scholarly journals Unification of aggregate growth models by emergence from cellular and intracellular mechanisms

2020 ◽  
Vol 7 (8) ◽  
pp. 192148
Author(s):  
T. J. Sego ◽  
James A. Glazier ◽  
Andres Tovar
Keyword(s):  
Growth Model ◽  
Growth Models ◽  
Classical Model ◽  
Aggregate Size ◽  
Mathematical Representation ◽  
Cell Type ◽  
Cellular Potts Model ◽  
Multicellular Aggregate ◽  
Classical Models ◽  
Aggregate Growth

Multicellular aggregate growth is regulated by nutrient availability and removal of metabolites, but the specifics of growth dynamics are dependent on cell type and environment. Classical models of growth are based on differential equations. While in some cases these classical models match experimental observations, they can only predict growth of a limited number of cell types and so can only be selectively applied. Currently, no classical model provides a general mathematical representation of growth for any cell type and environment. This discrepancy limits their range of applications, which a general modelling framework can enhance. In this work, a hybrid cellular Potts model is used to explain the discrepancy between classical models as emergent behaviours from the same mathematical system. Intracellular processes are described using probability distributions of local chemical conditions for proliferation and death and simulated. By fitting simulation results to a generalization of the classical models, their emergence is demonstrated. Parameter variations elucidate how aggregate growth may behave like one classical growth model or another. Three classical growth model fits were tested, and emergence of the Gompertz equation was demonstrated. Effects of shape changes are demonstrated, which are significant for final aggregate size and growth rate, and occur stochastically.

scholarly journals Incorporating Fuzzy Logic in Harrod’s Economic Growth Model

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2194
Author(s):  
Joan Carles Ferrer-Comalat ◽  
Salvador Linares-Mustarós ◽  
Ricard Rigall-Torrent
Keyword(s):  
Economic Growth ◽  
Fuzzy Logic ◽  
Growth Model ◽  
Growth Models ◽  
Classical Model ◽  
Economic Growth Model ◽  
Fuzzy Logic Theory ◽  
Endogenous Growth Models ◽  
Economic Growth Models ◽  
Equilibrium Growth

This paper suggests the possibility of incorporating the methodology of fuzzy logic theory into Harrod’s economic growth model, a classic model of economic dynamics for studying the growth of a developing economy based on the assumption that an economy with only savings and investment income is in equilibrium when savings are equal to investment. This model was the first precursor to exogenous growth models, which in turn gave rise to endogenous growth models. This article therefore represents a first step towards introducing fuzzy logic into economic growth models. The study concerned considers consumption and savings to depend on income by means of uncertain factors, and investment to depend on the variation of income through the accelerator factor, which we consider uncertain. These conditions are used to determine the equilibrium growth rate of income and investment, as well as the uncertain values for these variables in terms of fuzzy numbers. As a result, the new model is shown to expand the classical model by incorporating uncertainty into its variables.

scholarly journals Comparison of growth models to describe growth from birth to 6 years in a Beninese cohort of children with repeated measurements

BMJ Open ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. e035785
Author(s):  
Shukrullah Ahmadi ◽  
Florence Bodeau-Livinec ◽  
Roméo Zoumenou ◽  
André Garcia ◽  
David Courtin ◽  
...  
Keyword(s):  
Growth Model ◽  
Goodness Of Fit ◽  
Growth Models ◽  
Information Criterion ◽  
Height Growth ◽  
Sub Saharan Africa ◽  
Individual Growth ◽  
Secondary Outcome ◽  
Growth Trajectories ◽  
Best Fitting

ObjectiveTo select a growth model that best describes individual growth trajectories of children and to present some growth characteristics of this population.SettingsParticipants were selected from a prospective cohort conducted in three health centres (Allada, Sekou and Attogon) in a semirural region of Benin, sub-Saharan Africa.ParticipantsChildren aged 0 to 6 years were recruited in a cohort study with at least two valid height and weight measurements included (n=961).Primary and secondary outcome measuresThis study compared the goodness-of-fit of three structural growth models (Jenss-Bayley, Reed and a newly adapted version of the Gompertz growth model) on longitudinal weight and height growth data of boys and girls. The goodness-of-fit of the models was assessed using residual distribution over age and compared with the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The best-fitting model allowed estimating mean weight and height growth trajectories, individual growth and growth velocities. Underweight, stunting and wasting were also estimated at age 6 years.ResultsThe three models were able to fit well both weight and height data. The Jenss-Bayley model presented the best fit for weight and height, both in boys and girls. Mean height growth trajectories were identical in shape and direction for boys and girls while the mean weight growth curve of girls fell slightly below the curve of boys after neonatal life. Finally, 35%, 27.7% and 8% of boys; and 34%, 38.4% and 4% of girls were estimated to be underweight, wasted and stunted at age 6 years, respectively.ConclusionThe growth parameters of the best-fitting Jenss-Bayley model can be used to describe growth trajectories and study their determinants.

scholarly journals A Novel Approach to Modelling Stand-Level Growth of an Even-Aged Forest Using a Volume Productivity Index with Application to New Zealand-Grown Coast Redwood

Forests ◽  
2021 ◽  
Vol 12 (9) ◽  
pp. 1155 ◽  
Author(s):  
Mark O. Kimberley ◽  
Michael S. Watt
Keyword(s):  
New Zealand ◽  
Growth Model ◽  
Growth Models ◽  
Stand Density ◽  
Site Index ◽  
Growth And Yield ◽  
Productivity Index ◽  
Site Quality ◽  
Spatial And Temporal Variation ◽  
Coast Redwood

Empirical growth models are widely used to predict the growth and yield of plantation tree species, and the precise estimation of site quality is an important component of these models. The most commonly used proxy for site quality in growth models is Site Index (SI), which describes the mean height of dominant trees at a specified base age. Although SI is widely used, considerable research shows significant site-dependent variation in height for a given volume, with this latter variable more closely reflecting actual site productivity. Using a national dataset, this study develops and describes a stand-level growth and yield model for even-aged New Zealand-grown coast redwood (Sequoia sempervirens). We used a novel modelling approach that quantifies site quality using SI and a volume-based index termed the 300 Index, defined as the volume mean annual increment at age 30 years for a reference regime of 300 stems ha−1. The growth model includes a number of interrelated components. Mean top height is modelled from age and SI using a polymorphic Korf function. A modified anamorphic Korf function is used to describe tree quadratic mean diameter (Dq) as a function of age, stand density, SI and a diameter site index. As the Dq model includes stand density in its formulation, it can predict tree growth for different stand densities and thinning regimes. The mortality model is based on a simple attritional equation improved through incorporation of the Reineke stand density index to account for competition-induced mortality. Using these components, the model precisely estimates stand-level volume. The developed model will be of considerable value to growers for yield projection and regime evaluation. By more robustly describing the site effect, the growth model provides researchers with an improved framework for quantifying and understanding the causes of spatial and temporal variation in plantation productivity.

scholarly journals On the use of growth models for forecasting epidemic outbreaks with application to COVID-19 data

2020 ◽  
Author(s):  
Chenangnon F. TOVISSODE ◽  
Bruno E. LOKONON ◽  
Romain GLELE KAKAÏ
Keyword(s):  
Growth Model ◽  
Growth Models ◽  
Exponential Model ◽  
Limited Data ◽  
Model Framework ◽  
Phase Dynamics ◽  
Epidemic Dynamics ◽  
Isolation Measure ◽  
Containment Measures ◽  
Model Curve

The initial phase dynamics of an epidemic without containment measures is commonly well modeled using exponential growth models. However, in the presence of containment measures, the exponential model becomes less appropriate. Under the implementation of an isolation measure for detected infectives, we propose to model epidemic dynamics by fitting a flexible growth model curve to reported positive cases and to infer the overall epidemic dynamics by introducing information on the detection/testing effort and recovery and death rates. The resulting modeling approach is close to the SIQR (Susceptible- Infectious-Quarantined-Recovered) model framework. We focused on predicting the peaks (time and size) in positive cases, actives cases and new infections. We applied the approach to data from the COVID-19 outbreak in Italy. Fits on limited data before the observed peaks illustrate the ability of the flexible growth model to approach the estimates from the whole data.

The moment ratios of particle size distributions in some simple growth models

1980 ◽  
Vol 17 (4) ◽  
pp. 956-967 ◽  
Author(s):  
H. L. MacGillivray
Keyword(s):  
Particle Size ◽  
Size Distribution ◽  
Growth Model ◽  
Hazard Rate ◽  
Growth Models ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Initial Size ◽  
The Moment ◽  
Simple Growth

Important parameters of particle size distributions in dispersed systems in engineering and related fields are ratios of moments and inverse powers of these ratios, known as mean sizes. The variation in these parameters is examined for the simplest growth model in which the size distribution is translated, and the results for this process considered in relation to the problems of models of other growth processes. For initial size distributions with monotone hazard rate, the results are particularly significant, and the properties of the normalised moments of other distributions are also considered.

scholarly journals Real exchange rate and structural change in a Kaldorian balance of payments constrained growth model

2018 ◽  
Vol 38 (1) ◽  
pp. 48-69
Author(s):  
BERNARDO MATTOS SANTANA ◽  
JOSÉ LUIS OREIRO
Keyword(s):  
Exchange Rate ◽  
Structural Change ◽  
Real Exchange Rate ◽  
Growth Model ◽  
Manufacturing Industry ◽  
Growth Models ◽  
Dynamic Properties ◽  
Output Growth ◽  
Balance Of Payments ◽  
Over Time

ABSTRACT The objective of the present article is to develop a Kaldorian Growth model that (i) had a balance of payments constraint, in order to eliminate the inconsistency of balance of payments growth models; and (ii) defines a precise mechanism by which the level of real exchange rate can affect long-term growth. An important innovation introduced in the model is the idea that Kaldor-Verdoorn coefficient - that measures the sensibility of growth rate of labor productivity to output growth - depends on the share of manufacturing output on GDP. This hypothesis allowed us to introduce the possibility of structural change, defined as a dynamic process by which the share of manufacturing industry on real output could change over time. In this case, it will be possible to analyze the dynamic properties of the model either in the case where productive structure is kept constant (case with no structural change), as in the case where it evolves over time as a result of some economic process (case with structural change).

scholarly journals Incorporating temporal heterogeneity in environmental conditions into a somatic growth model

2017 ◽  
Vol 74 (3) ◽  
pp. 316-326 ◽  
Author(s):  
M.C. Dzul ◽  
C.B. Yackulic ◽  
J. Korman ◽  
M.D. Yard ◽  
J.D. Muehlbauer
Keyword(s):  
Food Availability ◽  
Growth Model ◽  
Environmental Conditions ◽  
Colorado River ◽  
Growth Models ◽  
Somatic Growth ◽  
Environmental Data ◽  
Fish Growth ◽  
Positive Temperature ◽  
Environmental Controls

Evaluating environmental effects on fish growth can be challenging because environmental conditions may vary at relatively fine temporal scales compared with sampling occasions. Here we develop a Bayesian state-space growth model to evaluate effects of monthly environmental data on growth of fish that are observed less frequently (e.g., from mark–recapture data where time between captures can range from months to years). We assess effects of temperature, turbidity, food availability, flow variability, and trout abundance on subadult humpback chub (Gila cypha) growth in two rivers, the Colorado River (CR) and the Little Colorado River (LCR), and we use out-of-sample prediction to rank competing models. Environmental covariates explained a high proportion of the variation in growth in both rivers; however, the best growth models were river-specific and included either positive temperature and turbidity duration effects (CR) or positive temperature and food availability effects (LCR). Our approach to analyzing environmental controls on growth should be applicable in other systems where environmental data vary over relatively short time scales compared with animal observations.

Aggregate size distributions in migration driven growth models

2003 ◽  
Vol 36 (3) ◽  
pp. 423-428 ◽  
Author(s):  
Jianhong Ke ◽  
Zhenquan Lin ◽  
Youyi Zhuang
Keyword(s):  
Growth Models ◽  
Aggregate Size ◽  
Size Distributions

Statistical modeling of baleen and body length at age in bowhead whales (Balaena mysticetus)

2012 ◽  
Vol 90 (8) ◽  
pp. 915-931 ◽  
Author(s):  
S.C. Lubetkin ◽  
J.E. Zeh ◽  
J.C. George
Keyword(s):  
Body Length ◽  
Growth Model ◽  
Growth Models ◽  
Information Criterion ◽  
Single Stage ◽  
Von Bertalanffy ◽  
Balaena Mysticetus ◽  
Bowhead Whales ◽  
Multi Stage ◽  
Age Estimates

We used baleen lengths and age estimates from 175 whales and body lengths and age estimates from 205 whales to test which of several single- and multi-stage growth models best characterized age-specific baleen and body lengths for bowhead whales ( Balaena mysticetus L., 1758) with the goal of determining which would be best for predicting whale age based on baleen or body length. Previous age estimates were compiled from several techniques, each of which is valid over a relatively limited set of physical characteristics. The best fitting single-stage growth model was a variation of the von Bertalanffy growth model for both baleen and body length data. Based on Bayesian information criterion, the two- and three-stage versions of the von Bertalanffy model fit the data better than did the single-stage models for both baleen and body length. The best baleen length models can be used to estimate expected ages for bowhead whales with up to 300–325 cm baleen, depending on sex, which correspond to age estimates approaching 60 years. The best body length models can be used to estimate expected ages for male bowhead whales up to 14 m, and female bowheads up to 15.5 m or ages up to approximately 40 years.

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