Horizontal innovation in the theory of growth and development

We analyze recent contributions to growth theory based on the model of expanding variety of Romer (1990). In the first part, we present different versions of the benchmark linear model with imperfect competition. These include the labequipment model, labor-for-intermediates and directed technical change . We review applications of the expanding variety framework to the analysis of international technology diffusion, trade, cross-country productivity differences, financial development and fluctuations. In many such applications, a key role is played by complementarities in the process of innovation.

Externalities and interdependent growth: Theory and evidence

I formulate and estimate a model of externalities within countriesand technological interdependence across countries. I find that externalreturns to scale to physical capital within countries are 8 percent; thata 10 percent increase of total factor productivity of a country's neighborsraises its total factor productivity by 6 percent; and that a 2 percentannual growth rate of labor productivity can be explained as an endogenousresponse to an exogenous 0.2 percent annual growth rate of total factorproductivity in the steady--state.

The growth and diffusion of knowlegde and the theory of the firm

We analyze the implications of a market imperfection related to the inability to establish intellectual property rights, that we label {\it unverifiable communication}. Employees are able to collude with external parties selling ``knowledge capital'' of the firm. The firm organizer engages in strategic interaction simultaneously with employees and competitors, as she introduces endogenous transaction costs in the market for information between those agents. Incentive schemes and communication costs are the key strategic variables used by the firm to induce frictions in collusive markets. Unverifiable communication introduces severe allocative distortions, both at internal product development and at intended sale of information (technology transfer). We derive implications of the model for observable decisions like characteristics of the employment relationship (full employment, incompatibility with other jobs), firms' preferences over cluster characteristics for location decisions, optimal size at entry, in--house development vs sale strategies for innovations and industry evolution.

Numerical algorithm for Ginzburg-Landau equations with multiplicative noise: Application to domain growth

We consider stochastic partial differential equations with multiplicative noise. We derive an algorithm for the computer simulation of these equations. The algorithm is applied to study domain growth of a model with a conserved order parameter. The numerical results corroborate previous analytical predictions obtained by linear analysis.

Pattern formation during mesophase growth in a homologous series

Remarkable differences in the shape of the nematic-smectic-B interface in a quasi-two-dimensional geometry have been experimentally observed in three liquid crystals of very similar molecular structure, i.e., neighboring members of a homologous series. In the thermal equilibrium of the two mesophases a faceted rectanglelike shape was observed with considerably different shape anisotropies for the three homologs. Various morphologies such as dendritic, dendriticlike, and faceted shapes of the rapidly growing smectic-B germ were also observed for the three substances. Experimental results were compared with computer simulations based on the phase field model. The pattern forming behavior of a binary mixture of two homologs was also studied.

From lattice-gas models to nonlinear diffusion models: A derivation of macroscopic equations and fluctuations

We derive nonlinear diffusion equations and equations containing corrections due to fluctuations for a coarse-grained concentration field. To deal with diffusion coefficients with an explicit dependence on the concentration values, we generalize the Van Kampen method of expansion of the master equation to field variables. We apply these results to the derivation of equations of phase-separation dynamics and interfacial growth instabilities.

Combinations of vascular endothelial growth factor pathway inhibitors with metronomic chemotherapy: Rational and current status.

Chemotherapy given in a metronomic manner can be administered with less adverse effects which are common with conventional schedules such as myelotoxicity and gastrointestinal toxicity and thus may be appropriate for older patients and patients with decreased performance status. Efficacy has been observed in several settings. An opportunity to improve the efficacy of metronomic schedules without significantly increasing toxicity presents with the addition of anti-angiogenic targeted treatments. These combinations rational stems from the understanding of the importance of angiogenesis in the mechanism of action of metronomic chemotherapy which may be augmented by specific targeting of the vascular endothelial growth factor (VEGF) pathway by antibodies or small tyrosine kinase inhibitors. Combinations of metronomic chemotherapy schedules with VEGF pathway targeting drugs will be discussed in this paper.

Trade-off between constitutive and inducible resistance against herbivores is only partially explained by gene expression and glucosinolate production.

The hypothesis that constitutive and inducible plant resistance against herbivores should trade-off because they use the same resources and impose costs to plant fitness has been postulated for a long time. Negative correlations between modes of deployment of resistance and defences have been observed across and within species in common garden experiments. It was therefore tested whether that pattern of resistance across genotypes follows a similar variation in patterns of gene expression and chemical defence production. Using the genetically tractable model Arabidopsis thaliana and different modes of induction, including the generalist herbivore Spodoptera littoralis, the specialist herbivore Pieris brassicae, and jasmonate application, constitutive and inducibility of resistance was measured across seven A. thaliana accessions that were previously selected based on constitutive levels of defence gene expression. According to theory, it was found that modes of resistance traded-off among accessions, particularly against S. littoralis, in which accessions investing in high constitutive resistance did not increase it substantially after attack and vice-versa. Accordingly, the average expression of eight genes involved in glucosinolate production negatively predicted larval growth across the seven accessions. Glucosinolate production and genes related to defence induction on healthy and herbivore-damaged plants were measured next. Surprisingly, only a partial correlation between glucosinolate production, gene expression, and the herbivore resistance results was found. These results suggest that the defence outcome of plants against herbivores goes beyond individual molecules or genes but stands on a complex network of interactions.

On Vessiot's Theory of Partial Differential Equations

The object of research presented here is Vessiot's theory of partial differential equations: for a given differential equation one constructs a distribution both tangential to the differential equation and contained within the contact distribution of the jet bundle. Then within it, one seeks n-dimensional subdistributions which are transversal to the base manifold, the integral distributions. These consist of integral elements, and these again shall be adapted so that they make a subdistribution which closes under the Lie-bracket. This then is called a flat Vessiot connection. Solutions to the differential equation may be regarded as integral manifolds of these distributions. In the first part of the thesis, I give a survey of the present state of the formal theory of partial differential equations: one regards differential equations as fibred submanifolds in a suitable jet bundle and considers formal integrability and the stronger notion of involutivity of differential equations for analyzing their solvability. An arbitrary system may (locally) be represented in reduced Cartan normal form. This leads to a natural description of its geometric symbol. The Vessiot distribution now can be split into the direct sum of the symbol and a horizontal complement (which is not unique). The n-dimensional subdistributions which close under the Lie bracket and are transversal to the base manifold are the sought tangential approximations for the solutions of the differential equation. It is now possible to show their existence by analyzing the structure equations. Vessiot's theory is now based on a rigorous foundation. Furthermore, the relation between Vessiot's approach and the crucial notions of the formal theory (like formal integrability and involutivity of differential equations) is clarified. The possible obstructions to involution of a differential equation are deduced explicitly. In the second part of the thesis it is shown that Vessiot's approach for the construction of the wanted distributions step by step succeeds if, and only if, the given system is involutive. Firstly, an existence theorem for integral distributions is proven. Then an existence theorem for flat Vessiot connections is shown. The differential-geometric structure of the basic systems is analyzed and simplified, as compared to those of other approaches, in particular the structure equations which are considered for the proofs of the existence theorems: here, they are a set of linear equations and an involutive system of differential equations. The definition of integral elements given here links Vessiot theory and the dual Cartan-Kähler theory of exterior systems. The analysis of the structure equations not only yields theoretical insight but also produces an algorithm which can be used to derive the coefficients of the vector fields, which span the integral distributions, explicitly. Therefore implementing the algorithm in the computer algebra system MuPAD now is possible.

On two rational difference equations

In this paper, we study the oscillating property of positive solutions and the global asymptotic stability of the unique equilibrium of the two rational difference equations [GRAPHICS] and [GRAPHICS] where a is a nonnegative constant. (c) 2005 Elsevier Inc. All rights reserved.

On the system of rational difference equations x(n) = A+(1)over-bar y(n-p), y(n) = A+(gamma(n-1))over-bar x(n-r)y(n-5)

In this paper, we study the behavior of the positive solutions of the system of two difference equations [GRAPHICS] where p >= 1, r >= 1, s >= 1, A >= 0, and x(1-r), x(2-r),..., x(0), y(1-max) {p.s},..., y(0) are positive real numbers. (c) 2005 Elsevier Inc. All rights reserved.