Allais-anonymity as an alternative to the discounted-sum criterion in the calculus of optimal growth II: Pareto optimality and some economic interpretations

This paper studies the Pareto-optimality of the consensual optimum established in "Allais-anonymity as an alternative to the discounted-sum criterion I: consensual optimality" (Mabrouk 2006a). For that, a Pareto-optimality criterion is set up by the application of the generalized Karush, Kuhn and Tucker theorem and thanks to the decomposition of the space of geometrically-growing real sequences. That makes it possible to find sufficient conditions so that a bequest-rule path is Pareto-optimal. Through an example, it is then shown that the golden rule must be checked to achieve Allais-anonymous optimality. The introduction of an additive altruism makes it possible to highlight the intergenerational-preference rate compatible with Allais-anonymous optimality. In this approach, it is not any more the optimality which depends on the intergenerational-preference rate, but the optimal intergenerational-preference rate which rises from Allais-anonymous optimality.Intergenerational anonymity; Allais-anonymity; Intergenerational equity; Optimal growth; Technical change; Time-preference; Discounted-sum criterion; Consensual criterion; Pareto-optimality; OG economy.

Allais-anonymity as an alternative to the discounted-sum criterion in the calculus of optimal growth I: Consensual optimality

The objective of this work is to try to define and calculate the optimal growth path, in the presence of exogenous technical change, without resorting to the discounted-sum criterion. The solution suggested is to consider an optimality criterion expressing an Allais-anonymous intergenerational consensus. The partial characterization of consensual optimality was made possible thanks to the decomposition of the dual of the space of sub-geometric sequences of reason p. The main finding is a relation between the marginal rate of substitution between bequest and heritage, and the growth rate, relation which is a necessary condition for consensual optimality. The necessary study of the Pareto-optimality of the consensual optimum is the subject of a forthcoming paper "Allais-anonymity as an alternative to the discounted-sum criterion in the calculus of optimal growth II: Pareto optimality and some economic interpretations".Intergenerational anonymity; Intergenerational equity; Optimal growth; Technical change; Time-preference; Discounted-sum criterion; Consensual criterion; OG economy

Intergenerational anonymity as an alternative to the discounted- sum criterion in the calculus of optimal growth I: Consensual optimality

The objective of this work is to try to define and calculate the optimal growth path, in the presence of exogenous technical change, without resorting to the discounted-sum criterion. The solution suggested is to consider an optimality criterion expressing an anonymous intergenerational consensus. The partial characterization of consensual optimality was made possible thanks to the decomposition of the dual of the space of sub-geometric sequences of reason p. The main finding is a relation between the marginal rate of substitution between bequest and heritage and the growth rate, relation which is a necessary condition for consensual optimality. The necessary study of the Pareto-optimality of the consensual optimum is the subject of a forthcoming paper « Intergenerational anonymity as an alternative to the discounted-sum criterion in the calculus of optimal growth II: Pareto-optimality and some economic interpretations »Intergenerational anonymity; Intergenerational equity; Optimal growth; Technical change; Time-preference; Discounted-sum criterion; Consensual criterion; OG economy

On the extension of a preorder under translation invariance

This paper proves the existence, for any preorder on a real vector space satisfying translation invariance, of a complete preorder extending the preorder and satisfying translation invariance. As application, the existence of a translation-invariant complete preorder on infinite utility streams satisfying strong Pareto and fixed-step anonymity, is established.Szpilrajn theorem; translation invariance

Translation invariance when utility streams are infinite and unbounded

The axiom translation invariance consists in asserting the invariance of the ranking of two utility streams if one applies the same translation to both. This axiom is significant in the characterization of utilitarian criteria in finite dimension. This characterization is achieved thanks to the "weak weighted utilitarianism theorem".The objective here is to propose a generalization of this theorem in a space of infinite and unbounded utility streams. A consequence of the suggested generalization is that, in the context of intergenerational choice, every maximal point with respect to a paretian utilitarian order granting comparable considerations to the present and the future, is also a maximal point with respect to some future-oriented criterion.Translation invariance; Infinite utility streams; Utilitarianism; Intergenerational equity

Social potential model to simulate emergent behaviour for swarm robots

Swarm robotics has a wide range of applications in numerous fields from space and sub-sea exploration to the deployment of teams of interacting artificial agents in disposal systems. In this paper, we introduce a model to simulate the emergent behaviour of multi-agent robot systems, based on principles from physical mechanics. The model is based on mutual interactions among the swarm individuals. The main elements of these interactions are repulsion forces, attraction forces, alignment forces and dissipative forces generated by the swarm members. Using statistical tools, which are used to investigate simulated group behaviour, we discuss the importance of introducing some dissipation to the system as well as the effect of the interaction parameters on various components of the model

On inversion and connection coefficients for basic hypergeometric polynomials

In this paper, we propose a general method to express explicitly the inversion and the connection coefficients between two basic hypergeometric polynomial sets. As application, we consider some $d$-orthogonal basic hypergeometric polynomials and we derive expansion formulae corresponding to all the families within the $q$-Askey scheme.Comment: 15 page

Optimal growth path in an OLG economy without time-preference assumptions : main results

The aim is to characterize optimal growth paths in an OLG economy where capital accumulation is achieved through bequests, without using the assumption of time preference theory on a social level, because such an assumption, that leads to use a discounted infinite horizon sum, introduce necessarily inequality between the different generations of the society. I investigated two optimality concepts: Pareto-optimality and consensual optimality. I considered the case without technical change. I found that all steady-state optimal growth paths converge necessarily to a level of capital where the marginal gain from a decrease of bequest is equal to the marginal loss from a similar decrease of heritage. With the use of an intergenerational altruistic utility, I showed that spontaneous equilibrium cannot be an optimal growth path unless generations feel (asymptotically) for their heirs as they feel for themselves.optimal growth, OLG economy, time-preference assumption, Pareto-optimality, egalitarianism, golden rule

Modeling and performance evaluation of free space optical link for ground-to-train communications

There is an increased demand for high-speed train (HSR) services. Consequently, onboard high-speed internet access needs increased as passengers travel to and from work. This sudden surge in demand introduced new challenges in delivering a seamless internet connection on-board fast-moving trains. Free Space Optical (FSO) Communications technology promises a bright future for various applications, due to its cost-effectiveness, ease of deployment, and huge unregulated bandwidth, which gives it an edge over contemporary technologies. However, there is a lack of significant research on FSO links for railway communications. In this thesis, straight, curved, and new double curved tracks mathematical models for FSO Ground-to-train (G2T-FSO) links have been proposed to overcome this issue and satisfy increased demand. G2T-FSO links feature base stations located beside the track to provide a LOS link for traveling trains. Moreover, FSO links comprise of intensity modulated transmitters with Direct detection receiver, that utilize RZ and NRZ OOK modulation formats at 2.5 Gbps. In addition, multiple transmitters concept has been implemented to enhance the link performance, in which single, dual, triple, and quad transmitters have been developed. Furthermore, geometrical parameters have been optimized to achieve optimal link performance. Measured meteorological data have been incorporated to simulate rain and fog weather attenuations. Performance evaluation has been conducted in terms of Received power, Q factor, SNR, BER, and Eye diagram patterns using MATLAB® and Optisystem®. Simulation results show significant effects of geometrical and atmospheric losses on single and dual transmitters link performances. However, Quad and triple transmitters have obtained a feasible error-free G2T-FSO link with BER of 10-9 for NRZ and RZ formats. Significantly enhanced ranges of up to 680m for straight track and 618m for curved track under clear weather condition have been achieved. G2T-FSO links promise an unmatched performance over contemporary HSR communications technology