Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Efficient simulation of a Tandem Jackson Network

The two-node tandem Jackson network serves as a convenient reference model for the analysis and testing of different methodologies and techniques in rare event simulation. In this paper we consider a new approach to efficiently estimate the probability that the content of the second buffer exceeds some high level L before it becomes empty, starting from a given state. The approach is based on a Markov additive process representation of the buffer processes, leading to an exponential change of measure to be used in an importance sampling procedure. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer. We prove that when the first buffer is finite, this method yields asymptotically efficient simulation for any set of arrival and service rates. In fact, the relative error is bounded independent of the level L; a new result which is not established for any other known method. When the first buffer is infinite, we propose a natural extension of the exponential change of measure for the finite buffer case. In this case, the relative error is shown to be bounded (independent of L) only when the second server is the bottleneck; a result which is known to hold for some other methods derived through large deviations analysis. When the first server is the bottleneck, experimental results using our method seem to suggest that the relative error is bounded linearly in L.

Rapid diagnosis in pediatric infectious diseases: The past, the present and the future

The focus of rapid diagnosis of infectious diseases of children in the last decade has shifted from variations of the conventional laboratory techniques of antigen detection, microscopy and culture to that of molecular diagnosis of infectious agents. Pediatricians will need to be able to interpret the use, limitations and results of molecular diagnostic techniques as they are increasingly integrated into routine clinical microbiology laboratory protocols. PCR is the best known and most successfully implemented diagnostic molecular technology to date. It can detect specific infectious agents and determine their virulence and antimicrobial genotypes with greater speed, sensitivity and specificity than conventional microbiology methods. Inherent technical limitations of PCR are present, although they are reduced in laboratories that follow suitable validation and quality control procedures. Variations of PCR together with advances in nucleic acid amplification technology have broadened its diagnostic capabilities in clinical infectious disease to now rival and even surpass traditional methods in some situations. Automation of all components of PCR is now possible. The completion of the genome sequencing projects for significant microbial pathogens, in combination with PCR and DNA chip technology, will revolutionize the diagnosis and management of infectious diseases.

Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (0(m)vertical bar alpha(n)) representations of U-q[gl(m vertical bar n)]

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (O-m\alpha(n)) families of highest-weight representations of the quantum superalgebras Uq[gl(m\n)]. These representations are irreducible, contain a free complex parameter a, and are 2(mn)-dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 2(4mn) components, each of which is in general an algebraic expression in the two complex variables q and a. Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in MATHEMATICA; illustrating our results with U-q [gl(3\1)]. (C) 2002 Published by Elsevier Science B.V.

Site-Directed Mutagenesis of Dimethyl Sulfoxide Reductase from Rhodobacter capsulatus: Characterization of a Y114 → F Mutant

A system for expressing site-directed mutants of the molybdenum enzyme dimethyl sulfoxide reductase from Rhodobacter capsulatus in the natural host was constructed. This system was used to Generate and express dimethyl sulfoxide reductase with a Y114F mutation. The Y114F mutant had an increased k(cat) and increased K-m toward both dimethyl sulfoxide and trimethylamine N-oxide compared to the native enzyme, and the value of k(cat)/K-m was lower for both substrates in the mutant enzyme. The Y114F mutant, as isolated, was able to oxidize dimethyl sulfide with phenazine ethosulfate as the electron acceptor but with a lower k(cat) than that of the native enzyme. The pH optimum of dimethyl sulfide: acceptor oxidoreductase activity in the Y114F mutant was shown to be shifted by +1 pH unit compared to the native enzyme. The Y114F mutant did not form a pink complex with dimethyl sulfide, which is characteristic of the native enzyme. The mutant enzyme showed a large increase in the K-d for DMS. Direct electrochemistry showed that the Mo(V)/Mo(IV) couple was unaffected by the Y114F mutant, but the midpoint potential of the Mo(VI)/Mo(V) couple was raised by about 50 mV. These data confirm that the Y114 residue plays a critical role in oxidation-reduction processes at the molybdenum active site and in oxygen atom transfer associated with sulfoxide reduction.

Communicating vegetation management science to land managers and other stakeholders

Science communication. including extension services. plays a key role in achieving sustainable native vegetation management. One of the pivotal aspects of the debate on sustainable vegetation management is the scientific information underpinning policy-making. In recent years. extension services have Shifted their focus from top-down technology transfer to bottom-up participation and empowerment. I here has also been a broadening of communication strategies to recognise the range of stakeholders involved in native vegetation management and to encompass environmental concerns. This paper examines the differences between government approaches to extension services to deliver policy and the need for effective communication to address broader science issues that underpin native vegetation management. The importance of knowing the learning styles of the stakeholders involved in native vegetation management is discussed at a time of increasing reliance on mass communication for information exchange and the importance of personal communication to achieve on-ground sustainable management. Critical factors for effective science-management communication are identified Such as: (i) undertaking scientific studies (research) with community involvement, acceptance and agreed understanding of project objectives (ii) realistic community consultation periods: (iii) matching communication channels with stakeholder needs; (iv) combining scientific with local knowledge in in holistic (biophysical and social) approach to understanding in issued and (v) regional partnerships. These communication factors are considered to be essential to implementing on-ground natural resource management strategics and actions, including those concerned with native vegetation management.

Rapid colour changes in multilayer reflecting stripes in the paradise whiptail, Pentapodus paradiseus

The Paradise whiptail (Pentapodus paradiseus) has distinct reflective stripes on its head and body. The reflective stripes contain a dense layer of physiologically active iridophores, which act as multilayer reflectors. The wavelengths reflected by these stripes can change from blue to red in 0.25 s. Transmission electron microscopy revealed that the iridophore cells contain plates that are, on average, 51.4 nm thick. This thickness produces a stack, which acts as an ideal quarter-wavelength multilayer reflector (equal optical thickness of plates and spaces) in the blue, but not the red, region of the spectrum. When skin preparations were placed into hyposmotic physiological saline, the peak wavelength of the reflected light shifted towards the longer (red) end of the visible spectrum. Hyperosmotic saline reversed this effect and shifted the peak wavelength towards shorter (blue/UV) wavelengths. Norepinephrine (100 mumol l(-1)) shifted the peak wavelength towards the longer end of the spectrum, while adenosine (100 mumol l(-1)) reversed the effects of norepinephrine. The results from this study show that the wavelength changes are elicited by a change of similar to70 nm in the distance between adjacent plates in the iridophore cells.