scholarly journals A Size-Perimeter Discrete Growth Model for Percolation Clusters

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Bendegúz Dezső Bak ◽  
Tamás Kalmár-Nagy
Keyword(s):  
Growth Model ◽  
Branching Process ◽  
Growth Models ◽  
Square Lattice ◽  
Cluster Growth ◽  
Invasion Percolation ◽  
Percolation Clusters ◽  
Proposed Model ◽  
Wide Range ◽  
The Mean

Cluster growth models are utilized for a wide range of scientific and engineering applications, including modeling epidemics and the dynamics of liquid propagation in porous media. Invasion percolation is a stochastic branching process in which a network of sites is getting occupied that leads to the formation of clusters (group of interconnected, occupied sites). The occupation of sites is governed by their resistance distribution; the invasion annexes the sites with the least resistance. An iterative cluster growth model is considered for computing the expected size and perimeter of the growing cluster. A necessary ingredient of the model is the description of the mean perimeter as the function of the cluster size. We propose such a relationship for the site square lattice. The proposed model exhibits (by design) the expected phase transition of percolation models, i.e., it diverges at the percolation threshold p c . We describe an application for the porosimetry percolation model. The calculations of the cluster growth model compare well with simulation results.

Processus de branchement en champ moyen et réaction PCR

2001 ◽  
Vol 33 (2) ◽  
pp. 391-403 ◽  
Author(s):  
Didier Piau
Keyword(s):  
Branching Process ◽  
Random Number ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Process Mean ◽  
Dna Mutations ◽  
Wide Range ◽  
The Mean ◽  
Efficiency Rate

Sun and Waterman model DNA mutations during the PCR reaction by a non-canonical branching process. Mean-field approximated values fit the simulated values surprisingly well. We prove this as a theoretical result, for a wide range of the parameters. Thus, we bound explicitly the biases, in law and in the mean, that the mean-field approximation induces in the random number of mutations of a DNA molecule, as a function of the initial number of molecules, of the number of PCR cycles, of the efficiency rate and of the mutation rate. The range where we prove that the approximation is good contains the observed mutation rates in many actual PCR reactions.

scholarly journals Alternative Strut and Tie Model for Reinforced Concrete Deep Beams

2018 ◽  
Vol 21 (1) ◽  
pp. 86
Author(s):  
Ahmed Faleh Al-Bayati
Keyword(s):  
Shear Strength ◽  
Reinforced Concrete ◽  
Test Results ◽  
Deep Beams ◽  
Strut And Tie ◽  
Codes Of Practice ◽  
Proposed Model ◽  
Wide Range ◽  
The Mean ◽  
Strut And Tie Model

This paper presents a simple strut and tie model to calculate the shear strength of reinforced concrete deep beams. The proposed model assumes that the shear strength is the algebraic sum of three strength components: concrete diagonal strut, vertical stirrups, and horizontal web reinforcements. The contribution of each strength components was calibrated with the test results of 305 deep beams compiled from previous studies with wide range of geometrical and material properties. The predictions of the proposed model were compared with those of the current codes of practice (ACI-318-14 and ASHTOO 2014) and those of existing model in the literature. Comparisons revealed that the proposed model provided better predictions than other models. The mean of predicted strength to test of the proposed model, the ACI-318-14 model, the ASHTOO 2014 model were 0.98, 0.79, and 0.75, respectively. The corresponding standard deviations were 0.17, 0.28, and 0.49, respectively.

Branching Process Modelling of COVID-19 Pandemic Including Immunity and Vaccination

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dimitar Atanasov ◽  
Vessela Stoimenova ◽  
Nikolay M. Yanev
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Data Availability ◽  
Model Parameters ◽  
Reproduction Rate ◽  
Direct Computation ◽  
Infection Dynamics ◽  
Secondary Infections ◽  
Proposed Model ◽  
The Mean

Abstract We propose modeling COVID-19 infection dynamics using a class of two-type branching processes. These models require only observations on daily statistics to estimate the average number of secondary infections caused by a host and to predict the mean number of the non-observed infected individuals. The development of the epidemic process depends on the reproduction rate as well as on additional facets as immigration, adaptive immunity, and vaccination. Usually, in the existing deterministic and stochastic models, the officially reported and publicly available data are not sufficient for estimating model parameters. An important advantage of the proposed model, in addition to its simplicity, is the possibility of direct computation of its parameters estimates from the daily available data. We illustrate the proposed model and the corresponding data analysis with data from Bulgaria, however they are not limited to Bulgaria and can be applied to other countries subject to data availability.

scholarly journals Fractional Growth Model Applied to COVID-19 Data

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1915
Author(s):  
Fernando Alcántara-López ◽  
Carlos Fuentes ◽  
Carlos Chávez ◽  
Fernando Brambila-Paz ◽  
Antonio Quevedo
Keyword(s):  
Fractional Derivative ◽  
Growth Model ◽  
Inflection Point ◽  
Growth Models ◽  
Coefficient Of Determination ◽  
Proposed Model ◽  
Inflection Points

Growth models have been widely used to describe behavior in different areas of knowledge; among them the Logistics and Gompertz models, classified as models with a fixed inflection point, have been widely studied and applied. In the present work, a model is proposed that contains these growth models as extreme cases; this model is generalized by including the Caputo-type fractional derivative of order 0<β≤1, resulting in a Fractional Growth Model which could be classified as a growth model with non-fixed inflection point. Moreover, the proposed model is generalized to include multiple sigmoidal behaviors and thereby multiple inflection points. The models developed are applied to describe cumulative confirmed cases of COVID-19 in Mexico, US and Russia, obtaining an excellent adjustment corroborated by a coefficient of determination R2>0.999.

scholarly journals On the Emergence of Islands in Complex Networks

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
J. Esquivel-Gómez ◽  
R. E. Balderas-Navarro ◽  
P. D. Arjona-Villicaña ◽  
P. Castillo-Castillo ◽  
O. Rico-Trejo ◽  
...  
Keyword(s):  
Complex Networks ◽  
Size Distribution ◽  
Growth Model ◽  
Power Law ◽  
Degree Distribution ◽  
Growth Models ◽  
Island Size ◽  
First Case ◽  
Proposed Model ◽  
Power Law Function

Most growth models for complex networks consider networks comprising a single connected block or island, which contains all the nodes in the network. However, it has been demonstrated that some large complex networks have more than one island, with an island size distribution (Is) obeying a power-law function Is~s-α. This paper introduces a growth model that considers the emergence of islands as the network grows. The proposed model addresses the following two features: (i) the probability that a new island is generated decreases as the network grows and (ii) new islands are created with a constant probability at any stage of the growth. In the first case, the model produces an island size distribution that decays as a power-law Is~s-α with a fixed exponent α=1 and in-degree distribution that decays as a power-law Qi~i-γ with γ=2. When the second case is considered, the model describes island size and in-degree distributions that decay as a power-law with 2<α<∞ and 2<γ<∞, respectively.

Greedy Network Growth Model of Social Network Service

2014 ◽  
Vol 18 (4) ◽  
pp. 590-597 ◽  
Author(s):  
Shohei Usui ◽  
◽  
Fujio Toriumi ◽  
Masato Matsuo ◽  
Takatsugu Hirayama ◽  
...  
Keyword(s):  
Social Network ◽  
Growth Model ◽  
Network Models ◽  
Network Services ◽  
Communication Tools ◽  
Network Growth ◽  
Social Network Service ◽  
Proposed Model ◽  
Wide Range ◽  
Target Network

As new network communication tools are developed, social network services (SNS) such as Facebook and Twitter are becoming part of a social phenomenon globally impacting on society. Many researchers are therefore studying the structure of relationship networks among users. We propose a greedy network growth model that appropriately increases nodes and links while automatically reproducing the target network. We handle a wide range of networks with high expressive ability. Results of experiments showed that we accurately reproduced 92.4% of 189 target networks from real services. The model also enabled us to reproduce 30 networks built up by existing network models. We thus show that the proposed model represents the expressiveness of many existing network models.

Characterization of the Growth of Corrosion Defects on Energy Pipelines Using Bayesian Dynamic Linear Model

2014 ◽  
Author(s):  
S. Zhang ◽  
W. Zhou ◽  
S. Kariyawasam ◽  
M. Al-Amin
Keyword(s):  
Linear Model ◽  
Growth Model ◽  
Growth Models ◽  
Model Parameters ◽  
Dynamic Linear Model ◽  
Average Growth ◽  
Imperfect Data ◽  
Natural Gas Pipeline ◽  
Proposed Model ◽  
Corrosion Defects

This paper describes the use of the second-order polynomial dynamic linear model (DLM) to characterize the growth of the depth of corrosion defects on energy pipelines using imperfect data obtained from multiple high-resolution in-line inspections (ILI). The growth model is formulated by incorporating the general form of the measurement error (including the biases and random scattering error) of the ILI tools as well as the correlations between the random scattering errors of different tools. The temporal variability of the corrosion growth is captured by allowing the average growth rate between two successive inspections to vary with time. The Markov Chain Monte Carlo simulation is employed to carry out the Bayesian updating of the growth model and evaluate the posterior distributions of the model parameters. An example involving real ILI data collected from an in-service natural gas pipeline is employed to illustrate and validate the growth model. The analysis results show that the defect depths predicted by the proposed model agree well with the actual depths and are more accurate than those predicted by the Gamma process-based growth models reported in the literature.

A Comparison of Physiological Demand between Self-Propelled and Motorized Treadmill Exercise

2018 ◽  
Vol 7 (4) ◽  
pp. 13-21
Author(s):  
Todd Backes ◽  
Charlene Takacs
Keyword(s):  
Respiratory Exchange Ratio ◽  
Treadmill Exercise ◽  
Cardiopulmonary Exercise Testing ◽  
Mean Value ◽  
The Self ◽  
Mixing Chamber ◽  
Wide Range ◽  
The Subject ◽  
The Mean ◽  
Computer Controlled

There are a wide range of options for individuals to choose from in order to engage in aerobic exercise; from outdoor running to computer controlled and self-propelled treadmills. Recently, self-propelled treadmills have increased in popularity and provide an alternative to a motorized treadmill. Twenty subjects (10 men, 10 women) ranging in age from 19-23 with a mean of 20.4 ± 0.8 SD were participants in this study. The subjects visited the laboratory on three occasions. The purpose of the first visit was to familiarize the subject with the self-propelled treadmill (Woodway Curve 3.0). The second visit, subjects were instructed to run on the self-propelled treadmill for 3km at a self-determined pace. Speed data were collected directly from the self-propelled treadmill. The third visit used speed data collected during the self-propelled treadmill run to create an identically paced 3km run for the subjects to perform on a motorized treadmill (COSMED T150). During both the second and third visit, oxygen consumption (VO2) and respiratory exchange ratio (R) data were collected with COSMED’s Quark cardiopulmonary exercise testing (CPET) metabolic mixing chamber system. The VO2 mean value for the self-propelled treadmill (44.90 ± 1.65 SE ml/kg/min) was significantly greater than the motorized treadmill (34.38 ± 1.39 SE ml/kg/min). The mean R value for the self-propelled treadmill (0.91 ± 0.01 SE) was significantly greater than the motorized treadmill (0.86 ± 0.01 SE). Our study demonstrated that a 3km run on a self-propelled treadmill does elicit a greater physiological response than a 3km run at on a standard motorized treadmill. Self-propelled treadmills provide a mode of exercise that offers increased training loads and should be considered as an alternative to motorized treadmills.

The way of value of Correlation of genomic DNA microsatellite loci and live weight of Chukchi reindeer

2020 ◽  
pp. 27-32
Author(s):  
V. Dodokhov ◽  
N. Pavlova ◽  
T. Rumyantseva ◽  
L. Kalashnikova
Keyword(s):  
Microsatellite Markers ◽  
Agricultural Production ◽  
Live Weight ◽  
Biodiversity Loss ◽  
Tribal Community ◽  
High Germination ◽  
Wide Range ◽  
The Mean ◽  
High Level ◽  
Dna Microsatellite

The article presents the genetic characteristic of the Chukchi reindeer breed. The object of the study was of the Chukchi reindeer. In recent years, the number of reindeer of the Chukchi breed has declined sharply. Reduced reindeer numbers could lead to biodiversity loss. The Chukchi breed of deer has good meat qualities, has high germination viability and is adapted in adverse tundra conditions of Yakutia. Herding of the Chukchi breed of deer in Yakutia are engaged only in the Nizhnekolymsky district. There are four generic communities and the largest of which is the agricultural production cooperative of nomadic tribal community «Turvaurgin», which was chosen to assess the genetic processes of breed using microsatellite markers: Rt6, BMS1788, Rt 30, Rt1, Rt9, FCB193, Rt7, BMS745, C 143, Rt24, OheQ, C217, C32, NVHRT16, T40, C276. It was found that microsatellite markers have a wide range of alleles and generally have a high informative value for identifying of genetic differences between animals and groups of animal. The number of identified alleles is one of the indicators of the genetic diversity of the population. The total number of detected alleles was 127. The Chukchi breed of deer is characterized by a high level of heterozygosity, and the random crossing system prevails over inbreeding in the population. On average, there were 7.9 alleles (Na) per locus, and the mean number of effective alleles (Ne) was 4.1. The index of fixation averaged 0.001. The polymorphism index (PIC) ranged from 0.217 to 0.946, with an average of 0.695.

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