scholarly journals Very fat geometric Galton-Watson trees

2020 ◽  
Vol 24 ◽  
pp. 294-314
Author(s):  
Romain Abraham ◽  
Aymen Bouaziz ◽  
Jean-François Delmas
Keyword(s):  
Infinite Number ◽  
Local Limit ◽  
Random Tree ◽  
Positive Sequence ◽  
Intermediate Regime ◽  
Offspring Distribution ◽  
Condensation Phenomenon ◽  
Branching Property

Let τn be a random tree distributed as a Galton-Watson tree with geometric offspring distribution conditioned on {Zn = an} where Zn is the size of the nth generation and (an, n ∈ ℕ*) is a deterministic positive sequence. We study the local limit of these trees τn as n →∞ and observe three distinct regimes: if (an, n ∈ ℕ*) grows slowly, the limit consists in an infinite spine decorated with finite trees (which corresponds to the size-biased tree for critical or subcritical offspring distributions), in an intermediate regime, the limiting tree is composed of an infinite skeleton (that does not satisfy the branching property) still decorated with finite trees and, if the sequence (an, n ∈ ℕ*) increases rapidly, a condensation phenomenon appears and the root of the limiting tree has an infinite number of offspring.

Asymptotics of the Hurwitz Binomial Distribution Related to Mixed Poisson Galton–Watson Trees

2001 ◽  
Vol 10 (3) ◽  
pp. 203-211 ◽  
Author(s):  
JÜRGEN BENNIES ◽  
JIM PITMAN
Keyword(s):  
Probability Distribution ◽  
Asymptotic Behaviour ◽  
Binomial Distribution ◽  
Random Tree ◽  
Binomial Theorem ◽  
Offspring Distribution

Hurwitz's extension of Abel's binomial theorem defines a probability distribution on the set of integers from 0 to n. This is the distribution of the number of non-root vertices of a fringe subtree of a suitably defined random tree with n + 2 vertices. The asymptotic behaviour of this distribution is described in a limiting regime in which the fringe subtree converges in distribution to a Galton–Watson tree with a mixed Poisson offspring distribution.

What is the purpose of cognition?

2020 ◽  
Vol 43 ◽  
Author(s):  
Aba Szollosi ◽  
Ben R. Newell
Keyword(s):  
Infinite Number ◽  
Human Cognition ◽  
The Way

Abstract The purpose of human cognition depends on the problem people try to solve. Defining the purpose is difficult, because people seem capable of representing problems in an infinite number of ways. The way in which the function of cognition develops needs to be central to our theories.

The Problem of Alternative Monotheisms: Another Serious Challenge to Theism

2018 ◽  
Vol 10 (1) ◽  
pp. 31-51
Author(s):  
Raphael Lataster
Keyword(s):  
Infinite Number ◽  
Current Evidence ◽  
God Concept ◽  
Classical Theism ◽  
The World ◽  
Divine Transcendence ◽  
Hiddenness Of God

Theistic and analytic philosophers of religion typically privilege classical theism by ignoring or underestimating the great threat of alternative monotheisms.[1] In this article we discuss numerous god-models, such as those involving weak, stupid, evil, morally indifferent, and non-revelatory gods. We find that theistic philosophers have not successfully eliminated these and other possibilities, or argued for their relative improbability. In fact, based on current evidence – especially concerning the hiddenness of God and the gratuitous evils in the world – many of these hypotheses appear to be more probable than theism. Also considering the – arguably infinite – number of alternative monotheisms, the inescapable conclusion is that theism is a very improbable god-concept, even when it is assumed that one and only one transcendent god exists.[1] I take ‘theism’ to mean ‘classical theism’, which is but one of many possible monotheisms. Avoiding much of the discussion around classical theism, I wish to focus on the challenges in arguing for theism over monotheistic alternatives. I consider theism and alternative monotheisms as entailing the notion of divine transcendence.

Author response for "A PID SRF‐PLL based algorithm for positive‐sequence synchrophasor measurements"

2020 ◽  
Author(s):  
Gabriel U. Carvalho ◽  
Gustavo W. Denardin ◽  
Rafael Cardoso ◽  
Flavio L. Grando
Keyword(s):  
Author Response ◽  
Positive Sequence

On Ramsey Minimal Graphs

10.37236/1184 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Tomasz Łuczak
Keyword(s):  
Infinite Number ◽  
Probabilistic Argument ◽  
Minimal Graphs

An elementary probabilistic argument is presented which shows that for every forest $F$ other than a matching, and every graph $G$ containing a cycle, there exists an infinite number of graphs $J$ such that $J\to (F,G)$ but if we delete from $J$ any edge $e$ the graph $J-e$ obtained in this way does not have this property.

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