Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

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.

Patterns of gene expression in the frontal cortex discriminate alcoholic from non-alcoholic individuals

Alcohol dependence is characterized by tolerance, physical dependence, and craving. The neuroadaptations underlying these effects of chronic alcohol abuse are likely due to altered gene expression. Previous gene expression studies using human post-mortem brain demonstrated that several gene families were altered by alcohol abuse. However, most of these changes in gene expression were small. It is not clear if gene expression profiles have sufficient power to discriminate control from alcoholic individuals and how consistent gene expression changes are when a relatively large sample size is examined. In the present study, microarray analysis (similar to 47 000 elements) was performed on the superior frontal cortex of 27 individual human cases ( 14 well characterized alcoholics and 13 matched controls). A partial least squares statistical procedure was applied to identify genes with altered expression levels in alcoholics. We found that genes involved in myelination, ubiquitination, apoptosis, cell adhesion, neurogenesis, and neural disease showed altered expression levels. Importantly, genes involved in neurodegenerative diseases such as Alzheimer's disease were significantly altered suggesting a link between alcoholism and other neurodegenerative conditions. A total of 27 genes identified in this study were previously shown to be changed by alcohol abuse in previous studies of human post-mortem brain. These results revealed a consistent re-programming of gene expression in alcohol abusers that reliably discriminates alcoholic from non-alcoholic individuals.

Demonstration of a simple entangling optical gate and its use in bell-state analysis

We demonstrate a new architecture for an optical entangling gate that is significantly simpler than previous realizations, using partially polarizing beam splitters so that only a single optical mode-matching condition is required. We demonstrate operation of a controlled-z gate in both continuous-wave and pulsed regimes of operation, fully characterizing it in each case using quantum process tomography. We also demonstrate a fully resolving, nondeterministic optical Bell-state analyzer based on this controlled-z gate. This new architecture is ideally suited to guided optics implementations of optical gates.

Approximate processing of massive continuous quantile queries over high-speed data streams

Quantile computation has many applications including data mining and financial data analysis. It has been shown that an is an element of-approximate summary can be maintained so that, given a quantile query d (phi, is an element of), the data item at rank [phi N] may be approximately obtained within the rank error precision is an element of N over all N data items in a data stream or in a sliding window. However, scalable online processing of massive continuous quantile queries with different phi and is an element of poses a new challenge because the summary is continuously updated with new arrivals of data items. In this paper, first we aim to dramatically reduce the number of distinct query results by grouping a set of different queries into a cluster so that they can be processed virtually as a single query while the precision requirements from users can be retained. Second, we aim to minimize the total query processing costs. Efficient algorithms are developed to minimize the total number of times for reprocessing clusters and to produce the minimum number of clusters, respectively. The techniques are extended to maintain near-optimal clustering when queries are registered and removed in an arbitrary fashion against whole data streams or sliding windows. In addition to theoretical analysis, our performance study indicates that the proposed techniques are indeed scalable with respect to the number of input queries as well as the number of items and the item arrival rate in a data stream.

Continuous variable tripartite entanglement from twin nonlinearities

In this work, we analyse and compare the continuous variable tripartite entanglement available from the use of two concurrent or cascaded X (2) nonlinearities. We examine both idealized travelling-wave models and more experimentally realistic intracavity models, showing that tripartite entangled outputs are readily producible. These may be a useful resource for applications such as quantum cryptography and teleportation.

Effect of temperature and free ammonia on nitrification and nitrite accumulation in landfill leachate and analysis of its nitrifying bacterial community by FISH

The cause of seasonal failure of a nitrifying municipal landfill leachate treatment plant utilizing a fixed biofilm was investigated by wastewater analyses and batch respirometric tests at every treatment stage. Nitrification of the leachate treatment plant was severely affected by the seasonal temperature variation. High free ammonia (NH3-N) inhibited not only nitrite oxidizing bacteria (NOB) but also ammonia oxidizing bacteria (AOB). In addition, high pH also increased free ammonia concentration to inhibit nitrifying activity especially when the NH4-N level was high. The effects of temperature and free ammonia of landfill leachate on nitrification and nitrite accumulation were investigated with a semi-pilot scale biofilm airlift reactor. Nitrification rate of landfill leachate increased with temperature when free ammonia in the reactor was below the inhibition level for nitrifiers. Leachate was completely nitrified up to a load of 1.5 kg NH4-N m(-3) d(-1) at 28 degrees C. The activity of NOB was inhibited by NH3-N resulting in accumulation of nitrite. NOB activity decreased more than 50% at 0.7 mg NH3-N L-1. Fluorescence in situ hybridization (FISH) was carried out to analyze the population of AOB and NOB in the nitrite accumulating nitrifying biofilm. NOB were located close to AOB by forming small clusters. A significant fraction of AOB identified by probe Nso1225 specifically also hybridized with the Nitrosonlonas specific probe Nsm156. The main NOB were Nitrobacter and Nitrospira which were present in almost equal amounts in the biofilm as identified by simultaneous hybridization with Nitrobacter specific probe Nit3 and Nitrospira specific probe Ntspa662. (c) 2005 Elsevier Ltd. All rights reserved.

The cross-entropy method for continuous multi-extremal optimization

In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including those with non-linear constraints.

Injuries associated with continuous miners, shuttle cars, load-haul-dump and personnel transport in New South Wales underground coal mines

In the three years to June 2005, 959 injuries associated with continuous miners (CMs), shuttle cars (SCs), load–haul–dump and personnel transport (PT) were reported by NSW underground coal mines, comprising 23% of all injuries reported. The present paper reports an analysis of the narrative field accompanying these reports to determine opportunities for controlling injury risks. The most common combinations of activity and mechanism were: strain while handling CM cable (96 injuries); caught between or struck by moving parts while bolting on a CM (86 injuries); strains while bolting on CM (54 injuries); and slipping off a CM during access, egress or other activity (60 injuries). For the other equipment considered, the common injury mechanism was the vehicle running over a pothole or other roadway abnormality causing the driver or passengers to be injured (169 injuries). Potential control measures include: monorails for CM services; hydraulic cable reelers; handrails on CM platforms; redesign of CM platforms and bolting rigs to reduce reach distances during drilling and bolting; improvements to guarding of bolting controls; standardisation and shape coding of bolting controls; two handed fast feed; improvements in underground roadway maintenance, vehicle suspension, visibility and seating; and pedestrian proximity warning devices.

Microarray and proteomic analysis of the human alcoholic brain

The superior frontal cortex (SFC) is selectively damaged in chronic alcohol abuse, with localized neuronal loss and tissue atrophy. Regions such as motor cortex show little neuronal loss except in severe co-morbidity (liver cirrhosis or WKS). Altered gene expression was found in microarray comparisons of alcoholic and control SFC samples [1]. We used Western blots and proteomic analysis to identify the proteins that also show differential expression. Tissue was obtained at autopsy under informed, written consent from uncomplicated alcoholics and age- and sex-matched controls. Alcoholics had consumed 80 g ethanol/day chronically (often, 200 g/day for 20 y). Controls either abstained or were social drinkers ( 20 g/day). All subjects had pathological confirmation of liver and brain diagnosis; none had been polydrug abusers. Samples were homogenized in water and clarified by brief centrifugation (1000g, 3 min) before storage at –80°C. For proteomics the thawed suspensions were centrifuged (15000g, 50 min) to prepare soluble fractions. Aliquots were pooled from SFC samples from the 5 chronic alcoholics and 5 matched controls used in the previous microarray study [1]. 2-Dimensional electrophoresis was performed in triplicate using 18 cm format pH 4–7 and pH 6–11 immobilized pH gradients for firstdimension isoelectric focusing. Following second-dimension SDS-PAGE the proteins were fluorescently stained and the images collected by densitometry. 182 proteins differed by 2-fold between cases and controls. 141 showed lower expression in alcoholics, 33 higher, and 8 were new or had disappeared. To date 63 proteins have been identified using MALDI-MS and MS-MS. Western blots were performed on uncentrifuged individual samples from 76 subjects (controls, uncomplicated alcoholics and cirrhotic alcoholics). A common standard was run on every gel. After transfer, immunolabeling, and densitometry, the intensities of the unknown bands were compared to those of the standards. We focused on proteins from transcripts that showed clear differences in a series of microarray studies, classified into common sets including Regulators of G-protein Signaling and Myelin-associated proteins. The preponderantly lower level of differentially expressed proteins in alcoholics parallels the microarray mRNA analysis in the same samples. We found that mRNA and protein expression do not frequently correspond; this may help identify pathogenic processes acting at the level of transcription, translation, or post-translationally.

Genomic and proteomic analysis of synaptic protein expression in the brains of human alcoholics

Alcoholism results in changes in the human brain which reinforce the cycle of craving and dependency, and these changes are manifest in the pattern of expression of mRNA and proteins in key cells and brain areas. Long-term alcohol abuse also results in damage to selected regions of the cortex. We have used cDNA microarrays to show that less than 1% of mRNA transcripts differ signifi cantly between cases and controls in the susceptible area and that the expression profi le of a subset of these transcripts is suffi cient to distinguish alcohol abusers from controls. In addition, we have utilized a 2D gel proteomics based approach to determine the identity of proteins in the superior frontal cortex (SFC) of the human brain that show differential expression in controls and long term alcohol abusers. Overall, 182 proteins differed by the criterion of > 2-fold between case and control samples. Of these, 139 showed signifi cantly lower expression in alcoholics, 35 showed signifi cantly higher expression, and 8 were new or had disappeared. To date 63 proteins have been identifi ed. The expression of one family of proteins, the synucleins, has been further characterized using Real Time PCR and Western Blotting. The expression of alpha-synuclein mRNA was signifi cantly lower in the SFC of alcoholics compared with the same area in controls (P = 0.01) whereas no such difference in expression was found in the motor cortex. The expression of beta- and gamma- synuclein were not signifi cantly different between alcoholics and controls. In contrast, the pattern of alphasynuclein protein expression differs from that of the corresponding RNA transcript. Because of the key role of synaptic proteins in the pathogenesis of alcoholism, we are developing 2-D DIGE based techniques to quantify expression changes in synaptosomes prepared from the SFC of controls and alcoholics.

Issues of robustness and high dimensionality in cluster analysis

Finite mixture models are being increasingly used to model the distributions of a wide variety of random phenomena. While normal mixture models are often used to cluster data sets of continuous multivariate data, a more robust clustering can be obtained by considering the t mixture model-based approach. Mixtures of factor analyzers enable model-based density estimation to be undertaken for high-dimensional data where the number of observations n is very large relative to their dimension p. As the approach using the multivariate normal family of distributions is sensitive to outliers, it is more robust to adopt the multivariate t family for the component error and factor distributions. The computational aspects associated with robustness and high dimensionality in these approaches to cluster analysis are discussed and illustrated.