Quasistationarity of continuous-time Markov chains with positive drift

We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity sets in. We will show how this 'quasi' stationary behaviour can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By way of a dual chain, obtained by killing the original process on last exit from 0, we invoke the theory of quasistationarity for absorbing Markov chains. We prove that the conditioned state probabilities of the original chain are equal to the state probabilities of its dual conditioned on non-absorption, thus allowing us to establish the simultaneous existence and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasistationary distribution in the usual sense, a similar statement is not possible for the original chain.

On the construction of integrable closed chains with quantum supersymmetry

We present a general prescription for the construction of integrable one-dimensional systems with closed boundary conditions and quantum supersymmetry.

On the Oberwolfach problem with two similar length cycles

For all in greater than or equal to 3, the Oberwolfach problem is solved for the case where the 2-factors consist of two cycles of lengths in and m + 1, and for the case where the 2-factors consist of two cycles of lengths m and m + 2.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Quantum-state engineering with continuous-variable postselection

We present a scheme to conditionally engineer an optical quantum system via continuous-variable measurements. This scheme yields high-fidelity squeezed single photons and a superposition of coherent states, from input single- and two-photon Fock states, respectively. The input Fock state is interacted with an ancilla squeezed vacuum state using a beam splitter. We transform the quantum system by postselecting on the continuous-observable measurement outcome of the ancilla state. We experimentally demonstrate the principles of this scheme using coherent states and experimentally measure fidelities that are only achievable using quantum resources.

Universal quantum computation with continuous-variable cluster states

We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multimode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.

Variation in length, fecundity and survival of pink wax scale, Ceroplastes rubens Maskell (Hemiptera: Coccidae), on umbrella trees

We investigated some of the factors that may lead to outbreaks of pink wax scale, Ceroplastes rubens Maskell, on umbrella trees, Schefflera actinophylla (Endl.). Estimates of birth and death rates of pink wax scale were high and variable within and among trees; variation in these rates was not related to scale density. Adult fecundity correlated significantly but weakly with adult test length; mean fecundity was 292 eggs per female with a range of 5-1178. Adult test length and its variance decreased weakly with increasing density. Field experiments showed that mortality of C. rubens is greatest during the first 24 hours after hatching when approximately half disappear. The rate of loss decreases over time with 0.3% of initial motile first-instar nymphs surviving to maturity. Rates of loss varied significantly between trees, indicating that some trees are more suitable for scale colonisation and survival.

Integrable multiparametric quantum spin chains

Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted boundary conditions, We illustrate how this general formalism applier; to construct multiparametric versions of the supersymmetric t-J and Li models.

Novel vascular graft grown within recipient's own peritoneal cavity

A method by which to overcome the clinical symptoms of atherosclerosis is the insertion of a graft to bypass an artery blocked or impeded by plaque. However, there may be insufficient autologous mammary artery for multiple or repeat bypass, saphenous vein may have varicose degenerative alterations that can lead to aneurysm in high-pressure sites, and small-caliber synthetic grafts are prone to thrombus induction and occlusion. Therefore, the aim of the present study was to develop an artificial blood conduit of any required length and diameter from the cells of the host for autologous transplantation. Silastic tubing, of variable length and diameter, was inserted into the peritoneal cavity of rats or rabbits. By 2 weeks, it had become covered by several layers of myofibroblasts, collagen matrix, and a single layer of mesothelium. The Silastic tubing was removed from the harvested implants, and the tube of living tissue was everted such that it now resembled a blood vessel with an inner lining of nonthrombotic mesothelial cells (the intima), with a media of smooth muscle-like cells (myofibroblasts), collagen, and elastin, and with an outer collagenous adventitia. The tube of tissue (10 to 20 mm long) was successfully grafted by end-to-end anastomoses into the severed carotid artery or abdominal aorta of the same animal in which they were grown. The transplant remained patent for at least 4 months and developed structures resembling elastic lamellae. The myofibroblasts gained a higher volume fraction of myofilaments and became responsive to contractile agonists, similar to the vessel into which they had been grafted. It is suggested that these nonthrombogenic tubes of living tissue, grown in the peritoneal cavity of the host, may be developed as autologous coronary artery bypass grafts or as arteriovenous access fistulae for hemodialysis patients.

Investigations into a power-combining structure using a reflect array of dual-feed aperture-coupled microstrip patch antennas

This paper details an investigation of a power combiner that uses a reflect array of dual-feed aperture-coupled microstrip patch antennas and a corporate-fed dual-polarized array as a signal distributing/combining device. In this configuration, elements of the reflect array receive a linearly polarized wave and retransmit it with an orthogonal polarization using variable-length sections of microstrip lines connecting receive and transmit ports. By applying appropriate lengths of these delay lines, the array focuses the transmitted wave onto the feed array. The operation of the combiner is investigated for a small-size circular reflect array for the cases of -3 dB, -6 dB and -10 dB edge illumination by the 2 x 2-element dual-polarized array.

Working memory correlates of three symptom clusters in schizophrenia

This study was designed to examine whether discrete working memory deficits underlie positive, negative and disorganised symptoms of schizophrenia. Symptom dimension ratings were assigned to 52 outpatients with schizophrenia (ICD-10 criteria), using items drawn from the Positive and Negative Syndrome Scale (PANSS). Linear regression and correlational analyses were conducted to examine whether symptom dimension scores were related to performance on several tests of working memory function. Severity of negative symptoms correlated with reduced production of words during a verbal fluency task, impaired ability to hold letter and number sequences on-line and manipulate them Simultaneously, reduced performance during a dual task, and compromised visuospatial working memory under distraction-free conditions. Severity of disorganisation symptoms correlated with impaired visuospatial working memory under conditions of distraction, failure of inhibition during a verbal fluency task, perseverative responding on a test of set-shifting ability, and impaired ability to judge the veracity of simple declarative statements. Severity of positive symptoms was uncorrelated with performance on any of the measures examined. The present study provides evidence that the positive, negative and disorganised symptom dimensions of the PANSS constitute independent clusters, associated with unique patterns of working memory impairment. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

CEDIA (R) sirolimus assay compared with HPLC-MS/MS and HPLC-UV in transplant recipient specimens

The role of the therapeutic drug monitoring laboratory in support of immunosuppressant drug therapy is well established, and the introduction of sirolimus (SRL) is a new direction in this field. The lack of an immunoassay for several years has restricted the availability of SRL assay services. The recent availability of a CEDIA (R) SRL assay has the potential to improve this situation. The present communication has compared the CEDIA (R) SRL method with 2 established chromatographic methods, HPLC-UV and HPLC-MS/MS. The CEDIA (R) method, run on a Hitachi 917 analyzer, showed acceptable validation criteria with within-assay precision of 9.1% and 3.3%, and bias of 17.1% and 5.8%, at SRL concentrations of 5.0 mu g/L and 20 mu g/L, respectively. The corresponding between-run precision values were 11.5% and 3.3% and bias of 7.1% and 2.9% at 5.0 mu g/L and 20 mu g/L, respectively, The lower limit of quantification was found to be 3.0 mu g/L. A series of 96 EDTA whole-blood samples predominantly from renal transplant recipients were assayed by the 3 methods for comparison. It was found that the CEDIA (R) method showed a Deming regression line of CEDIA = 1.20 X HPLC-MS/MS - 0.07 (r = 0.934, SEE = 1.47), with a mean bias of 20.4%. Serial blood samples from 8 patients included in this evaluation showed that the CEDIA (R) method reflected the clinical fluctuations in the chromatographic methods, albeit with the variable bias noted. The CEDIA (R) method on the H917 analyzer is therefore a useful adjunct to SRL dosage individualization in renal transplant recipients.

Optimal sampling strategy for estimation of spatial genetic structure in tree populations

Fine-scale spatial genetic structure (SGS) in natural tree populations is largely a result of restricted pollen and seed dispersal. Understanding the link between limitations to dispersal in gene vectors and SGS is of key interest to biologists and the availability of highly variable molecular markers has facilitated fine-scale analysis of populations. However, estimation of SGS may depend strongly on the type of genetic marker and sampling strategy (of both loci and individuals). To explore sampling limits, we created a model population with simulated distributions of dominant and codominant alleles, resulting from natural regeneration with restricted gene flow. SGS estimates from subsamples (simulating collection and analysis with amplified fragment length polymorphism (AFLP) and microsatellite markers) were correlated with the 'real' estimate (from the full model population). For both marker types, sampling ranges were evident, with lower limits below which estimation was poorly correlated and upper limits above which sampling became inefficient. Lower limits (correlation of 0.9) were 100 individuals, 10 loci for microsatellites and 150 individuals, 100 loci for AFLPs. Upper limits were 200 individuals, five loci for microsatellites and 200 individuals, 100 loci for AFLPs. The limits indicated by simulation were compared with data sets from real species. Instances where sampling effort had been either insufficient or inefficient were identified. The model results should form practical boundaries for studies aiming to detect SGS. However, greater sample sizes will be required in cases where SGS is weaker than for our simulated population, for example, in species with effective pollen/seed dispersal mechanisms.

Intramolecular disulphide bond arrangements in nonhomologous proteins

The presence and location of intramolecular disulphide bonds are a key determinant of the structure and function of proteins. Intramolecular disulphide bonds in proteins have previously been analyzed under the assumption that there is no clear relationship between disulphide arrangement and disulphide concentration. To investigate this, a set of sequence nonhomologous protein chains containing one or more intramolecular disulphide bonds was extracted from the Protein Data Bank, and the arrangements of the bonds, Protein Data Bank header, and Structural Characterization of Proteins fold were analyzed as a function of intramolecular, containing proteins were disulphide bond concentration. Two populations of intramolecular disulphide bond-containing identified, with a naturally occurring partition at 25 residues per bond. These populations were named intramolecular disulphide bond-rich and -poor. Benefits of partitioning were illustrated by three results: (1) rich chains most frequently contained three disulphides, explaining the plateaux in extant disulphide frequency distributions; (2) a positive relationship between median chain length and the number of disulphides, only seen when the data were partitioned-, and (3) the most common bonding pattern for chains with three disulphide bonds was based on the most common for two, only when the data were partitioned. The two populations had different headers, folds, bond arrangements, and chain lengths. Associations between IDSB concentration, IDSB bonding pattern, loop sizes, SCOP fold, and PDB header were also found. From this, we found that intramolecular disulphide bond-rich and -poor proteins follow different bonding rules, and must be considered separately to generate meaningful models of bond formation.