scholarly journals Combinatorial Analysis of Growth Models for Series-Parallel Networks

2018 ◽  
Vol 28 (4) ◽  
pp. 574-599
Author(s):  
MARKUS KUBA ◽  
ALOIS PANHOLZER
Keyword(s):  
Stochastic Models ◽  
Growth Process ◽  
Growth Models ◽  
Expected Number ◽  
Asymptotic Results ◽  
Tree Structures ◽  
Analytic Combinatorics ◽  
Source To Sink ◽  
Parallel Networks ◽  
Stochastic Growth Models

We give combinatorial descriptions of two stochastic growth models for series-parallel networks introduced by Hosam Mahmoud by encoding the growth process via recursive tree structures. Using decompositions of the tree structures and applying analytic combinatorics methods allows a study of quantities in the corresponding series-parallel networks. For both models we obtain limiting distribution results for the degree of the poles and the length of a random source-to-sink path, and furthermore we get asymptotic results for the expected number of source-to-sink paths. Moreover, we introduce generalizations of these stochastic models by encoding the growth process of the networks via further important increasing tree structures.

scholarly journals Realized Multi-Power Variation Process for Jump Detection in the Nigerian All Share Index

2021 ◽  
Vol 52 (3) ◽  
pp. 397-412
Author(s):  
Mabel Adeosun ◽  
Olabisi Ugbebor
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Models ◽  
Asymptotic Properties ◽  
Higher Order ◽  
Asymptotic Results ◽  
Jump Detection ◽  
Limit Distributions ◽  
Price Process ◽  
Variation Process ◽  
Asymptotic Variances

In this paper, we studied the particular cases of higher-order realized multipower variation process, their asymptotic properties comprising the probability limits and limit distributions were highlighted. The respective asymptotic variances of the limit distributions were obtained and jump detection models were developed from the asymptotic results. The models were obtained from the particular cases of the higher-order of the realized multipower variation process, in a class of continuous stochastic volatility semimartingale process. These are extensions of the method of jump detection by Barndorff-Nielsen and Shephard (2006), for large discrete data. An Empirical Application of the models to the Nigerian All Share Index (NASI) data shows that the models are robust to jumps and suggest that stochastic models with added jump components will give a better representation of the NASI price process.

Random Regular Expression Over Huge Alphabets

2021 ◽  
pp. 1-20
Author(s):  
Cyril Nicaud ◽  
Pablo Rotondo
Keyword(s):  
Regular Expression ◽  
Empty Word ◽  
Regular Expressions ◽  
Expected Number ◽  
Analytic Combinatorics ◽  
Transfer Theorem ◽  
Leading Term

In this article, we study some properties of random regular expressions of size [Formula: see text], when the cardinality of the alphabet also depends on [Formula: see text]. For this, we revisit and improve the classical Transfer Theorem from the field of analytic combinatorics. This provides precise estimations for the number of regular expressions, the probability of recognizing the empty word and the expected number of Kleene stars in a random expression. For all these statistics, we show that there is a threshold when the size of the alphabet approaches [Formula: see text], at which point the leading term in the asymptotics starts oscillating.

Analysing crack growth

1998 ◽  
Vol 212 (3) ◽  
pp. 157-166 ◽  
Author(s):  
M Newby
Keyword(s):  
Bayesian Analysis ◽  
Crack Length ◽  
Crack Growth ◽  
Failure Time ◽  
Growth Models ◽  
Accelerated Failure Time ◽  
Deterministic Models ◽  
Stochastic Growth Models ◽  
Standard Linear ◽  
Fully Bayesian

Deterministic models of crack growth can be fitted to experimental data. This paper shows that stochastic growth models are easy to use and provides a simple framework for data analysis. A simple transformation allows the standard linear regression model to be used and opens the way for a fully Bayesian analysis. The Bayesian analysis allows the incorporation of prior information and coherent predictions of crack length to be made. The parameters of the Paris-Erdogan model are readily evaluated directly from crack length data without the need for intermediate estimates of the crack growth rate. The approach lends itself to the analysis of properly designed experiments to determine the effect of environmental factors on the parameters of the Paris-Erdogan equation through the medium of accelerated failure time models. The paper also emphasizes the need for adequate communication between experimenter and statistician to ensure efficient experimental designs.

scholarly journals In-situ HRTEM observations of growth process of decagonal quasicrystals

2014 ◽  
Vol 70 (a1) ◽  
pp. C97-C97
Author(s):  
Keisuke Nagao ◽  
Kazue Nishimoto ◽  
Tomoaki Inuduka ◽  
Keiichi Edagawa
Keyword(s):  
Growth Mechanism ◽  
Growth Process ◽  
Structural Information ◽  
Growth Models ◽  
Experimental Studies ◽  
Unit Cell ◽  
Small Scale ◽  
Growth Processes ◽  
Decagonal Quasicrystals

Quasicrystals possess quasiperiodicity, where the structure cannot be described simply by the repetition of unit cell like conventional crystals. This fact raises the question of how quasicrystals grow, i.e., what physical mechanism makes the growth of quasicrystals possible. While crystals can grow by copying a unit cell via local atomic interactions, nonlocal structural information seems to be required in the growth of quasicrystals. This problem has attracted much attention ever since the first discovery of a quasicrystal in 1984, and several theoretical growth models [1] have been proposed. However, no experimental studies have so far been reported, and it is still unclear whether these theoretical growth models apply to real quasicrystals. In the present study, we have conducted in-situ high-temperature electron microscopic (HRTEM: High-Resolution Transmission Electron Microscopy) observations of the growth process of decagonal quasicrystals to elucidate the growth mechanism. The growth processes of a decagonal quasicrystal of Al70.8Ni19.7Co9.5were observed by HRTEM in the temperature range 1073-1173K. Tiling patterns with edge length of about 2nm were constructed from a series of HRTEM images. They were analysed in the framework of the projection method. Here, we followed the procedures in our previous work [2]. We have already reported the results of some observations and analyses elsewhere [3]. However, the growth processes of them were on a small scale, and the results were indefinite. Recently, we have succeeded in observing a growth process on a massive scale. In this paper, we present the results of this observation and subsequent analyses, and discuss the growth mechanism of the quasicrystal.

Limit theorems for stochastic growth models. I

1972 ◽  
Vol 4 (02) ◽  
pp. 193-232 ◽  
Author(s):  
Harry Kesten
Keyword(s):  
Fixed Point ◽  
Limit Theorem ◽  
Limit Theorems ◽  
Growth Models ◽  
Branching Processes ◽  
Random Variable ◽  
Present Situation ◽  
Stochastic Growth ◽  
Stochastic Growth Models ◽  
Zygotic Selection

We consider d-dimensional stochastic processes which take values in (R+) d . These processes generalize Galton-Watson branching processes, but the main assumption of branching processes, independence between particles, is dropped. Instead, we assume for some Here τ: (R+) d → R+, |x| = Σ1 d |x(i)| A = {x ∈ (R+) d : |x| = 1} and T: A → A. Under various assumptions on the maps τ and T it is shown that with probability one there exists a ρ > 1, a fixed point p ∈ A of T and a random variable w such that lim n→∞ Z n ρ−n = wp. This result is a generalization of the main limit theorem for super-critical branching processes; note, however, that in the present situation both p and ρ are random as well. The results are applied to a population genetical model for zygotic selection without mutation at one locus.

Limit theorems for stochastic growth models. II

1972 ◽  
Vol 4 (3) ◽  
pp. 393-428 ◽  
Author(s):  
Harry Kesten
Keyword(s):  
Limit Theorems ◽  
Growth Models ◽  
Branching Processes ◽  
Random Variable ◽  
Present Situation ◽  
Stochastic Growth ◽  
Stochastic Growth Models ◽  
Zygotic Selection ◽  
Image Position ◽  
Supercritical Branching Processes

We consider d-dimensional stochastic processes which take values in (R+)d These processes generalize Galton-Watson branching processes, but the main assumption of branching processes, independence between particles, is dropped. Instead, we assume for some Here τ:(R+)d→R +, |x| = σ1d |x(i)|, A {x ∈(R+)d: |x| 1} and T: A→A. Under various assumptions on the maps τ and T it is shown that with probability one there exists a ρ > 1, a fixed point p ∈ A of T and a random variable w such that limn→∞Zn|ρnwp. This result is a generalization of the main limit theorem for supercritical branching processes; note, however, that in the present situation both ρ and ρ are random as well. The results are applied to a population genetical model for zygotic selection without mutation at one locus.

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