A BB&R algorithm for minimizing total tardiness on a single machine with sequence dependent setup times

This paper presents a Branch, Bound, and Remember (BB&R) exact algorithm using the Cyclic Best First Search (CBFS) exploration strategy for solving the ${1|ST_{sd}|\sum T_{i}}$ scheduling problem, a single machine scheduling problem with sequence dependent setup times where the objective is to find a schedule with minimum total tardiness. The BB&R algorithm incorporates memory-based dominance rules to reduce the solution search space. The algorithm creates schedules in the reverse direction for problems where fewer than half the jobs are expected to be tardy. In addition, a branch and bound algorithm is used to efficiently compute tighter lower bounds for the problem. This paper also presents a counterexample for a previously reported exact algorithm in Luo and Chu (Appl Math Comput 183(1):575–588, 2006) and Luo et?al. (Int J Prod Res 44(17):3367–3378, 2006). Computational experiments demonstrate that the algorithm is two orders of magnitude faster than the fastest exact algorithm that has appeared in the literature. Computational experiments on two sets of benchmark problems demonstrate that the CBFS search exploration strategy can be used as an effective heuristic on problems that are too large to solve to optimality.     

The compound Poisson risk model with multiple thresholds

In this paper we consider a multi-threshold compound Poisson risk model. A piecewise integro-differential equation is derived for the Gerber-Shiu discounted penalty function. We then provide a recursive approach to obtain general solutions to the integro-differential equation and its generalizations. Finally, we use the probability of ruin to illustrate the applicability of the approach.     

A Post-Optimality Analysis Algorithm for Multi-Objective Optimization

Algorithms for multi-objective optimization problems are designed to generate a single Pareto optimum (non-dominated solution) or a set of Pareto optima that reflect the preferences of the decision-maker. If a set of Pareto optima are generated, then it is useful for the decision-maker to be able to obtain a small set of preferred Pareto optima using an unbiased technique of filtering solutions. This suggests the need for an efficient selection procedure to identify such a preferred subset that reflects the preferences of the decision-maker with respect to the objective functions. Selection procedures typically use a value function or a scalarizing function to express preferences among objective functions. This paper introduces and analyzes the Greedy Reduction (GR) algorithm for obtaining subsets of Pareto optima from large solution sets in multi-objective optimization. Selection of these subsets is based on maximizing a scalarizing function of the vector of percentile ordinal rankings of the Pareto optima within the larger set. A proof of optimality of the GR algorithm that relies on the non-dominated property of the vector of percentile ordinal rankings is provided. The GR algorithm executes in linear time in the worst case. The GR algorithm is illustrated on sets of Pareto optima obtained from five interactive methods for multi-objective optimization and three non-linear multi-objective test problems. These results suggest that the GR algorithm provides an efficient way to identify subsets of preferred Pareto optima from larger sets.     

Entropy increase in dynamical systems

The rate of increase of the non-equilibrium entropy introduced by Goldstein and Penrose, defined on nonstationary probability measures for an abstract dynamical system, is quantitatively related to the Kolmogorov-Sinai entropy of the system. It is shown in particular that for ergodic systems the asymptotic rate of entropy increase coincides with the Kolmogorov-Sinai entropy. Supported in part by NSF Grant No. PHY 78-03816.     

A concise synthesis of beta-asparaginyladenylate

Stable analogues of acyladenylate intermediates, such as N-acylphosphoramidates, are useful probes of tRNA aminoacylation and enzyme mechanism, and have potential application as enzyme inhibitors. We now report a concise, "one-pot" synthesis of beta-asparaginyladenylate using a novel coupling protocol that yields the target N-acylphosphoramidate in three reactions from readily available precursors. This simple synthetic procedure may represent a general approach for the preparation of functionalized N-acylphosphoramidates from amides that do not undergo coupling under the conditions of existing literature protocols.     

Cu(II)-nitroxyl radicals as catalytic galactose oxidase mimics

Results from Hammett correlation studies and primary kinetic isotope effects for the CuCl-TEMPO catalysed aerobic benzyl alcohol oxidations are inconsistent with an oxoammonium based mechanism. We postulate a copper-mediated dehydrogenation mechanism, in which TEMPO regenerates the active Cu(II)-species. This mechanism is analogous to that observed for Galactose Oxidase and mimics thereof.     

Sensitivity of MRI in metastatic neoplasia: a case report

Serial magnetic resonance imaging (MRI) and computed tomography (CT) were performed on a patient with metastatic lung cancer to brain. Magnetic resonance (MR) visualized two foci of intracerebral metastasis six weeks prior to CT.     

Remarks on the global Markov property

The global Markov property is established for the + state and the – state of attractive lattice systems (e.g., the ferromagnetic Ising model and most other systems for which the FKG inequalities are satisfied) and of the (continuum) Widom Rowlinson model.Supported in part by NSF Grant No. PHY 78-03816