Objects arranged randomly in space: an accessible theory

Richard Cowan

doi:10.2307/1427635

Objects arranged randomly in space: an accessible theory

Advances in Applied Probability ◽

10.1017/s0001867800018802 ◽

1989 ◽

Vol 21 (03) ◽

pp. 543-569 ◽

Cited By ~ 3

Author(s):

Richard Cowan

Keyword(s):

Statistical Properties ◽

Observation Window ◽

Size And Shape ◽

Expository Paper ◽

General Size ◽

Substantive Assumption

This expository paper deals with many problems concerning bounded objects arranged randomly in space. The objects are of rather general shapes and sizes, whilst the random mechanisms for positioning and orienting them are also fairly general. There are no restrictions on the dependence between shapes, sizes, orientations and positions of objects. The only substantive assumption is that the objects are distributed in a ‘statistically uniform' way throughout the whole of the space. We focus on the statistical properties of features seen in an observation window, itself of general size and shape.

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Changes in sources of shared variability of body size and shape in Egyptian local and New Zealand White breeds of rabbits during growth

Archives Animal Breeding ◽

10.5194/aab-45-269-2002 ◽

2002 ◽

Vol 45 (3) ◽

pp. 269-277

Author(s):

K. A. Shahin ◽

N. S. Hassan

Keyword(s):

Body Weight ◽

New Zealand ◽

General Factor ◽

Size Factor ◽

Shape Variation ◽

Thigh Circumference ◽

Size And Shape ◽

Stage Of Development ◽

Shape Characters ◽

General Size

Abstract. Correlations between body weight and measurements (body length, thigh circumference, shank length and chest width) at 6, 8, 10 and 12 weeks of age in New Zealand White (NZW), Red Baladi (RB), Black Baladi (BB) breeds of rabbits were studied by factor analysis to disclose the main sources of shared variability, to deduce the factors that describe these characteristics and to quantify breed differences in morphometric size and shape variation during growth. Differences and similarities between NZW and Egyptian rabbit breeds in factors describing variations in size and shape characters are discussed. At marketing age, compared with local breeds (RB and BB), NZW had higher communality (proportion of variance for a variable that is shared in common by other variables) for chest width and lower communality for body weight and other body shape characters. Compared with NZW, Egyptian breeds varied more in size and less in shape characters. Finding indicated that most of the common variability in live performance traits could be accounted for by two factors with the influence of general factor preponderating. Irrespective of breed, the first factor at various ages was interpreted as a general size factor. The second factor varies with breed and stage of development. In NZW, this factor at all ages (6 to 12 weeks) was described as chest width factor. The second factor in RB was designated to chest width (at 6 and 8 weeks) and a shank length at 10 and 12 weeks. In BB, the second factor was designated to chest width (at 6 weeks), a shank length (at 8 and 10 weeks) and to thigh circumference (at 12 weeks). The importance of the general size factor in relation to the second factor (shape) changes with age. The contribution of the general size factor to the total variance decreased with age in both NZW and RB, but it showed irregular pattern in BB. While that of the second factor increased with advancing age from 6 to 12 weeks in RB and from 6 to 10 weeks in NZW.

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Unbiased estimation of particle number and sizes using the new stereological tools: the disector, the fractionator, the selector, and the nucleator — or just point-sampled intercepts

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100104200 ◽

1988 ◽

Vol 46 ◽

pp. 428-429

Author(s):

H.J.G. Gundersen

Keyword(s):

Particle Number ◽

Small Distance ◽

Parallel Plane ◽

Unbiased Estimation ◽

Severe Problem ◽

New Era ◽

Size And Shape ◽

Distinct Property ◽

Sectioned Tissue

Previously, all stereological estimation of particle number and sizes were based on models and notoriously gave biased results, were very inefficient to use and difficult to justify. For all references to old methods and a direct comparison with unbiased methods see recent reviews.The publication in 1984 of the DISECTOR, the first unbiased stereological probe for sampling and counting 3—D objects irrespective of their size and shape, signalled the new era in stereology — and give rise to a number of remarkably simple and efficient techniques based on its distinct property: It is the only known way to obtain an unbiased sample of 3-D objects (cells, organelles, etc). The principle is simple: within a 2-D unbiased frame count or sample only cells which are not hit by a parallel plane at a known, small distance h.The area of the frame and h must be known, which might sometimes in itself be a problem, albeit usually a small one. A more severe problem may arise because these constants are known at the scale of the fixed, embedded and sectioned tissue which is often shrunken considerably.

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Ultrastructural Alterations in Sinusoidal Endothelial Fenestrae as a Result of Hypoxia

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100090828 ◽

1976 ◽

Vol 34 ◽

pp. 168-169

Author(s):

Waykin Nopanitaya ◽

Raeford E. Brown ◽

Joe W. Grisham ◽

Johnny L. Carson

Keyword(s):

Endothelial Cells ◽

Experimental Model ◽

Hepatic Lobule ◽

Ultrastructural Alterations ◽

Large Type ◽

Sinusoidal Endothelial Fenestrae ◽

General Size ◽

Sem Studies

Mammalian endothelial cells lining hepatic sinusoids have been found to be widely fenestrated. Previous SEM studies (1,2) have noted two general size catagories of fenestrations; large fenestrae were distributed randomly while the small type occurred in groups. These investigations also reported that large fenestrae were more numerous and larger in the endothelial cells at the afferent ends of sinusoids or around the portal areas, whereas small fenestrae were more numerous around the centrilobular portion of the hepatic lobule. It has been further suggested that under some physiologic conditions small fenestrae could fuse and subsequently become the large type, but this is, as yet, unproven.We have used a reproducible experimental model of hypoxia to study the ultrastructural alterations in sinusoidal endothelial fenestrations in order to investigate the origin of occurrence of large fenestrae.

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The influence of confocal microscope design on imaging performance

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100146564 ◽

1993 ◽

Vol 51 ◽

pp. 144-145

Author(s):

C J R Sheppard

Keyword(s):

Image Quality ◽

Fluorescence Imaging ◽

Confocal Microscope ◽

Industrial Applications ◽

Three Dimensions ◽

Design Parameters ◽

Weak Signals ◽

Size And Shape ◽

Imaging Performance ◽

Fundamental Limitation

The confocal microscope is now widely used in both biomedical and industrial applications for imaging, in three dimensions, objects with appreciable depth. There are now a range of different microscopes on the market, which have adopted a variety of different designs. The aim of this paper is to explore the effects on imaging performance of design parameters including the method of scanning, the type of detector, and the size and shape of the confocal aperture.It is becoming apparent that there is no such thing as an ideal confocal microscope: all systems have limitations and the best compromise depends on what the microscope is used for and how it is used. The most important compromise at present is between image quality and speed of scanning, which is particularly apparent when imaging with very weak signals. If great speed is not of importance, then the fundamental limitation for fluorescence imaging is the detection of sufficient numbers of photons before the fluorochrome bleaches.

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