Comment on "correlated noise in a logistic growth model"

We argue the results published by Bao-Quan Ai et al [Phys. Rev E 67, 022903 (2003)] on "correlated noise in a logistic growth model " are not correct. Their conclusion that for larger values of the correlation parameter, lambda, the cell population is peaked at x=0, which denotes the high extinction rate is also incorrect. We find the reverse behaviour corresponding to their results, that increasing lambda, promotes the stable growth of tumour cells. In particular, their results for steady-state probability, as a function of cell number, at different correlation strengths, presented in figures 1 and 2 show different behaviour than one would expect from the simple mathematical expression for the steady-state probability. Additionally, their interpretation at small values of cell number that the steady state probability increases as they increase the correlation parameter is also questionable. Another striking feature in their figures (1 and 3) is that for the same values of the parameter lambda and alpha, their simulation produces two different curves both qualitatively and quantitatively.

A conformal invariant growth model

We present a one-parameter extension of the raise and peel one-dimensional growth model. The model is defined in the configuration space of Dyck (RSOS) paths. Tiles from a rarefied gas hit the interface and change its shape. The adsorption rates are local but the desorption rates are non-local; they depend not only on the cluster hit by the tile but also on the total number of peaks (local maxima) belonging to all the clusters of the configuration. The domain of the parameter is determined by the condition that the rates are non-negative. In the finite-size scaling limit, the model is conformal invariant in the whole open domain. The parameter appears in the sound velocity only. At the boundary of the domain, the stationary state is an adsorbing state and conformal invariance is lost. The model allows us to check the universality of non-local observables in the raise and peel model. An example is given.

Public versus private provision of infrastructure in a neoclassical growth model

This article studies the welfare and long run allocation impacts of privatization. There are two types of capital in this model economy, one private and the other initially public (“infrastructure”). A positive externality due to infrastructure capital is assumed, so that the government could improve upon decentralized allocations internalizing the externality, but public investmentis …nanced through distortionary taxation. It is shown that privatization is welfare-improving for a large set of economies and that after privatization under-investment is optimal. When operation inefficiency in the public sectoror subsidy to infrastructure accumulation are introduced, gains from privatization are higherand positive for most reasonable combinations of parameters.

A competitive growth model with endogenous fertility

This paper investigates the interaction between endogenous fertility behavior and the distribution of income and wealth arnong farnilies in a competitive market economy. We construct a growth model in which altruistic dynasties are heterogeneous in their initial stocks of physical capital. Dynasties make choices of farnily size along with decisions about consumption and intergenerational transfers. We show that if the rate of time preference is increasing in the number of children and preferences over nurnber of children satisfy a norrnality assumption, all steady states are characterized by equality of capital stocks and consumption arnong families. We also provide sufficient conditions for uniqueness of the steady state. In order to illustrate these results, we present an example in which preferences over number of children are logarithrnic and the technology is Cobb-Douglas. For this combination of preferences and technology, there exists a unique egalitarian steady state. Moreover, the economy converges to this steady state in only one generation .

Debt and default in a growth model

This paper presents a small open economy model with capital accumulation and without commitment to repay debt. The optimal debt contract specifies debt relief following bad shocks and debt increase following good shocks and brings first order benefits if the country's borrowing constraint is binding. Countries with less capital (with higher marginal productivity of capital) have a higher debt-GDP ratio, are more likely to default on uncontingent bonds, require higher debt relief after bad shocks and pay a higher spread over treasury. Debt relief prescribed by the optimal contract following the interest rate hikes of 1980-81 is more than half of the debt forgiveness obtained by the main Latin American countries through the Brady agreements.

Richards growth model and viability indicators for populations subject to interventions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A low-growth model: informality as a structural constraint

Includes bibliography

Mean-Field critical behavior and ergodicity break in a nonequilibrium one-dimensional RSOS growth model

We investigate the nonequilibrium roughening transition of a one-dimensional restricted solid-on-solid model by directly sampling the stationary probability density of a suitable order parameter as the surface adsorption rate varies. The shapes of the probability density histograms suggest a typical Ginzburg-Landau scenario for the phase transition of the model, and estimates of the "magnetic" exponent seem to confirm its mean-field critical behavior. We also found that the flipping times between the metastable phases of the model scale exponentially with the system size, signaling the breaking of ergodicity in the thermodynamic limit. Incidentally, we discovered that a closely related model not considered before also displays a phase transition with the same critical behavior as the original model. Our results support the usefulness of off-critical histogram techniques in the investigation of nonequilibrium phase transitions. We also briefly discuss in the appendix a good and simple pseudo-random number generator used in our simulations.

On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, da parts per thousand yen1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.

Parameter estimation in a growth model for a biological population

The motivating problem concerns the estimation of the growth curve of solitary corals that follow the nonlinear Von Bertalanffy Growth Function (VBGF). The most common parameterization of the VBGF for corals is based on two parameters: the ultimate length L∞ and the growth rate k. One aim was to find a more reliable method for estimating these parameters, which can capture the influence of environmental covariates. The main issue with current methods is that they force the linearization of VBGF and neglect intra-individual variability. The idea was to use the hierarchical nonlinear model which has the appealing features of taking into account the influence of collection sites, possible intra-site measurement correlation and variance heterogeneity, and that can handle the influence of environmental factors and all the reliable information that might influence coral growth. This method was used on two databases of different solitary corals i.e. Balanophyllia europaea and Leptopsammia pruvoti, collected in six different sites in different environmental conditions, which introduced a decisive improvement in the results. Nevertheless, the theory of the energy balance in growth ascertains the linear correlation of the two parameters and the independence of the ultimate length L∞ from the influence of environmental covariates, so a further aim of the thesis was to propose a new parameterization based on the ultimate length and parameter c which explicitly describes the part of growth ascribable to site-specific conditions such as environmental factors. We explored the possibility of estimating these parameters characterizing the VBGF new parameterization via the nonlinear hierarchical model. Again there was a general improvement with respect to traditional methods. The results of the two parameterizations were similar, although a very slight improvement was observed in the new one. This is, nevertheless, more suitable from a theoretical point of view when considering environmental covariates.