General Growth Model Research Articles

Test of the accuracy of an age-height model for saguaro (Carnegiea gigantea)

A test of a general growth-model to estimate the age of Carnegiea gigantea, a keystone species of the Sonoran Desert, was conducted. Results suggest that standard errors are low (<2 years) and the model is robust for estimating age of establishment of the long-lived saguaro cactus.

Endogenous growth and intellectual property rights: A north–south modeling proposal

In this paper, we develop a general equilibrium endogenous growth model that emphasizes the IPR enforcement effects on growth, in a scenario of north–south technological knowledge diffusion. The economy consists of three sectors, and firms are engaged in step-by-step innovation. In line with the literature, we introduce an IPR parameter that makes imitation more difficult. We find that, in steady state, the increases in IPR protection result in decreases in the growth rate. This result is in line with the literature, which argues that the enforcement of IPR does not always have a positive effect on economic growth. To sum up, we present some suggestions for future research which can help to clarify the relationship between IPR and endogenous growth.

An archetypal mechanism for branching organogenesis

Branched structures are ubiquitous in nature, both in living and non-living systems. While the functional benefits of branching organogenesis are straightforward, the developmental mechanisms leading to the repeated branching of epithelia in surrounding mesoderm remain unclear. Both molecular and physical aspects of growth control seem to play a critical role in shape emergence and maintenance. On the molecular side, the existence of a gradient of growth-promoting ligand between epithelial tips and distal mesenchyme seems to be common to branched organs. On the physical side, the branching process seems to require a mechanism of real-time adaptation to local geometry, as suggested by the self-avoiding nature of branching events. In this paper, we investigate the outcomes of a general three-dimensional growth model, in which epithelial growth is implemented as a function of ligand income, while the mesenchyme is considered as a proliferating viscous medium. Our results suggest that the existence of a gradient of growth-promoting ligand between distal and proximal mesenchyme implies a growth instability of the epithelial sheet, resulting in spontaneous self-avoiding branching morphogenesis. While the general nature of the model prevents one from fitting the development of specific organs, it suggests that few ingredients are actually required to achieve branching organogenesis.

Structural transformation and the oil price

What part of the high oil price can be explained by structural transformation in the developing world? Will continued structural transformation in these countries result in a permanently higher oil price? To address these issues I identify an inverted-U shaped relationship in the data between aggregate oil intensity and the extent of structural transformation: countries in the middle stages of transition spend the highest fraction of their income on oil. I construct and calibrate a multi-sector, multi-country, general equilibrium growth model that accounts for this fact by generating an endogenously falling aggregate elasticity of substitution between oil and non-oil inputs. The model is used to measure and isolate the impact of changing sectoral composition in the developing world on global oil demand and the oil price in the OECD. I find that structural transformation in non-OECD countries accounts for up to 53% of the oil price increase in the OECD between 1970 and 2010. However, the impact of structural transformation is temporary. Continued structural transformation induces falling oil intensity and an easing of the upward pressure on the oil price. Since a standard one-sector growth model misses this non-linearity, to understand the impact of growth on the oil price, it is necessary to take a more disaggregated view than is standard in macroeconomics.

On a multiphase multicomponent model of biofilm growth.

Biofilms are formed when free-floating bacteria attach to a surface and secrete polysaccharide to form an extracellular polymeric matrix (EPS). A general model of biofilm growth needs to include the bacteria, the EPS, and the solvent within the biofilm region Ω(t), and the solvent in the surrounding region D(t). The interface between the two regions, Γ(t), is a free boundary. In this paper, we consider a mathematical model, which consists of a Stokes equation for the EPS with bacteria attached to it, and a Stokes equation for the solvent in Ω(t) and a different one for the solvent in D(t). The volume fraction of the EPS is another unknown satisfying a reaction-diffusion equation. The entire system is coupled nonlinearly within Ω(t), and across the free surface Γ(t). We prove the existence and uniqueness of solution, with a smooth surface Γ(t), for a small time interval.

General model for diffusive growth of nanostructures

General model for diffusive growth of nanostructures

Dynamical aspects of Information Production Processes

In this paper and talk we present a short proof of a theorem of Naranan stating that if sources grow exponentially and if items in sources also grow exponentially, then the system is Lotkaian, i.e. its size-frequency function is the law of Lotka. We apply this technique to the case of power law growth of sources and of items in sources and determine the size- and rank frequency functions in this case. These functions have a greater variety of shapes than in the classical Naranan case and we give practical examples. We also show that, in this context, the law of Heaps can be proved. We also further generalise this technique to general growth models of sources and items in sources.

A new method to estimate parameters of the growth model for metastatic tumours

PurposeKnowledge of natural tumour growth is valuable for understanding tumour biology, optimising screening programs, prognostication, optimal scheduling of chemotherapy, and assessing tumour spread. However, mathematical modelling in individuals is hampered by the limited data available. We aimed to develop a method to estimate parameters of the growth model and formation rate of metastases in individual patients.Materials and methodsData from one patient with liver metastases from a primary ileum carcinoid and one patient with lung metastases from a primary renal cell carcinoma were used to demonstrate this new method. Metastatic growth models were estimated by direct curve fitting, as well as with the new proposed method based on the relationship between tumour growth rate and tumour volume. The new model was derived from the Gompertzian growth model by eliminating the time factor (age of metastases), which made it possible to perform the calculations using data from all metastases in each patient. Finally, the formation time of each metastasis and, consecutively, the formation rate of metastases in each patient were estimated.ResultsWith limited measurements in clinical studies, fitting different growth curves was insufficient to estimate true tumour growth, even if patients were followed for several years. Growth of liver metastases was well described with a general growth model for all metastases. However, the lung metastases from renal cell carcinoma were better described by heterogeneous exponential growth with various growth rates.ConclusionAnalysis of the regression of tumour growth rate with the logarithm of tumour volume can be used to estimate parameters of the tumour growth model and metastasis formation rates, and therefore the number and size distribution of metastases in individuals.

Growth and Global Imbalances: The Role of Learning-by-Exporting

Rapidly growing developing economies are characterized by heavy exportation and current account surpluses. Empirical studies suggest that may be quantitatively important in developing countries and behind some of this dramatic growth. This paper explores if learning-by-exporting helps to explain key macroeconomic behavior of fast growing developing countries. To accomplish this, I build a two country general equilibrium growth model in which a developing economy benefits from learning-by-exporting as it trades with a developed economy. As the benchmark, I consider a setup in which policies are restricted by the World Trade Organization (WTO) to non-trade related policies and compare the outcome to a model with No-WTO restrictions. The optimal policies in the presence of WTO restrictions rationalize the observed current account surpluses of rapidly growing developing economies. However, if there were no WTO restrictions, developing countries would manipulate their terms of trade rather than their current account, which improves the welfare of both developing and developed countries. This highlights the fact that terms of trade manipulation can be win-win in the presence of learning-by-exporting. This paper also considers a Coordinated Policy problem to obtain the first-best outcome for the world. In this setup, the developing country's terms of trade deteriorate even further and it runs a greater current account deficit compared to the No-WTO Restrictions case.

Project Heterogeneity and Growth: The Impact of Selection

In the classical literature of innovation-based endogenous growth, the main engine of long run economic growth is firm entry. Nevertheless, when projects are heterogeneous, and good ideas are scarce, a mass-composition trade off is introduced into this link: larger cohorts are characterized by a lower average quality. As one of the roles of the financial system is to screen the quality of projects, the ability of financial intermediaries to detect promising projects shapes the strength of this trade-off. In order to study this relationship, we build a general equilibrium endogenous growth model with project heterogeneity and financial screening. To illustrate the relevance of the mass and composition margins we apply this framework to two important debates in the growth literature. First, we show that corporate taxation has only a weak effect in growth, but a strong effect on firm entry, both well known empirical regularities. A second illustration studies the effects of financial development in growth. A word of caution arises: for economies that are characterized by high rates of firm creation, domestic credit should not be used as a proxy of financial development, in contrast to most of the empirical literature.

COMPARATIVE ANALYSIS OF ANIMAL GROWTH: A PRIMATE CONTINUUM REVEALED BY A NEW DIMENSIONLESS GROWTH RATE COEFFICIENT

The comparative analysis of animal growth still awaits full integration into life-history studies, partially due to the difficulty of defining a comparable measure of growth rate across species. Using growth data from 50 primate species, we introduce a modified "general growth model" and a dimensionless growth rate coefficient β that controls for size scaling and phylogenetic effects in the distribution of growth rates. Our results contradict the prevailing idea that slow growth characterizes primates as a group: the observed range of β values shows that not all primates grow slowly, with galago species exhibiting growth rates similar or above the mammalian average, while other strepsirrhines and most New World monkeys show limited reduction in growth rates. Low growth rate characterizes apes and some papionines. Phylogenetic regressions reveal associations between β and life-history variables, providing tests for theories of primate growth evolution. We also show that primate slow growth is an exclusively postnatal phenomenon. Our study exemplifies how the dimensionless approach promotes the integration of growth rate data into comparative life-history analysis, and demonstrates its potential applicability to other cases of adaptive diversification of animal growth patterns.

Oxide Film Growth Kinetics on Metals and Alloys: II. Numerical Simulation of Transient Behavior

A number of passive film growth models have been advanced in the past, each founded on different assumptions and providing different rate laws. A new, generalized growth model has been developed and the numerical simulation of the transient behavior of oxide film growth on metals and alloys is reported here. This model is based on the transport of anions and cations (in a Cr2O3 film for stainless alloy). In contrast to most models up to date, it describes the time-variant behavior of film and film/solution potential differences. Because these potential differences are expressed as exponential functions of film thickness, asymptotic behaviors can be studied and it is shown that a square root law results for very thin and very thick films. Growth rate for intermediate films and during transient periods, on the other hand, is determined by numerical integration. Parameters which were introduced by the model and whose values are unknown are conveniently regrouped into only four lumped parameters, which are easily estimated by numerical optimisation. It is shown that experimental oxide film thickness measurements on stainless alloys in high-temperature aqueous environments can be reproduced. It is further shown that the diffusional rate expressions of all the species contributing to growth are analogous, explaining why it is possible to fit growth kinetics with a single type of point defect.

Cumulative Innovation, Growth and Welfare-Improving Patent Policy

We construct a tractable general equilibrium model of cumulative innovation and growth, in which new ideas strictly improve upon frontier technologies, and productivity improvements are drawn in a stochastic manner. The presence of positive knowledge spillovers implies that the decentralized equilibrium features an allocation of labor to R&D activity that is strictly lower than the social planner’s benchmark, which suggests a role for patent policy. We focus on a “non-infringing inventive step” requirement, which stipulates the minimum improvement to the best patented technology that a new idea needs to make for it to be patentable and non-infringing. We establish that there exists a finite required inventive step that maximizes the rate of innovation, as well as a separate optimal required inventive step that maximizes welfare, with the former being strictly greater than the latter. These conclusions are robust to allowing for the availability of an additional instrument in the form of patent length policy.

Degree distributions of evolving alphabetic bipartite networks and their projections

Many real-world systems are modeled as evolving bipartite networks and their one-mode projections. In particular, Discrete Combinatorial Systems (DCSs), which consist of a finite set of elementary units and different combinations of these units, can be modeled by a subclass of bipartite networks known as Alphabetic Bipartite Networks or α-BiNs, where the bottom partite-set contains a fixed number of nodes (the elementary units) and the top partite-set grows unboundedly with time through the addition of nodes (the combinations). The principal questions in the study of α-BiN evolution are to predict the degree distribution of the bottom set and that of the projection onto the bottom set (the bottom projection), from a knowledge of the bipartite growth dynamics. In this paper, we propose a realistic growth model for α-BiNs, where the degree distribution of the top set (i.e., the distribution of the number of elementary units in the composite entities in the DCS) can be any arbitrary distribution with finite first and second moments. Utilizing an exact correspondence between the preferential growth of α-BiNs and the Polya Urn scheme, we analytically solve the model to compute exact degree distributions of the bottom (fixed) set and the bottom projection. To the best of our knowledge, this is the first work which proposes and solves such a generalized growth model for α-BiNs. We also derive that the degree distributions of both the bottom set and the bottom projection, suitably normalized with time, converge to distributions that are invariant over time. We also verify that this improved model can accurately explain the degree distributions of several real-world DCSs and their projections.

A comparison of least squares and conditional maximum likelihood estimators under volume endpoint censoring in tumor growth experiments

Measurements in tumor growth experiments are stopped once the tumor volume exceeds a preset threshold: a mechanism we term volume endpoint censoring. We argue that this type of censoring is informative. Further, least squares (LS) parameter estimates are shown to suffer a bias in a general parametric model for tumor growth with an independent and identically distributed measurement error, both theoretically and in simulation experiments. In a linear growth model, the magnitude of bias in the LS growth rate estimate increases with the growth rate and the standard deviation of measurement error. We propose a conditional maximum likelihood estimation procedure, which is shown both theoretically and in simulation experiments to yield approximately unbiased parameter estimates in linear and quadratic growth models. Both LS and maximum likelihood estimators have similar variance characteristics. In simulation studies, these properties appear to extend to the case of moderately dependent measurement error. The methodology is illustrated by application to a tumor growth study for an ovarian cancer cell line.

Mechanical growth and morphogenesis of seashells

Seashells grow through the local deposition of mass along the aperture. Many mathematical descriptions of the shapes of shells have been provided over the years, and the basic logarithmic coiling seen in mollusks can be simulated with few parameters. However, the developmental mechanisms underlying shell coiling are largely not understood and the ubiquitous presence of ornamentation such as ribs, tubercles, or spines presents yet another level of difficulty. Here we develop a general model for shell growth based entirely on the local geometry and mechanics of the aperture and mantle. This local description enables us to efficiently describe both arbitrary growth velocities and the evolution of the shell aperture itself. We demonstrate how most shells can be simulated within this framework. We then turn to the mechanics underlying the shell morphogenesis, and develop models for the evolution of the aperture. We demonstrate that the elastic response of the mantle during shell deposition provides a natural mechanism for the formation of three-dimensional ornamentation in shells.

The impact of public goods and services and public R&D on the non-observed economy size, wages inequality and growth

We develop a general equilibrium endogenous growth model in which final goods can be produced either in the Non-Observed Economy (NOE) or in the Official Economy (OE). In particular, by solving transitional dynamics numerically towards the unique and stable steady state, we show that, by affecting the technological-knowledge bias in favour of the OE, productive public goods and services and public policies promoting R&D explain the simultaneous rise in the OE size, the wage premium in favour of OE workers and the economic growth rate. These results are mainly in line with empirical evidence for developed countries, since the 1990s.

Accounting for household heterogeneity in general equilibrium economic growth models

We describe and evaluate a new method of aggregating heterogeneous households that allows for the representation of changing demographic composition in a multi-sector economic growth model. The method is based on a utility and labor supply calibration that takes into account time variations in demographic characteristics of the population. We test the method using the Population-Environment-Technology (PET) model by comparing energy and emissions projections employing the aggregate representation of households to projections representing different household types explicitly. Results show that the difference between the two approaches in terms of total demand for energy and consumption goods is negligible for a wide range of model parameters. Our approach allows the effects of population aging, urbanization, and other forms of compositional change on energy demand and CO2 emissions to be estimated and compared in a computationally manageable manner using a representative household under assumptions and functional forms that are standard in economic growth models.

Non-scale endogenous growth effects of subsidies for exporters

We built a general equilibrium endogenous growth model in which final goods are produced either in the relatively skilled-labour intensive exports sector or in the relatively unskilled-labour intensive domestic sector. We show that, by affecting the technological-knowledge bias, subsidies explain the simultaneous rise in the exports sector, the skill wage premium and the economic growth rate. Then, to shed light upon the causal nexus between production-related subsidies and exports, we use a Portuguese longitudinal database (1996–2003) and implement a propensity score matching approach. Empirical results seem to prove the theoretical predictions: subsidies generate the rise in the wage premium of exporters and the increase in the relative size of export sector, even if no impact of subsidies is found in the capacity of transforming domestic firms into new exporters.

The Offspring-Development-Time/Offspring-Number Trade-Off

The metabolic theory of ecology (MTE) states that metabolic rate, ruled mainly by individual mass and temperature, determines many other biological rates. This view of ecology as ruled by the laws of physics and thermodynamics contrasts with life-history-optimization (LHO) theories, where traits are shaped by evolutionary processes. Integrating the MTE and LHO can lead, however, to a synthetic theory of ecology. In this work, we link the two theories to show that offspring development time is the result of both maternal investment in offspring and the metabolic constraints on offspring growth. We formulate a model that captures how offspring development time is the consequence of both offspring growth rate, determined by temperature and allometric scaling in accordance with the MTE, and the size reached by offspring at the end of the developmental period, determined mainly by LHO and reproductive strategies. We first extend the trade-off between offspring size and offspring number to ectotherms, showing that increased body temperatures result in increased resources available for reproduction. We then combine this trade-off with the general ontogenetic growth model to show that there is a trade-off between the number of offspring produced and offspring development time. The model predicts a shorter developmental time in organisms producing larger numbers of offspring.