GLODS: Global and Local Optimization using Direct Search

Locating and identifying points as global minimizers is, in general, a hard and time-consuming task. Difficulties increase in the impossibility of using the derivatives of the functions defining the problem. In this work, we propose a new class of methods suited for global derivative-free constrained optimization. Using direct search of directional type, the algorithm alternates between a search step, where potentially good regions are located, and a poll step where the previously located promising regions are explored. This exploitation is made through the launching of several instances of directional direct searches, one in each of the regions of interest. Differently from a simple multistart strategy, direct searches will merge when sufficiently close. The goal is to end with as many direct searches as the number of local minimizers, which would easily allow locating the global extreme value. We describe the algorithmic structure considered, present the corresponding convergence analysis and report numerical results, showing that the proposed method is competitive with currently commonly used global derivative-free optimization solvers.

Group decision making for selection of an information system in a business context

The main objective of this work is to report on the development of a multi-criteria methodology to support the assessment and selection of an Information System (IS) framework in a business context. The objective is to select a technological partner that provides the engine to be the basis for the development of a customized application for shrinkage reduction on the supply chains management. Furthermore, the proposed methodology di ers from most of the ones previously proposed in the sense that 1) it provides the decision makers with a set of pre-defined criteria along with their description and suggestions on how to measure them and 2)it uses a continuous scale with two reference levels and thus no normalization of the valuations is required. The methodology here proposed is has been designed to be easy to understand and use, without a specific support of a decision making analyst.

A framework for using real data with distributed low cost sensors

Currently, due to the widespread use of computers and the internet, students are trading libraries for the World Wide Web and laboratories with simulation programs. In most courses, simulators are made available to students and can be used to proof theoretical results or to test a developing hardware/product. Although this is an interesting solution: low cost, easy and fast way to perform some courses work, it has indeed major disadvantages. As everything is currently being done with/in a computer, the students are loosing the “feel” of the real values of the magnitudes. For instance in engineering studies, and mainly in the first years, students need to learn electronics, algorithmic, mathematics and physics. All of these areas can use numerical analysis software, simulation software or spreadsheets and in the majority of the cases data used is either simulated or random numbers, but real data could be used instead. For example, if a course uses numerical analysis software and needs a dataset, the students can learn to manipulate arrays. Also, when using the spreadsheets to build graphics, instead of using a random table, students could use a real dataset based, for instance, in the room temperature and its variation across the day. In this work we present a framework which uses a simple interface allowing it to be used by different courses where the computers are the teaching/learning process in order to give a more realistic feeling to students by using real data. A framework is proposed based on a set of low cost sensors for different physical magnitudes, e.g. temperature, light, wind speed, which are connected to a central server, that the students have access with an Ethernet protocol or are connected directly to the student computer/laptop. These sensors use the communication ports available such as: serial ports, parallel ports, Ethernet or Universal Serial Bus (USB). Since a central server is used, the students are encouraged to use sensor values results in their different courses and consequently in different types of software such as: numerical analysis tools, spreadsheets or simply inside any programming language when a dataset is needed. In order to do this, small pieces of hardware were developed containing at least one sensor using different types of computer communication. As long as the sensors are attached in a server connected to the internet, these tools can also be shared between different schools. This allows sensors that aren't available in a determined school to be used by getting the values from other places that are sharing them. Another remark is that students in the more advanced years and (theoretically) more know how, can use the courses that have some affinities with electronic development to build new sensor pieces and expand the framework further. The final solution provided is very interesting, low cost, simple to develop, allowing flexibility of resources by using the same materials in several courses bringing real world data into the students computer works.

Programação paralela estruturada aplicada a um problema de reconstrução de imagem

A Digital Breast Tomosynthesis (DBT) é uma técnica que permite obter imagens mamárias 3D de alta qualidade, que só podem ser obtidas através de métodos de re-construção. Os métodos de reconstrução mais rápidos são os iterativos, sendo no en-tanto computacionalmente exigentes, necessitando de sofrer muitas optimizações. Exis-tem optimizações que usam computação paralela através da implementação em GPUs usando CUDA. Como é sabido, o desenvolvimento de programas eficientes que usam GPUs é ainda uma tarefa demorada, dado que os modelos de programação disponíveis são de baixo nível, e a portabilidade do código para outras arquitecturas não é imedia-ta. É uma mais valia poder criar programas paralelos de forma rápida, com possibili-dade de serem usados em diferentes arquitecturas, sem exigir muitos conhecimentos sobre a arquitectura subjacente e sobre os modelos de programação de baixo nível. Para resolver este problema, propomos a utilização de soluções existentes que reduzam o esforço de paralelização, permitindo a sua portabilidade, garantindo ao mesmo tempo um desempenho aceitável. Para tal, vamos utilizar um framework (FastFlow) com suporte para Algorithmic Skeletons, que tiram partido da programação paralela estruturada, capturando esquemas/padrões recorrentes que são comuns na programação paralela. O trabalho realizado centrou-se na paralelização de uma das fases de reconstru-ção da imagem 3D – geração da matriz de sistema – que é uma das mais demoradas do processo de reconstrução; esse trabalho incluiu um método de ordenação modificado em relação ao existente. Foram realizadas diferentes implementações em CPU e GPU (usando OpenMP, CUDA e FastFlow) o que permitiu comparar estes ambientes de programação em termos de facilidade de desenvolvimento e eficiência da solução. A comparação feita permite concluir que o desempenho das soluções baseadas no FastFlow não é muito diferente das tradicionais o que sugere que ferramentas deste tipo podem simplificar e agilizar a implementação de um algoritmos na área de recons-trução de imagens 3D, mantendo um bom desempenho.

Local non-negative initial data scalar characterization of the Kerr solution

For any vacuum initial data set, we define a local, non-negative scalar quantity which vanishes at every point of the data hypersurface if and only if the data are Kerr initial data. Our scalar quantity only depends on the quantities used to construct the vacuum initial data set which are the Riemannian metric defined on the initial data hypersurface and a symmetric tensor which plays the role of the second fundamental form of the embedded initial data hypersurface. The dependency is algorithmic in the sense that given the initial data one can compute the scalar quantity by algebraic and differential manipulations, being thus suitable for an implementation in a numerical code. The scalar could also be useful in studies of the non-linear stability of the Kerr solution because it serves to measure the deviation of a vacuum initial data set from the Kerr initial data in a local and algorithmic way.

The Data Mining applied for the prediction of highway roughness due to overloaded trucks

Currently, the quality of the Indonesian national road network is inadequate due to several constraints, including overcapacity and overloaded trucks. The high deterioration rate of the road infrastructure in developing countries along with major budgetary restrictions and high growth in traffic have led to an emerging need for improving the performance of the highway maintenance system. However, the high number of intervening factors and their complex effects require advanced tools to successfully solve this problem. The high learning capabilities of Data Mining (DM) are a powerful solution to this problem. In the past, these tools have been successfully applied to solve complex and multi-dimensional problems in various scientific fields. Therefore, it is expected that DM can be used to analyze the large amount of data regarding the pavement and traffic, identify the relationship between variables, and provide information regarding the prediction of the data. In this paper, we present a new approach to predict the International Roughness Index (IRI) of pavement based on DM techniques. DM was used to analyze the initial IRI data, including age, Equivalent Single Axle Load (ESAL), crack, potholes, rutting, and long cracks. This model was developed and verified using data from an Integrated Indonesia Road Management System (IIRMS) that was measured with the National Association of Australian State Road Authorities (NAASRA) roughness meter. The results of the proposed approach are compared with the IIRMS analytical model adapted to the IRI, and the advantages of the new approach are highlighted. We show that the novel data-driven model is able to learn (with high accuracy) the complex relationships between the IRI and the contributing factors of overloaded trucks

Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

Multi-scale support vector algorithms for hot spot detection and modelling

The algorithmic approach to data modelling has developed rapidly these last years, in particular methods based on data mining and machine learning have been used in a growing number of applications. These methods follow a data-driven methodology, aiming at providing the best possible generalization and predictive abilities instead of concentrating on the properties of the data model. One of the most successful groups of such methods is known as Support Vector algorithms. Following the fruitful developments in applying Support Vector algorithms to spatial data, this paper introduces a new extension of the traditional support vector regression (SVR) algorithm. This extension allows for the simultaneous modelling of environmental data at several spatial scales. The joint influence of environmental processes presenting different patterns at different scales is here learned automatically from data, providing the optimum mixture of short and large-scale models. The method is adaptive to the spatial scale of the data. With this advantage, it can provide efficient means to model local anomalies that may typically arise in situations at an early phase of an environmental emergency. However, the proposed approach still requires some prior knowledge on the possible existence of such short-scale patterns. This is a possible limitation of the method for its implementation in early warning systems. The purpose of this paper is to present the multi-scale SVR model and to illustrate its use with an application to the mapping of Cs137 activity given the measurements taken in the region of Briansk following the Chernobyl accident.

Propagation connectivity of random hypergraphs

We study the concept of propagation connectivity on random 3-uniform hypergraphs. This concept is inspired by a simple linear time algorithm for solving instances of certain constraint satisfaction problems. We derive upper and lower bounds for the propagation connectivity threshold, and point out some algorithmic implications.

Simulador d'un processador amb Adobe Flash Player

Aquest Projecte pretén crear un simulador d’una màquina algorísmica, de caràcter didàctic amb Adobe Flash CS3 per a reproduir-lo amb Adobe Flash Lite Player, que és la versió per a dispositius mòbils. Simularà el comportament de la màquina algorísmica anomenada FEMTOPROC, que és capaç d’interpretar 4 instruccions molt senzilles: ADD, AND, NOT i JZ (jump if zero). Les diferents instruccions introduïdes que compondran un programa seran emmagatzemades en una memòria de 64 posicions de 8 bits cadascuna i hi haurà un Banc de Registres amb 8 registres de 8 bits, que es podrà inicialitzar al començament de la simulació.

Computing hypergraph width measures exactly

Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. A connection between these and tree decompositions is established. This enables us to almost seamlessly adapt the combinatorial and algorithmic results known for tree decompositions of graphs to the case of hypergraphs and obtain fast exact algorithms. As a consequence, we provide algorithms which, given a hypergraph H on n vertices and m hyperedges, compute the generalized hypertree-width of H in time O*(2n) and compute the fractional hypertree-width of H in time O(1.734601n.m).1

Study and implementation of some quantitative trading models

Quantitative or algorithmic trading is the automatization of investments decisions obeying a fixed or dynamic sets of rules to determine trading orders. It has increasingly made its way up to 70% of the trading volume of one of the biggest financial markets such as the New York Stock Exchange (NYSE). However, there is not a signi cant amount of academic literature devoted to it due to the private nature of investment banks and hedge funds. This projects aims to review the literature and discuss the models available in a subject that publications are scarce and infrequently. We review the basic and fundamental mathematical concepts needed for modeling financial markets such as: stochastic processes, stochastic integration and basic models for prices and spreads dynamics necessary for building quantitative strategies. We also contrast these models with real market data with minutely sampling frequency from the Dow Jones Industrial Average (DJIA). Quantitative strategies try to exploit two types of behavior: trend following or mean reversion. The former is grouped in the so-called technical models and the later in the so-called pairs trading. Technical models have been discarded by financial theoreticians but we show that they can be properly cast into a well defined scientific predictor if the signal generated by them pass the test of being a Markov time. That is, we can tell if the signal has occurred or not by examining the information up to the current time; or more technically, if the event is F_t-measurable. On the other hand the concept of pairs trading or market neutral strategy is fairly simple. However it can be cast in a variety of mathematical models ranging from a method based on a simple euclidean distance, in a co-integration framework or involving stochastic differential equations such as the well-known Ornstein-Uhlenbeck mean reversal ODE and its variations. A model for forecasting any economic or financial magnitude could be properly defined with scientific rigor but it could also lack of any economical value and be considered useless from a practical point of view. This is why this project could not be complete without a backtesting of the mentioned strategies. Conducting a useful and realistic backtesting is by no means a trivial exercise since the \laws" that govern financial markets are constantly evolving in time. This is the reason because we make emphasis in the calibration process of the strategies' parameters to adapt the given market conditions. We find out that the parameters from technical models are more volatile than their counterpart form market neutral strategies and calibration must be done in a high-frequency sampling manner to constantly track the currently market situation. As a whole, the goal of this project is to provide an overview of a quantitative approach to investment reviewing basic strategies and illustrating them by means of a back-testing with real financial market data. The sources of the data used in this project are Bloomberg for intraday time series and Yahoo! for daily prices. All numeric computations and graphics used and shown in this project were implemented in MATLAB^R scratch from scratch as a part of this thesis. No other mathematical or statistical software was used.

Bioreporters: gfp versus lux revisited and single-cell response.

Genetically engineered organisms expressing spectroscopically active reporter molecules in response to chemical effectors display great potential as living transducers in sensing applications. Green fluorescent protein (gfp gene) bioreporters have distinct advantages over luminescent couterparts (lux gene), including applicability at the single-cell level, but are typically less sensitive. Here we describe a gfp-bearing bioreporter that is sensitive to naphthalene (a poorly water soluble pollutant behaving like a large class of hydrophobic compounds), is suitable for use in chemical assays and bioavailability studies, and has detection limits comparable to lux-bearing bioreporters for higher efficiency detection strategies. Simultaneously, we find that the exploitation of population response data from single-cell analysis is not an algorithmic conduit to enhanced signal detection and hence lower effector detection limits, as normally assumed. The assay reported functions to equal effect with or without biocide.

On Certain Greedoid Polyhedra, Partially Indexable Scheduling Problems, and Extended Restless Bandit Allocation Indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid (whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then the problem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

On certain greedoid polyhedra, partially indexable scheduling problems and extended restless bandit allocation indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid(whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then theproblem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.