source and target manifolds when the source and target dimensions belong to the so-called nice dimensions, but outside this range of dimensions, smooth maps cannot generally be approximated by stable maps. This leads to the definition of topologically stable maps, where the smooth coordinate changes are replaced with homeomorphisms. The topologically stable maps are generic among proper maps for any dimensions of source and target. The purpose of this thesis is to investigate methods for proving topological stability by constructing extremely tame (E-tame) retractions onto the map in question from one of its smoothly stable unfoldings. In particular, we investigate how to use E-tame retractions from stable unfoldings to find topologically ministable unfoldings for certain weighted homogeneous maps or germs. Our first results are concerned with the construction of E-tame retractions and their relation to topological stability. We study how to construct the E-tame retractions from partial or local information, and these results form our toolbox for the main constructions. In the next chapter we study the group of right-left equivalences leaving a given multigerm f invariant, and show that when the multigerm is finitely determined, the group has a maximal compact subgroup and that the corresponding quotient is contractible. This means, essentially, that the group can be replaced with a compact Lie group of symmetries without much loss of information. We also show how to split the group into a product whose components only depend on the monogerm components of f. In the final chapter we investigate representatives of the E- and Z-series of singularities, discuss their instability and use our tools to construct E-tame retractions for some of them. The construction is based on describing the geometry of the set of points where the map is not smoothly stable, discovering that by using induction and our constructional tools, we already know how to construct local E-tame retractions along the set. The local solutions can then be glued together using our knowledge about the symmetry group of the local germs. We also discuss how to generalize our method to the whole E- and Z- series.

Bayesian statistical analysis of bacterial diversity

Bacteria play an important role in many ecological systems. The molecular characterization of bacteria using either cultivation-dependent or cultivation-independent methods reveals the large scale of bacterial diversity in natural communities, and the vastness of subpopulations within a species or genus. Understanding how bacterial diversity varies across different environments and also within populations should provide insights into many important questions of bacterial evolution and population dynamics. This thesis presents novel statistical methods for analyzing bacterial diversity using widely employed molecular fingerprinting techniques. The first objective of this thesis was to develop Bayesian clustering models to identify bacterial population structures. Bacterial isolates were identified using multilous sequence typing (MLST), and Bayesian clustering models were used to explore the evolutionary relationships among isolates. Our method involves the inference of genetic population structures via an unsupervised clustering framework where the dependence between loci is represented using graphical models. The population dynamics that generate such a population stratification were investigated using a stochastic model, in which homologous recombination between subpopulations can be quantified within a gene flow network. The second part of the thesis focuses on cluster analysis of community compositional data produced by two different cultivation-independent analyses: terminal restriction fragment length polymorphism (T-RFLP) analysis, and fatty acid methyl ester (FAME) analysis. The cluster analysis aims to group bacterial communities that are similar in composition, which is an important step for understanding the overall influences of environmental and ecological perturbations on bacterial diversity. A common feature of T-RFLP and FAME data is zero-inflation, which indicates that the observation of a zero value is much more frequent than would be expected, for example, from a Poisson distribution in the discrete case, or a Gaussian distribution in the continuous case. We provided two strategies for modeling zero-inflation in the clustering framework, which were validated by both synthetic and empirical complex data sets. We show in the thesis that our model that takes into account dependencies between loci in MLST data can produce better clustering results than those methods which assume independent loci. Furthermore, computer algorithms that are efficient in analyzing large scale data were adopted for meeting the increasing computational need. Our method that detects homologous recombination in subpopulations may provide a theoretical criterion for defining bacterial species. The clustering of bacterial community data include T-RFLP and FAME provides an initial effort for discovering the evolutionary dynamics that structure and maintain bacterial diversity in the natural environment.

Crystal structure of the amino acid-vitamin complex lysine pantothenatestar, open

L-Lysine d-pantothenate, a 1:1 amino acid-vitamin complex, crystallizes in the monoclinic space group P21 with Image Full-size image (1K) .The structure has been solved by direct methods and refined to an R value of 0.053 for 1868 observed reflections. The zwitterionic positively charged lysine molecules in the structure assume the sterically most favourable conformation with an all-trans side chain trans to the α-carboxylate group. The pantothenate anion has a somewhat folded conformation stabilised by an intramolecular bifurcated hydrogen bond. The unlike molecules aggregate into separate alternating layers. The molecules in the lysine layers form a head-to-tail sequence parallel to the a-axis. The interactions which hold the adjacent layers together include those between the side chain amino group of lysine and the carboxylate group in the pantothenate anion. The geometry of these interactions is such that each carboxylate group is sandwiched between two amino groups in a periodic arrangement of alternating carboxylate and amino groups.

Spatiotemporal aspects of Hendra Virus infection in Pteropid Bats (Flying-Foxes) in Eastern Australia

Hendra virus (HeV) causes highly lethal disease in horses and humans in the eastern Australian states of Queensland (QLD) and New South Wales (NSW), with multiple equine cases now reported on an annual basis. Infection and excretion dynamics in pteropid bats (flying-foxes), the recognised natural reservoir, are incompletely understood. We sought to identify key spatial and temporal factors associated with excretion in flying-foxes over a 2300 km latitudinal gradient from northern QLD to southern NSW which encompassed all known equine case locations. The aim was to strengthen knowledge of Hendra virus ecology in flying-foxes to improve spillover risk prediction and exposure risk mitigation strategies, and thus better protect horses and humans. Monthly pooled urine samples were collected from under roosting flying-foxes over a three-year period and screened for HeV RNA by quantitative RT-PCR. A generalised linear model was employed to investigate spatiotemporal associations with HeV detection in 13,968 samples from 27 roosts. There was a non-linear relationship between mean HeV excretion prevalence and five latitudinal regions, with excretion moderate in northern and central QLD, highest in southern QLD/northern NSW, moderate in central NSW, and negligible in southern NSW. Highest HeV positivity occurred where black or spectacled flying-foxes were present; nil or very low positivity rates occurred in exclusive grey-headed flying-fox roosts. Similarly, little red flying-foxes are evidently not a significant source of virus, as their periodic extreme increase in numbers at some roosts was not associated with any concurrent increase in HeV detection. There was a consistent, strong winter seasonality to excretion in the southern QLD/northern NSW and central NSW regions. This new information allows risk management strategies to be refined and targeted, mindful of the potential for spatial risk profiles to shift over time with changes in flying-fox species distribution.

Neutron-diffraction study of structure and conformation of nucleotide uridine-5 phosphate (disodium salt)

Acta Crystallographica Section A: Foundations of Crystallography covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.

The use of metabolomics to monitor simultaneous changes in metabolic variables following supramaximal low volume high intensity exercise

High Intensity Exercise (HIE) stimulates greater physiological remodeling when compared to workload matched low-moderate intensity exercise. This study utilized an untargeted metabolomics approach to examine the metabolic perturbations that occur following two workload matched supramaximal low volume HIE trials. In a randomized order, 7 untrained males completed two exercise protocols separated by one week; 1) HIE150%: 30 x 20s cycling at 150% VO2peak, 40s passive rest; 2) HIE300%: 30 x 10s cycling at 300% VO2peak, 50 s passive rest. Total exercise duration was 30 minutes for both trials. Blood samples were taken at rest, during and immediately following exercise and at 60 minutes post exercise. Gas chromatography-mass spectrometry (GC-MS) analysis of plasma identified 43 known metabolites of which 3 demonstrated significant fold changes (HIE300% compared to the HIE150% value) during exercise, 14 post exercise and 23 at the end of the recovery period. Significant changes in plasma metabolites relating to lipid metabolism [fatty acids: dodecanoate (p=0.042), hexadecanoate (p=0.001), octadecanoate (p=0.001)], total cholesterol (p=0.001), and glycolysis [lactate (p=0.018)] were observed following exercise and during the recovery period. The HIE300% protocol elicited greater metabolic changes relating to lipid metabolism and glycolysis when compared to HIE150% protocol. These changes were more pronounced throughout the recovery period rather than during the exercise bout itself. Data from the current study demonstrate the use of metabolomics to monitor intensity-dependent changes in multiple metabolic pathways following exercise. The small sample size indicates a need for further studies in a larger sample cohort to validate these findings.

Endoplasmic reticulum stress and cell death mechanisms in the cell model of Huntington’s disease

This thesis clarifies important molecular pathways that are activated during the cell death observed in Huntington’s disease. Huntington’s disease is one of the most common inherited neurodegenerative diseases, which is primarily inherited in an autosomal dominant manner. HD is caused by an expansion of CAG repeats in the first exon of the IT15 gene. IT15 encodes the production of a Huntington’s disease protein huntingtin. Mutation of the IT15 gene results in a long stretch of polyQ residues close to the amino-terminal region of huntingtin. Huntington’s disease is a fatal autosomal neurodegenerative disorder. Despite the current knowledge of HD, the precise mechanism behind the selective neuronal death, and how the disease propagates, still remains an enigma. The studies mainly focused on the control of endoplasmic reticulum (ER) stress triggered by the mutant huntingtin proteins. The ER is a delicate organelle having essential roles in protein folding and calcium regulation. Even the slightest perturbations on ER homeostasis are effective enough to trigger ER stress and its adaptation pathways, called unfolded protein response (UPR). UPR is essential for cellular homeostasis and it adapts ER to the changing environment and decreases ER stress. If adaptation processes fail and stress is excessive and prolonged; irreversible cell death pathways are engaged. The results showed that inhibition of ER stress with chemical agents are able to decrease cell death and formation of toxic cell aggregates caused by mutant huntingtin proteins. The study concentrated also to the NF-κB (nuclear factor-kappaB) pathway, which is activated during ER stress. NF-κB pathway is capable to regulate the levels of important cellular antioxidants. Cellular antioxidants provide a first line of defence against excess reactive oxygen species. Excess accumulation of reactive oxygen species and subsequent activation of oxidative stress damages motley of vital cellular processes and induce cell degeneration. Data showed that mutant huntingtin proteins downregulate the expression levels of NF-κB and vital antioxidants, which was followed by increased oxidative stress and cell death. Treatment with antioxidants and inhibition of oxidative stress were able to counteract these adverse effects. In addition, thesis connects ER stress caused by mutant huntingtin to the cytoprotective autophagy. Autophagy sustains cellular balance by degrading potentially toxic cell proteins and components observed in Huntington’s disease. The results revealed that cytoprotective autophagy is active at the early points (24h) of ER stress after expression of mutant huntingtin proteins. GADD34 (growth arrest and DNA damage-inducible gene 34), which is previously connected to the regulation of translation during cell stress, was shown to control the stimulation of autophagy. However, GADD34 and autophagy were downregulated at later time points (48h) during mutant huntingtin proteins induced ER stress, and subsequently cell survival decreased. Overexpression GADD34 enhanced autophagy and decreased cell death, indicating that GADD34 plays a critical role in cell protection. The thesis reveales new interesting data about the neuronal cell death pathways seen in Huntington’s disease, and how cell degeneration is partly counteracted by various therapeutic agents. Expression of mutant huntingtin proteins is shown to alter signaling events that control ER stress, oxidative stress and autophagy. Despite that Huntington’s disease is mainly an untreatable disorder; these findings offer potential targets and neuroprotective strategies in designing novel therapies for Huntington’s disease.

A deadline-constrained 802.11 MAC Protocol with QoS differentiation for soft real-time control

As one of the most widely used wireless network technologies, IEEE 802.11 wireless local area networks (WLANs) have found a dramatically increasing number of applications in soft real-time networked control systems (NCSs). To fulfill the real-time requirements in such NCSs, most of the bandwidth of the wireless networks need to be allocated to high-priority data for periodic measurements and control with deadline requirements. However, existing QoS-enabled 802.11 medium access control (MAC) protocols do not consider the deadline requirements explicitly, leading to unpredictable deadline performance of NCS networks. Consequentially, the soft real-time requirements of the periodic traffic may not be satisfied, particularly under congested network conditions. This paper makes two main contributions to address this problem in wireless NCSs. Firstly, a deadline-constrained MAC protocol with QoS differentiation is presented for IEEE 802.11 soft real-time NCSs. It handles periodic traffic by developing two specific mechanisms: a contention-sensitive backoff mechanism, and an intra-traffic-class QoS differentiation mechanism. Secondly, a theoretical model is established to describe the deadline-constrained MAC protocol and evaluate its performance of throughput, delay and packet-loss ratio in wireless NCSs. Numerical studies are conducted to validate the accuracy of the theoretical model and to demonstrate the effectiveness of the new MAC protocol.

Temporal: The artwork

The interactive artwork Temporal arose from a series of art-science investigations with some of Australia’s leading flying fox ecologists. It was designed as a gently evolving meditation upon the complex, periodic processes that mark Australia’s often irregular seasonal changes. In turn these changes directly govern the migratory movements of Australia’s keystone pollinating mammals - the mega bats (Flying Foxes). Temporal further called attention to our increasing capacity to profoundly disturb these partners within Australia’s complex, life-supporting systems

Analytical method for solving a set of infinite simultaneous equations

It is shown that a method based on the principle of analytic continuation can be used to solve a set of infinite simultaneous equations encountered in solving for the electric field of a periodic electrode structure.

Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.

Quasi-simple wave solutions for acoustic gravity waves

The special class of quasi-simple wave solutions is studied for the system of partial differential equations governing inviscid acoustic gravity waves. It is shown that these traveling wave solutions do not admit shocks. Periodic solutions are found to exist when there is no propagation in the vertical direction. The solutions for some particular cases are depicted graphically. Physics of Fluids is copyrighted by The American Institute of Physics.