scholarly journals On Asymptotics of the Beta Coalescents

2014 ◽  
Vol 46 (2) ◽  
pp. 496-515 ◽  
Author(s):  
Alexander Gnedin ◽  
Alexander Iksanov ◽  
Alexander Marynych ◽  
Martin Möhle
Keyword(s):  
Asymptotic Expansions ◽  
Branch Length ◽  
Wasserstein Distance ◽  
Stable Limit ◽  
Initial Number ◽  
Stable Law ◽  
Total Branch Length ◽  
Coalescent Tree ◽  
Number Of Particles

We show that the total number of collisions in the exchangeable coalescent process driven by the beta (1, b) measure converges in distribution to a 1-stable law, as the initial number of particles goes to ∞. The stable limit law is also shown for the total branch length of the coalescent tree. These results were known previously for the instance b = 1, which corresponds to the Bolthausen-Sznitman coalescent. The approach we take is based on estimating the quality of a renewal approximation to the coalescent in terms of a suitable Wasserstein distance. Application of the method to beta (a, b)-coalescents with 0 < a < 1 leads to a simplified derivation of the known (2 - a)-stable limit. We furthermore derive asymptotic expansions for the moments of the number of collisions and of the total branch length for the beta (1, b)-coalescent by exploiting the method of sequential approximations.

scholarly journals On Asymptotics of the Beta Coalescents

2014 ◽  
Vol 46 (02) ◽  
pp. 496-515 ◽  
Author(s):  
Alexander Gnedin ◽  
Alexander Iksanov ◽  
Alexander Marynych ◽  
Martin Möhle
Keyword(s):  
Asymptotic Expansions ◽  
Branch Length ◽  
Wasserstein Distance ◽  
Stable Limit ◽  
Initial Number ◽  
Stable Law ◽  
Total Branch Length ◽  
Coalescent Tree ◽  
Number Of Particles

We show that the total number of collisions in the exchangeable coalescent process driven by the beta (1,b) measure converges in distribution to a 1-stable law, as the initial number of particles goes to ∞. The stable limit law is also shown for the total branch length of the coalescent tree. These results were known previously for the instanceb= 1, which corresponds to the Bolthausen-Sznitman coalescent. The approach we take is based on estimating the quality of a renewal approximation to the coalescent in terms of a suitable Wasserstein distance. Application of the method to beta (a,b)-coalescents with 0 &lt;a&lt; 1 leads to a simplified derivation of the known (2 -a)-stable limit. We furthermore derive asymptotic expansions for the moments of the number of collisions and of the total branch length for the beta (1,b)-coalescent by exploiting the method of sequential approximations.

Distribution of epicormic branches and foliage on Douglas-fir as influenced by adjacent canopy gaps

2018 ◽  
Vol 48 (11) ◽  
pp. 1320-1330
Author(s):  
John W. Punches ◽  
Klaus J. Puettmann
Keyword(s):  
Branch Length ◽  
Canopy Gaps ◽  
Douglas Fir ◽  
Canopy Gap ◽  
Tree Age ◽  
Gap Size ◽  
Terminal Bud ◽  
Total Branch Length ◽  
A Minor ◽  
Epicormic Branches

The influence of adjacent canopy gaps on spatial distribution of epicormic branches and delayed foliage (originating from dormant buds) was investigated in 65-year-old coastal Douglas-fir (Pseudotsuga menziesii var. menziesii (Mirb.) Franco). Sample trees were selected across a broad range of local densities (adjacent canopy gap sizes) from a repeatedly thinned stand in which gaps had been created 12 years prior to our study. Lengths and stem locations of original and epicormic branches were measured within the south-facing crown quadrant, along with extents to which branches were occupied by sequential (produced in association with terminal bud elongation) and (or) delayed foliage. Epicormic branches, while prevalent throughout crowns, contributed only 10% of total branch length and 2% of total foliage mass. In contrast, delayed foliage occupied over 75% of total branch length, accounted for nearly 39% of total foliage mass, and often overlapped with sequential foliage. Canopy gap size did not influence original or epicormic branch length or location. On original branches, larger gaps may have modestly negatively influenced the relative extent of sequential foliage on branches and (or) slightly positively influenced delayed foliage mass. Delayed foliage appears to contribute substantially to Douglas-fir crown maintenance at this tree age, but canopy gap size had a minor influence, at least in the short term.

Parametric computational study of particle trajectory deviation probabilistic nature influencing the unevenness of their localization in the model tract

2021 ◽  
Author(s):  
A.V. Voronetskiy ◽  
K.Yu. Arefiev ◽  
M.A. Abramov
Keyword(s):  
Computational Study ◽  
Circular Cross Section ◽  
Cylindrical Part ◽  
Two Phase ◽  
Dispersed Particles ◽  
Alloy Particles ◽  
Model Channel ◽  
Probabilistic Nature ◽  
Number Of Particles

The purpose of this research was to investigate the spatial structure of a two-phase flow in a supersonic model channel of circular cross-section with a diameter of the cylindrical part of ~10 mm. For modeling, we used the Euler-Lagrange approach in combination with a probabilistic estimate of the dispersed particles deviation from their base trajectory. Chromium-nickel alloy particles with a diameter of 15 to 40 μm move in the channel in a special way, which was considered in the paper. Furthermore, we analyzed how the nature of the distribution function of the particle’s root-mean-square deviation from its base trajectory influences the quality of mixing of the dispersed phase with the flow and the number of particles interacting with the walls of the flow path.

Some Functional Stable Limit Theorems

1973 ◽  
Vol 16 (2) ◽  
pp. 173-177 ◽  
Author(s):  
D. R. Beuerman
Keyword(s):  
Weak Convergence ◽  
Limit Theorems ◽  
Stable Process ◽  
Random Variables ◽  
Domain Of Attraction ◽  
Stable Processes ◽  
Stable Limit ◽  
Stable Law ◽  
Partial Sum Process ◽  
Image Position

Let Xl,X2,X3, … be a sequence of independent and identically distributed (i.i.d.) random variables which belong to the domain of attraction of a stable law of index α≠1. That is,1whereandwhere L(n) is a function of slow variation; also take S0=0, B0=l.In §2, we are concerned with the weak convergence of the partial sum process to a stable process and the question of centering for stable laws and drift for stable processes.

Selection of flood-resistant and susceptible seedlings of Populustrichocarpa Torr. & Gray

1988 ◽  
Vol 18 (2) ◽  
pp. 271-275 ◽  
Author(s):  
Barbara A. Smit
Keyword(s):  
Leaf Area ◽  
Marked Reduction ◽  
Branch Length ◽  
Stomatal Resistance ◽  
Growth And Survival ◽  
Seed Collection ◽  
Individual Leaf ◽  
Total Branch Length ◽  
Collection Sites ◽  
Selection Of

To identify Populustrichocarpa plants with contrasting levels of resistance to flooding, seedlings from five diverse riparian sites were evaluated for growth and survival under flooding conditions. All seedlings survived 6 or 8 weeks of flooding. Total branch length and leaf number were reduced in all flooded plants relative to nonflooded controls. There was also a marked reduction in individual leaf area and increased stomatal resistance of flooded plants compared with nonflooded controls. Growth of flooded and nonflooded plants was highly variable within populations and no significant trends were found among populations. Therefore differential responses to flooding can be selected for within any of the seed collection sites. Plants that were rated as particularly resistant or susceptible fo flooding were selected for further study.

OVERWINTERING SPRUCE BUDWORM ON BLACK SPRUCE: SAMPLE-UNIT SIZE AND POPULATION DISTRIBUTION

1985 ◽  
Vol 117 (4) ◽  
pp. 395-399 ◽  
Author(s):  
Daniel J. Robison ◽  
Lawrence P. Abrahamson ◽  
Miroslaw M. Czapowskyj ◽  
Edwin H. White ◽  
Douglas C. Allen
Keyword(s):  
Population Distribution ◽  
Black Spruce ◽  
Branch Length ◽  
Spruce Budworm ◽  
Unit Size ◽  
Optimum Size ◽  
Sample Unit ◽  
Larval Distribution ◽  
Total Branch Length ◽  
Branch Distribution

AbstractOptimum size of a sample unit and within-branch distribution of overwintering spruce budworm were determined for black spruce in northern Maine. No significant differences in sample reliability were found between whole-branch and 45-cm branch-tip samples. Larval distribution on branches varied with total branch length and a model was developed to estimate the whole-branch population from a 45-cm branch tip. Use of a 45-cm branch-tip sample unit is recommended because it is biologically and statistically valid and reduces sampling costs.

scholarly journals THE MEASUREMENT AND DISTRIBUTION OF WOOD DUST

2010 ◽  
Vol 41 (1) ◽  
pp. 25 ◽  
Author(s):  
Andrea Rosario Proto ◽  
Giuseppe Zimbalatti ◽  
Martino Negri
Keyword(s):  
Health And Safety ◽  
Qualitative Assessment ◽  
Dust Particles ◽  
Wood Dust ◽  
High Concentration ◽  
Dust Emissions ◽  
Carcinogenic Agents ◽  
Prevention Model ◽  
Number Of Particles

In Italy, the woodworking industry presents many issues in terms of occupational health and safety. This study on exposure to wood dust could contribute to the realization of a prevention model in order to limit exposure to carcinogenic agents to the worker. The sampling methodology illustrated the analysis of dust emissions from the woodworking machinery in operation throughout the various processing cycles. The quantitative and qualitative assessment of exposure was performed using two different methodologies. The levels of wood dust were determined according to EN indications and sampling was conducted using IOM and Cyclon personal samplers. The qualitative research of wood dust was performed using an advanced laser air particle counter. This allowed the number of particles present to be counted in real time. The results obtained allowed for an accurate assessment of the quality of the dust emitted inside the workplace during the various processing phases. The study highlighted the distribution of air particles within the different size classes, the exact number of both thin and ultra-thin dusts, and confirmed the high concentration of thin dust particles which can be very harmful to humans.

A simple proof of a random stable limit theorem

1970 ◽  
Vol 7 (2) ◽  
pp. 502-504 ◽  
Author(s):  
Stephen R. Kimbleton
Keyword(s):  
Limit Theorem ◽  
Elementary Proof ◽  
General Theorem ◽  
Natural Extension ◽  
Sufficient Conditions ◽  
Domain Of Attraction ◽  
Stable Limit ◽  
Stable Law ◽  
Sufficient Conditions For Convergence ◽  
Necessary And Sufficient

Random stable limit theorems have been obtained by several authors, e.g., [3], [4]. The purpose of this note is to give a rather elementary proof of the basic version of this theorem. Our proof may be viewed as the natural extension to stable laws of the method used by Rényi [2] in obtaining a random central limit theorem. Indeed, the only “outside” theorems used are Kolmogorov's inequality (which Rényi also uses) and a general theorem on necessary and sufficient conditions for convergence of a triangular array. It will also be observed that in the present theorem, the consideration of random variables in the domain of attraction of a stable law of index α = 1, introduces no additional difficulties.

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