Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

A mixture model-based approach to the clustering of microarray expression data

Motivation: This paper introduces the software EMMIX-GENE that has been developed for the specific purpose of a model-based approach to the clustering of microarray expression data, in particular, of tissue samples on a very large number of genes. The latter is a nonstandard problem in parametric cluster analysis because the dimension of the feature space (the number of genes) is typically much greater than the number of tissues. A feasible approach is provided by first selecting a subset of the genes relevant for the clustering of the tissue samples by fitting mixtures of t distributions to rank the genes in order of increasing size of the likelihood ratio statistic for the test of one versus two components in the mixture model. The imposition of a threshold on the likelihood ratio statistic used in conjunction with a threshold on the size of a cluster allows the selection of a relevant set of genes. However, even this reduced set of genes will usually be too large for a normal mixture model to be fitted directly to the tissues, and so the use of mixtures of factor analyzers is exploited to reduce effectively the dimension of the feature space of genes. Results: The usefulness of the EMMIX-GENE approach for the clustering of tissue samples is demonstrated on two well-known data sets on colon and leukaemia tissues. For both data sets, relevant subsets of the genes are able to be selected that reveal interesting clusterings of the tissues that are either consistent with the external classification of the tissues or with background and biological knowledge of these sets.

Woodstoves uncovered: a paediatric problem

Objectives: To document and describe the effects of woodstove burns in children. To identify how these accidents occur so that a prevention strategy can be devised. Design, Patients and Setting: Retrospective departmental database and case note review of all children with woodstove burns seen at the Burns Unit of a Tertiary Referral Children's Hospital between January 1997 and September 2001. Main outcome measures: Number and ages of children burned: circumstances of the accidents; injuries-sustained, treatment-required and long-term sequelae. Results. Eleven children, median age 1.0 year, sustained burns, usually to the hands, of varying thickness. Two children required skin grafting and five required scar therapy. Seven children intentionally placed their hands onto the Outside of the stove. In all children, burns occurred despite adult supervision Conclusions: Woodstoves area cause of burns in children. These injuries are associated with significant morbidity and financial costs. Through public education, woodstove burns can easily be prevented utilising simple safety measures. (C) 2002 Elsevier Science Ltd and ISBI All rights reserved.

Development of a mungbean (Vigna radiata) RFLP linkage map and its comparison with lablab (Lablab purpureus) revelas a high level of colinearity between the two genomes

A genetic linkage map of mungbean (Vigna radiata, 2n = 2x = 22) consisting of 255 RFLP loci was developed using a recombinant inbred population of 80 individuals. The population was derived from an intersubspecific cross between the cultivated mungbean variety 'Berken' and a wild mungbean genotype 'ACC 41' (V radiata subsp. sublobata). The total length of the map, which comprised 13 linkage groups, spanned 737.9 cM with an average distance between markers of 3.0 cM and a maximum distance between linked markers of 15.4 cM. The mungbean map was compared to a previously published map of lablab (Lablab purpureus, 2n = 2x = 24) using a common set of 65 RFLP probes. In contrast to some other comparative mapping studies among members of the Fabaceae, where a high level of chromosomal rearrangement has been observed, marker order between mungbean and lablab was found to be highly conserved. However, the two genomes have apparently accumulated a large number of duplications/deletions after they diverged.

On the importance function in splitting simulation

The splitting method is a simulation technique for the estimation of very small probabilities. In this technique, the sample paths are split into multiple copies, at various stages in the simulation. Of vital importance to the efficiency of the method is the Importance Function (IF). This function governs the placement of the thresholds or surfaces at which the paths are split. We derive a characterisation of the optimal IF and show that for multi-dimensional models the natural choice for the IF is usually not optimal. We also show how nearly optimal splitting surfaces can be derived or simulated using reverse time analysis. Our numerical experiments illustrate that by using the optimal IF, one can obtain a significant improvement in simulation efficiency.

Interlabial contact pressures exhibited in dysarthria following traumatic brain injury during speech and nonspeech tasks

A miniature pressure transducer was used to assess the interlabial contact pressures produced by a group of 19 adults (mean age 30.6 years) with dysarthria following severe traumatic brain injury (TBI) during a set of speech and nonspeech tasks. Ten parameters relating to lip strength, endurance, rate of movement and lip pressure accuracy and stability were measured from the nonspeech tasks. The results attained by the TBI group were compared against a group of 19 age- and sex-matched control subjects. Significant differences between the groups were found for maximum interlabial contact pressure, maximum rate of repetition of maximum pressure, and lip pressure accuracy at 50 and 10% levels of maximum pressure. In regards to speech, the interlabial contact pressures generated by the TBI group and control group did not differ significantly. When expressed as percentages of maximum pressure, however, the TBI group's interlabial pressures appeared to have been generated with greater physiological effort. Copyright (C) 2002 S. Karger AG, Basel.

Two-dimensional balanced sampling plans excluding contiguous units

A balanced sampling plan excluding contiguous units (or BSEC for short) was first introduced by Hedayat, Rao and Stufken in 1988. These designs can be used for survey sampling when the units are arranged in one-dimensional ordering and the contiguous units in this ordering provide similar information. In this paper, we generalize the concept of a BSEC to the two-dimensional situation and give constructions of two-dimensional BSECs with block size 3. The existence problem is completely solved in the case where lambda = 1.

Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

A comparison of peak power in the shoulder press and shoulder throw

The ability to generate peak power is central for performance in many sports. Currently two distinct resistance training methods are used to develop peak power, the heavy weight/slow velocity and light weight/fast velocity regimes. When using the light weight/fast velocity power training method it was proposed that peak power would be greater in a shoulder throw exercise compared with a normal shoulder press. Nine males performed three lifts in the shoulder press and shoulder throw at 30% and 40% of their one repetition maximum (1RM). These lifts were performed identically, except for the release of the bar in the throw condition. A potentiometer attached to the bar measured displacement and duration of the lifts. The time of bar release in the shoulder throw was determined with a pressure switch. ANOVA was used to examine statistically significant differences where the level of acceptance was set at p