Approximation algorithms and hardness results for labeled connectivity problems

Let G=(V,E) be a connected multigraph, whose edges are associated with labels specified by an integer-valued function ℒ:E→ℕ. In addition, each label ℓ∈ℕ has a non-negative cost c(ℓ). The minimum label spanning tree problem (MinLST) asks to find a spanning tree in G that minimizes the overall cost of the labels used by its edges. Equivalently, we aim at finding a minimum cost subset of labels I⊆ℕ such that the edge set {e∈E:ℒ(e)∈I} forms a connected subgraph spanning all vertices. Similarly, in the minimum label s – t path problem (MinLP) the goal is to identify an s–t path minimizing the combined cost of its labels. The main contributions of this paper are improved approximation algorithms and hardness results for MinLST and MinLP.     

Minimization of maximum lateness under linear deterioration

This paper considers a single-machine scheduling problem to minimize the maximum lateness. The processing time of each job is a linear function of the time when the job starts processing. This problem is known to be -hard in the literature. In this paper, we design a branch-and-bound algorithm for deriving exact solutions by incorporating several properties concerning dominance relations and lower bounds. These properties produce synergic effects in accelerating the solution finding process such that the algorithm can solve problems of 100 jobs within 1 min on average. To compose approximate solutions, we revise a heuristic algorithm available in the literature and propose several hybrid variants. Numerical results evince that the proposed approaches are very effective in successfully reporting optimal solutions for most of the test cases.     

Assessing Uncertainty in Small Area Forecasts: State of the Practice and Implementation Strategy

Forecasts are needed for everyday decisions and must be in the form of numbers. Yet forecasts invariably turn out to be different than the numbers that actually occur. Yet, most producers of forecasts only present a deterministic view of the future in the form of point predictions. However, the presence of uncertainty is inherent in management or policy decisions and there is often concern that benefits are overstated and risks are understated. Such concerns are difficult to address by providing only point forecasts with no assessment of their uncertainty. Having a better understanding of uncertainty can enhance the usefulness of forecasts and make the work of forecasting agencies an even more valuable product for planners, policy makers, and the public. The purpose of this paper is twofold. First, it presents an overview of the current state-of-the-practice is assessing forecast uncertainty. Second, it offers a guidelines and options for implementing and building uncertainty into small area forecasting processes. There are options for assessing forecasting uncertainty that can and should be implemented by most, if not all, producers of forecasts.     

The optimum growth rate for population under critical-level utilitarianism

We characterize optimal consumption, capital, and population growth of a production economy under critical-level utilitarianism. First, we show that neither classical utilitarianism nor average utilitarianism can avoid a corner solution for the population growth rate, in that under the former, population grows at the maximum speed (the so-called repugnant conclusion) while under the latter, it grows at the minimum. Second, we show that critical level utilitarianism yields an interior solution for the population growth rate provided the critical level belongs to a positive, open interval. Finally, we characterize the transition to the steady state and perform comparative dynamics analysis.     

Progressive multi-state models for informatively incomplete longitudinal data

Progressive multi-state models provide a convenient framework for characterizing chronic disease processes where the states represent the degree of damage resulting from the disease. Incomplete data often arise in studies of such processes, and standard methods of analysis can lead to biased parameter estimates when observation of data is response-dependent. This paper describes a joint analysis useful for fitting progressive multi-state models to data arising in longitudinal studies in such settings. Likelihood based methods are described and parameters are shown to be identifiable. An EM algorithm is described for parameter estimation, and variance estimation is carried out using the Louis’ method. Simulation studies demonstrate that the proposed method works well in practice under a variety of settings. An application to data from a smoking prevention study illustrates the utility of the method.     

Life test sampling plans for Weibull distributed lifetimes under accelerated hybrid censoring

Life test sampling plans (LSPs) for the Weibull distribution are usually developed under the assumptions that the shape parameter is known and the life test is conducted at an accelerated condition for which the acceleration factor (AF) is known. However, the sensitivities of a plan to the assumed shape parameter and AF have been rarely investigated. This paper considers the case where the life test is hybrid censored and develops attributes LSPs under the above assumptions. Then, sensitivity analyses are conducted to assess the effects of the uncertainties in the assumed AF and shape parameter on the actual producer and consumer risks. A method is also developed for constructing LSPs that can accommodate these uncertainties.     

Modeling longitudinal binomial responses: implications from two dueling paradigms

The generalized estimating equations (GEEs) and generalized linear mixed-effects model (GLMM) are the two most popular paradigms to extend models for cross-sectional data to a longitudinal setting. Although the two approaches yield well-interpreted models for continuous outcomes, it is quite a different story when applied to binomial responses. We discuss major modeling differences between the GEE- and GLMM-derived models by presenting new results regarding the model-driven differences. Our results show that GLMM induces some artifacts in the marginal models at assessment times, making it inappropriate when applied to such responses from real study data. The different interpretations of parameters resulting from the conceptual difference between the two modeling approaches also carry quite significant implications and ramifications with respect to data and power analyses. Although a special case involving a scale difference in parameters between GEE and GLMM has been noted in the literature, its implications in real data analysis has not been thoroughly addressed. Further, this special case has a very limited covariate structure and does not apply to most real studies, especially multi-center clinical trials. The new results presented fill a substantial gap in the literature regarding the model-driven differences between the two dueling paradigms.     

On a problem with singularity in comparison of linear experiments

For consistency, the parameter space in the Gauss-Markov model with singular covariance matrix is usually restricted by observation vector. This restriction arises some difficulties in comparison of linear experiments. To avoid it we reduce the problem of comparison from singular to nonsingular case.