Motivated by Bland's linear programming (LP) generalization of the renowned Edmonds-Karp efficient refinement of the Ford-Fulkerson maximum flow algorithm, we analyze three closely related natural augmentation rules for LP and integer-linear programming (ILP) augmentation algorithms. For all three rules and in both contexts, LP and ILP, we bound the number of augmentations. Extending Bland's "discrete steepest-descent" augmentation rule (i.e., choosing directions with the best ratio of cost improvement per unit 1-norm length, and then making maximal augmentations in such directions) from LP to ILP, we (i) show that the number of discrete steepest-descent augmentations is bounded by the number of elements in the Graver basis of the problem matrix and (ii) give the first strongly polynomial-time algorithm for N-fold ILP. For LP, two of the rules can suffer from a "zig-zagging" phenomenon, and so in those cases we apply the rules more subtly to achieve good bounds. Our results improve on what is known for such augmentation algorithms for LP (e.g., extending the style of bounds found by Kitahara and Mizuno for the number of steps in the simplex method) and are closely related to research on the diameters of polytopes and the search for a strongly polynomial-time simplex or augmentation algorithm.

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.

The unique properties of lasers create an enormous potential for specific treatment of chronic ear disease. Despite the widespread acceptance and use of the laser, however, a complete understanding of the time- and space-dependent temperature distribution in otic capsule bone immediately after pulsed laser exposure has not been elucidated. Using a liquid nitrogen-cooled mercury-cadmium telluride infrared detector, the temperature distribution in human cadaveric otic capsule bone was determined immediately after pulsed (100 msec) carbon dioxide laser exposure (0.3 to 4.0 W; 200 microm spot diameter). The time- and space-dependent temperature increases and thermal diffusion were determined as a function of the laser power density and were found to vary linearly.

Previous studies have reported altered dentinal structure and properties after laser irradiation. It was the aim of this investigation to determine the thermal and ablative effects of XeCl irradiation in dentin and then to investigate microstructural and physicochemical changes in the residual dentin structure. Extracted human molar tooth roots were bisected and coated with acid-resistant varnish, leaving a window. After irradiation of one half at 1 Hz, 15 ns pulse durations, fluences of 0.5 - 2 J/cm2, both halves were subjected to acidified gelatin gel at pH 4.5. The carious lesions were bisected and used to perform SEM and microhardness measurements.