Circles in the Water: Towards Island Group Labeling

Many algorithmic results are known for automated label placement on maps. However, algorithms to compute labels for groups of features, such as island groups, are largely missing. In this paper we address this issue by presenting new, efficient algorithms for island label placement in various settings. We consider straight-line and circular-arc labels that may or may not overlap a given set of islands. We concentrate on computing the line or circle that minimizes the maximum distance to the islands, measured by the closest distance. We experimentally test whether the generated labels are reasonable for various real-world island groups, and compare different options. The results are positive and validate our geometric formalizations

Multi-objective design optimization of a mobile-bearing total disc arthroplasty considering spinal kinematics, facet joint loads, and metal-on-polyethylene contact mechanics

Total disc arthroplasty (TDA) is a motion-preserving surgical technique used to treat spinal disorders, when more conservative medical therapies fail. Unfortunately, a high incidence of revision surgery exists due to postoperative complications including abnormal kinematics, facet joint arthritis, and implant failures. However, TDA is still an attractive option, since an optimally designed artificial disc is expected to reproduce native segmental biomechanics. Correspondingly, it would mitigate the development of adjacent segment diseases (a major concern of spinal fusion) caused by altered segmental biomechanics. Design optimization is a process of finding the best design parameters for a component/system to satisfy one/multiple design requirements using optimization algorithms. The shape of a candidate design is parametrized using computer-aided design, such that design parameters are manipulated to minimize one/multiple objective functions subject to performance constraints and design space bounds. Optimization algorithms typically require the gradients of the objective/constraint functions with respect to each design variable. In the traditional design optimization, due to the high computational cost to calculate the gradients by performing finite element analysis in each optimization iteration, it often results in a slow process to seek the optimal solution. To address the problem, an artificial neural network (ANN) was implemented to derive the analytical expressions of the objective/constraint function and their gradients. By incorporating analytical gradients, we successfully developed a multiobjective optimization (MOO) framework considering three performance metrics simultaneously. Furthermore, a new mobile-bearing TDA design concept featuring a biconcave polyethylene (PE) core was proposed, to strengthen the PE rim, where a high risk of fracture exists. It was hypothesized that there is a trade-off relationship among postoperative performance metrics in terms of spinal kinematics, facet joint loading, and metal-on-polyethylene contact mechanics. We tested this hypothesis by refining the new TDA to match normal segmental biomechanics and alleviate PE core stress. After performing MOO, the best-trade-off TDA design was determined by the solved three-dimensional Pareto frontier. The novel MOO framework can be also used to improve existing TDA designs, as well as to push the cutting edge of surgical techniques for the treatment of spinal disorders

Capturing points with a rotating polygon (and a 3D extension)

This is a post-peer-review, pre-copyedit version of an article published in Theory of computing systems: an international journal. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00224-018-9885-yWe study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this problem where the rotation center is a given point or lies on a segment or a line. We also solve an extension to 3D where we rotate a polyhedron around a given point to contain the maximum number of elements from a set of points in the space.Peer ReviewedPostprint (author's final draft

Analyzing the Biomechanical Nature of Thoracic Kyphosis and Other Mid-Sagittal Spinal Deformities Using Finite Element Analysis

Thoracic kyphosis is the mid-sagittal misalignment in the human thoracic spine. Occurring in both adults and children, this spinal deformity is caused by the likes of poor posture, genetics, osteoporosis and intervertebral disc degeneration. This disease results in the patient having a rounded or hump back appearance causing strain on muscles, internal organs and improper walking gate. Corrections for this condition involve surgical implantation of metallic hardware to straighten the patient\u27s posture. However, this treatment does not come without its own drawbacks such as a retrogressive forward head posture (FHP) which can occur post-surgery. With the assistance of computer aided design and finite element analysis, we propose to link the cause of FHP to the surgical realignment of the thoracic spine

A Semi-Analytical Model for Gravitational Microlensing

This thesis describes the theory and implementation of a semi-analytical model for gravitational microlensing. Gravitational microlensing is observed when a distant background `source' star comes into close alignment with an intermediate `lens' star. The gravitational eld of the lens de ects the paths of light emitted from the source, which causes an increase in its observed brightness. As the alignment of the two stars changes with time, the apparent magni cation of the source follows a well de ned `lightcurve'. A companion body (such as a planet) orbiting the lens star can introduce large deviations from the standard lightcurve, which can be modelled to determine a mass ratio and separation for the companion(s). This provides a means to detect extrasolar planets orbiting the lens star. We show, from basic principles, the development of the standard model of a mi- crolensing event, including the e ect of multiple lens masses and orbital motion. We discuss the two, distinctly di erent, numerical approaches that are used to calculate theoretical lightcurves using this model. The `ray shooting' approaches are discussed with reference to the previously developed modelling code (MLENS), which implemented them. This is followed by a comprehensive description of the `semi-analytical' approaches used in the new software (mlens2) developed during this thesis programme; a key feature of these techniques is the determination of the source magni cation from the roots of a high order polynomial. We also discuss the process of nding the best- t model for an observed microlensing event, with respect to the mlens2 software package. Finally, we demonstrate the capabilities of our semi-analytical model by generating theoretical lightcurves for the microlensing events OGLE-2005-BLG-390 and OGLE-2006-BLG-109 and comparing them to the observational data and published models

Building on Oldroyd’s viscoplastic legacy: Perspectives and new developments

The decade following the second world war heralded the publication of a collection of important papers on non-Newtonian fluid mechanics; Oldroyd’s work featured heavily in this collection. Not only did these articles establish important results, but Oldroyd’s style and methods set the scene for subsequent work in the area, exploiting mathematical analysis to formulate problems, establish results and guide further research. While Oldroyd’s name will forever be linked with the study of elastic fluids, the purpose of the present paper is to offer a modern perspective on a number of Oldroyd’s papers on viscoplastic fluids from 1947–1951 [1], [2], [3], [4], [5], [6], [7], [8]. Along the way, we sprinkle in a brief review of some of the subsequent developments stemming from Oldroyd’s advances, together with a few new results guided by his work. Following the approach of most of Oldroyd’s original papers, we focus on unidirectional flow down conduits. In an Appendix, we complement this discussion with a lubrication analysis, extending, clarifying and correcting the important original analysis of Walton and Bittleston (1991) [9]; although lubrication theory was not directly utilized by Oldroyd, the methodology aligns with his philosophy of using asymptotic and analytical approaches

Mechanical design automation: a case study on plastic extrusion die tooling

The Skills Gap in Mechanical Engineering (ME) Design has been widening with the increasing number of baby boomers retiring (Silver Tsunami) and the lack of a new generation to acquire, practice and perfect their knowledge base. This growing problem has been addressed with several initiatives focused on attracting and retaining young talent; however, these types of initiatives may not be timely for this new group to be trained by an established Subject Matter Expert (SME) group. Automated Engineering Design provides a potential pathway to address not only the Skills Gap but also the transfer of information from SMEs to a new generation of engineers. Automation has been at the heart of the Advanced Manufacturing Industry, and has been successful at accomplishing repetitive tasks with processes, software and equipment. The next stage in Advanced Manufacturing is further integrating Machine Learning techniques (Artificial Intelligence (AI)) in order to mimic human decision making. These initiatives are clear for the type of mechanized systems and repetitive processes present in the manufacturing world, but the question remains if they can be effectively applied to the decision heavy area of ME Design. A collaboration with an industry partner New Jersey Precision Technologies (NJPT) was established in order to address this question. This thesis presents an ME Design Automation process involving a multi-stage approach: Design Definition, Task Differentiation, Workflow Generation and Expert System Development. This process was executed on plastic extrusion tooling design. A Computer Aided Design (CAD) based Expert System was developed for the Automation of design, and the generation of a database towards future Machine Learning work. This system was run on 6 extrusion product examples previously designed by NJPT through traditional methods. The time needed to generate the design was reduced by 95-98%. This thesis demonstrates the capability of automating ME design, the potential impact in industry and next steps towards the application of AI