The Galton-Watson process conditioned on the total progeny

1975 ◽  
Vol 12 (4) ◽  
pp. 800-806 ◽  
Author(s):  
Douglas P. Kennedy
Keyword(s):  
Marked Contrast ◽  
Total Progeny ◽  
Limiting Behaviour ◽  
Watson Process

Let Zk denote the number in the kth generation of a Galton-Watson process initiated by one individual and let N be the total progeny, i.e., As n → ∞ the limiting behaviour of the process {Zk, 0 ≦ k ≦ n} conditioned on the event {N =n} is studied. The results obtained are of exactly the same form for the subcritical, critical and supercritical cases. This is in marked contrast to the analogous situation got by conditioning on non-extinction by the nth generation and letting n → ∞. In the latter case the limiting results differ in form for the critical and non-critical cases.

The Galton-Watson process conditioned on the total progeny

1975 ◽  
Vol 12 (04) ◽  
pp. 800-806 ◽  
Author(s):  
Douglas P. Kennedy
Keyword(s):  
Marked Contrast ◽  
Total Progeny ◽  
Limiting Behaviour ◽  
Watson Process

Let Zk denote the number in the kth generation of a Galton-Watson process initiated by one individual and let N be the total progeny, i.e., As n → ∞ the limiting behaviour of the process {Zk, 0 ≦ k ≦ n} conditioned on the event {N =n} is studied. The results obtained are of exactly the same form for the subcritical, critical and supercritical cases. This is in marked contrast to the analogous situation got by conditioning on non-extinction by the nth generation and letting n → ∞. In the latter case the limiting results differ in form for the critical and non-critical cases.

The multi-type Galton-Watson process with immigration

1970 ◽  
Vol 7 (02) ◽  
pp. 411-422 ◽  
Author(s):  
M. P. Quine
Keyword(s):  
Recurrence Relation ◽  
Limiting Behaviour ◽  
Watson Process

Summary We consider the limiting behaviour of a k-type (k < ∞) Galton-Watson process which is augmented at each generation by a stochastic immigration component. In Section 2, conditions for ergodicity are found for a subclass of such processes. In Section 3, expressions are derived for the first two moments of the nth generation (by way of a recurrence relation) and for the first two asymptotic moments, in a manner which to some extent generalises previous results.

The multi-type Galton-Watson process with immigration

1970 ◽  
Vol 7 (2) ◽  
pp. 411-422 ◽  
Author(s):  
M. P. Quine
Keyword(s):  
Recurrence Relation ◽  
Limiting Behaviour ◽  
Watson Process

SummaryWe consider the limiting behaviour of a k-type (k < ∞) Galton-Watson process which is augmented at each generation by a stochastic immigration component. In Section 2, conditions for ergodicity are found for a subclass of such processes. In Section 3, expressions are derived for the first two moments of the nth generation (by way of a recurrence relation) and for the first two asymptotic moments, in a manner which to some extent generalises previous results.

FT-IR microspectroscopic analysis of diseased white matter brain tissues

1995 ◽  
Vol 53 ◽  
pp. 968-969
Author(s):  
Steven M. Le Vine ◽  
David L. Wetzel
Keyword(s):  
White Matter ◽  
Gray Matter ◽  
Twitcher Mouse ◽  
Grid Pattern ◽  
Marked Contrast ◽  
Spatially Resolved ◽  
Ft Ir ◽  
Ir Microspectroscopy ◽  
Chemical Evidence

In situ FT-IR microspectroscopy has allowed spatially resolved interrogation of different parts of brain tissue. In previous work the spectrrscopic features of normal barin tissue were characterized. The white matter, gray matter and basal ganglia were mapped from appropriate peak area measurements from spectra obtained in a grid pattern. Bands prevalent in white matter were mostly associated with the lipid. These included 2927 and 1469 cm-1 due to CH2 as well as carbonyl at 1740 cm-1. Also 1235 and 1085 cm-1 due to phospholipid and galactocerebroside, respectively (Figs 1and2). Localized chemical changes in the white matter as a result of white matter diseases have been studied. This involved the documentation of localized chemical evidence of demyelination in shiverer mice in which the spectra of white matter lacked the marked contrast between it and gray matter exhibited in the white matter of normal mice (Fig. 3).The twitcher mouse, a model of Krabbe’s desease, was also studied. The purpose in this case was to look for a localized build-up of psychosine in the white matter caused by deficiencies in the enzyme responsible for its breakdown under normal conditions.

TEM observations of surface-step and hole-edge faceting in acid-etched and annealed MgO thin foils

1993 ◽  
Vol 51 ◽  
pp. 1134-1135
Author(s):  
Simon King ◽  
C. Barry Carter
Keyword(s):  
Marked Contrast ◽  
Aqua Regia ◽  
Surface Step ◽  
Smoke Particle ◽  
Hole Edge ◽  
Thin Foils ◽  
Surface Steps ◽  
Unit Cells ◽  
Reflection Electron Microscopy ◽  
Similar Preparation

Surface-steps formed during the cleavage of MgO on {100} planes, the smaller steps of which may be of atomic height, have been observed in Reflection-Electron Microscopy investigations to be accurately aligned along <001> directions. Steps of atomic height also have been identified on MgO smoke-particle platelets; these steps may be curved or straight, with the straight steps showing evidence for faceting along <001>. Reference also is made to faceting along <011> and <012> directions. Straight steps ∼2 unit cells high, with edges along <100> also have been imaged by High-Resolution Profile-Imaging at the peripheries of MgO smoke microcubes. After etching in aqua-regia and annealing in air, however, high densities of “large” steps several unit cells high, as well as numerous holes, are formed. It is faceting in these foils that is reported here.As can be seen in fig 1, obvious faceting of the surface-step traces is extremely rare in these foils, in marked contrast to substrates such as LaAlO3 and SrTiO3, on which surface-step traces facet readily after a similar preparation treatment.

Corporate Sustainability: Challenge to Managerial Orthodoxies

2003 ◽  
Vol 9 (1) ◽  
pp. 2-11 ◽  
Author(s):  
Dexter Dunphy
Keyword(s):  
Case Studies ◽  
Corporate Sustainability ◽  
Central Place ◽  
Marked Contrast ◽  
Sustainability Management

ABSTRACTThis paper addresses the issue of corporate sustainability. It examines why achieving sustainability is becoming an increasingly vital issue for society and organisations, defines sustainability and then outlines a set of phases through which organisations can move to achieve increasing levels of sustainability. Case studies are presented of organisations at various phases indicating the benefits, for the organisation and its stakeholders, which can be made at each phase. Finally the paper argues that there is a marked contrast between the two competing philosophies of neo-conservatism (economic rationalism) and the emerging philosophy of sustainability. Management schools have been strongly influenced by economic rationalism, which underpins the traditional orthodoxies presented in such schools. Sustainability represents an urgent challenge for management schools to rethink these traditional orthodoxies and give sustainability a central place in the curriculum.

Growth, Development and Innate Capacity for Increase in Aphytis Chrysomphali Mercet and A. Melinus Debach, Parasites of California Red Scale, Aonidiella Aurantii (Mask.), In Relation to Temperature.

1974 ◽  
Vol 22 (2) ◽  
pp. 213 ◽  
Author(s):  
I Abdelrahman
Keyword(s):  
Negative Relationship ◽  
Differential Mortality ◽  
Female Progeny ◽  
Annual Fluctuation ◽  
Adaptation To Cold ◽  
Rate Of Increase ◽  
Total Progeny ◽  
Searching Ability ◽  
Pupal Mortality ◽  
Threshold Of Development

A, melinus produced more female progeny and more than twice as many total progeny as A. chrysomphali; it also destroyed almost twice as many hosts through oviposition and mutiliation. A. chrysomphali had a longer post-oviposition period than A. melinus, especially at 30�C. The proportion of single progeny in a host was higher for A, chrysomphali than for A. melinus at all temperatures, and was related to temperature positively in A. chrysomphali and inversely in A. melinus. Large old female A. melinus produced only males at the end of their lives; they did not mate at that stage when offered males, not because they were aged but because they mate only once in their lives. As temperature decreased, female A. melznus ceased producing females earlier, probably because temperature affected either longevity of sperms or the mechanism controlling their release. Differential mortality, temperature, and age of mothers all influenced sex ratio. Pupal mortality was inversely related to temperature within the observed range 20-30�C; in female pupae of A. chrysomphali it was lower than that in either female or male pupae of A. melinus; it was higher in male than female pupae in A. melinus. A. melinus lived longer than A. chrysomphali at all temperatures. Duration of development was longer for A. chrysomphali than for A. melinus at 30�C, but shorter at 20 and 25�C. The threshold of development was 8.5C for A. chrysomphali and 11C for A. melinus. A. chrysomphali had a higher rm at 20 and 25�C than A. melinus, but much lower at 30�C. The highest rate of increase was at > 30�C for A. melinus, and at about 25�C for A. chrysomphali. The rm of the parasites was 3.1-5.0 times that of red scale, depending on parasite species and temperature. A. chrysomphali is smaller than A. melinus, and from the positive relationship between adaptation to cold and speed of development, and the negative relationship between speed of development and size, a negative relationship between size and adaptation to cold within Aphytis spp. may be postulated. A. chrysomphali is more adapted to cold and less to heat than A. melinus. This explains the seasonal and annual fluctuation in their relative abundance in southern Australia. The species would complement each other in controlling red scale; from the data presented here it is possible that Aphytis spp. in Australia may have evolved into more efficient control agents of red scale than elsewhere. Knowledge on the searching ability of Aphytis at different host densities is wanting.

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