Exact Solution of Bayes and Minimax Change-Detection Problems

The challenge of detecting a change in the distribution of data is a sequential decision problem that is relevant to many engineering solutions, including quality control and machine and process monitoring. This dissertation develops techniques for exact solution of change-detection problems with discrete time and discrete observations. Change-detection problems are classified as Bayes or minimax based on the availability of information on the change-time distribution. A Bayes optimal solution uses prior information about the distribution of the change time to minimize the expected cost, whereas a minimax optimal solution minimizes the cost under the worst-case change-time distribution. Both types of problems are addressed. The most important result of the dissertation is the development of a polynomial-time algorithm for the solution of important classes of Markov Bayes change-detection problems. Existing techniques for epsilon-exact solution of partially observable Markov decision processes have complexity exponential in the number of observation symbols. A new algorithm, called constellation induction, exploits the concavity and Lipschitz continuity of the value function, and has complexity polynomial in the number of observation symbols. It is shown that change-detection problems with a geometric change-time distribution and identically- and independently-distributed observations before and after the change are solvable in polynomial time. Also, change-detection problems on hidden Markov models with a fixed number of recurrent states are solvable in polynomial time. A detailed implementation and analysis of the constellation-induction algorithm are provided. Exact solution methods are also established for several types of minimax change-detection problems. Finite-horizon problems with arbitrary observation distributions are modeled as extensive-form games and solved using linear programs. Infinite-horizon problems with linear penalty for detection delay and identically- and independently-distributed observations can be solved in polynomial time via epsilon-optimal parameterization of a cumulative-sum procedure. Finally, the properties of policies for change-detection problems are described and analyzed. Simple classes of formal languages are shown to be sufficient for epsilon-exact solution of change-detection problems, and methods for finding minimally sized policy representations are described.

Is sustainable development a motor or a constraint for the professionalization of the pearl oyster industry in tahiti?

This article reports the results of a survey of the pearl oyster industry in French Polynesia territory. Its purpose is to examine the perceptions of the priorities for the development of this industry towards sustainable development. These perceptions were apprehended by a survey of pearl oyster farmers and other stakeholders of the sector (management authorities, scientists). After describing the methodological protocol of these investigations, it comes to confront the priorities chosen by professionals (i.e. pearl farmers) concerning sustainable development, with the perceptions of others stakeholders in the sector. Secondly it comes to build a typology of the priorities of pearl farmers concerning sustainable development. This analysis enables the assessment of the degree of convergence within the sector, which is the base material for defining a shared action plan at the territory scale. This is the first study compiling data of surveys of various professionals and stakeholders of the pearl farming industry in such a large area in French Polynesia.

MAGIC observations of the February 2014 flare of 1ES 1011+496 and ensuing constraint of the EBL density

Context. In February-March 2014, the MAGIC telescopes observed the high-frequency peaked BL Lac 1ES 1011+496 (z=0.212) in flaring state at very-high energy (VHE, E>100GeV). The flux reached a level more than 10 times higher than any previously recorded flaring state of the source. Aims. Description of the characteristics of the flare presenting the light curve and the spectral parameters of the night-wise spectra and the average spectrum of the whole period. From these data we aim at detecting the imprint of the Extragalactic Background Light (EBL) in the VHE spectrum of the source, in order to constrain its intensity in the optical band. Methods. We analyzed the gamma-ray data from the MAGIC telescopes using the standard MAGIC software for the production of the light curve and the spectra. For the constraining of the EBL we implement the method developed by the H.E.S.S. collaboration in which the intrinsic energy spectrum of the source is modeled with a simple function (< 4 parameters), and the EBL-induced optical depth is calculated using a template EBL model. The likelihood of the observed spectrum is then maximized, including a normalization factor for the EBL opacity among the free parameters. Results. The collected data allowed us to describe the flux changes night by night and also to produce di_erential energy spectra for all nights of the observed period. The estimated intrinsic spectra of all the nights could be fitted by power-law functions. Evaluating the changes in the fit parameters we conclude that the spectral shape for most of the nights were compatible, regardless of the flux level, which enabled us to produce an average spectrum from which the EBL imprint could be constrained. The likelihood ratio test shows that the model with an EBL density 1:07 (-0.20,+0.24)stat+sys, relative to the one in the tested EBL template (Domínguez et al. 2011), is preferred at the 4:6 σ level to the no-EBL hypothesis, with the assumption that the intrinsic source spectrum can be modeled as a log-parabola. This would translate into a constraint of the EBL density in the wavelength range [0.24 μm,4.25 μm], with a peak value at 1.4 μm of λF_ = 12:27^(+2:75)_ (-2:29) nW m^(-2) sr^(-1), including systematics.

Filling in gaps of Drosophila melanogaster urate degradation metabolic pathway using metabolomics approaches: towards the core metabolome of the fruit fly

The primary goal of systems biology is to integrate complex omics data, and data obtained from traditional experimental studies in order to provide a holistic understanding of organismal function. One way of achieving this aim is to generate genome-scale metabolic models (GEMs), which contain information on all metabolites, enzyme-coding genes, and biochemical reactions in a biological system. Drosophila melanogaster GEM has not been reconstructed to date. Constraint-free genome-wide metabolic model of the fruit fly has been reconstructed in our lab, identifying gaps, where no enzyme was identified and metabolites were either only produced or consume. The main focus of the work presented in this thesis was to develop a pipeline for efficient gap filling using metabolomics approaches combined with standard reverse genetics methods, using 5-hydroxyisourate hydrolase (5-HIUH) as an example. 5-HIUH plays a role in urate degradation pathway. Inability to degrade urate can lead to inborn errors of metabolism (IEMs) in humans, including hyperuricemia. Based on sequence analysis Drosophila CG30016 gene was hypothesised to encode 5- HIUH. CG30016 knockout flies were examined to identify Malpighian tubules phenotype, and shortened lifespan might reflect kidney disorders in hyperuricemia in humans. Moreover, LC-MS analysis of mutant tubules revealed that CG30016 is involved in purine metabolism, and specifically urate degradation pathway. However, the exact role of the gene has not been identified, and the complete method for gap filling has not been developed. Nevertheless, thanks to the work presented here, we are a step closer towards the development of a gap-filling pipeline in Drosophila melanogaster GEM. Importantly, the areas that require further optimisation were identified and are the focus of future research. Moreover, LC-MS analysis confirmed that tubules rather than the whole fly were more suitable for metabolomics analysis of purine metabolism. Previously, Dow/Davies lab has generated the most complete tissue-specific transcriptomic atlas for Drosophila – FlyAtlas.org, which provides data on gene expression across multiple tissues of adult fly and larva. FlyAtlas revealed that transcripts of many genes are enriched in specific Drosophila tissues, and that it is possible to deduce the functions of individual tissues within the fly. Based on FlyAtlas data, it has become clear that the fly (like other metazoan species) must be considered as a set of tissues, each 2 with its own distinct transcriptional and functional profile. Moreover, it revealed that for about 30% of the genome, reverse genetic methods (i.e. mutation in an unknown gene followed by observation of phenotype) are only useful if specific tissues are investigated. Based on the FlyAtlas findings, we aimed to build a primary tissue-specific metabolome of the fruit fly, in order to establish whether different Drosophila tissues have different metabolomes and if they correspond to tissue-specific transcriptome of the fruit fly (FlyAtlas.org). Different fly tissues have been dissected and their metabolome elucidated using LC-MS. The results confirmed that tissue metabolomes differ significantly from each other and from the whole fly, and that some of these differences can be correlated to the tissue function. The results illustrate the need to study individual tissues as well as the whole organism. It is clear that some metabolites that play an important role in a given tissue might not be detected in the whole fly sample because their abundance is much lower in comparison to other metabolites present in all tissues, which prevent the detection of the tissue-specific compound.

Exact solutions to the short sea shipping distribution problem

Short sea shipping has several advantages over other means of transportation, recognized by EU members. The maritime transportation could be dealt like a combination of two well-known problems: the container stowage problem and routing planning problem. The integration of these two well-known problems results in a new problem CSSRP (Container stowage and ship routing problem) that is also an hard combinatorial optimization problem. The aim of this work is to solve the CSSRP using a mixed integer programming model. It is proved that regardless the complexity of this problem, optimal solutions could be achieved in a reduced computational time. For testing the mathematical model some problems based on real data were generated and a sensibility analysis was performed.

Exact solutions for cluster-growth kinetics with evolving size and shape profiles

In this paper we construct a model for the simultaneous compaction by which clusters are restructured, and growth of clusters by pairwise coagulation. The model has the form of a multicomponent aggregation problem in which the components are cluster mass and cluster diameter. Following suitable approximations, exact explicit solutions are derived which may be useful for the verification of simulations of such systems. Numerical simulations are presented to illustrate typical behaviour and to show the accuracy of approximations made in deriving the model. The solutions are then simplified using asymptotic techniques to show the relevant timescales of the kinetic processes and elucidate the shape of the cluster distribution functions at large times.

Equivalence of quantum field theories related by the θ-exact Seiberg-Witten map

The equivalence of the noncommutative U(N) quantum field theories related by the θ-exact Seiberg-Witten maps is, in this paper, proven to all orders in the perturbation theory with respect to the coupling constant. We show that this holds for super Yang-Mills theories with N=0, 1, 2, 4 supersymmetry. A direct check of this equivalence relation is performed by computing the one-loop quantum corrections to the quadratic part of the effective action in the noncommutative U(1) gauge theory with N=0, 1, 2, 4 supersymmetry.

Lot production size problem and simulation of urban transport

OBJECTIVES AND STUDY METHOD: There are two subjects in this thesis: “Lot production size for a parallel machine scheduling problem with auxiliary equipment” and “Bus holding for a simulated traffic network”. Although these two themes seem unrelated, the main idea is the optimization of complex systems. The “Lot production size for a parallel machine scheduling problem with auxiliary equipment” deals with a manufacturing setting where sets of pieces form finished products. The aim is to maximize the profit of the finished products. Each piece may be processed in more than one mold. Molds must be mounted on machines with their corresponding installation setup times. The key point of our methodology is to solve the single period lot-sizing decisions for the finished products together with the piece-mold and the mold-machine assignments, relaxing the constraint that a single mold may not be used in two machines at the same time. For the “Bus holding for a simulated traffic network” we deal with One of the most annoying problems in urban bus operations is bus bunching, which happens when two or more buses arrive at a stop nose to tail. Bus bunching reflects an unreliable service that affects transit operations by increasing passenger-waiting times. This work proposes a linear mathematical programming model that establishes bus holding times at certain stops along a transit corridor to avoid bus bunching. Our approach needs real-time input, so we simulate a transit corridor and apply our mathematical model to the data generated. Thus, the inherent variability of a transit system is considered by the simulation, while the optimization model takes into account the key variables and constraints of the bus operation. CONTRIBUTIONS AND CONCLUSIONS: For the “Lot production size for a parallel machine scheduling problem with auxiliary equipment” the relaxation we propose able to find solutions more efficiently, moreover our experimental results show that most of the solutions verify that molds are non-overlapping even if they are installed on several machines. We propose an exact integer linear programming, a Relax&Fix heuristic, and a multistart greedy algorithm to solve this problem. Experimental results on instances based on real-world data show the efficiency of our approaches. The mathematical model and the algorithm for the lot production size problem, showed in this research, can be used for production planners to help in the scheduling of the manufacturing. For the “Bus holding for a simulated traffic network” most of the literature considers quadratic models that minimize passenger-waiting times, but they are harder to solve and therefore difficult to operate by real-time systems. On the other hand, our methodology reduces passenger-waiting times efficiently given our linear programming model, with the characteristic of applying control intervals just every 5 minutes.

Exact solutions for the agricultural and the two-dimensional packing problems

Objectives and study method: The objective of this study is to develop exact algorithms that can be used as management tools for the agricultural production planning and to obtain exact solutions for two of the most well known twodimensional packing problems: the strip packing problem and the bin packing problem. For the agricultural production planning problem we propose a new hierarchical scheme of three stages to improve the current agricultural practices. The objective of the first stage is to delineate rectangular and homogeneous management zones into the farmer’s plots considering the physical and chemical soil properties. This is an important task because the soil properties directly affect the agricultural production planning. The methodology for this stage is based on a new method called “Positions and Covering” that first generates all the possible positions in which the plot can be delineated. Then, we use a mathematical model of linear programming to obtain the optimal physical and chemical management zone delineation of the plot. In the second stage the objective is to determine the optimal crop pattern that maximizes the farmer’s profit taken into account the previous management zones delineation. In this case, the crop pattern is affected by both management zones delineation, physical and chemical. A mixed integer linear programming is used to solve this stage. The objective of the last stage is to determine in real-time the amount of water to irrigate in each crop. This stage takes as input the solution of the crop planning stage, the atmospheric conditions (temperature, radiation, etc.), the humidity level in plots, and the physical management zones of plots, just to name a few. This procedure is made in real-time during each irrigation period. A linear programming is used to solve this problem. A breakthrough happen when we realize that we could propose some adaptations of the P&C methodology to obtain optimal solutions for the two-dimensional packing problem and the strip packing. We empirically show that our methodologies are efficient on instances based on real data for both problems: agricultural and two-dimensional packing problems. Contributions and conclusions: The exact algorithms showed in this study can be used in the making-decision support for agricultural planning and twodimensional packing problems. For the agricultural planning problem, we show that the implementation of the new hierarchical approach can improve the farmer profit between 5.27% until 8.21% through the optimization of the natural resources. An important characteristic of this problem is that the soil properties (physical and chemical) and the real-time factors (climate, humidity level, evapotranspiration, etc.) are incorporated. With respect to the two-dimensional packing problems, one of the main contributions of this study is the fact that we have demonstrate that many of the best solutions founded in literature by others approaches (heuristics approaches) are the optimal solutions. This is very important because some of these solutions were up to now not guarantee to be the optimal solutions.

Eficácia dos protocolos modificados de constraint induced movement therapy na função motora e desempenho de atividades diárias

Projeto de Graduação apresentado à Universidade Fernando Pessoa como parte dos requisitos para obtenção do grau de Licenciada em Fisioterapia

Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element

We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We construct a deformation function based on an interpolation of transformations at the nodes of the finite element. In the case of the geometrically exact planar Bernoulli beam element presented in this work, these transformation functions at the nodes are given as rotations. However, due to an intrinsic coupling between rotational and translational components of the deformation function, the formulation provides for a good approximation of the deflection of the beam, as well as of the resultant forces and moments. As both the translational and the rotational components of the deformation function are defined on the logarithmic space, we propose to refer to the novel approach as the “Logarithmic finite element method”, or “LogFE” method.