In this paper, we extend the work by Sato devoted to the development of economic growth models within the framework of the Lie group theory. We propose a new growth model based on the assumption of logistic growth in factors and derive the corresponding production functions, as well as a compatible notion of wage share. In the process, it is shown that the new functions compare reasonably well against relevant economic data. The corresponding problem of maximisation of profit under conditions of perfect competition is solved with the aid of one of these functions. In addition, it is explained in reasonably rigorous mathematical terms why Bowley’s law no longer holds true in the post-1960 data.

Was there really a debt-fuelled ‘liberal growth model’ that preceded the 2008 financial crisis? The accepted narrative about the pre-crisis boom is that some liberal countries relied on domestic consumption to fuel economic growth, and on household debt to fuel this consumption. In this, they contrasted with coordinated economies. While eventually unsustainable, the growth strategy was politically necessary to maintain middle-class living standards in the context of increasing income inequality. In this article, I take these contentions to the data. Economic evidence from 1995–2007 and political data from the Comparative Manifesto Project Database undermine this received wisdom: while household debt increased in the liberal countries, it does not differentiate this particular growth model. Further, there is no evidence that politicians in liberal countries advocate different economic policies, including those concerning borrowing, to claim credit and stay in power. Differences in the importance of finance between countries, however, suggest a more elite-driven divergence.

Plants, algae, and fungi are essential for nearly all life on earth. Throughphotosynthesis, plants and algae convert solar energy to chemical energy in the form oforganic compounds that sustains essentially all life on earth. In addition, plants andalgae convert the carbon dioxide produced by respiring organisms to oxygen that is neededfor respiration. Fungi decompose complex organic compounds produced by respiring organismsso that molecules can be recycled in photosynthesis and respiration. Plants, algae, andfungi have one important feature in common, their cells have walls. Expansive growth andits regulation are central to the life and development of plant, algal, and fungal cells,i.e. cells with walls. In recent decades there has been an explosion of informationrelevant to expansive growth of cells with walls. Mathematical models have beenconstructed in an attempt to organize and evaluate this information, to gain insight, toevaluate hypotheses, and to assist in the selection and development of new experimentalstudies. In this article some of the mathematical models constructed to study expansivegrowth of cells with walls are reviewed. It is nearly impossible to review all relevantresearch conducted in this area. Instead, the review focuses on the development ofmathematical equations that have been used to model expansive growth, morphogenesis, andgrowth rate regulation of cells with walls. Also, relevant experimental findings arereviewed, conceptual models are presented, and suggestions for future research areproposed. The authors have attempted to provide an overview that is accessible toresearchers that are not working in this field.

According to AK growth models, permanent changes in investment rates have permanent effects on a country's rate of economic growth. Jones (Quarterly Journal of Economics, 1995, 110, 495-525) finds strong evidence against this prediction studying the time series properties of GDP growth rates and investment output ratios in fifteen OECD countries for the period 1950-1988. In this paper, we test the same hypothesis in four OECD countries using a longer span of data (1870-2002 for Canada, the UK and the US, and 1885-2002 for Japan). Moreover, instead of using classic approaches, which are based on stationary I(0) or unit roots I(1) processes, we use methodologies based on fractional integration. After examining the order of integration of GDP growth rates and non-residential investment ratios for these countries, we do not find much evidence against the “growth effects” prediction of AK models. In fact, we only find clear evidence against this theory for the UK case.

Predicting the response of poultry to nutrients has progressed to a stage where it is now not only possible to predict voluntary feed intake accurately, but broiler feeds and feeding programmes may now be optimised using the more advanced simulation models. Development of such prediction models has stimulated useful and purposeful research targeted at filling the gaps in our knowledge of critical aspects of the theory incorporated into these models. The aim of this paper was to review some of these past developments, discuss the controversy that exists in designing and interpreting response experiments, and highlight some of the most recent challenges related to the prediction of responses to nutrients by poultry. These latter include differences, brought about by selection for diverse goals, that have become apparent between modern broiler strains in their responses in feed intake and mortality, which are not independent of level of feeding or strain of broiler, as was previously believed. Uniformity, an important quality criterion in broiler processing, is also not independent of level of feeding, and the effect may now be predicted using stochastic models. It is not yet clear whether breast meat yield, the carcass component of broilers yielding the highest returns, is a function of the strain of broiler or simply that of the protein weight of the bird when processed. An important aspect of response prediction is dealing with constraints to performance: whereas it is relatively straightforward to simulate the potential performance of a broiler, such performance is often constrained by the physical, social and infectious environment, among others, providing a challenge to modellers attempting to predict actual performance. Some of these constraints to potential performance have not yet been adequately described, but are now receiving attention, suggesting that nutrient responses in poultry have the potential to be more accurately predicted in the future.

Fascioliasis pathogenesis depends on fluke burden. In human hyperendemic zones, individual infection intensities reach very high levels and the majority of infected subjects should be in the advanced chronic phase. The rat model offers a useful approach for pathological research in the advanced chronic period. The influence of infection intensity per rat on fluke development, pre-patent period and egg shedding (eggs/g faeces/worm) was analysed in 3 groups (I: 1–3 worms/rat; II: 4–6; III: 7–9). Ontogenetic trajectories of fluke body measures followed a logistic model. Results showed that when the burden increases, the maximum values of fluke measures decrease. The crowding effect is manifest when fluke measures approximate their maximums in the advanced chronic stage. The pre-patent period and egg production decrease when the burden increases. This means that measurements of eggs per gramme of faeces tend to underestimate the fluke burden. The present study demonstrates how to quantify the fascioliasis experimental rat model crowding effect on adult growth, pre-patent period and egg production. This quantification may be of great interest in epidemiological studies and in experimental research on the in vivo actions of different anthelminthic drugs and vaccines, pathology, immunology and resistance studies.

Economic values for average ad libitum food intake capacity (FIC) were estimated with two different linear-plateau models. One model based on a constant minimum fat to protein deposition ratio (Rmin). The other model relied on a constant minimum marginal ratio between fat and protein deposition (MR). Economic values were used to define aggregate genotypes where the driving variables of the growth models were considered as traits. The consequences of a possible implementation of such aggregate genotypes were evaluated with a comparison of the expected selection responses for the different traits.

Economic values for the traits under the two models indicated the same direction of selection and differed only slightly in their magnitude. For a FIC below its optimum, FIC had a positive and Rmin or MR a negative, economic value. In this situation the maximum protein deposition rate Pdmax had no influence on the production costs and therefore an economic value of zero. Selection emphasis is then mainly put on FIC which leads to an increase in average daily gain (ADG). If FIC is above its optimum, economic values for FIC were negative, positive for Pdmax and equal to zero for Rmin or MR. Practically no differences between the selection responses under the two growth models were observed.

The use of growth models to estimate economic values for FIC allowed to attribute a positive economic value to this trait if it is below its optimum. This is not possible when economic values are estimated with an economic production model.

A biological growth model was developed to study economic values for average ad libitum food intake capacity (FIC) in growing pigs. The model was based on the linear/plateau relationship between protein deposition and food intake. Input variables were: minimum fat to protein deposition ratio (R), maximum protein deposition rate (Pdmax)and food intake (FI). Output variables were production traits and production costs.

Economic values (under commercial conditions with ad libitum feeding) were derived with the growth model for each of the traits FIC, R, and Pdmax keeping the other two traits constant, for three alternative levels of FIC. If FIC was too low to realize Pdmax, FIC had a positive economic value, R had a negative economic value and the value of Pdmax was zero. If FIC was higher than necessary to realize Pdmax, economic values were negative, zero and positive for FIC, R, and Pdmax respectively. If FIC was just sufficient to realise Pdmax, the lowest production costs occurred. Now, R had a negative economic value and Pdmax had a positive economic value.

With a restricted feeding regimen under commercial conditions a daily food supply just sufficient to realize Pdmax should be pursued. It was concluded that use of a biological growth model to estimate economic values for FIC would give more insight into correct selection strategies than would the use of an economic model.

Stochastic optimization of semimartingales which permit a dynamic description, like a stochastic differential equation, leads normally to dynamic programming procedures. The resulting Bellman equation is often of a very genera! nature, and analytically hard to solve. The models in the present paper are formulated in terms of the relative change, and the optimality criterion is to maximize the expected rate of growth. We show how this can be done in a simple way, where we avoid using the Bellman equation. An application is indicated.

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.

A rigorous treatment is given for a construction via Markov chains of a binary (0–1) stationary homogeneous Markov random field on Z × Z. The resulting process possesses rather interesting properties. For example, its correlation structure is geometric and it may be easily simulated. Some of the results are rather unintuitive — indeed counter-intuitive — but their demonstration is straightforward involving only the most elementary properties of Markov chains.

We consider d-dimensional stochastic processes which take values in (R+)d These processes generalize Galton-Watson branching processes, but the main assumption of branching processes, independence between particles, is dropped. Instead, we assume for some

Here τ:(R+)d→R +, |x| = σ1d |x(i)|, A {x ∈(R+)d: |x| 1} and T: A→A. Under various assumptions on the maps τ and T it is shown that with probability one there exists a ρ > 1, a fixed point p ∈ A of T and a random variable w such that limn→∞Zn|ρnwp. This result is a generalization of the main limit theorem for supercritical branching processes; note, however, that in the present situation both ρ and ρ are random as well. The results are applied to a population genetical model for zygotic selection without mutation at one locus.

We consider d-dimensional stochastic processes which take values in (R+)d. These processes generalize Galton-Watson branching processes, but the main assumption of branching processes, independence between particles, is dropped. Instead, we assume for some

Here τ: (R+)d → R+, |x| = Σ1d |x(i)| A = {x ∈ (R+)d: |x| = 1} and T: A → A. Under various assumptions on the maps τ and T it is shown that with probability one there exists a ρ > 1, a fixed point p ∈ A of T and a random variable w such that limn→∞Znρ−n = wp. This result is a generalization of the main limit theorem for super-critical branching processes; note, however, that in the present situation both p and ρ are random as well. The results are applied to a population genetical model for zygotic selection without mutation at one locus.