On the effect of topology on cellular automata rule spaces

This thesis presents an empirical study of the effects of topology on cellular automata rule spaces. The classical definition of a cellular automaton is restricted to that of a regular lattice, often with periodic boundary conditions. This definition is extended to allow for arbitrary topologies. The dynamics of cellular automata within the triangular tessellation were analysed when transformed to 2-manifolds of topological genus 0, genus 1 and genus 2. Cellular automata dynamics were analysed from a statistical mechanics perspective. The sample sizes required to obtain accurate entropy calculations were determined by an entropy error analysis which observed the error in the computed entropy against increasing sample sizes. Each cellular automata rule space was sampled repeatedly and the selected cellular automata were simulated over many thousands of trials for each topology. This resulted in an entropy distribution for each rule space. The computed entropy distributions are indicative of the cellular automata dynamical class distribution. Through the comparison of these dynamical class distributions using the E-statistic, it was identified that such topological changes cause these distributions to alter. This is a significant result which implies that both global structure and local dynamics play a important role in defining long term behaviour of cellular automata.

Development and validation of the ankle fracture outcome of rehabilitation measure (A-FORM)

Study Design Delphi panel and cohort study. Objective To develop and refine a condition-specific, patient-reported outcome measure, the Ankle Fracture Outcome of Rehabilitation Measure (A-FORM), and to examine its psychometric properties, including factor structure, reliability, and validity, by assessing item fit with the Rasch model. Background To our knowledge, there is no patient-reported outcome measure specific to ankle fracture with a robust content foundation. Methods A 2-stage research design was implemented. First, a Delphi panel that included patients and health professionals developed the items and refined the item wording. Second, a cohort study (n = 45) with 2 assessment points was conducted to permit preliminary maximum-likelihood exploratory factor analysis and Rasch analysis. Results The Delphi panel reached consensus on 53 potential items that were carried forward to the cohort phase. From the 2 time points, 81 questionnaires were completed and analyzed; 38 potential items were eliminated on account of greater than 10% missing data, factor loadings, and uniqueness. The 15 unidimensional items retained in the scale demonstrated appropriate person and item reliability after (and before) removal of 1 item (anxious about footwear) that had a higher-than-ideal outfit statistic (1.75). The “anxious about footwear” item was retained in the instrument, but only the 14 items with acceptable infit and outfit statistics (range, 0.5–1.5) were included in the summary score. Conclusion This investigation developed and refined the A-FORM (Version 1.0). The A-FORM items demonstrated favorable psychometric properties and are suitable for conversion to a single summary score. Further studies utilizing the A-FORM instrument are warranted. J Orthop Sports Phys Ther 2014;44(7):488–499. Epub 22 May 2014. doi:10.2519/jospt.2014.4980

Approximate Bayesian Computation for astronomical model analysis : a case study in galaxy demographics and morphological transformation at high redshift

Approximate Bayesian Computation’ (ABC) represents a powerful methodology for the analysis of complex stochastic systems for which the likelihood of the observed data under an arbitrary set of input parameters may be entirely intractable – the latter condition rendering useless the standard machinery of tractable likelihood-based, Bayesian statistical inference [e.g. conventional Markov chain Monte Carlo (MCMC) simulation]. In this paper, we demonstrate the potential of ABC for astronomical model analysis by application to a case study in the morphological transformation of high-redshift galaxies. To this end, we develop, first, a stochastic model for the competing processes of merging and secular evolution in the early Universe, and secondly, through an ABC-based comparison against the observed demographics of massive (Mgal > 1011 M⊙) galaxies (at 1.5 < z < 3) in the Cosmic Assembly Near-IR Deep Extragalatic Legacy Survey (CANDELS)/Extended Groth Strip (EGS) data set we derive posterior probability densities for the key parameters of this model. The ‘Sequential Monte Carlo’ implementation of ABC exhibited herein, featuring both a self-generating target sequence and self-refining MCMC kernel, is amongst the most efficient of contemporary approaches to this important statistical algorithm. We highlight as well through our chosen case study the value of careful summary statistic selection, and demonstrate two modern strategies for assessment and optimization in this regard. Ultimately, our ABC analysis of the high-redshift morphological mix returns tight constraints on the evolving merger rate in the early Universe and favours major merging (with disc survival or rapid reformation) over secular evolution as the mechanism most responsible for building up the first generation of bulges in early-type discs.

Spatial and temporal patterns of locally-acquired dengue transmission in northern Queensland, Australia, 1993-2012

BACKGROUND: Dengue has been a major public health concern in Australia since it re-emerged in Queensland in 1992-1993. We explored spatio-temporal characteristics of locally-acquired dengue cases in northern tropical Queensland, Australia during the period 1993-2012. METHODS: Locally-acquired notified cases of dengue were collected for northern tropical Queensland from 1993 to 2012. Descriptive spatial and temporal analyses were conducted using geographic information system tools and geostatistical techniques. RESULTS: 2,398 locally-acquired dengue cases were recorded in northern tropical Queensland during the study period. The areas affected by the dengue cases exhibited spatial and temporal variation over the study period. Notified cases of dengue occurred more frequently in autumn. Mapping of dengue by statistical local areas (census units) reveals the presence of substantial spatio-temporal variation over time and place. Statistically significant differences in dengue incidence rates among males and females (with more cases in females) (χ(2) = 15.17, d.f.  = 1, p<0.01). Differences were observed among age groups, but these were not statistically significant. There was a significant positive spatial autocorrelation of dengue incidence for the four sub-periods, with the Moran's I statistic ranging from 0.011 to 0.463 (p<0.01). Semi-variogram analysis and smoothed maps created from interpolation techniques indicate that the pattern of spatial autocorrelation was not homogeneous across the northern Queensland. CONCLUSIONS: Tropical areas are potential high-risk areas for mosquito-borne diseases such as dengue. This study demonstrated that the locally-acquired dengue cases have exhibited a spatial and temporal variation over the past twenty years in northern tropical Queensland, Australia. Therefore, this study provides an impetus for further investigation of clusters and risk factors in these high-risk areas.

Approximation of Bayesian predictive p-values with regression ABC

In the Bayesian framework a standard approach to model criticism is to compare some function of the observed data to a reference predictive distribution. The result of the comparison can be summarized in the form of a p-value, and it's well known that computation of some kinds of Bayesian predictive p-values can be challenging. The use of regression adjustment approximate Bayesian computation (ABC) methods is explored for this task. Two problems are considered. The first is the calibration of posterior predictive p-values so that they are uniformly distributed under some reference distribution for the data. Computation is difficult because the calibration process requires repeated approximation of the posterior for different data sets under the reference distribution. The second problem considered is approximation of distributions of prior predictive p-values for the purpose of choosing weakly informative priors in the case where the model checking statistic is expensive to compute. Here the computation is difficult because of the need to repeatedly sample from a prior predictive distribution for different values of a prior hyperparameter. In both these problems we argue that high accuracy in the computations is not required, which makes fast approximations such as regression adjustment ABC very useful. We illustrate our methods with several samples.

Statistical methods for electromyography data and associated problems

This thesis proposes three novel models which extend the statistical methodology for motor unit number estimation, a clinical neurology technique. Motor unit number estimation is important in the treatment of degenerative muscular diseases and, potentially, spinal injury. Additionally, a recent and untested statistic to enable statistical model choice is found to be a practical alternative for larger datasets. The existing methods for dose finding in dual-agent clinical trials are found to be suitable only for designs of modest dimensions. The model choice case-study is the first of its kind containing interesting results using so-called unit information prior distributions.

A novel ambiguity acceptance test threshold determination method with controllable failure rate

Ambiguity validation as an important procedure of integer ambiguity resolution is to test the correctness of the fixed integer ambiguity of phase measurements before being used for positioning computation. Most existing investigations on ambiguity validation focus on test statistic. How to determine the threshold more reasonably is less understood, although it is one of the most important topics in ambiguity validation. Currently, there are two threshold determination methods in the ambiguity validation procedure: the empirical approach and the fixed failure rate (FF-) approach. The empirical approach is simple but lacks of theoretical basis. The fixed failure rate approach has a rigorous probability theory basis, but it employs a more complicated procedure. This paper focuses on how to determine the threshold easily and reasonably. Both FF-ratio test and FF-difference test are investigated in this research and the extensive simulation results show that the FF-difference test can achieve comparable or even better performance than the well-known FF-ratio test. Another benefit of adopting the FF-difference test is that its threshold can be expressed as a function of integer least-squares (ILS) success rate with specified failure rate tolerance. Thus, a new threshold determination method named threshold function for the FF-difference test is proposed. The threshold function method preserves the fixed failure rate characteristic and is also easy-to-apply. The performance of the threshold function is validated with simulated data. The validation results show that with the threshold function method, the impact of the modelling error on the failure rate is less than 0.08%. Overall, the threshold function for the FF-difference test is a very promising threshold validation method and it makes the FF-approach applicable for the real-time GNSS positioning applications.

Efficient minimax strategies for square loss games

We consider online prediction problems where the loss between the prediction and the outcome is measured by the squared Euclidean distance and its generalization, the squared Mahalanobis distance. We derive the minimax solutions for the case where the prediction and action spaces are the simplex (this setup is sometimes called the Brier game) and the \ell_2 ball (this setup is related to Gaussian density estimation). We show that in both cases the value of each sub-game is a quadratic function of a simple statistic of the state, with coefficients that can be efficiently computed using an explicit recurrence relation. The resulting deterministic minimax strategy and randomized maximin strategy are linear functions of the statistic.

Proportionality : a valid alternative to correlation for relative data

Relative abundance data is common in the life sciences, but appreciation that it needs special analysis and interpretation is scarce. Correlation is popular as a statistical measure of pairwise association but should not be used on data that carry only relative information. Using timecourse yeast gene expression data, we show how correlation of relative abundances can lead to conclusions opposite to those drawn from absolute abundances, and that its value changes when different components are included in the analysis. Once all absolute information has been removed, only a subset of those associations will reliably endure in the remaining relative data, specifically, associations where pairs of values behave proportionally across observations. We propose a new statistic φ to describe the strength of proportionality between two variables and demonstrate how it can be straightforwardly used instead of correlation as the basis of familiar analyses and visualization methods.

Arabic translation, adaptation and modification of the dialysis symptom index for chronic kidney disease stages four and five

Background Symptom burden in chronic kidney disease (CKD) is poorly understood. To date, the majority of research focuses on single symptoms and there is a lack of suitable multidimensional symptom measures. The purpose of this study was to modify, translate, cross-culturally adapt and psychometrically analyse the Dialysis Symptom Index (DSI). Methods The study methods involved four phases: modification, translation, pilot-testing with a bilingual non-CKD sample and then psychometric testing with the target population. Content validity was assessed using an expert panel. Inter-rater agreement, test-retest reliability and Cronbach’s alpha coefficient were calculated to demonstrate reliability of the modified DSI. Discriminative and convergent validity were assessed to demonstrate construct validity. Results Content validity index during translation was 0.98. In the pilot study with 25 bilingual students a moderate to perfect agreement (Kappa statistic = 0.60-1.00) was found between English and Arabic versions of the modified DSI. The main study recruited 433 patients CKD with stages 4 and 5. The modified DSI was able to discriminate between non-dialysis and dialysis groups (p < 0.001) and demonstrated convergent validity with domains of the Kidney Disease Quality of Life short form. Excellent test-retest and internal consistency (Cronbach’s α = 0.91) reliability were also demonstrated. Conclusion The Arabic version of the modified DSI demonstrated good psychometric properties, measures the multidimensional nature of symptoms and can be used to assess symptom burden at different stages of CKD. The modified instrument, renamed the CKD Symptom Burden Index (CKD-SBI), should encourage greater clinical and research attention to symptom burden in CKD.

Spatiotemporal analysis of indigenous and imported dengue fever cases in Guangdong province, China

Background Dengue fever has been a major public health concern in China since it re-emerged in Guangdong province in 1978. This study aimed to explore spatiotemporal characteristics of dengue fever cases for both indigenous and imported cases during recent years in Guangdong province, so as to identify high-risk areas of the province and thereby help plan resource allocation for dengue interventions. Methods Notifiable cases of dengue fever were collected from all 123 counties of Guangdong province from 2005 to 2010. Descriptive temporal and spatial analysis were conducted, including plotting of seasonal distribution of cases, and creating choropleth maps of cumulative incidence by county. The space-time scan statistic was used to determine space-time clusters of dengue fever cases at the county level, and a geographical information system was used to visualize the location of the clusters. Analysis were stratified by imported and indigenous origin. Results 1658 dengue fever cases were recorded in Guangdong province during the study period, including 94 imported cases and 1564 indigenous cases. Both imported and indigenous cases occurred more frequently in autumn. The areas affected by the indigenous and imported cases presented a geographically expanding trend over the study period. The results showed that the most likely cluster of imported cases (relative risk = 7.52, p < 0.001) and indigenous cases (relative risk = 153.56, p < 0.001) occurred in the Pearl River Delta Area; while a secondary cluster of indigenous cases occurred in one district of the Chao Shan Area (relative risk = 471.25, p < 0.001). Conclusions This study demonstrated that the geographic range of imported and indigenous dengue fever cases has expanded over recent years, and cases were significantly clustered in two heavily urbanised areas of Guangdong province. This provides the foundation for further investigation of risk factors and interventions in these high-risk areas.

Spatial incidence of dengue infections in Queensland, Australia - reply

This study aimed to investigate the spatial clustering and dynamic dispersion of dengue incidence in Queensland, Australia. We used Moran's I statistic to assess the spatial autocorrelation of reported dengue cases. Spatial empirical Bayes smoothing estimates were used to display the spatial distribution of dengue in postal areas throughout Queensland. Local indicators of spatial association (LISA) maps and logistic regression models were used to identify spatial clusters and examine the spatio-temporal patterns of the spread of dengue. The results indicate that the spatial distribution of dengue was clustered during each of the three periods of 1993–1996, 1997–2000 and 2001–2004. The high-incidence clusters of dengue were primarily concentrated in the north of Queensland and low-incidence clusters occurred in the south-east of Queensland. The study concludes that the geographical range of notified dengue cases has significantly expanded in Queensland over recent years.

Tensor-based analysis of genetic influences on brain integrity using DTI in 100 twins

Information from the full diffusion tensor (DT) was used to compute voxel-wise genetic contributions to brain fiber microstructure. First, we designed a new multivariate intraclass correlation formula in the log-Euclidean framework. We then analyzed used the full multivariate structure of the tensor in a multivariate version of a voxel-wise maximum-likelihood structural equation model (SEM) that computes the variance contributions in the DTs from genetic (A), common environmental (C) and unique environmental (E) factors. Our algorithm was tested on DT images from 25 identical and 25 fraternal twin pairs. After linear and fluid registration to a mean template, we computed the intraclass correlation and Falconer's heritability statistic for several scalar DT-derived measures and for the full multivariate tensors. Covariance matrices were found from the DTs, and inputted into SEM. Analyzing the full DT enhanced the detection of A and C effects. This approach should empower imaging genetics studies that use DTI.

Translation and psychometric properties of the Chinese version of the Leeds Attitudes to Concordance II scale

Background Concordance is characterised as a negotiation-like health communication approach based on an equal and collaborative partnership between patients and health professionals. The Leeds Attitudes to Concordance II (LATCon II) scale was developed to measure the attitudes towards concordance. The purpose of this study was to translate the LATCon II into Chinese and psychometrically test the Chinese version of LATCon II (C-LATCon II). Methods The study involved three phases: i) translation and cross-cultural adaptation; ii) pilot study, and; iii) a cross-sectional survey (n = 366). Systematic random sampling was used to recruit hypertensive patients from nine communities covering around 78,000 residents in China. Tests of psychometric properties included content validity, construct validity, criteria-related validity (correlation between the C-LATCon II and the Therapeutic Adherence Scale for Hypertensive Patients (TASHP)), internal reliability, and test-retest reliability (n = 30). Results The study found that the C-LATCon II had a satisfactory content validity (item-level Content Validity Index (CVI) = 0.83-1, scale-level CVI/universal agreement = 0.89, and scale-level CVI/averaging calculation = 0.98), construct validity (four components extracted explained 56.66% of the total variance), internal reliability (Cronbach’s alpha of overall scale and four components was 0.78 and 0.66-0.84, respectively), and test-retest reliability (Pearson’s correlation coefficient = 0.82, p < 0.001; interclass correlation coefficient = 0.82, p < 0.001; linear weighted kappa3 statistic for each item = 0.40-0.65, p < 0.05). Criteria-related validity showed a weak association (Pearson’s correlation coefficient = 0.11, p < 0.05) between patients’ attitudes towards concordance during health communication and their health behaviours for hypertension management. Conclusions The C-LATCon II is a validated and reliable instrument which can be used to evaluate the attitudes to concordance in Chinese populations. Four components (health professionals’ attitudes, partnership between two parties, therapeutic decision making, and patients’ involvement) describe the attitudes towards concordance during health communication.

Spatiotemporal transmission dynamics of hemorrhagic fever with renal syndrome in China, 2005-2012

Background Hemorrhagic fever with renal syndrome (HFRS) is a rodent-borne disease caused by many serotypes of hantaviruses. In China, HFRS has been recognized as a severe public health problem with 90% of the total reported cases in the world. This study describes the spatiotemporal dynamics of HFRS cases in China and identifies the regions, time, and populations at highest risk, which could help the planning and implementation of key preventative measures. Methods Data on all reported HFRS cases at the county level from January 2005 to December 2012 were collected from Chinese Center for Disease Control and Prevention. Geographic Information System-based spatiotemporal analyses including Local Indicators of Spatial Association and Kulldorff's space-time scan statistic were performed to detect local high-risk space-time clusters of HFRS in China. In addition, cases from high-risk and low-risk counties were compared to identify significant demographic differences. Results A total of 100,868 cases were reported during 2005–2012 in mainland China. There were significant variations in the spatiotemporal dynamics of HFRS. HFRS cases occurred most frequently in June, November, and December. There was a significant positive spatial autocorrelation of HFRS incidence during the study periods, with Moran's I values ranging from 0.46 to 0.56 (P<0.05). Several distinct HFRS cluster areas were identified, mainly concentrated in northeastern, central, and eastern of China. Compared with cases from low-risk areas, a higher proportion of cases were younger, non-farmer, and floating residents in high-risk counties. Conclusions This study identified significant space-time clusters of HFRS in China during 2005–2012 indicating that preventative strategies for HFRS should be particularly focused on the northeastern, central, and eastern of China to achieve the most cost-effective outcomes.