Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft

This paper considers left-invariant control systems defined on the Lie groups SU(2) and SO(3). Such systems have a number of applications in both classical and quantum control problems. The purpose of this paper is two-fold. Firstly, the optimal control problem for a system varying on these Lie Groups, with cost that is quadratic in control is lifted to their Hamiltonian vector fields through the Maximum principle of optimal control and explicitly solved. Secondly, the control systems are integrated down to the level of the group to give the solutions for the optimal paths corresponding to the optimal controls. In addition it is shown here that integrating these equations on the Lie algebra su(2) gives simpler solutions than when these are integrated on the Lie algebra so(3).

Ring-chain interconversion in high-performance polymer systems. 3. Cyclodepolymerization of poly(m-phenylene isophthalamide) (Nomex) and entropically driven ring-opening polymerization of the macrocyclic oligomers so produced

A homologous series of macrocyclic oligoamides has been prepared in high yield by reaction of isophthaloyl chloride with m-phenylenediamine under pseudo-high-dilution conditions. The products were characterized by infrared and H-1 NMR spectroscopies, matrix assisted laser desorption-ionization time-of-flight mass spectrometry, and gel permeation chromatography (GPC). A series of linear oligomers was prepared for comparison. The macrocycles ranged in size from the cyclic trimer up to at least the cyclic nonamer (90 ring atoms). The same homologous series of macrocyclic oligomers was prepared in high yield by the cyclodepolymerization of poly(m-phenylene isophthalamide) (Nomex). Cyclodepolymerization was best achieved by treating a 1% w/v solution of the polymer in dimethyl sulfoxide containing calcium chloride or lithium chloride with 3-4 mol % of sodium hydride or the sodium salt of benzanilide at 150 degreesC for 70 h. Treatment of a concentrated solution of the macrocyclic oligomers (25% w/v) with 4 mol % of sodium hydride or the sodium salt of benzanilide in a solution of lithium chloride in dimethyl sulfoxide at 170 degreesC for 6 h resulted in efficient entropically driven ring-opening polymerizations to give poly(m-phenylene isophthalamide), characterized by infrared and H-1 NMR spectroscopies and by GPC. The molecular weights obtained were comparable with those of the commercial polymer.

Integrating Hamiltonian systems defined on the Lie groups SO(4) and SO(1,3)

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E³, the spheres S³ and the hyperboloids H³ with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions is illustrated.

Long-chain n−3 PUFA: plant v. marine sources

Increasing recognition of the importance of the long-chain n-3 PUFA, EPA and DHA, to cardiovascular health, and in the case of DHA to normal neurological development in the fetus and the newborn, has focused greater attention on the dietary supply of these fatty acids. The reason for low intakes of EPA and DHA in most developed countries (0 center dot 1-0 center dot 5hairspg/d) is the low consumption of oily fish, the richest dietary source of these fatty acids. An important question is whether dietary intake of the precursor n-3 fatty acid, alpha-linolenic acid (alpha LNA), can provide sufficient amounts of tissue EPA and DHA by conversion through the n-3 PUFA elongation-desaturation pathway. alpha LNA is present in marked amounts in plant sources, including green leafy vegetables and commonly-consumed oils such as rape-seed and soyabean oils, so that increased intake of this fatty acid would be easier to achieve than via increased fish consumption. However, alpha LNA-feeding studies and stable-isotope studies using alpha LNA, which have addressed the question of bioconversion of alpha LNA to EPA and DHA, have concluded that in adult men conversion to EPA is limited (approximately 8%) and conversion to DHA is extremely low (< 0 center dot 1%). In women fractional conversion to DHA appears to be greater (9%), which may partly be a result of a lower rate of utilisation of alpha LNA for beta-oxidation in women. However, up-regulation of the conversion of EPA to DHA has also been suggested, as a result of the actions of oestrogen on Delta 6-desaturase, and may be of particular importance in maintaining adequate provision of DHA in pregnancy. The effect of oestrogen on DHA concentration in pregnant and lactating women awaits confirmation.

Proteornics analysis unravels the functional repertoire of coronavirus nonstructural protein 3

Severe acute respiratory syndrome (SARS) coronavirus infection and growth are dependent on initiating signaling and enzyme actions upon viral entry into the host cell. Proteins packaged during virus assembly may subsequently form the first line of attack and host manipulation upon infection. A complete characterization of virion components is therefore important to understanding the dynamics of early stages of infection. Mass spectrometry and kinase profiling techniques identified nearly 200 incorporated host and viral proteins. We used published interaction data to identify hubs of connectivity with potential significance for virion formation. Surprisingly, the hub with the most potential connections was not the viral M protein but the nonstructurall protein 3 (nsp3), which is one of the novel virion components identified by mass spectrometry. Based on new experimental data and a bioinformatics analysis across the Coronaviridae, we propose a higher-resolution functional domain architecture for nsp3 that determines the interaction capacity of this protein. Using recombinant protein domains expressed in Escherichia coli, we identified two additional RNA-binding domains of nsp3. One of these domains is located within the previously described SARS-unique domain, and there is a nucleic acid chaperone-like domain located immediately downstream of the papain-like proteinase domain. We also identified a novel cysteine-coordinated metal ion-binding domain. Analyses of interdomain interactions and provisional functional annotation of the remaining, so-far-uncharacterized domains are presented. Overall, the ensemble of data surveyed here paint a more complete picture of nsp3 as a conserved component of the viral protein processing machinery, which is intimately associated with viral RNA in its role as a virion component.

Distributed space-time block coding for 3 and 4 relay nodes: Imperfect synchronisation and a solution

Most research on distributed space time block coding (STBC) has so far focused on the case of 2 relay nodes and assumed that the relay nodes are perfectly synchronised at the symbol level. By applying STBC to 3-or 4-relay node systems, this paper shows that imperfect synchronisation causes significant performance degradation to the conventional detector. To this end, we propose a new STBC detection solution based on the principle of parallel interference cancellation (PIC). The PIC detector is moderate in computational complexity but is very effective in suppressing the impact of imperfect synchronisation.

Synthesis of 3 '-S-phosphorothiolate oligonucleotides for their potential use in RNA interference

The potency of RNA interference (RNAi) undoubtedly can be improved through chemical modifications to the small interfering RNAs (siRNA). By incorporation of the 3′-S-phosphorothiolate modification into strands of RNA, it is hoped that specific regions of a siRNA duplex can be stabilised to enhance the target binding affinity of a selected antisense strand into the activated RNA-induced silencing complex (RISC*). Oligonucleotides composed entirely of this modification are desirable so unconventional 5′ → 3′ synthesis is investigated, with initial solution-phase testing proving successful. The phosphoroamidite monomer required for solid-phase synthesis has also been produced.

Marine omega-3 fatty acids and coronary heart disease

Purpose of review: To provide an overview of the key earlier intervention studies with marine omega-3 fatty acids and to review and comment on recent studies reporting on mortality outcomes and on selected underlying mechanisms of action. Recent findings: Studies relating marine omega-3 fatty acid status to current or future outcomes continue to indicate benefits, for example, on incident heart failure, congestive heart failure, acute coronary syndrome, and all-cause mortality. New mechanistic insights into the actions of marine omega-3 fatty acids have been gained. Three fairly large secondary prevention trials have not confirmed the previously reported benefit of marine omega-3 fatty acids towards mortality in survivors of myocardial infarction. Studies of marine omega-3 fatty acids in atrial fibrillation and in cardiac surgery-induced atrial fibrillation have produced inconsistent findings and meta-analyses demonstrate no benefit. A study confirmed that marine omega-3 fatty acids reduce the inflammatory burden with advanced atherosclerotic plaques, so inducing greater stability. Summary: Recent studies of marine omega-3 fatty acids on morbidity of, and mortality from, coronary and cardiovascular disease have produced mixed findings. These studies raise new issues to be addressed in future research.

ATD: a multiplatform for semiautomatic 3-D detection of kidneys and their pathology in real time

This research presents a novel multi-functional system for medical Imaging-enabled Assistive Diagnosis (IAD). Although the IAD demonstrator has focused on abdominal images and supports the clinical diagnosis of kidneys using CT/MRI imaging, it can be adapted to work on image delineation, annotation and 3D real-size volumetric modelling of other organ structures such as the brain, spine, etc. The IAD provides advanced real-time 3D visualisation and measurements with fully automated functionalities as developed in two stages. In the first stage, via the clinically driven user interface, specialist clinicians use CT/MRI imaging datasets to accurately delineate and annotate the kidneys and their possible abnormalities, thus creating “3D Golden Standard Models”. Based on these models, in the second stage, clinical support staff i.e. medical technicians interactively define model-based rules and parameters for the integrated “Automatic Recognition Framework” to achieve results which are closest to that of the clinicians. These specific rules and parameters are stored in “Templates” and can later be used by any clinician to automatically identify organ structures i.e. kidneys and their possible abnormalities. The system also supports the transmission of these “Templates” to another expert for a second opinion. A 3D model of the body, the organs and their possible pathology with real metrics is also integrated. The automatic functionality was tested on eleven MRI datasets (comprising of 286 images) and the 3D models were validated by comparing them with the metrics from the corresponding “3D Golden Standard Models”. The system provides metrics for the evaluation of the results, in terms of Accuracy, Precision, Sensitivity, Specificity and Dice Similarity Coefficient (DSC) so as to enable benchmarking of its performance. The first IAD prototype has produced promising results as its performance accuracy based on the most widely deployed evaluation metric, DSC, yields 97% for the recognition of kidneys and 96% for their abnormalities; whilst across all the above evaluation metrics its performance ranges between 96% and 100%. Further development of the IAD system is in progress to extend and evaluate its clinical diagnostic support capability through development and integration of additional algorithms to offer fully computer-aided identification of other organs and their abnormalities based on CT/MRI/Ultra-sound Imaging.