scholarly journals Asymptotic shape in a continuum growth model

2003 ◽  
Vol 35 (02) ◽  
pp. 303-318 ◽  
Author(s):  
Maria Deijfen
Keyword(s):  
Growth Model ◽  
Expected Value ◽  
The State ◽  
Rotational Invariance ◽  
Euclidean Ball ◽  
Bounded Support ◽  
Asymptotic Shape

A continuum growth model is introduced. The state at time t, S t , is a subset of ℝ d and consists of a connected union of randomly sized Euclidean balls, which emerge from outbursts at their centre points. An outburst occurs somewhere in S t after an exponentially distributed time with expected value |S t |-1 and the location of the outburst is uniformly distributed over S t . The main result is that, if the distribution of the radii of the outburst balls has bounded support, then S t grows linearly and S t /t has a nonrandom shape as t → ∞. Due to rotational invariance the asymptotic shape must be a Euclidean ball.

scholarly journals Asymptotic shape in a continuum growth model

2003 ◽  
Vol 35 (2) ◽  
pp. 303-318 ◽  
Author(s):  
Maria Deijfen
Keyword(s):  
Growth Model ◽  
Expected Value ◽  
The State ◽  
Rotational Invariance ◽  
Euclidean Ball ◽  
Bounded Support ◽  
Asymptotic Shape

A continuum growth model is introduced. The state at time t, St, is a subset of ℝd and consists of a connected union of randomly sized Euclidean balls, which emerge from outbursts at their centre points. An outburst occurs somewhere in St after an exponentially distributed time with expected value |St|-1 and the location of the outburst is uniformly distributed over St. The main result is that, if the distribution of the radii of the outburst balls has bounded support, then St grows linearly and St/t has a nonrandom shape as t → ∞. Due to rotational invariance the asymptotic shape must be a Euclidean ball.

scholarly journals Modeling on population growth and its adaptation: A comparative analysis between Bangladesh and India

2020 ◽  
Vol 12 (4) ◽  
pp. 688-701
Author(s):  
A.N.M. Rezaul Karim ◽  
Mohammed Nizam Uddin ◽  
Masud Rana ◽  
Mayeen Uddin Khandaker ◽  
M. R. I. Faruque ◽  
...  
Keyword(s):  
Population Growth ◽  
Growth Model ◽  
21St Century ◽  
Least Square Method ◽  
Exponential Model ◽  
The State ◽  
Least Square ◽  
Logistic Growth ◽  
Projection Data ◽  
Logistic Growth Model

The biggest challenge in the world is population growth and determining how society and the state adapt to it as it directly affects the fundamental human rights such as food, clothing, housing, education, medical care, etc. The population estimates of any country play an important role in making the right decision about socio-economic and population development projects. Unpredictable population growth can be a curse. The purpose of this research article is to compare the accuracy process and proximity of three mathematical model such as Malthusian or exponential growth model, Logistic growth model and Least Square model to make predictions about the population growth of Bangladesh and India at the end of 21st century. Based on the results, it has been observed that the population is expected to be 429.32(in million) in Bangladesh and 3768.53 (in million) in India by exponential model, 211.70(in million) in Bangladesh and 1712.94(in million) in India by logistic model and 309.28 (in million) in Bangladesh and 2686.30 (in million) in India by least square method at the end of 2100. It was found that the projection data from 2000 to 2020 using the Logistic Growth Model was very close to the actual data. From that point of view, it can be predicted that the population will be 212 million in Bangladesh and 1713 million in India at the end of the 21st century. Although transgender people are recognized as the third sex but their accurate statistics data is not available. The work also provides a comparative scenario of how the state has adapted to the growing population in the past and how they will adapt in the future.

On the Williams-Bjerknes tumour growth model: II

1980 ◽  
Vol 88 (2) ◽  
pp. 339-357 ◽  
Author(s):  
Maury Bramson ◽  
David Griffeath
Keyword(s):  
Growth Model ◽  
Tumour Growth ◽  
Interacting Particle Systems ◽  
Dual Processes ◽  
Planar Lattice ◽  
Cellular Division ◽  
Asymptotic Shape ◽  
Regularity Properties ◽  
Abnormal Cells ◽  
Tumour Growth Model

AbstractWilliams and Bjerknes introduced in 1972 a stochastic model for the spread of cancer cells. Cells, normal and abnormal (cancerous), are situated on a planar lattice. With each cellular division, one daughter cell stays put, while the other usurps the position of a neighbour; abnormal cells reproduce at a faster rate than normal cells. We are interested in the long-term behaviour of this system. We showed in ‘On the Williams-Bjerknes Tumour Growth Model I’ (1) that, provided it lives forever, the tumour will eventually contain a ball of linearly expanding radius. Here it is shown that the rate of expansion is actually linear, and that the region of infection has an asymptotic shape which is given by some (unknown) norm. To demonstrate that the tumour contains a ball of linearly expanding radius, we applied in (1) certain techniques common to the field of interacting particle systems; in particular we made use of certain auxiliary Markov chains which are imbedded in the dual processes of our model. Here different techniques are applied. We show that the first infection times of different sites are almost subadditive, and we exhibit various regularity properties of the infection times such as bounds on their moments. These properties of the Williams-Bjerknes process allow one to follow the outline prescribed by Richardson in (7), where he showed that such a process does indeed exhibit a linear growth whose shape is prescribed by a norm.

The transformation of the state extensive growth model in Cuba's sugarcane agriculture

1996 ◽  
Vol 13 (1) ◽  
pp. 59-68
Author(s):  
L�zaro Pe�a Castellanos ◽  
Jose Alvarez
Keyword(s):  
Growth Model ◽  
The State ◽  
Extensive Growth

Introduction

2021 ◽  
pp. 1-22
Author(s):  
Jack Copley
Keyword(s):  
Growth Model ◽  
Ad Hoc ◽  
Financial Liberalization ◽  
Economic Restructuring ◽  
The State ◽  
The World ◽  
State Archives ◽  
The City ◽  
Political Backlash

This chapter introduces the concept of financialization, surveys the scholarly literature on this topic, and makes the case for this book’s novel contribution to these debates. It is widely recognized that the world economy has become financialized, yet the role of states in furthering this process has been underexamined. While many accounts point out that states were crucial in propelling financialization through policies of financial liberalization, these accounts tend to argue that the state did so either due to the lobbying power of financial elites and the influence of neoliberal norms or because policymakers were seeking to construct an alternative growth model based on financial accumulation. These two accounts of the role of states in spurring financialization—which can be termed interest-based and ideational explanations and functionalist explanations—fail to capture the reactive and ad hoc nature of the policymaking that resulted in financial liberalization. In the case of Britain, the agenda of financial liberalization in the 1970s and 1980s that propelled the City of London’s ascent was not chiefly driven by lobbying or ideology, nor was it intended to inaugurate a financialized growth model. Instead, by analysing declassified state archives, this book shows that policymakers pursued such policies as short-term measures to navigate through the stagflation crisis of that era. Financial liberalization was deployed in a messy fashion, either to postpone the worst effects of the crisis so as to maintain governing legitimacy, or to enact painful economic restructuring in a manner that shielded the state from political backlash.

scholarly journals Slot Machine Payback Percentages: The Devil is in the Moment

2014 ◽  
Vol 8 (2) ◽  
pp. 55-71
Author(s):  
Robert Scott Farrow ◽  
Jackson Costa
Keyword(s):  
Slot Machine ◽  
Expected Value ◽  
The State ◽  
Slot Machines ◽  
Significant Shift ◽  
The Moment ◽  
The Devil ◽  
Payback Percentage

The average payback percentage from slot machines is important to gamblers, casinos and governments.  While apparently simple to define several complications can exist, among them which measure to average and potentially misleading formulas to calculate the average.  Daily slot machine data from the state of Maryland for 19 months are analyzed for the expected value of the average payback ratio per machine and per dollar gambled.  On a per dollar gambled basis, the payback percentage meets legislative requirements that the gaming floor payback be at least 90 percent. On a per machine basis, that requirement is not met which can imply a significant shift of money from gamblers to casino operators and the state. Other payback measures are hypothesized to also be less than the per-dollar gambled measure but data are lacking.

scholarly journals A Bayesian Logistic Growth Model for the Spread of COVID-19 in New York

2020 ◽  
Author(s):  
Svetoslav Bliznashki
Keyword(s):  
New York ◽  
Bayesian Estimation ◽  
Growth Model ◽  
The State ◽  
The Other ◽  
Logistic Growth ◽  
Short Term ◽  
Normal Error ◽  
Data Points ◽  
Logistic Growth Model

AbstractWe use Bayesian Estimation for the logistic growth model in order to estimate the spread of the coronavirus epidemic in the state of New York. Models weighting all data points equally as well as models with normal error structure prove inadequate to model the process accurately. On the other hand, a model with larger weights for more recent data points and with t-distributed errors seems reasonably capable of making at least short term predictions.

Validated ageing methods for blue warehou (Seriolella brama) and white warehou (S. caerulea) in New Zealand waters

2001 ◽  
Vol 52 (3) ◽  
pp. 297 ◽  
Author(s):  
P. L. Horn
Keyword(s):  
New Zealand ◽  
Growth Model ◽  
The State ◽  
Von Bertalanffy ◽  
Ageing Methods

Blue warehou (Seriolella brama) and white warehou (Seriolella caerulea) (Stromateoidei : Centrolophidae) from New Zealand waters were aged from counts of zones in cross-sectioned otoliths, a technique that was validated for both species by examining the state of otolith margins from fish sampled regularly throughout the year. Von Bertalanffy parameters were calculated for blue warehou on the Stewart-Snares shelf. The fish grew rapidly up to the time of first spawning (~4 –5 years) , but growth was negligible after ~10 –12 years. A maximum age of 22 years was recorded. Von Bertalanffy parameters were calculated for white warehou from the Chatham Rise and the Campbell Plateau;there were no significant differences in growth between areas. The fish grew rapidly up to the time of first spawning (~3 –4 years) , but growth was negligible after ~6 –8 years. A maximum age of 21 years was recorded. Females of both species grow significantly faster than males. A revised growth model for silver warehou (Seriolella punctata) is also presented.

Modelling counts with state-dependent zero inflation

2018 ◽  
Vol 20 (2) ◽  
pp. 127-147 ◽  
Author(s):  
Tobias A MÖller ◽  
Christian H Weiß ◽  
Hee-Young Kim
Keyword(s):  
Time Series ◽  
The State ◽  
Zero Inflation ◽  
Count Time Series ◽  
Flexible Approach ◽  
Bounded Support ◽  
Excessive Demand ◽  
Parent Distribution ◽  
State Dependent ◽  
Stochastic Properties

We introduce a state-dependent zero-inflation mechanism for count distributions with unbounded or bounded support. Instead of uniformly downweighting the parent distribution, this flexible approach allows us to generate most of the zeros from either low or high counts. We derive the stochastic properties of the inflated distributions and discuss special instances designed for zero inflation caused by, for example, excessive demand or underreporting. Furthermore, we apply the state-dependent zero-inflation mechanism to generalize existing models for count time series with bounded support.

Sign in / Sign up

Export Citation Format

Share Document