Complex 3D digital objects are used in many domains such as animation films, scientific visualization, medical imaging and computer vision. These objects are usually represented by triangular meshes with many triangles. The simplification of those objects in order to keep them as close as possible to the original has received a lot of attention in the recent years. In this context, we propose a simplification algorithm which is focused on the accuracy of the simplifications. The mesh simplification uses edges collapses with vertex relocation by minimizing an error metric. Accuracy is obtained with the two error metrics we use: the Accurate Measure of Quadratic Error (AMQE) and the Symmetric Measure of Quadratic Error (SMQE). AMQE is computed as the weighted sum of squared distances between the simplified mesh and the original one. Accuracy of the measure of the geometric deviation introduced in the mesh by an edge collapse is given by the distances between surfaces. The distances are computed in between sample points of the simplified mesh and the faces of the original one. SMQE is similar to the AMQE method but computed in the both, direct and reverse directions, i.e. simplified to original and original to simplified meshes. The SMQE approach is computationnaly more expensive than the AMQE but the advantage of computing the AMQE in a reverse fashion results in the preservation of boundaries, sharp features and isolated regions of the mesh. For both measures we obtain better results than methods proposed in the literature.

This dissertation investigates optimization approaches applied to radiation therapy in cancer treatment. Since cancerous cells are surrounded by critical organs and normal tissues, there is conflicting objectives in the treatment design of providing sufficient radiation dose to tumor region, while avoiding normal healthy cells. In general, the goal of radiation therapy is to conform the spatial distribution of the prescribed dose to the tumor volume while minimizing the dose to the surrounding normal structures. A recent advanced technology, using multi-leaf collimator integrated into linear accelerator, provides much better opportunities to achieve this goal: the radiotherapy based on non-uniform radiation beams intensities is called Intensity-Modulated Radiation Therapy. My dissertation research offers a quadratic mixed integer programming approach to determine optimal beam orientations and beamlets intensity simultaneously. The problems generated from real patient cases are large-scale dense instances due to the physics of dose contributions from beamlets to volume elements. The research highlights computational techniques to improve solution times for these intractable instances. Furthermore, results from this research will provide plans that are clinically acceptable and superior in plan quality, thus directly improve the curity rate and lower the normal tissue complication for cancer patients.

Submitted by Daniele Amaral (daniee_ni@hotmail.com) on 2016-09-12T18:53:29Z No. of bitstreams: 1 DissCAC.pdf: 4343040 bytes, checksum: e2ee4b69c3269f2aca979c23c21e6c9a (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-13T18:39:11Z (GMT) No. of bitstreams: 1 DissCAC.pdf: 4343040 bytes, checksum: e2ee4b69c3269f2aca979c23c21e6c9a (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-13T18:39:22Z (GMT) No. of bitstreams: 1 DissCAC.pdf: 4343040 bytes, checksum: e2ee4b69c3269f2aca979c23c21e6c9a (MD5) / Made available in DSpace on 2016-09-13T18:39:31Z (GMT). No. of bitstreams: 1 DissCAC.pdf: 4343040 bytes, checksum: e2ee4b69c3269f2aca979c23c21e6c9a (MD5) Previous issue date: 2015-05-22 / Não recebi financiamento / This work presents the development and implementation of a didactic sequence in order to motivate and teach school students quadratic functions. To do this, we built a cannon made of tiner cans and prepared a serie of activities that have been subdivided into three phases: construction, competition and activities with the use of the software GeoGebra. The work done with students in these aroused a greater interest in the matter and was extremely valuable because students did not forget the acquired learning. / Neste trabalho apresentamos o desenvolvimento e a implementação de uma sequência didática a fim de motivar e ensinar os alunos do Ensino Médio o tema funções quadráticas. Para isto, construímos um canhão feito de latas de tiner e preparamos uma série de atividades que foram subdivididas em 3 fases: a construção, a competição e atividades com o uso do software GeoGebra. O trabalho realizado com os alunos despertou nestes um maior interesse pela matéria e foi de extrema valia, pois os alunos não se esqueceram do aprendizado adquirido.

The pressure from high population density leads to the creation of high-rise structures within urban areas. Consequently, the design of facilities which confront the challenges of emergency evacuation from high-rise buildings become a complex concern. This paper proposes an embedded program which combines a deterministic (GMAFLAD) and stochastic model (M/G/C/C State Dependent Queueing model) into one program, GMAF_MGCC, to solve an evacuation problem. An evacuation problem belongs to Quadratic Assignment Problem (QAP) class which will be formulated as a Quadratic Set Packing model (QSP) including the random flow out of the building and the random pairwise traffic flow among activities. The procedure starts with solving the QSP model to find all potential optimal layouts for the problem. Then, the stochastic model calculates an evacuation time of each solution which is the primary decision variable to figure the best design for the building. Here we also discuss relevant topics to the new program including the computational accuracy and the correlation between a successful rate of solving and problems’ scale. This thesis examines the relationship of independent variables including arrival rate, population and a number of stories with the dependent variable, evacuation time. Finally, the study also analyzes the probability distribution of an evacuation time for a wide range of problem scale.

The main topic of this thesis is integer quadratic programming with applications to problems arising in the areas of automatic control and communication. One of the most widespread modern control principles is the discrete-time method Model Predictive Control (MPC). The main advantage with MPC, compared to most other control principles, is that constraints on control signals and states can easily be handled. In each time step, MPC requires the solution of a Quadratic Programming (QP) problem. To be able to use MPC for large systems, and at high sampling rates, optimization routines tailored for MPC are used. In recent years, the range of application of MPC has been extended from constrained linear systems to so-called hybrid systems. Hybrid systems are systems where continuous dynamics interact with logic. When this extension is made, binary variables are introduced in the problem. As a consequence, the QP problem has to be replaced by a far more challenging Mixed Integer Quadratic Programming (MIQP) problem. Generally, for this type of optimization problems, the computational complexity is exponential in the number of binary optimization variables. In modern communication systems, multiple users share a so-called multi-access channel, where the information sent by different users is separated by using almost orthogonal codes. Since the codes are not completely orthogonal, the decoded information at the receiver is slightly correlated between different users. Further, noise is added during the transmission. To estimate the information originally sent, a maximum likelihood problem involving binary variables is solved. The process of simultaneously estimating the information sent by multiple users is called multiuser detection. In this thesis, the problem to efficiently solve MIQP problems originating from MPC is addressed. Two different algorithms are presented. First, a polynomial complexity preprocessing algorithm for binary quadratic programming problems is presented. By using the algorithm, some, or all, binary variables can be computed efficiently already in the preprocessing phase. In simulations, the algorithm is applied to unconstrained MPC problems with a mixture of real and binary control signals. It has also been applied to the multiuser detection problem, where simulations have shown that the bit error rate can be significantly reduced by using the proposed algorithm as compared to using common suboptimal algorithms. Second, an MIQP algorithm tailored for MPC is presented. The algorithm uses a branch and bound method where the relaxed node problems are solved by a dual active set QP algorithm. In this QP algorithm, the KKT-systems are solved using Riccati recursions in order to decrease the computational complexity. Simulation results show that both the QP solver and the MIQP solver proposed have lower computational complexity than corresponding generic solvers. / <p>Report code: LiU-TEK-LIC-2005:71.</p>

This thesis explores the integration of sustainability into Modern Portfolio Theory (MPT) optimization by introducing stepwise filtration and optimization. This study acknowledges the growing importance of sustainability in investment strategies and modifies the traditional MPT framework to include environmental, social, and governance (ESG) factors. A systematic filtration process is conducted where each asset undergoes a step-by-step filtration based on different ESG criteria. For each filtration step, portfolio optimization is performed to find the most efficient portfolios under the filtered criteria. The effect of each filtration on portfolio risk and return profile provides insights into the trade-offs between financial performance and sustainability impacts. The findings indicate that investors considering the ethical aspects of ESG can achieve these goals without significantly affecting the portfolio risk and return. However, investors incorporating all aspects of ESG will experience a higher drop in the efficient frontier. Moreover, while investigating an additional index, including more companies, investors can attain a better portfolio profile while incorporating all aspects of ESG. A central ambition of this study has been enlighten investors regarding the different aspects of ESG and the trade-offs of integrating sustainability into investment practices. Thus, this study seeks to refine the investor decision-making process and encourage investors to make more informed sustainable decisions. / Detta examensarbete undersöker hur hållbarhet kan integreras i Modern Portfolio Theory (MPT) genom att introducera en stegvis filtrering och optimering. Denna studie framhäver den växande betydelsen av hållbarhet inom investeringsstrategier och modifierar det tradionella ramverket för MPT för att inkludera miljön, socialt ansvar och bolagsstyrning (ESG). En systematisk filtreringsprocess genomförs där varje tillgång genomför en iterativ filtrering baserad på ESG-kriterier. För varje filtreringssteg utförs portföljdoptimering för att hitta de mest effektiva portföljerna under den filtrerade kriterierna. Denna process ger insikt i avvägningarna mellan finansiell avkastning och hållbarhetseffekter. Resultaten indikerar att investerare som beaktar de etiska aspekter kan uppnå dessa mål utan att nämnvärt påverka portföljens risk och avkastningsprofil. Dock, investerare som beaktar samtliga aspekter av ESG kommer att uppleva en större minskning av den effektiva fronten. Dessutom kan investerare, genom utforskning av ett kompletterande index som innefattar ett större urval av företag, uppnå en förbättrad portföljprofiler samtidigt som alla ESG-aspekter beaktas. En central ambition för denna studie har varit att upplysa investerare om de olika aspekterna av ESG och avvägningarna med att integrera hållbarhet i investeringspraxis. Således, strävar denna studie efter att förbättra investerarnas beslutprocess och uppmuntra investerare till att fatta med informerade hållbara beslut.

Quadratic curvature terms are commonly introduced in the action as first-order corrections of General Relativity, and, in this thesis, we investigated their impact on the most simple isolated objects, that are the static and spherically symmetric ones. Most of the work has been done in the context of Stelle's theory of gravity, in which the most general quadratic contractions of curvature tensors are added to the action of General Relativity without a cosmological constant. We studied this theory's possible static, spherically symmetric and asymptotically flat solutions with both analytical approximations and numerical methods. We found black holes with Schwarzschild and non-Schwarzschild nature, naked singularities which can have either an attractive or repulsive gravitational potential in the origin, non-symmetric wormholes which connects an asymptotically flat spacetime with an asymptotically singular one, and non-vacuum solutions modeled by perfect fluids with different equations of state. We described the general geometrical properties of these solutions and linked these short-scale behaviors to the values of the parameters which characterize the gravitational field at large distances. We studied linear perturbations of these solutions, finding that most are unstable, and presented a first attempt to picture the parameter space of stable solutions. We also studied the Thermodynamics of black holes and described their evaporation process: we found that either evaporation leads black holes to unstable configurations, or the predictions of quadratic gravity are unphysical. We also considered the possibility of generalizing Stelle's theory by removing the dependence from the only mass-scale present by including a new dynamical scalar field, making the theory scale invariant. Having a more complex theory, we did not investigate exotic solutions but limited ourselves to the impact of the new additional degrees of freedom on known analytical solutions. It was already known that in a cosmological setting this theory admits a transition between two de Sitter configurations; we analyzed the same problem in the context of static and spherically symmetric solutions and found a transition between two Schwarzschild-de Sitter configurations. In order to do that, we studied both linear perturbations and the semiclassical approximation of the path integral formulation of Euclidean quantum gravity. At last, we tried to extract some phenomenological signatures of the exotic solutions. In particular, we investigated the shadow of an object on background free-falling light, and a possible way of determining the behavior close to the origin using mass measurements that rely on different physical processes. We show that, whenever these measurements are applied to the case of compact stars, in principle it could be possible to distinguish solutions where different equations of state describe the fluid.

Doctor of Philosophy / Department of Electrical and Computer Engineering / Balasubramaniam Natarajan / For any automated surveillance operation to be successful, it is critical to have sensing resources strategically positioned to observe, interpret, react and maybe even predict events.In many practical scenarios, it is also expected that different zones within a surveillance area may have different probability of event detection (or false alarm) requirements. The operational objective in such surveillance systems is to optimize resources (number of sensors and the associated cost) and their deployment while guaranteeing a certain assured level of detection/false alarm performance. In this dissertation, we study two major challenges related to sensor deployment in distributed sensor networks (DSNs) for detection applications. The first problem we study is the sensor deployment problem in which we ask the following question: Given a finite number of sensors (with a known sensing profile), how can we deploy these sensors such that we best meet the detection and false alarm requirements in a DSN employing a specific information fusion rule? Even though sensor deployment has garnered significant interest in the past, a unified, analytical framework to model and study sensor deployment is lacking. Additionally, the algorithms proposed in literature are typically heuristic in nature and are limited to (1) simplistic DSN fusion architectures, and (2) DSNs with uniform detection/false alarm requirements. In this dissertation, we propose a novel treatment of the sensor deployment problem using concepts from optimal control theory. Specifically, the deployment problem is formulated as a linear quadratic regulator (LQR) problem which provides a rigorous and analytical framework to study the deployment problem. We develop new sensor deployment algorithms that are applicable to a wide range of DSN architectures employing different fusion rules such as (1) logical OR fusion; (2) value fusion; (3) majority decision fusion, and (4) optimal decision fusion. In all these cases, we demonstrate that our proposed control theoretic deployment approach is able to significantly outperform previously proposed algorithms. The second problem considered in this dissertation is the “self healing” problem in which we ask the following question: After the failure of a number of sensors, how can one reconfigure the DSN such that the performance degradation due to sensor loss is minimized? Prior efforts in tackling the self healing problem typically rely on assumptions that don’t accurately capture the behavior of practical sensors/networks and focus on minimizing performance degradation at a local area of the network instead of considering overall performance of the DSN. In this work, we propose two self healing strategies the first approach relies on adjusting decision thresholds at the fusion center. The second approach involves sensor redeployment based on our control theoretic deployment framework. Simulation results illustrate that the proposed algorithms are effective in alleviating the performance degradation due to sensor loss.

This study investigates to what extent educators’ pedagogical content knowledge affects learners’ achievement in quadratic functions. The components of pedagogical content knowledge (PCK) examined are: (i) mathematical content knowledge (MCK), (ii) knowledge of learners’ conceptions, and misconceptions, and (iii) knowledge of strategies. The participants were seventeen mathematics educators and ten learners from each educator’s class. The sample of educators was a convenient sample, while the sample of learners was selected by means of random sampling. A mixed method design was used to execute the study. Data about educators’ MCK, and knowledge of learners’ misconceptions were collected by means of a questionnaire. An interview was used to gather data about educators’ knowledge of strategies. Data on learners’ achievements and misconceptions was collected by means of a questionnaire. Descriptive statistics were used to describe the effect of each component of the educators’ PCK on learners’ achievements. The result indicates that the achievement of learners who are taught by educators who have strong PCK is higher than the achievement of learners who are taught by educators who have weak PCK. / Mathematical Sciences / M. Ed. (Mathematics Education)

This thesis develops techniques for the design and analysis of controllers to achieve sub-micron accuracy on the position of electron beams for the optimal performance of synchrotrons. The techniques have been applied to Diamond Light Source, the UK's national synchrotron facility. Electron beam motion in synchrotrons is considered as a large-scale, two-dimensional process and by using basis functions, controllable modes of the process are identified which are independent and allow the design to be approached in terms of a family of single-input, single-output transfer functions. This thesis develops techniques for the design and analysis of controllers to achieve sub-micron accuracy on the position of electron beams for the optimal performance of synchrotrons. The techniques have been applied to Diamond Light Source, the UK's national synchrotron facility. Electron beam motion in synchrotrons is considered as a large-scale, two-dimensional process and by using basis functions, controllable modes of the process are identified which are independent and allow the design to be approached in terms of a family of single-input, single-output transfer functions. In this thesis, loop shaping concepts for dynamical systems are applied to the two-dimensional frequency domain to meet closed loop specifications. Spatial uncertainties are modelled by complex Fourier matrices and the closed loop robust stability, in the presence of spatial uncertainties is analysed within an Integral Quadratic Constraint framework. Two extensions to the unconstrained, single-actuator array controller design are considered. The first being anti-windup augmentation to give satisfactory performance when rate limit constraints are imposed on the actuators and the second being a strategy to account for two arrays of actuators with different dynamics. The resulting control schemes offer both stability and performance guarantees within structures that are feasible for online computation in real time.