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.

High dependency units: Issues to consider in their planning

This review discusses the issues to be considered in establishing new or extending existing high dependency unit (HDU) services. A defined high dependency service becomes cost-effective when patient care requires more than one nurse for three patients. Professional guidelines for HDUs vary and there are no national accreditation criteria. Casemix and service delivery specifications for the HDU need to be defined and agreed upon within the institution. Establishing a new HDU service requires changes to care delivery. Many potential HDU patients are currently managed in general wards or in the intensive care unit. The service should be discussed widely and marketed within the institution, and the development of defined working relationships with the ICU and primary care teams oil the wards is mandatory.

Exogenous Slit2 does not affect ureteric branching or nephron formation during kidney development

In an attempt to elucidate the role of Slit2 invertebrate kidney development, the effect of adding exogenous human Slit2 protein (hSlit2) to developing murine metanephric kidney explants was examined. To confirm the activity of the recombinant Slit2 protein, neurons from 8 day old chick sympathetic nerve chain dorsal root ganglia were cultured with hSlit2 protein, which induced significant neurite branching and outgrowth. Using kidney explants as a model system, metanephric development in the presence of hSlit2 protein was examined. Addition of hSlit2 up to a final concentration of 1 mug/ml had no detectable effect on the formation of nephrons or on branching morphogenesis of the ureteric tree after 2 or 4 days in culture, as assessed via immunofluorescence for the markers WT1 and calbindin 28K respectively. Similarly, maturation of the nephrogenic mesenchyme occurred in a phenotypically normal fashion. In situ analysis of the Slit receptors, Robot and Robot, the vasculogenic markers VEGFA and Flk-1, and the stromal cell marker BF2 displayed no difference in comparison to controls.

MAX4 and RMS1 are orthologous dioxygenase-like genes that regulate shoot branching in Arabidopsis and pea

Shoot branching is inhibited by auxin transported down the stem from the shoot apex. Auxin does not accumulate in inhibited buds and so must act indirectly. We show that mutations in the MAX4 gene of Arabidopsis result in increased and auxin-resistant bud growth. Increased branching in max4 shoots is restored to wild type by grafting to wild-type rootstocks, suggesting that MAX4 is required to produce a mobile branch-inhibiting signal, acting downstream of auxin. A similar role has been proposed for the pea gene, RMS1. Accordingly, MAX4 and RMS1 were found to encode orthologous, auxin-inducible members of the polyene dioxygenase family.

Dendritic branching of pyramidal cells in the visual cortex of the nocturnal owl monkey: A fractal analysis

The branching structure of neurones is thought to influence patterns of connectivity and how inputs are integrated within the arbor. Recent studies have revealed a remarkable degree of variation in the branching structure of pyramidal cells in the cerebral cortex of diurnal primates, suggesting regional specialization in neuronal function. Such specialization in pyramidal cell structure may be important for various aspects of visual function, such as object recognition and color processing. To better understand the functional role of regional variation in the pyramidal cell phenotype in visual processing, we determined the complexity of the dendritic branching pattern of pyramidal cells in visual cortex of the nocturnal New World owl monkey. We used the fractal dilation method to quantify the branching structure of pyramidal cells in the primary visual area (V1), the second visual area (V2) and the caudal and rostral subdivisions of inferotemporal cortex (ITc and ITr, respectively), which are often associated with color processing. We found that, as in diurnal monkeys, there was a trend for cells of increasing fractal dimension with progression through these cortical areas. The increasing complexity paralleled a trend for increasing symmetry. That we found a similar trend in both diurnal and nocturnal monkeys suggests that it was a feature of a common anthropoid ancestor.

Application to quantify fetal lung branching on rat explants

Recently, regulating mechanisms of branching morphogenesis of fetal lung rat explants have been an essential tool for molecular research. The development of accurate and reliable segmentation techniques may be essential to improve research outcomes. This work presents an image processing method to measure the perimeter and area of lung branches on fetal rat explants. The algorithm starts by reducing the noise corrupting the image with a pre-processing stage. The outcome is input to a watershed operation that automatically segments the image into primitive regions. Then, an image pixel is selected within the lung explant epithelial, allowing a region growing between neighbouring watershed regions. This growing process is controlled by a statistical distribution of each region. When compared with manual segmentation, the results show the same tendency for lung development. High similarities were harder to obtain in the last two days of culture, due to the increased number of peripheral airway buds and complexity of lung architecture. However, using semiautomatic measurements, the standard deviation was lower and the results between independent researchers were more coherent

Automated image analysis of lung branching morphogenesis from microscopic images of fetal rat explants

Background: Regulating mechanisms of branching morphogenesis of fetal lung rat explants have been an essential tool for molecular research. This work presents a new methodology to accurately quantify the epithelial, outer contour and peripheral airway buds of lung explants during cellular development from microscopic images. Methods: The outer contour was defined using an adaptive and multi-scale threshold algorithm whose level was automatically calculated based on an entropy maximization criterion. The inner lung epithelial was defined by a clustering procedure that groups small image regions according to the minimum description length principle and local statistical properties. Finally, the number of peripheral buds were counted as the skeleton branched ends from a skeletonized image of the lung inner epithelial. Results: The time for lung branching morphometric analysis was reduced in 98% in contrast to the manual method. Best results were obtained in the first two days of cellular development, with lesser standard deviations. Non-significant differences were found between the automatic and manual results in all culture days. Conclusions: The proposed method introduces a series of advantages related to its intuitive use and accuracy, making the technique suitable to images with different lightning characteristics and allowing a reliable comparison between different researchers.

Automated image analysis of lung branching morphogenesis

Regulating mechanisms of branchingmorphogenesis of fetal lung rat explants have been an essential tool formolecular research.This work presents a new methodology to accurately quantify the epithelial, outer contour, and peripheral airway buds of lung explants during cellular development frommicroscopic images. Methods.Theouter contour was defined using an adaptive and multiscale threshold algorithm whose level was automatically calculated based on an entropy maximization criterion. The inner lung epithelium was defined by a clustering procedure that groups small image regions according to the minimum description length principle and local statistical properties. Finally, the number of peripheral buds was counted as the skeleton branched ends from a skeletonized image of the lung inner epithelia. Results. The time for lung branching morphometric analysis was reduced in 98% in contrast to themanualmethod. Best results were obtained in the first two days of cellular development, with lesser standard deviations. Nonsignificant differences were found between the automatic and manual results in all culture days. Conclusions. The proposed method introduces a series of advantages related to its intuitive use and accuracy, making the technique suitable to images with different lighting characteristics and allowing a reliable comparison between different researchers.

Application to quantify fetal lung branching on rat explant

Recently, regulating mechanisms of branching morphogenesis of fetal lung rat explants have been an essential tool for molecular research. The development of accurate and reliable segmentation techniques may be essential to improve research outcomes. This work presents an image processing method to measure the perimeter and area of lung branches on fetal rat explants. The algorithm starts by reducing the noise corrupting the image with a pre-processing stage. The outcome is input to a watershed operation that automatically segments the image into primitive regions. Then, an image pixel is selected within the lung explant epithelial, allowing a region growing between neighbouring watershed regions. This growing process is controlled by a statistical distribution of each region. When compared with manual segmentation, the results show the same tendency for lung development. High similarities were harder to obtain in the last two days of culture, due to the increased number of peripheral airway buds and complexity of lung architecture. However, using semiautomatic measurements, the standard deviation was lower and the results between independent researchers were more coherent.

Scheduling of head-dependent cascaded reservoirs considering discharge ramping constraints and start/stop of units

This paper is on the problem of short-term hydro scheduling (STHS), particularly concerning head-dependent reservoirs under competitive environment. We propose a novel method, based on mixed-integer nonlinear programming (MINLP), for optimising power generation efficiency. This method considers hydroelectric power generation as a nonlinear function of water discharge and of the head. The main contribution of this paper is that discharge ramping constraints and start/stop of units are also considered, in order to obtain more realistic and feasible results. The proposed method has been applied successfully to solve two case studies based on Portuguese cascaded hydro systems, providing a higher profit at an acceptable computation time in comparison with classical optimisation methods based on mixed-integer linear programming (MILP).

Comparison of fungal contamination between hospitals and companies food units

A descriptive study was developed to compare air and surfaces fungal contamination in ten hospitals’ food units and two food units from companies. Fifty air samples of 250 litres through impaction method were collected from hospitals’ food units and 41 swab samples from surfaces were also collected, using a 10 by 10 cm square stencil. Regarding the two companies, ten air samples and eight surface samples were collected. Air and surface samples were collected in food storage facilities, kitchen, food plating and canteen. Outdoor air was also collected since this is the place regarded as a reference. Simultaneously, temperature, relative humidity and meal numbers were registered. Concerning air from hospitals’ food units, 32 fungal species were identified, being the two most commonly isolated genera Penicillium sp.