Efficient Recursions for General Factorisable Models

Let n S-valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant and other summations. A saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution, with maximum computational efficiency as the subsets attain their minimum size. If each subset contains at most r+1 of the n components in the joint distribution, we term this a lag-r model, whose normalising constant can be computed using a forward recursion in O(Sr+1) computations, as opposed to O(Sn) for the direct computation. We show how a lag-r model represents a Markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood. We illustrate the method by showing how the normalising constant of the Ising or autologistic model can be computed

Cloud and Star Formation in Spiral Arms

We present the results from simulations of GMC formation in spiral galaxies. First we discuss cloud formation by cloud-cloud collisions, and gravitational instabilities, arguing that the former is prevalent at lower galactic surface densities and the latter at higher. Cloud masses are also limited by stellar feedback, which can be effective before clouds reach their maximum mass. We show other properties of clouds in simulations with different levels of feedback. With a moderate level of feedback, properties such as cloud rotations and virial parameters agree with observations. Without feedback, an unrealistic population of overly bound clouds develops. Spiral arms are not found to trigger star formation, they merely gather gas into more massive GMCs. We discuss in more detail interactions of clouds in the ISM, and argue that these are more complex than early ideas of cloud-cloud collisions. Finally we show ongoing work to determine whether the Milky Way is a flocculent or grand design spiral.Comment: 10 pages, 5 figures, to be published in Seychelles conference "Lessons from the Local Group", ed. K. C. Freeman, B. G. Elmegreen, D. L. Block, and M. Woolway (Dordrecht: Springer), 201

The contribution of electrostatic interactions to the collapse of oligoglycine in water

Protein solubility and conformational stability are a result of a balance of interactions both within a protein and between protein and solvent. The electrostatic solvation free energy of oligoglycines, models for the peptide backbone, becomes more favorable with an increasing length, yet longer peptides collapse due to the formation of favorable intrapeptide interactions between CO dipoles, in some cases without hydrogen bonds. The strongly repulsive solvent cavity formation is balanced by van der Waals attractions and electrostatic contributions. In order to investigate the competition between solvent exclusion and charge interactions we simulate the collapse of a long oligoglycine comprised of 15 residues while scaling the charges on the peptide from zero to fully charged. We examine the effect this has on the conformational properties of the peptide. We also describe the approximate thermodynamic changes that occur during the scaling both in terms of intrapeptide potentials and peptide-water potentials, and estimate the electrostatic solvation free energy of the system.Comment: 10 pages, 7 figure

Bars and spirals in tidal interactions with an ensemble of galaxy mass models

We present simulations of the gaseous and stellar material in several different galaxy mass models under the influence of different tidal fly-bys to assess the changes in their bar and spiral morphology. Five different mass models are chosen to represent the variety of rotation curves seen in nature. We find a multitude of different spiral and bar structures can be created, with their properties dependent on the strength of the interaction. We calculate pattern speeds, spiral wind-up rates, bar lengths, and angular momentum exchange to quantify the changes in disc morphology in each scenario. The wind-up rates of the tidal spirals follow the 2:1 resonance very closely for the flat and dark matter dominated rotation curves, whereas the more baryon dominated curves tend to wind-up faster, influenced by their inner bars. Clear spurs are seen in most of the tidal spirals, most noticeable in the flat rotation curve models. Bars formed both in isolation and interactions agree well with those seen in real galaxies, with a mixture of "fast" and "slow" rotators. We find no strong correlation between bar length or pattern speed and the interaction strength. Bar formation is, however, accelerated/induced in four out of five of our models. We close by briefly comparing the morphology of our models to real galaxies, easily finding analogues for nearly all simulations presenter here, showing passages of small companions can easily reproduce an ensemble of observed morphologies.Comment: 30 pages, 29 colour figures, accepted for publication in MNRAS. Videos of simulations can be found at http://www.youtube.com/playlist?list=PLQKy--XcWrIVBc1sS2RNc-ekyfeBsGtD

Driving performance impairments due to hypovigilance on monotonous roads

Drivers' ability to react to unpredictable events deteriorates when exposed to highly predictable and uneventful driving tasks. Highway design reduces the driving task mainly to a lane-keeping manoeuvre. Such a task is monotonous, providing little stimulation and this contributes to crashes due to inattention. Research has shown that driver's hypovigilance can be assessed with EEG measurements and that driving performance is impaired during prolonged monotonous driving tasks. This paper aims to show that two dimensions of monotony - namely road design and road side variability - decrease vigilance and impair driving performance. This is the first study correlating hypovigilance and driver performance in varied monotonous conditions, particularly on a short time scale (a few seconds). We induced vigilance decrement as assessed with an EEG during a monotonous driving simulator experiment. Road monotony was varied through both road design and road side variability. The driver's decrease in vigilance occurred due to both road design and road scenery monotony and almost independently of the driver's sensation seeking level. Such impairment was also correlated to observable measurements from the driver, the car and the environment. During periods of hypovigilance, the driving performance impairment affected lane positioning, time to lane crossing, blink frequency, heart rate variability and non-specific electrodermal response rates. This work lays the foundation for the development of an in-vehicle device preventing hypovigilance crashes on monotonous roads

Dynamic simulations of water at constant chemical potential

The grand molecular dynamics (GMD) method has been extended and applied to examine the density dependence of the chemical potential of a three-site water model. The method couples a classical system to a chemical potential reservoir of particles via an ansatz Lagrangian. Equilibrium properties such as structure and thermodynamics, as well as dynamic properties such as time correlations and diffusion constants, in open systems at a constant chemical potential, are preserved with this method. The average number of molecules converges in a reasonable amount of computational effort and provides a way to estimate the chemical potential of a given model force field

Statistical modelling of neuron degeneration

SUMMARY: Parkinson’s disease, Huntington’s disease, Amyotrophic lateral sclerosis (ALS) and Alzheimer’s disease are all examples of neurodegenerative disorders that result from the premature death of nerve cells or neurons. In order to understand the mechanisms through which these diseases advance, a number of models have been put forward to describe the decline in the numbers of surviving neurons. Such work has been hampered by the poor quality of estimates of the numbers of surviving neurons and also by questionable model selection techniques. Recent work has favoured the adoption of the exponential model to explain neurodegenerative decline. We present in this paper a methodology for challenging this model, using data from patients with ALS. We use a two stage procedure to study motor unit numbers. The first stage involves determining the number of motor units in a muscle on several occasions over a period of time. The method of Ridall et al. (2007) is used which makes use of reversible jump Markov chain Monte Carlo (RJMCMC). The second stage involves the analysis of the RJMCMC output by using a hiddenMarkov process of decline. Two such processes of decline are compared. The first is the exponential where the rate parameter is constant. This is compared to a more general semi-parametric process where the rate parameter is allowed to vary over time. The rate is set to be piecewise constant between recordings where the magnitudes of the change in rate are weakly constrained by the length of the interval between recording occasions. Between model comparisons are based on electrophysiological data collected from a group of ALS patients where motor units (MUs) are gradually lost leading to progressive muscle weakness. By calculating marginal likelihoods, we find the Bayes factor in support of the exponential decline model against the more general alternative. This approach is illustrated with four ALS patients. Prediction of MU numbers lost, which incorporates both models, can also be made. Our methods, we therefore believe, have a role in formulating and evaluating biological models for neural degeneration of the motor system in ALS patients

Automatic assembly design project 1968/9 :|breport of economic planning committee

Investigations into automatic assembly systems have been carried out. The conclusions show the major features to be considered by a company operating the machine to assemble the contact block with regard to machine output and financial aspects. The machine system has been shown to be economically viable for use under suitable conditions, but the contact block is considered to be unsuitable for automatic assembly. Data for machine specification, reliability and maintenance has been provided