Nonrigid Structure-From-Motion From 2-D Images Using Markov Chain Monte Carlo

In this paper we present a new method for simultaneously determining three dimensional (3-D) shape and motion of a non-rigid object from uncalibrated two dimensional (2- D) images without assuming the distribution characteristics. A non-rigid motion can be treated as a combination of a rigid rotation and a non-rigid deformation. To seek accurate recovery of deformable structures, we estimate the probability distribution function of the corresponding features through random sampling, incorporating an established probabilistic model. The fitting between the observation and the projection of the estimated 3-D structure will be evaluated using a Markov chain Monte Carlo based expectation maximisation algorithm. Applications of the proposed method to both synthetic and real image sequences are demonstrated with promising results.

Interlaboratory comparison of real-time polymerase chain reaction methods to detect Coxiella burnetii, the causative agent of Q fever

The bacterium Coxiella burnetii, which has a wide host range, causes Q fever. Infection with C burnetii can cause abortions, stillbirth, and the delivery of weak offspring in ruminants. Coxiella burnetii infection is zoonotic, and in human beings it can cause chronic, potentially fatal disease. Real-time polymerase chain reaction (PCR) is increasingly being used to detect the organism and to aid in diagnosis both in human and animal cases. Many different real-time PCR methods, which target different genes, have been described. To assess the comparability of the C. burnetii real-time PCR assays in use in different European laboratories, a panel of nucleic acid extracts was dispatched to 7 separate testing centers. The testing centers included laboratories from both human and animal health agencies. Each laboratory tested the samples using their in-house real-time PCR methods. The results of this comparison show that the most common target gene for real-time PCR assays is the IS1111 repeat element that is present in multiple copies in the C. burnetii genome. Many laboratories also use additional real-time PCR tests that target single-copy genes. The results of the current study demonstrate that the assays in use in the different laboratories are comparable, with general agreement of results for the panel of samples.

Identification of Pseudomonas aeruginosa by a duplex real-time polymerase chain reaction assay targeting the ecfX and the gyrB genes

Phenotypic identification of Gram-negative bacteria from respiratory specimens of patients with cystic fibrosis carries a high risk of misidentification. Molecular identification techniques that use single-gene targets are also susceptible to error, including cross-reaction issues with other Gram-negative organisms. In this study, we have designed a Pseudomonas aeruginosa duplex real-time polymerase chain reaction (PCR) (PAduplex) assay targeting the ecfX and the gyrB genes. The PAduplex was evaluated against a panel of 91 clinical and environmental isolates that were presumptively identified as P. aeruginosa. The results were compared with those obtained using a commercial biochemical identification kit and several other P. aeruginosa PCR assays. The results showed that the PAduplex assay is highly suitable for routine identification of P. aeruginosa isolates from clinical or environmental samples. The 2-target format provides simultaneous confirmation of P. aeruginosa identity where both the ecfX and gyrB PCR reactions are positive and may also reduce the potential for false negatives caused by sequence variation in primer or probe targets.

Rapid detection of health-care-associated bloodstream infection in critical care using multipathogen real-time polymerase chain reaction technology: a diagnostic accuracy study and systematic review

Background: There is growing interest in the potential utility of real-time polymerase chain reaction (PCR) in diagnosing bloodstream infection by detecting pathogen deoxyribonucleic acid (DNA) in blood samples within a few hours. SeptiFast (Roche Diagnostics GmBH, Mannheim, Germany) is a multipathogen probe-based system targeting ribosomal DNA sequences of bacteria and fungi. It detects and identifies the commonest pathogens causing bloodstream infection. As background to this study, we report a systematic review of Phase III diagnostic accuracy studies of SeptiFast, which reveals uncertainty about its likely clinical utility based on widespread evidence of deficiencies in study design and reporting with a high risk of bias. 

Objective: Determine the accuracy of SeptiFast real-time PCR for the detection of health-care-associated bloodstream infection, against standard microbiological culture. 

Design: Prospective multicentre Phase III clinical diagnostic accuracy study using the standards for the reporting of diagnostic accuracy studies criteria. 

Setting: Critical care departments within NHS hospitals in the north-west of England. 

Participants: Adult patients requiring blood culture (BC) when developing new signs of systemic inflammation. 

Main outcome measures: SeptiFast real-time PCR results at species/genus level compared with microbiological culture in association with independent adjudication of infection. Metrics of diagnostic accuracy were derived including sensitivity, specificity, likelihood ratios and predictive values, with their 95% confidence intervals (CIs). Latent class analysis was used to explore the diagnostic performance of culture as a reference standard. 

Results: Of 1006 new patient episodes of systemic inflammation in 853 patients, 922 (92%) met the inclusion criteria and provided sufficient information for analysis. Index test assay failure occurred on 69 (7%) occasions. Adult patients had been exposed to a median of 8 days (interquartile range 4–16 days) of hospital care, had high levels of organ support activities and recent antibiotic exposure. SeptiFast real-time PCR, when compared with culture-proven bloodstream infection at species/genus level, had better specificity (85.8%, 95% CI 83.3% to 88.1%) than sensitivity (50%, 95% CI 39.1% to 60.8%). When compared with pooled diagnostic metrics derived from our systematic review, our clinical study revealed lower test accuracy of SeptiFast real-time PCR, mainly as a result of low diagnostic sensitivity. There was a low prevalence of BC-proven pathogens in these patients (9.2%, 95% CI 7.4% to 11.2%) such that the post-test probabilities of both a positive (26.3%, 95% CI 19.8% to 33.7%) and a negative SeptiFast test (5.6%, 95% CI 4.1% to 7.4%) indicate the potential limitations of this technology in the diagnosis of bloodstream infection. However, latent class analysis indicates that BC has a low sensitivity, questioning its relevance as a reference test in this setting. Using this analysis approach, the sensitivity of the SeptiFast test was low but also appeared significantly better than BC. Blood samples identified as positive by either culture or SeptiFast real-time PCR were associated with a high probability (> 95%) of infection, indicating higher diagnostic rule-in utility than was apparent using conventional analyses of diagnostic accuracy. 

Conclusion: SeptiFast real-time PCR on blood samples may have rapid rule-in utility for the diagnosis of health-care-associated bloodstream infection but the lack of sensitivity is a significant limiting factor. Innovations aimed at improved diagnostic sensitivity of real-time PCR in this setting are urgently required. Future work recommendations include technology developments to improve the efficiency of pathogen DNA extraction and the capacity to detect a much broader range of pathogens and drug resistance genes and the application of new statistical approaches able to more reliably assess test performance in situation where the reference standard (e.g. blood culture in the setting of high antimicrobial use) is prone to error.

The effect of clock jitter on the performance of continuous-time delta-sigma ADC for GNSS signals

Next generation Global Navigation Satellite System (GNSS) receivers will operate in multiple navigation bands. An efficient way to achieve this with lower power and cost is to employ BandPass Sampling (BPS); nevertheless, the sampling operation injects large amounts of jitter noise, which degrades the performance of the receiver. Continuous–Time (CT) Delta–Sigma (ΔΣ) modulators are capable of suppressing this noise but the impact of clock jitter at the output of the Digital– to–Analog Converter (DAC) in the feedback path of the modulator should be taken into account. This paper presents an analytical approach for describing clock jitter in GNSS receivers when a CT–ΔΣ modulator is utilized for Analog–to–Digital Conversion (ADC). The validity of the presented approach is verified through time–domain simulations using a behavioural model of the fourth–order CT–ΔΣ modulator with 1–bit NRZ DAC feedback pulse.

Forecasting overseas visitors into the United Kingdom using continuous time and autoregressive fractional integrated moving average models with discrete data

This paper applies Gaussian estimation methods to continuous time models for modelling overseas visitors into the UK. The use of continuous time modelling is widely used in economics and finance but not in tourism forecasting. Using monthly data for 1986–2010, various continuous time models are estimated and compared to autoregressive integrated moving average (ARIMA) and autoregressive fractionally integrated moving average (ARFIMA) models. Dynamic forecasts are obtained over different periods. The empirical results show that the ARIMA model performs very well, but that the constant elasticity of variance (CEV) continuous time model has the lowest root mean squared error (RMSE) over a short period.

An FPGA based decimation filter processor design for real-time continuous-time Σ−Δ modulator performance measurement and evaluation

This paper reports on a Field Programmable Gate Array (FPGA) implementation as well as prototyping for real-time testing of a low complexity high efficiency decimation filter processor which is deployed in conjunction with a custom built low-power jitter insensitive Continuous Time (CT) Sigma-Delta (Σ-Δ) Modulator to measure and assess its performance. The CT Σ-Δ modulator/decimation filter cascade can be used in integrated all-digital microphone interfaces for a variety of applications including mobile phone handsets, wireless handsets as well as other applications requiring all-digital microphones. The work reported here concentrates on the design and implementation as well as prototyping on a Xilinx Spartan 3 FPGA development system and real-time testing of the decimation processing part deploying All-Pass based structures to process the bit stream coming from CT Σ-Δ modulator hence measuring in real-time and fully assessing the modulator's performance.

Investigations on Stochastic Storage Systems with Positive Service Time

In this thesis the queueing-inventory models considered are analyzed as continuous time Markov chains in which we use the tools such as matrix analytic methods. We obtain the steady-state distributions of various queueing-inventory models in product form under the assumption that no customer joins the system when the inventory level is zero. This is despite the strong correlation between the number of customers joining the system and the inventory level during lead time. The resulting quasi-birth-anddeath (QBD) processes are solved explicitly by matrix geometric methods

An Extension to the Tactical Planning Model for a Job Shop: Continuous-Time Control

We develop an extension to the tactical planning model (TPM) for a job shop by the third author. The TPM is a discrete-time model in which all transitions occur at the start of each time period. The time period must be defined appropriately in order for the model to be meaningful. Each period must be short enough so that a job is unlikely to travel through more than one station in one period. At the same time, the time period needs to be long enough to justify the assumptions of continuous workflow and Markovian job movements. We build an extension to the TPM that overcomes this restriction of period sizing by permitting production control over shorter time intervals. We achieve this by deriving a continuous-time linear control rule for a single station. We then determine the first two moments of the production level and queue length for the workstation.

Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completely absent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involved parts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method is introduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that the theoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approach has reasonable properties from a compositional point of view. In particular, it is “natural” in the sense that it recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in the same paper a substitution method for missing values on compositional data sets is introduced

Continuous Time Finance

Exercises, exams and solutions for a third year finance course.

Detecting recombination in 4-taxa DNA sequence alignments with Bayesian hidden Markov models and Markov chain Monte Carlo

This article presents a statistical method for detecting recombination in DNA sequence alignments, which is based on combining two probabilistic graphical models: (1) a taxon graph (phylogenetic tree) representing the relationship between the taxa, and (2) a site graph (hidden Markov model) representing interactions between different sites in the DNA sequence alignments. We adopt a Bayesian approach and sample the parameters of the model from the posterior distribution with Markov chain Monte Carlo, using a Metropolis-Hastings and Gibbs-within-Gibbs scheme. The proposed method is tested on various synthetic and real-world DNA sequence alignments, and we compare its performance with the established detection methods RECPARS, PLATO, and TOPAL, as well as with two alternative parameter estimation schemes.

Robustness and applicability of Markov chain Monte Carlo algorithms for eigenvalue problems

In this paper we analyse applicability and robustness of Markov chain Monte Carlo algorithms for eigenvalue problems. We restrict our consideration to real symmetric matrices. Almost Optimal Monte Carlo (MAO) algorithms for solving eigenvalue problems are formulated. Results for the structure of both - systematic and probability error are presented. It is shown that the values of both errors can be controlled independently by different algorithmic parameters. The results present how the systematic error depends on the matrix spectrum. The analysis of the probability error is presented. It shows that the close (in some sense) the matrix under consideration is to the stochastic matrix the smaller is this error. Sufficient conditions for constructing robust and interpolation Monte Carlo algorithms are obtained. For stochastic matrices an interpolation Monte Carlo algorithm is constructed. A number of numerical tests for large symmetric dense matrices are performed in order to study experimentally the dependence of the systematic error from the structure of matrix spectrum. We also study how the probability error depends on the balancing of the matrix. (c) 2007 Elsevier Inc. All rights reserved.