A measure of non-convexity in the plane and the Minkowski sum

In this paper a measure of non-convexity for a simple polygonal region in the plane is introduced. It is proved that for "not far from convex" regions this measure does not decrease under the Minkowski sum operation, and guarantees that the Minkowski sum has no "holes".Comment: 5 figures; Discrete and Computational Geometry, 201

Constructive procedures to solve 2-dimensional bin packing problems with irregular pieces and guillotine cuts

This paper presents an approach for solving a new real problem in cutting and packing. At its core is an innovative mixed integer programme model that places irregular pieces and defines guillotine cuts. The two-dimensional irregular shape bin packing problem with guillotine constraints arises in the glass cutting industry, for example, the cutting of glass for conservatories. Almost all cutting and packing problems that include guillotine cuts deal with rectangles only, where all cuts are orthogonal to the edges of the stock sheet and a maximum of two angles of rotation are permitted. The literature tackling packing problems with irregular shapes largely focuses on strip packing i.e. minimizing the length of a single fixed width stock sheet, and does not consider guillotine cuts. Hence, this problem combines the challenges of tackling the complexity of packing irregular pieces with free rotation, guaranteeing guillotine cuts that are not always orthogonal to the edges of the stock sheet, and allocating pieces to bins. To our knowledge only one other recent paper tackles this problem. We present a hybrid algorithm that is a constructive heuristic that determines the relative position of pieces in the bin and guillotine constraints via a mixed integer programme model. We investigate two approaches for allocating guillotine cuts at the same time as determining the placement of the piece, and a two phase approach that delays the allocation of cuts to provide flexibility in space usage. Finally we describe an improvement procedure that is applied to each bin before it is closed. This approach improves on the results of the only other publication on this problem, and gives competitive results for the classic rectangle bin packing problem with guillotine constraint

Tibiofemoral Contact Forces in the Anterior Cruciate Ligament-Reconstructed Knee.

PURPOSE: To investigate differences in ACL reconstructed (ACLR) and healthy individuals in terms of the magnitude of the tibiofemoral contact forces, as well as the relative muscle and external load contributions to those contact forces, during walking, running and sidestepping gait tasks. METHODS: A computational electromyography-driven neuromusculoskeletal model was used to estimate the muscle and tibiofemoral contact forces in those with combined semitendinosus and gracilis tendon autograft ACLR (n=104, 29.7±6.5 years, 78.1±14.4 kg) and healthy controls (n=60, 27.5±5.4 years, 67.8±14.0 kg) during walking (1.4±0.2 ms), running (4.5±0.5 ms) and sidestepping (3.7±0.6 ms). Within the computational model, the semitendinosus of ACLR participants was adjusted to account for literature reported strength deficits and morphological changes subsequent to autograft harvesting. RESULTS: ACLRs had smaller maximum total and medial tibiofemoral contact forces (~80% of control values, scaled to bodyweight) during the different gait tasks. Compared to controls, ACLRs were found to have a smaller maximum knee flexion moment, which explained the smaller tibiofemoral contact forces. Similarly, compared to controls, ACLRs had both a smaller maximum knee flexion angle and knee flexion excursion during running and sidestepping, which may have concentrated the articular contact forces to smaller areas within the tibiofemoral joint. Mean relative muscle and external load contributions to the tibiofemoral contact forces were not significantly different between ACLRs and controls. CONCLUSION: ACLRs had lower bodyweight-scaled tibiofemoral contact forces during walking, running and sidestepping, likely due to lower knee flexion moments and straighter knee during the different gait tasks. The relative contributions of muscles and external loads to the contact forces were equivalent between groups

Ownership and control in a competitive industry

We study a differentiated product market in which an investor initially owns a controlling stake in one of two competing firms and may acquire a non-controlling or a controlling stake in a competitor, either directly using her own assets, or indirectly via the controlled firm. While industry profits are maximized within a symmetric two product monopoly, the investor attains this only in exceptional cases. Instead, she sometimes acquires a noncontrolling stake. Or she invests asymmetrically rather than pursuing a full takeover if she acquires a controlling one. Generally, she invests indirectly if she only wants to affect the product market outcome, and directly if acquiring shares is profitable per se. --differentiated products,separation of ownership and control,private benefits of control

A comparative review of 3D container loading algorithms

Three-dimensional cutting and packing problems have a range of important applications and are of particular relevance to the transportation of cargo in the form of container loading problems. Recent years has seen a marked increase in the number of papers examining a variant of the container loading problem ranging from largely theoretical to implementations that focus on meeting the many critical real world constraints. In this paper we review the literature focusing on the solution methodologies employed by researchers, with the aim of providing insight into some of the critical algorithmic design issues. In addition we provide an extensive comparison of algorithm performance across the benchmark literatur