The constrained compartmentalized knapsack problem: mathematical models and solution methods

The constrained compartmentalized knapsack problem can be seen as an extension of the constrained knapsack problem. However, the items are grouped into different classes so that the overall knapsack has to be divided into compartments, and each compartment is loaded with items from the same class. Moreover, building a compartment incurs a fixed cost and a fixed loss of the capacity in the original knapsack, and the compartments are lower and upper bounded. The objective is to maximize the total value of the items loaded in the overall knapsack minus the cost of the compartments. This problem has been formulated as an integer non-linear program, and in this paper, we reformulate the non-linear model as an integer linear master problem with a large number of variables. Some heuristics based on the solution of the restricted master problem are investigated. A new and more compact integer linear model is also presented, which can be solved by a branch-and-bound commercial solver that found most of the optimal solutions for the constrained compartmentalized knapsack problem. On the other hand, heuristics provide good solutions with low computational effort. (C) 2011 Elsevier BM. All rights reserved.

Seasonal drought stress in the Amazon: Reconciling models and observations

The Amazon Basin is crucial to global circulatory and carbon patterns due to the large areal extent and large flux magnitude. Biogeophysical models have had difficulty reproducing the annual cycle of net ecosystem exchange (NEE) of carbon in some regions of the Amazon, generally simulating uptake during the wet season and efflux during seasonal drought. In reality, the opposite occurs. Observational and modeling studies have identified several mechanisms that explain the observed annual cycle, including: (1) deep soil columns that can store large water amount, (2) the ability of deep roots to access moisture at depth when near-surface soil dries during annual drought, (3) movement of water in the soil via hydraulic redistribution, allowing for more efficient uptake of water during the wet season, and moistening of near-surface soil during the annual drought, and (4) photosynthetic response to elevated light levels as cloudiness decreases during the dry season. We incorporate these mechanisms into the third version of the Simple Biosphere model (SiB3) both singly and collectively, and confront the results with observations. For the forest to maintain function through seasonal drought, there must be sufficient water storage in the soil to sustain transpiration through the dry season in addition to the ability of the roots to access the stored water. We find that individually, none of these mechanisms by themselves produces a simulation of the annual cycle of NEE that matches the observed. When these mechanisms are combined into the model, NEE follows the general trend of the observations, showing efflux during the wet season and uptake during seasonal drought.

COM-Poisson cure rate survival models and an application to a cutaneous melanoma data

In this paper, we develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow the Conway-Maxwell Poisson distribution. This model includes as special cases some of the well-known cure rate models discussed in the literature. Next, we discuss the maximum likelihood estimation of the parameters of this cure rate survival model. Finally, we illustrate the usefulness of this model by applying it to a real cutaneous melanoma data. (C) 2009 Elsevier B.V. All rights reserved.

Package models and the information crisis of prebiotic evolution

The coexistence between different types of templates has been the choice solution to the information crisis of prebiotic evolution, triggered by the finding that a single RNA-like template cannot carry enough information to code for any useful replicase. In principle, confining d distinct templates of length L in a package or protocell, whose Survival depends on the coexistence of the templates it holds in, could resolve this crisis provided that d is made sufficiently large. Here we review the prototypical package model of Niesert et al. [1981. Origin of life between Scylla and Charybdis. J. Mol. Evol. 17, 348-353] which guarantees the greatest possible region of viability of the protocell population, and show that this model, and hence the entire package approach, does not resolve the information crisis. In particular, we show that the total information stored in a viable protocell (Ld) tends to a constant value that depends only on the spontaneous error rate per nucleotide of the template replication mechanism. As a result, an increase of d must be followed by a decrease of L, so that the net information gain is null. (C) 2008 Elsevier Ltd. All rights reserved.