Path integrals for continuous-time Markov chains

This note presents a method of evaluating the distribution of a path integral for Markov chains on a countable state space.

A simulated annealing algorithm for finding consensus sequences

Motivation: A consensus sequence for a family of related sequences is, as the name suggests, a sequence that captures the features common to most members of the family. Consensus sequences are important in various DNA sequencing applications and are a convenient way to characterize a family of molecules. Results: This paper describes a new algorithm for finding a consensus sequence, using the popular optimization method known as simulated annealing. Unlike the conventional approach of finding a consensus sequence by first forming a multiple sequence alignment, this algorithm searches for a sequence that minimises the sum of pairwise distances to each of the input sequences. The resulting consensus sequence can then be used to induce a multiple sequence alignment. The time required by the algorithm scales linearly with the number of input sequences and quadratically with the length of the consensus sequence. We present results demonstrating the high quality of the consensus sequences and alignments produced by the new algorithm. For comparison, we also present similar results obtained using ClustalW. The new algorithm outperforms ClustalW in many cases.

A cognitive complexity metric applied to cognitive development

Two experiments tested predictions from a theory in which processing load depends on relational complexity (RC), the number of variables related in a single decision. Tasks from six domains (transitivity, hierarchical classification, class inclusion, cardinality, relative-clause sentence comprehension, and hypothesis testing) were administered to children aged 3-8 years. Complexity analyses indicated that the domains entailed ternary relations (three variables). Simpler binary-relation (two variables) items were included for each domain. Thus RC was manipulated with other factors tightly controlled. Results indicated that (i) ternary-relation items were more difficult than comparable binary-relation items, (ii) the RC manipulation was sensitive to age-related changes, (iii) ternary relations were processed at a median age of 5 years, (iv) cross-task correlations were positive, with all tasks loading on a single factor (RC), (v) RC factor scores accounted for 80% (88%) of age-related variance in fluid intelligence (compositionality of sets), (vi) binary- and ternary-relation items formed separate complexity classes, and (vii) the RC approach to defining cognitive complexity is applicable to different content domains. (C) 2002 Elsevier Science (USA). All rights reserved.

A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.

Consensus neuropathological diagnosis of common dementia syndromes: testing and standardising the use of multiple diagnostic criteria

The aim of this study was to assess the variation between neuropathologists in the diagnosis of common dementia syndromes when multiple published protocols are applied. Fourteen out of 18 Australian neuropathologists participated in diagnosing 20 cases (16 cases of dementia, 4 age-matched controls) using consensus diagnostic methods. Diagnostic criteria, clinical synopses and slides from multiple brain regions were sent to participants who were asked for case diagnoses. Diagnostic sensitivity, specificity, predictive value, accuracy and variability were determined using percentage agreement and kappa statistics. Using CERAD criteria, there was a high inter-rater agreement for cases with probable and definite Alzheimer's disease but low agreement for cases with possible Alzheimer's disease. Braak staging and the application of criteria for dementia with Lewy bodies also resulted in high inter-rater agreement. There was poor agreement for the diagnosis of frontotemporal dementia and for identifying small vessel disease. Participants rarely diagnosed more than one disease in any case. To improve efficiency when applying multiple diagnostic criteria, several simplifications were proposed and tested on 5 of the original 210 cases. Inter-rater reliability for the diagnosis of Alzheimer's disease and dementia with Lewy bodies significantly improved. Further development of simple and accurate methods to identify small vessel lesions and diagnose frontotemporal dementia is warranted.

Prediction of Golgi Type II membrane proteins based on their transmembrane domains

Motivation: A major issue in cell biology today is how distinct intracellular regions of the cell, like the Golgi Apparatus, maintain their unique composition of proteins and lipids. The cell differentially separates Golgi resident proteins from proteins that move through the organelle to other subcellular destinations. We set out to determine if we could distinguish these two types of transmembrane proteins using computational approaches. Results: A new method has been developed to predict Golgi membrane proteins based on their transmembrane domains. To establish the prediction procedure, we took the hydrophobicity values and frequencies of different residues within the transmembrane domains into consideration. A simple linear discriminant function was developed with a small number of parameters derived from a dataset of Type II transmembrane proteins of known localization. This can discriminate between proteins destined for Golgi apparatus or other locations (post-Golgi) with a success rate of 89.3% or 85.2%, respectively on our redundancy-reduced data sets.

A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

Bridging the gap between different statistical approaches: An integrated framework for modelling

This paper proposes a template for modelling complex datasets that integrates traditional statistical modelling approaches with more recent advances in statistics and modelling through an exploratory framework. Our approach builds on the well-known and long standing traditional idea of 'good practice in statistics' by establishing a comprehensive framework for modelling that focuses on exploration, prediction, interpretation and reliability assessment, a relatively new idea that allows individual assessment of predictions. The integrated framework we present comprises two stages. The first involves the use of exploratory methods to help visually understand the data and identify a parsimonious set of explanatory variables. The second encompasses a two step modelling process, where the use of non-parametric methods such as decision trees and generalized additive models are promoted to identify important variables and their modelling relationship with the response before a final predictive model is considered. We focus on fitting the predictive model using parametric, non-parametric and Bayesian approaches. This paper is motivated by a medical problem where interest focuses on developing a risk stratification system for morbidity of 1,710 cardiac patients given a suite of demographic, clinical and preoperative variables. Although the methods we use are applied specifically to this case study, these methods can be applied across any field, irrespective of the type of response.

Haemodynamic response to TENS applied to upper thoracic nerve roots in normal subjects

This study investigated the haemodynamic response to the 90-minute application of 85 Hz transcutaneous electrical nerve stimulation (TENS) to the T1 and T5 nerve roots. Comparison was made between 20 healthy subjects who had TENS stimulation and a separate group of 20 healthy subjects who rested for 90 minutes. Pulse and blood pressure were measured just prior to the start of TENS stimulation, after 30 minutes of stimulation, and after 90 minutes of stimulation (immediately after stopping TENS) or at completion of the rest time depending on group allocation. The rate pressure product was calculated from the pulse and systolic blood pressure data. Multivariate repeated measures analysis showed a significant group effect for TENS (p = 0.048). Univariate repeated measures analyses showed a significant group by time effect due to TENS on systolic blood pressure over the 90-minute time period (p = 0.028). Separate group repeated measures ANOVA showed a significant decline in heart rate (p = 0.000), systolic blood pressure (p = 0.013) and rate pressure product (p = 0.000) for the TENS group, while the control resting group showed a significant decline in heart rate only (p = 0.04). The application of 85 Hz TENS to the upper thoracic nerve roots causes no adverse haemodynamic effects in healthy subjects.

Mouse proteome analysis

A general overview of the protein sequence set for the mouse transcriptome produced during the FANTOM2 sequencing project is presented here. We applied different algorithms to characterize protein sequences derived from a nonredundant representative protein set (RPS) and a variant protein set (VPS) of the mouse transcriptome. The functional characterization and assignment of Gene Ontology terms was done by analysis of the proteome using InterPro. The Superfamily database analyses gave a detailed structural classification according to SCOP and provide additional evidence for the functional characterization of the proteome data. The MDS database analysis revealed new domains which are not presented in existing protein domain databases. Thus the transcriptome gives us a unique source of data for the detection of new functional groups. The data obtained for the RPS and VPS sets facilitated the comparison of different patterns of protein expression. A comparison of other existing mouse and human protein sequence sets (e.g., the International Protein Index) demonstrates the common patterns in mammalian proteornes. The analysis of the membrane organization within the transcriptome of multiple eukaryotes provides valuable statistics about the distribution of secretory and transmembrane proteins

Two-locus Linkage Analysis Applied to Putative Quantitative Trait Loci for Lipoprotein(a) Levels

Plasma levels of lipoprotein(a) _ Lp(a) _ are associated with cardiovascular risk (Danesh et al., 2000) and were long believed to be influenced by the LPA locus on chromosome 6q27 only. However, a recent report of Broeckel et al. (2002) suggested the presence of a second quantitative trait locus on chromosome 1 influencing Lp(a) levels. Using a two-locus model, we found no evidence for an additional Lp(a) locus on chromosome 1 in a linkage study among 483 dizygotic twin pairs.

Stereological and other methods applied to rock joint size estimation - Does Crofton's theorem apply?

A number of authors concerned with the analysis of rock jointing have used the idea that the joint areal or diametral distribution can be linked to the trace length distribution through a theorem attributed to Crofton. This brief paper seeks to demonstrate why Crofton's theorem need not be used to link moments of the trace length distribution captured by scan line or areal mapping to the moments of the diametral distribution of joints represented as disks and that it is incorrect to do so. The valid relationships for areal or scan line mapping between all the moments of the trace length distribution and those of the joint size distribution for joints modeled as disks are recalled and compared with those that might be applied were Crofton's theorem assumed to apply. For areal mapping, the relationship is fortuitously correct but incorrect for scan line mapping.