A Homotopy Method for Equilibrium Programming under Uncertainty

We consider a homotopy method for solving stochastic Nash equilibrium models. The algorithm works by following, via a predictor-corrector method, the one-dimensional manifold of the homotopy constructed to connect the systems of equations describing the solution set of the scenario equilibrium model (no nonanticipativity constraints) and the stochastic equilibrium model. The predictor and corrector phases of this homotopy method require the usual solutions of large linear systems, a computationally expensive task, which we render less difficult through our use of Jacobi techniques designed to take advantage of the problem's near separability across scenarios

Pathways of Economic Development in an Uncertain Environment: A Finite Scenario Approach to the U.S. Region Under Carbon Emission Restrictions

Prediction of future economic behavior is increasingly important for both public and private economic planning. This prediction is, however, increasingly fraught with difficulties because of the uncertainty surrounding the future state of so many key economic parameters. In this paper we consider how stochastic programming may be a valuable tool in the analysis of these kinds of problems. Using the U.S. region of Alan Manne and Richard Richels Global 2100 five region world trade model and a set of eight future state-of-the-world scenarios, we observe how the development paths of several key variables predicted by stochastic programming differ in interesting ways from the paths predicted using deterministic methods. We conclude that the explicit way in which stochastic programming models uncertainty may prove useful to economic analysis efforts and provide additional insight into the nature of economic development in an uncertain environment

Large-Scale Convex Optimization via Saddle Point Computation

This article proposes large-scale convex optimization problems to be solved via saddle points of the standard Lagrangian. A recent approach for saddle point computation is specialized, by way of a specific perturbation technique and unique scaling method, to convex optimization problems with differentiable objective and constraint functions. In each iteration the update directions for primal and dual variables are determined by gradients of the Lagrangian. These gradients are evaluated at perturbed points which are generated from current points via auxiliary mappings. The resulting algorithm suits massively parallel computing. Sparsity can be exploited efficiently. Employing simulation of parallel computations, an experimental code embedded into GAMS is tested on two sets of nonlinear problems. The first set arises from multi-stage stochastic optimization of the US energy economy. The second set consists of multi-currency bond portfolio problems. In such stochastic optimization problems the serial time appears approximatively proportional to the number of scenarios, while the parallel time seems independent of the number of scenarios. Thus, we observe that the serial time of our approach in comparison with Minos increases slower with the problem size. Consequently, for large problems with reasonable precision requirements, our method appears faster than Minos even in a serial computer

On Augmented Lagrangian Decomposition Methods for Multistage Stochastic Programs

A general decomposition framework for large convex optimization problems based on augmented Lagrangians is described. The approach is then applied to multistage stochastic programming problems in two different ways: by decomposing the problem into scenarios and by decomposing it into nodes corresponding to stages. Theoretical convergence properties of the two approaches are derived and a computational illustration is presented

Addressing the Issue of Uncertainty Within the Egyptian Agricultural Sector

In this paper we use the static EASM model of the Egyptian agricultural sector and stochastic programming methodology to explore what level of uncertainty Egyptian decision makers presently perceive regarding the value of their produce on international markets. We also investigate how Egyptian cropping patterns might change in response to changing annual water availability and a changing perception of uncertainty

Mesoscopic models for DNA stretching under force: new results and comparison to experiments

Single molecule experiments on B-DNA stretching have revealed one or two structural transitions, when increasing the external force. They are characterized by a sudden increase of DNA contour length and a decrease of the bending rigidity. It has been proposed that the first transition, at forces of 60--80 pN, is a transition from B to S-DNA, viewed as a stretched duplex DNA, while the second one, at stronger forces, is a strand peeling resulting in single stranded DNAs (ssDNA), similar to thermal denaturation. But due to experimental conditions these two transitions can overlap, for instance for poly(dA-dT). We derive analytical formula using a coupled discrete worm like chain-Ising model. Our model takes into account bending rigidity, discreteness of the chain, linear and non-linear (for ssDNA) bond stretching. In the limit of zero force, this model simplifies into a coupled model already developed by us for studying thermal DNA melting, establishing a connexion with previous fitting parameter values for denaturation profiles. We find that: (i) ssDNA is fitted, using an analytical formula, over a nanoNewton range with only three free parameters, the contour length, the bending modulus and the monomer size; (ii) a surprisingly good fit on this force range is possible only by choosing a monomer size of 0.2 nm, almost 4 times smaller than the ssDNA nucleobase length; (iii) mesoscopic models are not able to fit B to ssDNA (or S to ss) transitions; (iv) an analytical formula for fitting B to S transitions is derived in the strong force approximation and for long DNAs, which is in excellent agreement with exact transfer matrix calculations; (v) this formula fits perfectly well poly(dG-dC) and $\lambda$-DNA force-extension curves with consistent parameter values; (vi) a coherent picture, where S to ssDNA transitions are much more sensitive to base-pair sequence than the B to S one, emerges.Comment: 14 pages, 9 figure

Scarabaeoidea (Insecta : Coleoptera) in the Brazilian Cerrado : current state of knowledge

Besouros pertencentes à superfamília Scarabaeoidea ocupam habitats variados, possuem hábitos alimentares diversifi cados, desempenham importante papel ecológico e diversas espécies apresentam importância agrícola. No entanto, estudos com esse grupo na região do Cerrado são escassos. Nesta revisão realizou-se um levantamento dos artigos publicados nos últimos 30 anos a respeito dos Scarabaeoidea no Cerrado. Foram recuperados 64 artigos, realizados em nove unidades da federação, que focavam quatro temas principais espécies praga, aspectos bioecológicos, biodiversidade e importância ecológica, e técnicas e metodologias de coleta de Scarabaeoidea. Os resultados desta revisão indicam que poucos estudos foram realizados com os Scarabaeoidea no Cerrado brasileiro nas últimas décadas frente à importância e diversidade desse grupo de insetos.Beetles belonging to the superfamily Scarabaeoidea occupy different habitats, present feeding habits diversifi ed, play an important ecological role and several species have agricultural importance. However, studies with this group in the Brazilian Cerrado are scarce. In this review we carried out a survey of scientifi c articles published in the past 30 years concerning Scarabaeoidea in the Cerrado. Were found 64 studies in nine Brazilian states. The studies focused on four main topics: pest species, bioecology, biodiversity and ecological importance, techniques and methodologies for collecting Scarabaeoidea. The results of this review indicate that few studies have been conducted with Scarabaeoidea in the Cerrado in recent decades compared to the importance and diversity of this group of insects