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.

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.

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.

Integrals for continuous-time Markov chains

This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process. (C) 2002 Elsevier Science Inc. All rights reserved.

Multiple axon guidance cues establish the olfactory topographic map: how do these cues interact?

Each primary olfactory neuron stochastically expresses one of similar to1000 odorant receptors. The total population of these neurons therefore consists of similar to1,000 distinct subpopulations, each of which are mosaically dispersed throughout one of four semi-annular zones in the nasal cavity. The axons of these different subpopulations are initially intermingled within the olfactory nerve. However, upon reaching the olfactory bulb, they sort out and converge so that axons expressing the same odorant receptor typically target one or two glomeruli. The spatial location of each of these 1800 glomeruli are topographically-fixed in the olfactory bulb and are invariant from animal to animal. Thus, while odorant receptors are expressed mosaically by neurons throughout the olfactory neuroepithelium their axons sort out, converge and target the same glomerulus within the olfactory bulb. How is such precise and reproducible topographic targeting generated? While some of the mechanisms governing the growth cone guidance of olfactory sensory neurons are understood, the cues responsible for homing axons to their target site remain elusive.

The paternity of the price-quality 'value map'

In the literature on firm strategy and product differentiation, consumer price-quality trade-offs are sometimes represented using consumer 'value maps'. These involve the geometric representation of indifferent price and quality combinations as points along curves that are concave to the 'quality' axis. In this paper, it is shown that the value map for price-quality tradeoffs may be derived from a Hicksian compensated demand curve for product quality. The paper provides the theoretical link between analytical methods employed in the existing literature on firm strategy and competitive advantage with the broader body of economic analysis.

Epitope map for a growth hormone receptor agonist monoclonal antibody, MAb 263

Monoclonal antibody (MAb) 263 is a widely used monoclonal antibody that recognizes the extracellular domain (ECD) of the GH receptor. It has been shown to act as a GH agonist both in vitro and in vivo, and we report here that it must be divalent to exert its effect on the full-length receptor. To understand the mechanism of its agonist action, we have determined the precise epitope for this antibody using a novel random PCR mutagenesis approach together with expression screening in yeast. A library of 5200 clones of rabbit GH receptor ECD mutants were screened both with MAb 263 and with an anticarboxy-tag antibody to verify complete ECD expression. Sequencing for clones that expressed complete ECD but were not MAb 263 positive identified 20 epitope residues distributed in a discontinuous manner throughout the ECD. The major part of the epitope, as revealed after mapping onto the crystal structure model of the ECD molecule, was located on the side and upper portion of domain 1, particularly within the D - E strand disulfide loop 79 - 96. Molecular dynamics docking of an antibody of the same isotype as MAb 263 was used to dock the bivalent antibody to the 1528-Angstrom(2) epitope and to visualize the likely consequences of MAb binding. The minimized model enables the antibody to grasp two receptors in a pincer-like movement from opposite sides, facilitating alignment of the receptor dimerization domains in a manner similar to, but not identical with, GH.

A genetic map of macadamia based on randomly amplified DNA fingerprinting (RAF) markers

The first genetic linkage map of macadamia (Macadamia integrifolia and M. tetraphylla) is presented. The map is based on 56 F-1 progeny of cultivars 'Keauhou' and 'A16'. Eighty-four percent of the 382 markers analysed segregated as Mendelian loci. The two-way pseudo-testcross mapping strategy allowed construction of separate parental cultivar maps. Ninety bridging loci enabled merging of these maps to produce a detailed genetic map of macadamia, 1100 cM in length and spanning 70-80% of the genome. The combined map comprised 24 linkage groups with 265 framework markers: 259 markers from randomly amplified DNA fingerprinting (RAF), five random amplified polymorphic DNA (RAPD), and one sequence-tagged microsatellite site (STMS). The RAF marker system unexpectedly revealed 16 codominant markers, one of them a putative microsatellite locus and exhibiting four distinct alleles in the cross. This molecular study is the most comprehensive examination to date of genetic loci of macadamia, and is a major step towards developing marker-assisted selection for this crop.

Building a bicycle suitability map for Coimbra

The adoption of faster modes of transportation (mainly the private car) has changed profoundly the spatial organisation of cities. The increase in distance covered due to increased speed of travel and to urban sprawl leads to an increase in energy consumption, being the transportation sector a huge consumer responsible for 61.5% of total world oil consumption and a global final energy consumption of 31.6% in EU-27 (2007). Due to unsustainable transportation conditions, many cities suffer from congestion and various other traffic problems. Such situations get worse with solutions mostly seen in the development of new infrastructure for motorized modes of transportation, and construction of car parking structures. The bicycle, considered the most efficient among all modes of transportation including walking, is a travel mode that can be adopted in most cities contributing for urban sustainability given the associated environmental, economic and social advantages. In many nations a large number of policy initiatives have focused on discouraging the use of private cars, encouraging the use of sustainable modes of transportation, like public transportation and other forms such as bicycling. Given the importance of developing initiatives that favour the use of bicycle as an urban transportation mode, an analysis of city suitability, including distances and slopes of street network, is crucial in order to help decision-makers to plan the city for bicycle. In this research Geographical Information Systems (GIS) technology was used for this purpose and some results are presented concerning the city of Coimbra.

Harvesting dynamic aspects from a real rational map : the bulb of period 5

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Spatial operators for collaborative map handling

MSC Dissertation in Computer Engineering

Urban land use change analysis and modelling: a case study of Setubal-Sesimbra, Portugal

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies