On the index system of well-rounded lattices

Let \Lb be a lattice in an $n$-dimensional Euclidean space $E$ and let \Lb' be a Minkowskian sublattice of \Lb, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of \Lb. We consider the set of possible quotients \Lb/\Lb' which may exists in a given dimension or among not too large values of the index [\Lb:\Lb'], indeed [\Lb:\Lb']\le 4, or dimension $n\le 8$.Comment: 17 page

Finite size effects and equilibration in Bose-Hubbard chains with central well dephasing

We investigate Bose-Hubbard chains in a central depleted well configuration, with dephasing in the middle well. We look at equilibration of populations, pseudo-entropy, and entanglement measures. Using stochastic integration in the truncated Wigner representation, we find that the initial quantum states of the occupied wells has an influence on the subsequent dynamics, and that with more than three wells, the chains do not reach a full equilibrium, with edge effects becoming important, and the time to reach the steady state becoming longer. The evolutions with and without phase diffusion are qualitatively different. We find no convincing evidence of entanglement in the final states with phase diffusion. Although at least one accepted measure indicates the presence of mode entanglement, we are easily able to show that it can give ambiguous predictions.Comment: 20 pages, 12 figures, theor

Agricultural land-use and biological conservation

Land use change is a main driver of biodiversity erosion, especially in agricultural landscapes. Incentive-based land-use policies aim at influence land-use pattern, and are usually evaluated with habitat suitability scores, without accounting explicitly for the ecology of the studied population. In this paper, we propose a methodology to define and evaluate agricultural land-use policies with respect to their ecological outcomes directly. We use an ecological-economic model to link the regional abundance of a bird species to the economic context. Policies based on such ecological economics approaches appear to be more efficient than that based on landscape evaluation, from both economic and ecological viewpoints.Ecological-economic model, agriculture, land-use, landscape, conservation

An Environmental-Economic Measure of Sustainable Development

A central issue in the study of sustainable development is the interplay of growth and sacrifice in a dynamic economy. This paper investigates the relationship among current consumption, growth, and sustained consumption in two canonical, stylized economies and in a more general context. It is found that the maximin value measures what is sustainable and provides the limit to growth. Maximin value is interpreted as an environmental-economic carrying capacity and current consumption or utility as an environmental-economic footprint. The time derivative of maximin value is interpreted as net investment in sustainability improvement. It is called durable savings to distinguish it from genuine savings, usually computed with discounted utilitarian prices.sustained development, growth, maximin, sustainability indicator

Chaotic and regular motion around generalized Kalnajs discs

The motion of test particles in the gravitational fields generated by the first four members of the infinite family of generalized Kalnajs discs, is studied. In first instance, we analyze the stability of circular orbits under radial and vertical perturbations and describe the behavior of general equatorial orbits and so we find that radial stability and vertical instability dominate such disc models. Then we study bounded axially symmetric orbits by using the Poincare surfaces of section and Lyapunov characteristic numbers and find chaos in the case of disc-crossing orbits and completely regular motion in other cases

Combining Rights and Welfarism: A New Approach to Intertemporal Evaluation of Social Alternatives

We propose a new criterion which reflects both the concern for welfare (utility) and the concern for rights in the evaluation of economic development paths. The concern for rights is captured by a pre-ordering over combinations of thresholds (floors or ceilings on various quantitative indicators) that serve as constraints on actions and on levels of state variables. These thresholds are interpreted as minimal rights to be guaranteed to all generations. They are endogenously chosen within the set of all feasible thresholds, accounting for the “cost in terms of welfare” of achieving these rights. We apply the criterion to several examples, including the standard Dasgupta-Heal-Solow model of resource extraction and capital accumulation. We show that if the weight given to rights in the criterion is sufficiently high, the optimal solution may be on the threshold possibility frontier. The development path is then “driven” by the rights. In particular, if a minimal consumption is considered as a right, constant consumption can be optimal even with a positive utility discount rate. The shadow prices of thresholds play an important role in the determination of the rate of discount to be applied to social investment projects.rights, intergenerational equity, welfare, sustainability