Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets

Analytically or computationally intractable likelihood functions can arise in complex statistical inferential problems making them inaccessible to standard Bayesian inferential methods. Approximate Bayesian computation (ABC) methods address such inferential problems by replacing direct likelihood evaluations with repeated sampling from the model. ABC methods have been predominantly applied to parameter estimation problems and less to model choice problems due to the added difficulty of handling multiple model spaces. The ABC algorithm proposed here addresses model choice problems by extending Fearnhead and Prangle (2012, Journal of the Royal Statistical Society, Series B 74, 1–28) where the posterior mean of the model parameters estimated through regression formed the summary statistics used in the discrepancy measure. An additional stepwise multinomial logistic regression is performed on the model indicator variable in the regression step and the estimated model probabilities are incorporated into the set of summary statistics for model choice purposes. A reversible jump Markov chain Monte Carlo step is also included in the algorithm to increase model diversity for thorough exploration of the model space. This algorithm was applied to a validating example to demonstrate the robustness of the algorithm across a wide range of true model probabilities. Its subsequent use in three pathogen transmission examples of varying complexity illustrates the utility of the algorithm in inferring preference of particular transmission models for the pathogens.

J-Circos : an interactive Circos plotter

Circos plots are graphical outputs that display three dimensional chromosomal interactions and fusion transcripts. However, the Circos plot tool is not an interactive visualization tool, but rather a figure generator. For example, it does not enable data to be added dynamically, nor does it provide information for specific data points interactively. Recently, an R-based Circos tool (RCircos) has been developed to integrate Circos to R, but similarly, Rcircos can only be used to generate plots. Thus, we have developed a Circos plot tool (J-Circos) that is an interactive visualization tool that can plot Circos figures, as well as being able to dynamically add data to the figure, and providing information for specific data points using mouse hover display and zoom in/out functions. J-Circos uses the Java computer language to enable it to be used on most operating systems (Windows, MacOS, Linux). Users can input data into JCircos using flat data formats, as well as from the GUI. J-Circos will enable biologists to better study more complex chromosomal interactions and fusion transcripts that are otherwise difficult to visualize from next-generation sequencing data.

A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

Variable phenotype in 16p duplication within a family

Background More individuals are now being identified with very rare genetic syndromes. We present a family with an inherited duplication of 16p11.2 to 16q12.1 in ring formation. Three of the four children, (aged 15 months to 10 years), mother, uncle, and grandmother are affected. Our aim was to provide preliminary evidence of possible phenotypic patterns of learning and behaviour associated with this chromosome anomaly. Method Psychometric assessments were undertaken with all four children. The mother and uncle also agreed to participate in the study. Measures of development (Bayley or Mullen), intellectual ability (WISC-IV or WAIS-III), academic achievement (WIAT-II), adaptive behaviour (Vinelands), and other relevant aspects of functioning (e.g., Children’s Memory Scale) were administered. Results. The first-born child is the only one who is unaffected. Her intellectual ability was assessed as being within the superior range. The second child experienced early difficulties with speech and motor skills. Although his intelligence is average, he has learning difficulties and significant auditory memory problems. The third child’s speech and motor milestones were markedly delayed. He has a complex medical history that includes a vitamin B12 deficiency. On the Mullen Scales at age 4 his scores ranged from average to very low. The development of the youngest child (aged 15 months), who also had a B12 deficiency but was treated early, was assessed as being within typical limits. Conclusions There is considerable developmental variability among the three children with this inherited 16p duplication. We discuss the intriguing similarities and differences, considering common features that may reflect phenotypic patterns and speculating about possible explanations for the variable presentations.

Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

Damned to fame: The moral rights of the Beckett estate

The Company B production of Samuel Beckett's Waiting for Godot raises important questions about copyright law, moral rights, and dramatic works. The playwright's nephew and executor, Edward Beckett, threatened to bring a legal action against the Sydney company for breach of contract on the grounds that unauthorised music appeared in the production. The Company B production denied that the contract made any such express provisions. The director Neil Armfield complained: 'In coming here with its narrow prescriptions, its dead controlling hand, the Beckett estate seems to me to be the enemy of art'. In the biography Damned to fame, James Knowlson documents a number of other proceedings taken by Beckett and his agents to control the productions of his work: 'He was often represented as a tyrannical figure, an arch-controller of his work, ready to unleash fiery thunderbolts onto the head of any bold, innovative director, unwilling to follow his text and stage directions to the last counted dot and precisely timed pause.' However, Knowlson notes that Beckett was inconsistent in his willingness to use legal action: 'It made a tremendous difference if he liked and respected the persons involved or if he had been able to listen to their reasons for wanting to attempt something highly innovative or even slightly different'. Famously, in 1988, Beckett brought legal action against a Dutch theatre company, which wanted to stage a production of Waiting for Godot, with women acting all the roles. His lawyer argued that the integrity of the text was violated because actresses were substituted for the male actors asked for in the text. The judge in the Haarlem court ruled that the integrity of the play had not been violated, because the performance showed fidelity to the dialogue and the stage directions of the play. By contrast, in 1992, a French court held a stage director was liable for an infringement of Beckett's moral right of integrity because the director had staged Waiting for Godot with the two lead roles played by women. In 1998, a United States production of Waiting for Godot with a racially mixed cast attracted legal threats amid accusations it had 'injected race into the play'. In the 2000 New York Fringe Festival, a company made light of this ongoing conflict between the Beckett estate and artistic directors. The work was entitled: The complete lost works of Samuel Beckett as found in an envelope (partially burned) in a dustbin in Paris labelled 'Never to be performed. Never. Ever. EVER! Or I'll sue! I'LL SUE FROM THE GRAVE!'. The plot concerned a fight between three producers and the Beckett estate. In the wake of such disputes, Beckett and later his estate sought to tighten production contracts to state that no additions, omissions or alterations should be made to the text of the play or the stage directions and that no music, special effects or other supplements should be added without prior consent.

Investigating the population structure of Queensland invasive Streptococcus pneumoniae isolates in children: Using a modified multi-locus variable number of tandem repeat analysis and a novel minimum SNPs capsular typing method

This research investigated the use of DNA fingerprinting to characterise the bacteria Streptococcus pneumoniae or pneumococcus, and hence gain insight into the development of new vaccines or antibiotics. Different bacterial DNA fingerprinting methods were studied, and a novel method was developed and validated, which characterises different cell coatings that pneumococci produce. This method was used to study the epidemiology of pneumococci in Queensland before and after the introduction of the current pneumococcal vaccine. This study demonstrated that pneumococcal disease is highly prevalent in children under four years, that the bacteria can `switch' its cell coating to evade the vaccine, and that some DNA fingerprinting methods are more discriminatory than others. This has an impact on understanding which strains are more prone to cause invasive disease. Evidence of the excellent research findings have been published in high impact internationally refereed journals.

Numerical analysis of a new space-time variable fractional order advection-dispersion equation

Many physical processes appear to exhibit fractional order behavior that may vary with time and/or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider a new space–time variable fractional order advection–dispersion equation on a finite domain. The equation is obtained from the standard advection–dispersion equation by replacing the first-order time derivative by Coimbra’s variable fractional derivative of order α(x)∈(0,1]α(x)∈(0,1], and the first-order and second-order space derivatives by the Riemann–Liouville derivatives of order γ(x,t)∈(0,1]γ(x,t)∈(0,1] and β(x,t)∈(1,2]β(x,t)∈(1,2], respectively. We propose an implicit Euler approximation for the equation and investigate the stability and convergence of the approximation. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Variable-Temperature EPR and Transport Studies on Poly(4,4'-methylenedianiline): Evidence for Bipolarons

The correlation between magnetic and transport properties is examined by studying poly(4,4'-methylenedianiline)(PMDA) salts and their bases using EPR and conductivity measurements. Five different PMDA salts (doped polymers)were prepared by chemical polymerization of 4,4'-methylenedianiline using different protonic acids. The PMDA bases were obtained by dedoping the salts using ammonium hydroxide. Ambient temperature electrical conductivity measurements show evidence for the doped PMDA system to be highly disordered. The EPR spectra of the samples were recorded in the range 20-200 "C, and the results were analyzed on the basis of the polaron-bipolaron model, which is typical of nondegenerate systems. Both PMDA salts and their bases consist of self-trapped, highly mobile polarons or radical cations. EPR studies on PMDA salts show evidence for the presence of thermally activated and temperature independent (or Pauli type) paramagnetism while the bases show thermally activated, Pauli and Curie-Weiss types of paramagnetism. The paramagnetism arises due to polarons.It is proposed that charge transport takes place through both polarons and bipolarons.

Species-area and species-individual relationships for tropical trees: A comparison of three 50-ha plots

1 Species-accumulation curves for woody plants were calculated in three tropical forests, based on fully mapped 50-ha plots in wet, old-growth forest in Peninsular Malaysia, in moist, old-growth forest in central Panama, and in dry, previously logged forest in southern India. A total of 610 000 stems were identified to species and mapped to < Im accuracy. Mean species number and stem number were calculated in quadrats as small as 5 m x 5 m to as large as 1000 m x 500 m, for a variety of stem sizes above 10 mm in diameter. Species-area curves were generated by plotting species number as a function of quadrat size; species-individual curves were generated from the same data, but using stem number as the independent variable rather than area. 2 Species-area curves had different forms for stems of different diameters, but species-individual curves were nearly independent of diameter class. With < 10(4) stems, species-individual curves were concave downward on log-log plots, with curves from different forests diverging, but beyond about 104 stems, the log-log curves became nearly linear, with all three sites having a similar slope. This indicates an asymptotic difference in richness between forests: the Malaysian site had 2.7 times as many species as Panama, which in turn was 3.3 times as rich as India. 3 Other details of the species-accumulation relationship were remarkably similar between the three sites. Rectangular quadrats had 5-27% more species than square quadrats of the same area, with longer and narrower quadrats increasingly diverse. Random samples of stems drawn from the entire 50 ha had 10-30% more species than square quadrats with the same number of stems. At both Pasoh and BCI, but not Mudumalai. species richness was slightly higher among intermediate-sized stems (50-100mm in diameter) than in either smaller or larger sizes, These patterns reflect aggregated distributions of individual species, plus weak density-dependent forces that tend to smooth the species abundance distribution and 'loosen' aggregations as stems grow. 4 The results provide support for the view that within each tree community, many species have their abundance and distribution guided more by random drift than deterministic interactions. The drift model predicts that the species-accumulation curve will have a declining slope on a log-log plot, reaching a slope of O.1 in about 50 ha. No other model of community structure can make such a precise prediction. 5 The results demonstrate that diversity studies based on different stem diameters can be compared by sampling identical numbers of stems. Moreover, they indicate that stem counts < 1000 in tropical forests will underestimate the percentage difference in species richness between two diverse sites. Fortunately, standard diversity indices (Fisher's sc, Shannon-Wiener) captured diversity differences in small stem samples more effectively than raw species richness, but both were sample size dependent. Two nonparametric richness estimators (Chao. jackknife) performed poorly, greatly underestimating true species richness.

Determination of coefficient of consolidation from early stage of log t plot

The standard curve-fitting methods, Casagrande's log t method and Taylor's root t method, for the determination of the coefficient of consolidation use the later part of the consolidation curve and are influenced by secondary compression effects. Literature shows that secondary compression is concurrent with primary consolidation and that its effect is to decrease the value of the coefficient of consolidation. If the early part of the time-compression data is used, the values obtained will be less influenced by secondary compression effects. A method that uses the early part of the log t plot is proposed in this technical note. As the influence of secondary compression is reduced, the value obtained by this method is greater than that yielded by both the standard methods. The permeability values computed from C-v (obtained from the proposed method) rue more in agreement with the measured values than the standard methods showing that the effects of secondary compression are minimized. Time-compression data for a shorter duration is sufficient for the determination of C-v if the coefficient of secondary compression is not required.

Fast Multiple Access Selection through variable power transmissions

Many wireless applications demand a fast mechanism to detect the packet from a node with the highest priority ("best node") only, while packets from nodes with lower priority are irrelevant. In this paper, we introduce an extremely fast contention-based multiple access algorithm that selects the best node and requires only local information of the priorities of the nodes. The algorithm, which we call Variable Power Multiple Access Selection (VP-MAS), uses the local channel state information from the accessing nodes to the receiver, and maps the priorities onto the receive power. It is based on a key result that shows that mapping onto a set of discrete receive power levels is optimal, when the power levels are chosen to exploit packet capture that inherently occurs in a wireless physical layer. The VP-MAS algorithm adjusts the expected number of users that contend in each step and their respective transmission powers, depending on whether previous transmission attempts resulted in capture, idle channel, or collision. We also show how reliable information regarding the total received power at the receiver can be used to improve the algorithm by enhancing the feedback mechanism. The algorithm detects the packet from the best node in 1.5 to 2.1 slots, which is considerably lower than the 2.43 slot average achieved by the best algorithm known to date.

Effect of a magnetic field on the flow and blood oxygenation in channels of variable cross-section

The effect of a magnetic field on the flow and oxygenation of an incompressible Newtonian conducting fluid in channels with irregular boundaries has been investigated. The geometric parameter δ, which is a ratio of the mean half width of the channel d to the characteristic length λ along the channel over which the significant changes in the flow quantities occur, has been used for perturbing the governing equations. Closed form solutions of the various order equations are presented for the stream function. The equations for oxygen partial pressure remain nonlinear even after perturbation, therefore a numerical solution is presented. The expressions for shear stress at a wall and pressure distributions are derived. Here the separation in the flow occurs at a higher Reynolds number than the corresponding non-magnetic case. It is found that the magnetic field has an effect on local oxygen concentration but has a little effect on the saturation length.