Tensor Completion for Multidimensional Inverse Problems with Applications to Magnetic Resonance Relaxometry

This thesis deals with tensor completion for the solution of multidimensional inverse problems. We study the problem of reconstructing an approximately low rank tensor from a small number of noisy linear measurements. New recovery guarantees, numerical algorithms, non-uniform sampling strategies, and parameter selection algorithms are developed. We derive a fixed point continuation algorithm for tensor completion and prove its convergence. A restricted isometry property (RIP) based tensor recovery guarantee is proved. Probabilistic recovery guarantees are obtained for sub-Gaussian measurement operators and for measurements obtained by non-uniform sampling from a Parseval tight frame. We show how tensor completion can be used to solve multidimensional inverse problems arising in NMR relaxometry. Algorithms are developed for regularization parameter selection, including accelerated k-fold cross-validation and generalized cross-validation. These methods are validated on experimental and simulated data. We also derive condition number estimates for nonnegative least squares problems. Tensor recovery promises to significantly accelerate N-dimensional NMR relaxometry and related experiments, enabling previously impractical experiments. Our methods could also be applied to other inverse problems arising in machine learning, image processing, signal processing, computer vision, and other fields.

Myocardial flow reserve by Rb-82 cardiac PET improves the selection of patients eligible for invasive coronary angiography

Aim: We asked whether myocardial flow reserve (MFR) by Rb-82 cardiac PET improve the selection of patients eligible for invasive coronary angiography (ICA). Material and Methods: We enrolled 26 consecutive patients with suspected or known coronary artery disease who performed dynamic Rb-82 PET/CT and (ICA) within 60 days; 4 patients who underwent revascularization or had any cardiovascular events between PET and ICA were excluded. Myocardial blood flow at rest (rMBF), at stress with adenosine (sMBF) and myocardial flow reserve (MFR=sMBF/rMBF) were estimated using the 1-compartment Lortie model (FlowQuant) for each coronary arteries territories. Stenosis severity was assessed using computer-based automated edge detection (QCA). MFR was divided in 3 groups: G1:MFR<1.5, G2:1.5≤MFR<2 and G3:2≤MFR. Stenosis severity was graded as non-significant (<50% or FFR ≥0.8), intermediate (50%≤stenosis<70%) and severe (≥70%). Correlation between MFR and percentage of stenosis were assessed using a non-parametric Spearman test. Results: In G1 (44 vessels), 17 vessels (39%) had a severe stenosis, 11 (25%) an intermediate one, and 16 (36%) no significant stenosis. In G2 (13 vessels), 2 (15%) vessels presented a severe stenosis, 7 (54%) an intermediate one, and 4 (31%) no significant stenosis. In G3 (9 vessels), 0 vessel presented a severe stenosis, 1 (11%) an intermediate one, and 8 (89%) no significant stenosis. Of note, among 11 patients with 3-vessel low MFR<1.5 (G1), 9/11 (82%) had at least one severe stenosis and 2/11 (18%) had at least one intermediate stenosis. There was a significant inverse correlation between stenosis severity and MFR among all 66 territories analyzed (rho= -0.38, p=0.002). Conclusion: Patients with MFR>2 could avoid ICA. Low MFR (G1, G2) on a vessel-based analysis seems to be a poor predictor of severe stenosis severity. Patients with 3-vessel low MFR would benefit from ICA as they are likely to present a significant stenosis in at least one vessel.

Effects of species turnover on reserve site selection in a fragmented landscape

Changes in species composition is an important process in many ecosystems but rarely considered in systematic reserve site selection. To test the influence of temporal variability in species composition on the establishment of a reserve network, we compared network configurations based on species data of small mammals and frogs sampled during two consecutive years in a fragmented Atlantic Forest landscape (SE Brazil). Site selection with simulated annealing was carried out with the datasets of each single year and after merging the datasets of both years. Site selection resulted in remarkably divergent network configurations. Differences are reflected in both the identity of the selected fragments and in the amount of flexibility and irreplaceability in network configuration. Networks selected when data for both years were merged did not include all sites that were irreplaceable in one of the 2 years. Results of species number estimation revealed that significant changes in the composition of the species community occurred. Hence, temporal variability of community composition should be routinely tested and considered in systematic reserve site selection in dynamic systems.

Simultaneous spectrometric determination of Cu2+, Mn2+ and Zn2+ in polivitaminic/polimineral drug using SPA and GA algorithms for variable selection

Este artigo apresenta uma aplicação do método para determinação espectrofotométrica simultânea dos íons divalentes de cobre, manganês e zinco à análise de medicamento polivitamínico/polimineral. O método usa 4-(2-piridilazo) resorcinol (PAR), calibração multivariada e técnicas de seleção de variáveis e foi otimizado o empregando-se o algoritmo das projeções sucessivas (APS) e o algoritmo genético (AG), para escolha dos comprimentos de onda mais informativos para a análise. Com essas técnicas, foi possível construir modelos de calibração por regressão linear múltipla (RLM-APS e RLM-AG). Os resultados obtidos foram comparados com modelos de regressão em componentes principais (PCR) e nos mínimos quadrados parciais (PLS). Demonstra-se a partir do erro médio quadrático de previsão (RMSEP) que os modelos apresentam desempenhos semelhantes ao prever as concentrações dos três analitos no medicamento. Todavia os modelos RLM são mais simples pois requerem um número muito menor de comprimentos de onda e são mais fáceis de interpretar que os baseados em variáveis latentes.

Optimal dispatch of spinning reserve in a competitive electricity market using genetic algorithms

Ancillary service plays a key role in maintaining operation security of the power system in a competitive electricity market. The spinning reserve is one of the most important ancillary services that should be provided effectively. This paper presents the design of an integrated market for energy and spinning reserve service with particular emphasis on coordinated dispatch of bulk power and spinning reserve services. A new market dispatching mechanism has been developed to minimize the cost of service while maintaining system security. Genetic algorithms (GA) are used for finding the global optimal solutions for this dispatch problem. Case studies and corresponding analyses have been carried out to demonstrate and discuss the efficiency and usefulness of the proposed method.

A Taxonomy for Locality Algorithms on Peer-to-Peer Networks

The continuous growth of peer-to-peer networks has made them responsible for a considerable portion of the current Internet traffic. For this reason, improvements in P2P network resources usage are of central importance. One effective approach for addressing this issue is the deployment of locality algorithms, which allow the system to optimize the peers` selection policy for different network situations and, thus, maximize performance. To date, several locality algorithms have been proposed for use in P2P networks. However, they usually adopt heterogeneous criteria for measuring the proximity between peers, which hinders a coherent comparison between the different solutions. In this paper, we develop a thoroughly review of popular locality algorithms, based on three main characteristics: the adopted network architecture, distance metric, and resulting peer selection algorithm. As result of this study, we propose a novel and generic taxonomy for locality algorithms in peer-to-peer networks, aiming to enable a better and more coherent evaluation of any individual locality algorithm.

Accelerating autonomous learning by using heuristic selection of actions

This paper investigates how to make improved action selection for online policy learning in robotic scenarios using reinforcement learning (RL) algorithms. Since finding control policies using any RL algorithm can be very time consuming, we propose to combine RL algorithms with heuristic functions for selecting promising actions during the learning process. With this aim, we investigate the use of heuristics for increasing the rate of convergence of RL algorithms and contribute with a new learning algorithm, Heuristically Accelerated Q-learning (HAQL), which incorporates heuristics for action selection to the Q-Learning algorithm. Experimental results on robot navigation show that the use of even very simple heuristic functions results in significant performance enhancement of the learning rate.

Reconfiguration of distribution networks to minimize loss and disruption costs using genetic algorithms

In this paper a computational implementation of an evolutionary algorithm (EA) is shown in order to tackle the problem of reconfiguring radial distribution systems. The developed module considers power quality indices such as long duration interruptions and customer process disruptions due to voltage sags, by using the Monte Carlo simulation method. Power quality costs are modeled into the mathematical problem formulation, which are added to the cost of network losses. As for the EA codification proposed, a decimal representation is used. The EA operators, namely selection, recombination and mutation, which are considered for the reconfiguration algorithm, are herein analyzed. A number of selection procedures are analyzed, namely tournament, elitism and a mixed technique using both elitism and tournament. The recombination operator was developed by considering a chromosome structure representation that maps the network branches and system radiality, and another structure that takes into account the network topology and feasibility of network operation to exchange genetic material. The topologies regarding the initial population are randomly produced so as radial configurations are produced through the Prim and Kruskal algorithms that rapidly build minimum spanning trees. (C) 2009 Elsevier B.V. All rights reserved.

Genetic algorithms for continuous optimization problems - a concept of parameter-space size adjustment

The concept of parameter-space size adjustment is pn,posed in order to enable successful application of genetic algorithms to continuous optimization problems. Performance of genetic algorithms with six different combinations of selection and reproduction mechanisms, with and without parameter-space size adjustment, were severely tested on eleven multiminima test functions. An algorithm with the best performance was employed for the determination of the model parameters of the optical constants of Pt, Ni and Cr.

Materialized view selection under the maintenance time constraint

A data warehouse is a data repository which collects and maintains a large amount of data from multiple distributed, autonomous and possibly heterogeneous data sources. Often the data is stored in the form of materialized views in order to provide fast access to the integrated data. One of the most important decisions in designing a data warehouse is the selection of views for materialization. The objective is to select an appropriate set of views that minimizes the total query response time with the constraint that the total maintenance time for these materialized views is within a given bound. This view selection problem is totally different from the view selection problem under the disk space constraint. In this paper the view selection problem under the maintenance time constraint is investigated. Two efficient, heuristic algorithms for the problem are proposed. The key to devising the proposed algorithms is to define good heuristic functions and to reduce the problem to some well-solved optimization problems. As a result, an approximate solution of the known optimization problem will give a feasible solution of the original problem. (C) 2001 Elsevier Science B.V. All rights reserved.

Mathematical methods for spatially cohesive reserve design

The problem of designing spatially cohesive nature reserve systems that meet biodiversity objectives is formulated as a nonlinear integer programming problem. The multiobjective function minimises a combination of boundary length, area and failed representation of the biological attributes we are trying to conserve. The task is to reserve a subset of sites that best meet this objective. We use data on the distribution of habitats in the Northern Territory, Australia, to show how simulated annealing and a greedy heuristic algorithm can be used to generate good solutions to such large reserve design problems, and to compare the effectiveness of these methods.