Optimization in a Simulation Setting: Use of Function Approximation in Debt Strategy Analysis

The stochastic simulation model suggested by Bolder (2003) for the analysis of the federal government's debt-management strategy provides a wide variety of useful information. It does not, however, assist in determining an optimal debt-management strategy for the government in its current form. Including optimization in the debt-strategy model would be useful, since it could substantially broaden the range of policy questions that can be addressed. Finding such an optimal strategy is nonetheless complicated by two challenges. First, performing optimization with traditional techniques in a simulation setting is computationally intractable. Second, it is necessary to define precisely what one means by an "optimal" debt strategy. The authors detail a possible approach for addressing these two challenges. They address the first challenge by approximating the numerically computed objective function using a function-approximation technique. They consider the use of ordinary least squares, kernel regression, multivariate adaptive regression splines, and projection-pursuit regressions as approximation algorithms. The second challenge is addressed by proposing a wide range of possible government objective functions and examining them in the context of an illustrative example. The authors' view is that the approach permits debt and fiscal managers to address a number of policy questions that could not be fully addressed with the current stochastic simulation engine.Debt management; Econometric and statistical methods; Fiscal policy; Financial markets

Modeling and hexahedral meshing of cerebral arterial networks from centerlines

Computational fluid dynamics (CFD) simulation provides valuable information on blood flow from the vascular geometry. However, it requires extracting precise models of arteries from low-resolution medical images, which remains challenging. Centerline-based representation is widely used to model large vascular networks with small vessels, as it encodes both the geometric and topological information and facilitates manual editing. In this work, we propose an automatic method to generate a structured hexahedral mesh suitable for CFD directly from centerlines. We addressed both the modeling and meshing tasks. We proposed a vessel model based on penalized splines to overcome the limitations inherent to the centerline representation, such as noise and sparsity. The bifurcations are reconstructed using a parametric model based on the anatomy that we extended to planar n-furcations. Finally, we developed a method to produce a volume mesh with structured, hexahedral, and flow-oriented cells from the proposed vascular network model. The proposed method offers better robustness to the common defects of centerlines and increases the mesh quality compared to state-of-the-art methods. As it relies on centerlines alone, it can be applied to edit the vascular model effortlessly to study the impact of vascular geometry and topology on hemodynamics. We demonstrate the efficiency of our method by entirely meshing a dataset of 60 cerebral vascular networks. 92% of the vessels and 83% of the bifurcations were meshed without defects needing manual intervention, despite the challenging aspect of the input data. The source code is released publicly

The Relation of Finite Element and Finite Difference Methods

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods

Building a Parameterized 4D Cardiac Model with Respiratory Motion from 2D MR Time Series

Projecte final de carrera fet en col.laboració amb Northeastern UniversityAtrial fibrillation (AF) is a growing problem in modern societies with an enormous impact in both short term quality of life and long term survival. A recently developed promising approach to cure AF uses radiofrequency (RF) ablation to carry out "pulmonary vein antrum isolation" (PVAI), electrically isolating the pulmonary veins from the rest of the atrium. However, the lack of proper 3D surgery training, planning, and guidance, along with current limitations in understanding of the true causes and mechanisms of AF, makes this surgery a very difficult task for the surgeons. Therefore recurrence rates and even failures of the procedure, as well as the risk for the patient, increase. The purpose of this work is to develop methods for automatically segmenting and tracking the heart in 4-D cardiac MRI datasets. The reconstructed heart surface will serve as a virtual computer model for the 3D surgery training, planning and guidance. The method used in this project is based on an active contour model for segmentation, followed by a spatial-time post-filtering and processing of the data obtained by the segmentation

Automatic parametric digital design of custom-fit bicycle helmets based on 3D anthropometry and novel clustering algorithm

Bicycle helmets can provide valuable protective effects to the wearer’s head in the event of a crash. However, the level of protection that helmets offer varies greatly between the users for similar impacts. Although these discrepancies can be due to many causes, several researchers highlighted the poor fit of helmets experienced by some users as a possible explanation. Poor helmet fit may be attributed to two main causes. First, the helmet could be worn incorrectly, with the helmet either worn back to front, or tilted forward or backward. The chin strap could also be unfastened. Second, helmet sizes and shapes available to the public might not be suitable for the full range of head morphologies observed in the population. Indeed, for some users, there could either be a large gap and/or pressure points between the inner surfaces of the helmet and the head, or a low coverage of the skull area with significant unprotected regions of the head. While the poorly informed usage of bicycle helmets is partly rectifiable through education programs, the mismatch between the head and the helmet’s inside surfaces primarily relates to the conventional design method and manufacturing techniques used in the industry today. In addition to the safety concerns described above, poorly fitted helmets can cause significant discomfort and may lead people to cycle infrequently or even not cycle altogether. Such a reaction could be somewhat detrimental to the user since the health benefits of regular cycling are significant. Some organisations and institutions even believe that the risks involved in cycling without a helmet (in not-extreme practices such as mountain biking) might be outweighed by the health benefits of consistent physical workout that the activity procures. However, this is impractical in countries such as Australia where mandatory helmet laws (MHL) are in place. Improper helmet fit coupled with MHL might be the reason why Australians cycle less than formerly, despite many initiatives undertaken by the government to grow the activity. In summary, current commercially available bicycle helmets suffer from the lack of fit accuracy, are uncomfortable, and consequently can discourage riding activities in the community, especially in populations like Australia where MHL exist. Therefore, the main purpose of this research has been to develop an innovative method to produce bicycle helmet models that provide a highly accurate fit to the wearer’s head. To achieve this goal, a mass customisation (MC) framework was initiated. MC systems enable the association of the small unit costs of mass production with the compliance of individual customisation. Although MC is defined as the use of both computer-aided design and manufacturing systems to produce custom output, it was decided to focus exclusively, in this study, on the design part of the MC framework of bicycle helmets. More specifically, I tried to answer the following central research question: How can one automatically create commercially ready, custom-fit digital 3D models of bicycle helmets based on 3D anthropometric data? One objective was to create certified design models, since helmets must comply with relevant safety regulations to be sold in a country. Safety standards generally determine the amount of energy a helmet must absorb during a crash, which mostly affects the thickness of its foam liner. Since customisation plays a major role in the helmet liner’s thickness, special considerations on how the automatic process should affect the helmet’s shape were provided. Contrary to conventional helmet production techniques, this method was based on state of the art technologies and techniques, such as three-dimensional (3D) anthropometry, supervised and unsupervised machine-learning methods, and fully parametric design models. Indeed, until today, traditional 1D anthropometric data (e.g., head circumference, head length, and head breath) have been the primary sources of information used by ergonomists for the design of user-centred products such as helmets. Although these data are simple to use and understand, they only provide univariate measures of key dimensions, and these tend to only partially represent the actual shape characteristics of the head. However, 3D anthropometric data can capture the full shape of a scanned surface, thereby providing meaningful information for the design of properly fitted headgear. However, the interpretation of these data can be complicated due to the abundance of information they contain (i.e., a 3D head scan can contain up to several million data points). In recent years, the use of 3D measurements for product design has become more appealing thanks to the advances in mesh parameterization, multivariate analyses, and clustering algorithms. Such analyses and algorithms have been adopted in this project. To the author’s knowledge, this is the first time that these methods have been applied to the design of helmets within a mass customisation framework. As a result, a novel method has been developed to automatically create a complete, certified custom-fit 3D model of a bicycle helmet based on the 3D head scan of a specific individual. Even though the manufacturing of the generated customised helmets is not discussed in detail in this research, it is envisaged that the models could be fabricated using either advanced subtractive and additive manufacturing technologies (e.g., numerical control machining and 3D printing.), standard moulding techniques, or a combination of both. The proposed design framework was demonstrated using a case study where customised helmet models were created for Australian cyclists. The computed models were evaluated and validated using objective (digital models) fit assessments. Thus, a significant improvement in terms of fit accuracy was observed compared to commercially available helmet models. More specifically, a set of new techniques and algorithms were developed, which successively: (i) clean, repair, and transform a digitized head scan to a registered state; (ii) compare it to the population of interest and categorize it into a predefined group; and (iii) modify the group’s generic helmet 3D model to precisely follow the head shape considered. To successfully implement the described steps, a 3D anthropometric database comprising 222 Australian cyclists was first established using a cutting edge handheld white light 3D scanner. Subsequently, a clustering algorithm, called 3D-HEAD-CLUSTERING, was introduced to categorize individuals with similar head shapes into groups. The algorithm successfully classified 95% of the sample into four groups. A new supervised learning method was then developed to classify new customers into one of the four computed groups. It was named the 3D-HEAD-CLASSIFIER. Generic 3D helmet models were then generated for each of the computed groups using the minimum, maximum, and mean shapes of all the participants classified inside a group. The generic models were designed specifically to comply with the relevant safety standard when accounting for all the possible head shape variations within a group. Furthermore, a novel quantitative method that investigates the fit accuracy of helmets was presented. The creation of the new method was deemed necessary, since the scarce computational methods available in the literature for fit assessment of user-centred products were inadequate for the complex shapes of today’s modern bicycle helmets. The HELMET-FIT-INDEX (HFI) was thus introduced, providing a fit score ranging on a scale from 0 (excessively poor fit) to 100 (perfect fit) for a specific helmet and a specific individual. In-depth analysis of three commercially available helmets and 125 participants demonstrated a consistent correlation between subjective assessment of helmet fit and the index. The HFI provided a detailed understanding of helmet efficiency regarding fit. For example, it was shown that females and Asians experience lower helmet fit accuracy than males and Caucasians, respectively. The index was used during the MC design process to validate the high fit accuracy of the generated customised helmet models. As far as the author is aware, HFI is the first method to successfully demonstrate an ability to evaluate users’ feelings regarding fit using computational analysis. The user-centred framework presented in this work for the customisation of bicycle helmet models is proved to be a valuable alternative to the current standard design processes. With the new approach presented in this research study, the fit accuracy of bicycle helmets is optimised, improving both the comfort and the safety characteristics of the headgear. Notwithstanding the fact that the method is easily adjustable to other helmet types (e.g., motorcycle, rock climbing, football, military, and construction), the author believes that the development of similar MC frameworks for user-centred products such as shoes, glasses and gloves could be adapted effortlessly. Future work should first emphasise the fabrication side of the proposed MC system and describe how customised helmet models can be accommodated in a global supply chain model. Other research projects could focus on adjusting the proposed customisation framework to other user-centred products

AutoGraff: towards a computational understanding of graffiti writing and related art forms.

The aim of this thesis is to develop a system that generates letters and pictures with a style that is immediately recognizable as graffiti art or calligraphy. The proposed system can be used similarly to, and in tight integration with, conventional computer-aided geometric design tools and can be used to generate synthetic graffiti content for urban environments in games and in movies, and to guide robotic or fabrication systems that can materialise the output of the system with physical drawing media. The thesis is divided into two main parts. The first part describes a set of stroke primitives, building blocks that can be combined to generate different designs that resemble graffiti or calligraphy. These primitives mimic the process typically used to design graffiti letters and exploit well known principles of motor control to model the way in which an artist moves when incrementally tracing stylised letter forms. The second part demonstrates how these stroke primitives can be automatically recovered from input geometry defined in vector form, such as the digitised traces of writing made by a user, or the glyph outlines in a font. This procedure converts the input geometry into a seed that can be transformed into a variety of calligraphic and graffiti stylisations, which depend on parametric variations of the strokes

Tank gunnery prediction systems

This thesis is concerned with fire control prediction schemes for tanks employed in a defensive role against moving targets. The problem is considered in three parts: the determination of likely target movement patterns in an operational setting; the assessment and modelling of human operator response to those motions; and the utilisation of this response in optimal prediction schemes. In the first part the results from war games, tactical exercises and field trials are collated, and a method is devised for generating test target tracks for human operator study and prediction scheme evaluation. In the second part previous approaches to operator modelling are reviewed, laboratory experiments are described and a mathematical model of human response is developed. In the third part the general statistical properties of predictors are examined, a new class of predictive algorithm called the 'threshold' algorithm is devised, and this type of algorithm is then evaluated using the results of the previous two parts. The thesis ends with some consideration of further research requirements or possibilities, and of the steps needed to validate the results obtained so far.<p

Building a Parameterized 4D Cardiac Model with Respiratory Motion from 2D MR Time Series

Projecte final de carrera fet en col.laboració amb Northeastern UniversityAtrial fibrillation (AF) is a growing problem in modern societies with an enormous impact in both short term quality of life and long term survival. A recently developed promising approach to cure AF uses radiofrequency (RF) ablation to carry out "pulmonary vein antrum isolation" (PVAI), electrically isolating the pulmonary veins from the rest of the atrium. However, the lack of proper 3D surgery training, planning, and guidance, along with current limitations in understanding of the true causes and mechanisms of AF, makes this surgery a very difficult task for the surgeons. Therefore recurrence rates and even failures of the procedure, as well as the risk for the patient, increase. The purpose of this work is to develop methods for automatically segmenting and tracking the heart in 4-D cardiac MRI datasets. The reconstructed heart surface will serve as a virtual computer model for the 3D surgery training, planning and guidance. The method used in this project is based on an active contour model for segmentation, followed by a spatial-time post-filtering and processing of the data obtained by the segmentation